TSTP Solution File: SWW173+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW173+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 23:21:01 EDT 2022
% Result : Timeout 300.07s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW173+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 03:55:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.93/1.52 *** allocated 10000 integers for termspace/termends
% 0.93/1.52 *** allocated 10000 integers for clauses
% 0.93/1.52 *** allocated 10000 integers for justifications
% 0.93/1.52 *** allocated 15000 integers for termspace/termends
% 0.93/1.52 *** allocated 22500 integers for termspace/termends
% 0.93/1.52 *** allocated 33750 integers for termspace/termends
% 0.93/1.52 Bliksem 1.12
% 0.93/1.52
% 0.93/1.52
% 0.93/1.52 Automatic Strategy Selection
% 0.93/1.52
% 0.93/1.52 *** allocated 50625 integers for termspace/termends
% 0.93/1.52 *** allocated 75937 integers for termspace/termends
% 0.93/1.52 *** allocated 113905 integers for termspace/termends
% 0.93/1.52
% 0.93/1.52 Clauses:
% 0.93/1.52
% 0.93/1.52 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.93/1.52 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.93/1.52 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.93/1.52 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.93/1.52 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.93/1.52 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.93/1.52 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.93/1.52 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.93/1.52 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.93/1.53 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.93/1.53 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.93/1.53 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.93/1.53 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.93/1.53 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.93/1.53 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.93/1.53 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.93/1.53 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.93/1.53 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.93/1.53 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 0.93/1.53 ) = c_Int_OPls }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 0.93/1.53 ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) )
% 0.93/1.53 , Y ) = Y }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls
% 0.93/1.53 ) ) ) = Y }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.93/1.53 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.93/1.53 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.93/1.53 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.93/1.53 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.93/1.53 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.53 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) }.
% 0.93/1.53 { ! Z = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 tc_RealDef_Oreal, Y, X ), Z = c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 tc_RealDef_Oreal, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.53 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.93/1.53 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 X ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ) }.
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) ), X ) ) }.
% 0.93/1.53 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.93/1.53 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.53 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.53 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.53 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.53 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.53 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.93/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.53 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.53 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.93/1.53 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.93/1.53 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.93/1.53 ( X ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.53 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.93/1.53 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.53 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.53 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Z, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.53 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.53 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ), X ), X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.53 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.53 ), U = Z, T = Y }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.93/1.53 ) ), T ), Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.93/1.53 ) ), Z ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.53 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.53 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.53 ), ! U = T }.
% 0.93/1.53 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.93/1.53 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.93/1.53 ), ! Z = Y }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.53 = Y }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.53 = Y }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.93/1.53 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.93/1.53 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Nat_Onat ) ) = Y }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 }.
% 0.93/1.53 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.93/1.53 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.93/1.53 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.93/1.53 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.93/1.53 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.93/1.53 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.93/1.53 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.53 = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Nat_Onat ) ) = Y }.
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) }.
% 0.93/1.53 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.53 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Nat_Onat, Z, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.93/1.53 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha35( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha1( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha35( X, Y, Z, T ), !
% 0.93/1.53 alpha1( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.93/1.53 { ! alpha35( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.93/1.53 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha35( X, Y, Z, T ) }.
% 0.93/1.53 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha35(
% 0.93/1.53 X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha36( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha2( X, Y, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha36( X, Y, Z, T ), !
% 0.93/1.53 alpha2( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha36(
% 0.93/1.53 X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha2( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { Y = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.93/1.53 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.93/1.53 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.93/1.53 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.93/1.53 ) ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) }.
% 0.93/1.53 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.93/1.53 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.53 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.53 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.93/1.53 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.93/1.53 .
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.93/1.53 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.93/1.53 .
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit1( Y
% 0.93/1.53 ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ), X ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.93/1.53 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.93/1.53 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.93/1.53 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.53 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.93/1.53 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.93/1.53 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ), alpha37( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.93/1.53 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ), alpha3( X, Y, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 alpha37( X, Y, Z, T ), ! alpha3( X, Y, T ), T =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Y ) ) }.
% 0.93/1.53 { ! alpha37( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ) = Z }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ), alpha37( X, Y, Z, T ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z, alpha37( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha3( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.53 .
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ), alpha3( X, Y, Z ) }.
% 0.93/1.53 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha38( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha4( X, Y, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 alpha38( X, Y, Z, T ), ! alpha4( X, Y, T ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! alpha38( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , T ) ), Y ) = Z }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha38( X, Y, Z, T ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) = Z, alpha38( X, Y, Z, T
% 0.93/1.53 ) }.
% 0.93/1.53 { ! alpha4( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) }.
% 0.93/1.53 { Y = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ), alpha4( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), alpha39( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), alpha5( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 alpha39( X, Y, Z, T ), ! alpha5( X, Y, Z ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.93/1.53 { ! alpha39( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.93/1.53 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 0.93/1.53 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha39( X, Y, Z, T ) }
% 0.93/1.53 .
% 0.93/1.53 { ! alpha5( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) }.
% 0.93/1.53 { Z = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ), alpha5( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Z ) ) = Y, alpha40( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Z ) ) = Y, alpha6( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.93/1.53 alpha40( X, Y, Z, T ), ! alpha6( X, Y, Z ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Z ) ) = Y }.
% 0.93/1.53 { ! alpha40( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ) ) }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ), alpha40( X, Y, Z, T ) }.
% 0.93/1.53 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha40( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha6( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.53 .
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ), alpha6( X, Y, Z ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.93/1.53 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, c_Int_OPls ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1
% 0.93/1.53 ( c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = X }.
% 0.93/1.53 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.93/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.93/1.53 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), c_Nat_OSuc(
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.93/1.53 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.53 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.53 ), c_Nat_OSuc( hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.93/1.53 ( c_Int_OPls ) ) ) ), Y ) ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.53 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.53 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.93/1.53 { ! v_y____ = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.93/1.53 ( tc_Int_Oint ) }.
% 0.93/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.53 { c_Int_OMin = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Int_Oint ), X ) = X }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Int_Oint ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.93/1.53 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.93/1.53 ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.93/1.53 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ), Y ) }.
% 0.93/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.93/1.53 ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ) ) = X }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.93/1.53 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.93/1.53 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.93/1.53 ( tc_Int_Oint ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.93/1.53 = X }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ) ) }.
% 0.93/1.53 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.93/1.53 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ), X ) }.
% 0.93/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.93/1.53 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.93/1.53 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ) ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.93/1.53 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.53 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OMin
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0
% 0.93/1.53 ( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0(
% 0.93/1.53 X ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 0.93/1.53 .
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.93/1.53 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.53 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.53 X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.93/1.53 tc_Int_Oint, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Int_OMin ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OMin
% 0.93/1.53 ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OPls ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OMin ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1
% 0.93/1.53 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1(
% 0.93/1.53 X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.53 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.53 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OMin ), X
% 0.93/1.53 ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.93/1.53 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.93/1.53 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.93/1.53 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.93/1.53 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha7( X, Y
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha41( X,
% 0.93/1.53 Y ) }.
% 0.93/1.53 { ! alpha7( X, Y ), ! alpha41( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.93/1.53 { ! alpha41( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha41( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha41( X, Y ) }.
% 0.93/1.53 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha7( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha7( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.93/1.53 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.93/1.53 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ) =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), Y ) =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 X, W, Z ) ), U ), T ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.93/1.53 ( X, Z, W ) ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.53 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OMin ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.93/1.53 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.53 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.93/1.53 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, c_Int_OMin ) ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.93/1.53 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.93/1.53 , X ) ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.93/1.53 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.93/1.53 , X ) ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.93/1.53 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.93/1.53 , X ) ) }.
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OMin ) = c_Int_OBit1
% 0.93/1.53 ( c_Int_OPls ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.53 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.93/1.53 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.93/1.53 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Int_OPls ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha8( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.53 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.93/1.53 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha8( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha8( X
% 0.93/1.53 , Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.93/1.53 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.93/1.53 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.93/1.53 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.53 ( X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.53 ) ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.53 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.93/1.53 ( X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.93/1.53 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.93/1.53 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.93/1.53 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.53 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.53 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.53 ), Y ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.93/1.53 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.93/1.53 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.93/1.53 ) }.
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls ) = c_Int_OPls }
% 0.93/1.53 .
% 0.93/1.53 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 0.93/1.53 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.93/1.53 { ! c_Int_OBit1( X ) = c_Int_OMin, X = c_Int_OMin }.
% 0.93/1.53 { ! X = c_Int_OMin, c_Int_OBit1( X ) = c_Int_OMin }.
% 0.93/1.53 { ! c_Int_OMin = c_Int_OBit1( X ), c_Int_OMin = X }.
% 0.93/1.53 { ! c_Int_OMin = X, c_Int_OMin = c_Int_OBit1( X ) }.
% 0.93/1.53 { c_Int_OBit1( c_Int_OMin ) = c_Int_OMin }.
% 0.93/1.53 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 0.93/1.53 { ! c_Int_OPls = c_Int_OMin }.
% 0.93/1.53 { ! c_Int_OMin = c_Int_OPls }.
% 0.93/1.53 { ! c_Int_OBit0( X ) = c_Int_OMin }.
% 0.93/1.53 { ! c_Int_OMin = c_Int_OBit0( X ) }.
% 0.93/1.53 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.53 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.93/1.53 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.53 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.53 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.93/1.53 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.93/1.53 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.53 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.93/1.53 ( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.93/1.53 tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha9( X, Y ), alpha42( X, Y )
% 0.93/1.53 }.
% 0.93/1.53 { ! alpha9( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.93/1.53 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! alpha42( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.93/1.53 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! alpha42( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! alpha42( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.93/1.53 c_Int_OMin ) }.
% 0.93/1.53 { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X =
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha42( X,
% 0.93/1.53 Y ) }.
% 0.93/1.53 { ! alpha9( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! alpha9( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha9( X, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.53 .
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.53 c_Int_OBit1( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.93/1.53 }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.53 ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.53 c_Int_OBit0( X ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.53 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.93/1.53 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.93/1.53 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.53 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.93/1.53 ( X, Z ) }.
% 0.93/1.53 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.53 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.53 Z ) ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.53 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.53 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.93/1.53 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.53 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.93/1.53 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.93/1.53 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.93/1.53 , c_Rings_Oinverse__class_Odivide( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , c_Int_OMin ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) )
% 0.93/1.53 }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), alpha43( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), alpha67( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.93/1.53 , T ), ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.53 { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), alpha79( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.53 , alpha67( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha79( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha79( X, Y, Z, T ), alpha91( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha79( X, Y, Z, T ), alpha10( X, Y, T ) }.
% 0.93/1.53 { ! alpha91( X, Y, Z, T ), ! alpha10( X, Y, T ), alpha79( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha91( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 alpha91( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha91( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha43( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 alpha43( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha43( X, Y, Z, T )
% 0.93/1.53 }.
% 0.93/1.53 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , alpha10( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), alpha10( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Z ), Y ), alpha44( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Z ), Y ), alpha68( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.93/1.53 , T ), ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.93/1.53 { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), alpha80( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.53 , alpha68( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha80( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha80( X, Y, Z, T ), alpha92( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha80( X, Y, Z, T ), alpha11( X, Y, Z ) }.
% 0.93/1.53 { ! alpha92( X, Y, Z, T ), ! alpha11( X, Y, Z ), alpha80( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha92( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 alpha92( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha92( X, Y, Z, T )
% 0.93/1.53 }.
% 0.93/1.53 { ! alpha44( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.93/1.53 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.53 alpha44( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha44( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , alpha11( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , Y ), alpha11( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.53 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.93/1.53 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.93/1.53 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 0.93/1.53 ( c_Int_OPls ) ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.93/1.53 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.93/1.53 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 0.93/1.53 tc_Int_Oint, Y ) ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.93/1.53 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.93/1.53 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Y ) ) ), alpha45( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Y ) ) ), alpha69( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! alpha45( X, Y, Z, T ), ! alpha69( X, Y, Z, T )
% 0.93/1.53 , c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Y ) ) ) }.
% 0.93/1.53 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ) ), alpha81( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha69( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha81( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha81( X, Y, Z, T ), alpha12( X, Y, T ) }.
% 0.93/1.53 { ! alpha93( X, Y, Z, T ), ! alpha12( X, Y, T ), alpha81( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Groups_Ozero__class_Ozero( X ) ), alpha93( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ) ), alpha93( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha45( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ), Z ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha45( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ), Z ), alpha45( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), alpha12( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), alpha46( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.53 ( X, Z, Y ) ), alpha70( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! alpha46( X, Y, Z, T ), ! alpha70( X, Y, Z, T )
% 0.93/1.53 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.53 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), alpha82( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.53 , alpha70( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha82( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha82( X, Y, Z, T ), alpha13( X, Y, T ) }.
% 0.93/1.53 { ! alpha94( X, Y, Z, T ), ! alpha13( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 alpha94( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), Y ) ), alpha94( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha46( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 alpha46( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), Y ), Z ), alpha46( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , alpha13( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha47( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha71( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! alpha47( X, Y, Z, T ), ! alpha71( X, Y, Z, T )
% 0.93/1.53 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), alpha83( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.53 , alpha71( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha83( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha83( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha83( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 0.93/1.53 { ! alpha95( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 alpha95( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ), Z ), T ), alpha95( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.93/1.53 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.53 alpha47( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ), Z ) ), alpha47( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , alpha14( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha14( X, Y, Z ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Z ) ), Y ), alpha48( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.53 X, Z ) ), Y ), alpha72( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.53 class_Int_Onumber( X ), ! alpha48( X, Y, Z, T ), ! alpha72( X, Y, Z, T )
% 0.93/1.53 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.93/1.53 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.93/1.53 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ) ), alpha84( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha72( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha84( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha84( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha84( X, Y, Z, T ), alpha15( X, Y, Z ) }.
% 0.93/1.53 { ! alpha96( X, Y, Z, T ), ! alpha15( X, Y, Z ), alpha84( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ) ), T ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ), c_Groups_Ozero__class_Ozero( X ) ), alpha96( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ) ), T ), alpha96( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ) ) ) }.
% 0.93/1.53 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha48( X, Y, Z, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Z ) ) ), alpha48( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , Y ), alpha15( X, Y, Z ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.53 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.53 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.93/1.53 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.93/1.53 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 , Y ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.93/1.53 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.93/1.53 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.93/1.53 ) ) ) }.
% 0.93/1.53 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.93/1.53 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.93/1.53 .
% 0.93/1.53 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.53 c_Int_OPls ) ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.53 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.53 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.93/1.53 Z ) ), U ), T ) = Y }.
% 0.93/1.53 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.93/1.53 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.53 W ) ), U ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.93/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Z ), U ), Y ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.93/1.53 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.93/1.53 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.53 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.93/1.53 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.53 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.93/1.53 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.93/1.53 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.93/1.53 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.53 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.93/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.53 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.53 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.93/1.53 ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.53 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.93/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.93/1.53 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.53 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.53 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.93/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.53 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.53 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.93/1.53 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha16( X, Y, Z, T ),
% 0.93/1.53 alpha49( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha49( X, Y, Z, T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha49( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.93/1.53 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.93/1.53 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha16( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha17( X, Y, Z, T ),
% 0.93/1.53 alpha50( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha50( X, Y, Z, T ),
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.53 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha50( X, Y, Z, T ) }.
% 0.93/1.53 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.53 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.93/1.53 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.53 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha17( X, Y, Z, T ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.53 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.53 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.93/1.53 .
% 0.93/1.53 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.53 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ), alpha18( X, Y, Z ), alpha51( X, Y, Z ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha51( X, Y, Z ),
% 0.93/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.53 ( X ) ) }.
% 0.93/1.53 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.53 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( X ), Y ), alpha51( X, Y, Z ) }.
% 0.93/1.54 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha19( X, Y
% 0.93/1.54 , Z ), alpha52( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha52( X, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.54 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha52( X, Y, Z ) }.
% 0.93/1.54 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha19( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.93/1.54 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.93/1.54 ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.93/1.54 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.93/1.54 ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.93/1.54 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.93/1.54 , X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.54 ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Y, Z ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Y, Z ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.93/1.54 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ), alpha53( X,
% 0.93/1.54 Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha20( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha53( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha53( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha53( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), alpha53( X, Y, Z ) }.
% 0.93/1.54 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.54 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 ), alpha20( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha21( X, Y, Z ), alpha54
% 0.93/1.54 ( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha21( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha54( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 ), alpha54( X, Y, Z ) }.
% 0.93/1.54 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.54 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), alpha21( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ), alpha55
% 0.93/1.54 ( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha22( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha55( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( X ), Y ), alpha55( X, Y, Z ) }.
% 0.93/1.54 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha23( X, Y, Z ), alpha56
% 0.93/1.54 ( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha23( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha56( X, Y, Z
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), alpha56( X, Y, Z ) }.
% 0.93/1.54 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.93/1.54 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha23( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.93/1.54 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.54 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.93/1.54 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 0.93/1.54 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.93/1.54 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.93/1.54 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.54 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.93/1.54 ( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.93/1.54 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.93/1.54 ( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.54 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.93/1.54 X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.54 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.54 c_Int_OBit1( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.54 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.93/1.54 c_Int_OBit1( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.54 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.93/1.54 c_Int_OPls ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.93/1.54 c_Int_OPls ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.93/1.54 X ) ) }.
% 0.93/1.54 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.93/1.54 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.93/1.54 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.54 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.93/1.54 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.93/1.54 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.93/1.54 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 Z, Y ) }.
% 0.93/1.54 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.54 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.93/1.54 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.54 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.54 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.93/1.54 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ), alpha57( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ), alpha73( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha57( X, Y, Z
% 0.93/1.54 , T ), ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha85( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.54 , alpha73( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha85( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha85( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha85( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 0.93/1.54 { ! alpha97( X, Y, Z, T ), ! alpha24( X, Y, T ), alpha85( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.54 alpha97( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha97( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.54 alpha57( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha57( X, Y, Z, T )
% 0.93/1.54 }.
% 0.93/1.54 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha24( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha24( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Z ), Y ), alpha58( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Z ), Y ), alpha74( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha58( X, Y, Z
% 0.93/1.54 , T ), ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.93/1.54 { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), alpha86( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.54 , alpha74( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha86( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha86( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha86( X, Y, Z, T ), alpha25( X, Y, Z ) }.
% 0.93/1.54 { ! alpha98( X, Y, Z, T ), ! alpha25( X, Y, Z ), alpha86( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.54 alpha98( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha98( X, Y, Z, T )
% 0.93/1.54 }.
% 0.93/1.54 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.54 alpha58( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha58( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha25( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.54 , alpha25( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Y ), Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Y ), Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 Z, Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Y ), Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.93/1.54 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.93/1.54 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.93/1.54 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.93/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 X ), Y ), Z = Y }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.93/1.54 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.93/1.54 ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.93/1.54 }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 X, Z ) ), Y ), alpha59( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 X, Z ) ), Y ), alpha75( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! alpha59( X, Y, Z, T ), ! alpha75( X, Y, Z, T )
% 0.93/1.54 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.93/1.54 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.54 ) ), alpha87( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha75( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha87( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha87( X, Y, Z, T ), alpha99( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha87( X, Y, Z, T ), alpha26( X, Y, Z ) }.
% 0.93/1.54 { ! alpha99( X, Y, Z, T ), ! alpha26( X, Y, Z ), alpha87( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha99( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Z ) ), T ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.54 ), c_Groups_Ozero__class_Ozero( X ) ), alpha99( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Z ) ), T ), alpha99( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Z ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha59( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Z ) ) ), alpha59( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.54 , alpha26( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha60( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha76( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! alpha60( X, Y, Z, T ), ! alpha76( X, Y, Z, T )
% 0.93/1.54 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.93/1.54 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.93/1.54 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), alpha88( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.54 , alpha76( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha88( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha88( X, Y, Z, T ), alpha100( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha88( X, Y, Z, T ), alpha27( X, Y, Z ) }.
% 0.93/1.54 { ! alpha100( X, Y, Z, T ), ! alpha27( X, Y, Z ), alpha88( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha100( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.54 alpha100( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 Y ) ), Z ), T ), alpha100( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.93/1.54 alpha60( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 Y ) ), Z ) ), alpha60( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.54 ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha27( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha27( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Z, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.93/1.54 ( X, Z, Y ) ), alpha77( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! alpha61( X, Y, Z, T ), ! alpha77( X, Y, Z, T )
% 0.93/1.54 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.93/1.54 { ! alpha77( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), alpha89( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.93/1.54 , alpha77( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha89( X, Y, Z, T ), alpha77( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha89( X, Y, Z, T ), alpha101( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha89( X, Y, Z, T ), alpha28( X, Y, T ) }.
% 0.93/1.54 { ! alpha101( X, Y, Z, T ), ! alpha28( X, Y, T ), alpha89( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha101( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.54 alpha101( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 T ) ), Y ) ), alpha101( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.54 alpha61( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 T ) ), Y ), Z ), alpha61( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha28( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha28( X, Y, Z ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 X, Y ) ) ), alpha62( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 X, Y ) ) ), alpha78( X, Y, Z, T ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber( X ), ! alpha62( X, Y, Z, T ), ! alpha78( X, Y, Z, T )
% 0.93/1.54 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 0.93/1.54 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.93/1.54 { ! alpha78( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.54 ) ), alpha90( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha78( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha90( X, Y, Z, T ), alpha78( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha90( X, Y, Z, T ), alpha102( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha90( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 0.93/1.54 { ! alpha102( X, Y, Z, T ), ! alpha29( X, Y, T ), alpha90( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha102( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Y ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.54 ), c_Groups_Ozero__class_Ozero( X ) ), alpha102( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Y ) ) ), alpha102( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Y ) ), Z ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha62( X, Y, Z, T ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( X, Y ) ), Z ), alpha62( X, Y, Z, T ) }.
% 0.93/1.54 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.54 , alpha29( X, Y, Z ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.93/1.54 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.54 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.93/1.54 ), Y ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.93/1.54 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.54 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.54 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.93/1.54 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.54 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.54 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.93/1.54 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.54 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.54 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.93/1.54 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), Y ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.93/1.54 ) ) ) ) ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.93/1.54 ) ) ) ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( X ), Y ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.93/1.54 ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) = c_Rings_Oinverse__class_Odivide(
% 0.93/1.54 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) = c_Rings_Oinverse__class_Odivide(
% 0.93/1.54 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y )
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.93/1.54 ( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), Z = Y }.
% 0.93/1.54 { ! class_Rings_Olinordered__semidom( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.54 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.93/1.54 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.93/1.54 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.54 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.54 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.93/1.54 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.93/1.54 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.93/1.54 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) ) }.
% 0.93/1.54 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), Y ) ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.93/1.54 class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.93/1.54 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.93/1.54 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.54 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.54 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.93/1.54 ( tc_Int_Oint ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.54 X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.54 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.93/1.54 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.93/1.54 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.93/1.54 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.93/1.54 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.93/1.54 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.54 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.93/1.54 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.93/1.54 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.93/1.54 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { alpha103( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.93/1.54 { alpha103( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 0.93/1.54 hAPP( X, Y ), Z ) ) }.
% 0.93/1.54 { ! alpha103( X, Y, Z ), alpha104( X, Y, Z ), Z = Y }.
% 0.93/1.54 { ! alpha103( X, Y, Z ), alpha104( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ),
% 0.93/1.54 Z ) ) }.
% 0.93/1.54 { ! alpha104( X, Y, Z ), alpha103( X, Y, Z ) }.
% 0.93/1.54 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha103( X, Y, Z ) }.
% 0.93/1.54 { ! alpha104( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.93/1.54 }.
% 0.93/1.54 { ! alpha104( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.93/1.54 X, Y ), Z ) ), alpha104( X, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.93/1.54 , c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.93/1.54 c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.93/1.54 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 tc_RealDef_Oreal, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.93/1.54 , c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.93/1.54 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.93/1.54 c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.93/1.54 { c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) )
% 0.93/1.54 = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.93/1.54 ) ) }.
% 0.93/1.54 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.93/1.54 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.93/1.54 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.93/1.54 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.93/1.54 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.93/1.54 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.93/1.54 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.93/1.54 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.93/1.54 .
% 0.93/1.54 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) )
% 0.93/1.54 , c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.93/1.54 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) ), X ) }.
% 0.93/1.54 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X
% 0.93/1.54 ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.93/1.54 ( Y ), c_NthRoot_Osqrt( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.93/1.54 .
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.93/1.54 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Int_Oint ) ) }.
% 0.93/1.54 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.93/1.54 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.93/1.54 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.93/1.54 { ! c_Nat_OSuc( X ) = X }.
% 0.93/1.54 { ! X = c_Nat_OSuc( X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.93/1.54 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.93/1.54 c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.93/1.54 , c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.93/1.54 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.93/1.54 .
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.93/1.54 .
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.93/1.54 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.54 X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.93/1.54 }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.93/1.54 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 0.93/1.54 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.93/1.54 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.93/1.54 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.54 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.93/1.54 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.93/1.54 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.93/1.54 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.93/1.54 .
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.93/1.54 , X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.54 c_NthRoot_Osqrt( X ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = X,
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.93/1.54 ( c_Int_OPls ) ) ) ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.93/1.54 ( c_Int_OPls ) ) ) ) = X }.
% 0.93/1.54 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_NthRoot_Osqrt( X ) = Y }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.93/1.54 ( c_Int_OPls ) ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ), X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X )
% 0.93/1.54 ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), T ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.93/1.54 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.93/1.54 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.93/1.54 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.54 c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.93/1.54 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 0.93/1.54 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.93/1.54 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.54 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.54 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! alpha30( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.93/1.54 c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! alpha30( X, Y ), Y = c_Nat_OSuc( skol4( Z, Y ) ) }.
% 0.93/1.54 { ! alpha30( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol4( X,
% 0.93/1.54 Y ), X ) }.
% 0.93/1.54 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.93/1.54 ), alpha30( X, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol5( X ) ) }.
% 0.93/1.54 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.93/1.54 ) ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.93/1.54 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.54 , ! alpha31( X, Y, Z ) }.
% 0.93/1.54 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.54 , ! alpha63( X, Y, Z ) }.
% 0.93/1.54 { alpha31( X, Y, Z ), alpha63( X, Y, Z ), hBOOL( hAPP( Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.54 { ! alpha63( X, Y, Z ), ! hBOOL( hAPP( Z, skol6( T, U, Z ) ) ) }.
% 0.93/1.54 { ! alpha63( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.54 skol6( X, Y, Z ) ) }.
% 0.93/1.54 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.93/1.54 ) ), alpha63( X, Y, Z ) }.
% 0.93/1.54 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.93/1.54 }.
% 0.93/1.54 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha31( X, Y, Z ) }.
% 0.93/1.54 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.54 , alpha32( X, Y, Z ) }.
% 0.93/1.54 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.93/1.54 , alpha64( X, Y, Z ) }.
% 0.93/1.54 { ! alpha32( X, Y, Z ), ! alpha64( X, Y, Z ), hBOOL( hAPP( Z,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.54 { ! alpha64( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.93/1.54 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.93/1.54 { ! hBOOL( hAPP( Z, skol7( T, U, Z ) ) ), alpha64( X, Y, Z ) }.
% 0.93/1.54 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol7( X, Y, Z ) ),
% 0.93/1.54 alpha64( X, Y, Z ) }.
% 0.93/1.54 { ! alpha32( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.93/1.54 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha32( X, Y, Z ) }
% 0.93/1.54 .
% 0.93/1.54 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha32
% 0.93/1.54 ( X, Y, Z ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), X ) = X }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ) ) = X }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) ) }.
% 0.93/1.54 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.93/1.54 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.54 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.93/1.54 .
% 0.93/1.54 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.93/1.54 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.54 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.93/1.54 .
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.54 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.54 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 Y ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.93/1.54 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.93/1.54 ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.93/1.54 ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.93/1.54 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.93/1.54 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.54 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.54 ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.54 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.93/1.54 ), X ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Int_Oint ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Int_Oint, X, Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.93/1.54 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.93/1.54 , Y ), X ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Nat_Onat ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.93/1.54 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 0.93/1.54 tc_RealDef_Oreal, Z, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 0.93/1.54 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.54 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.54 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.93/1.54 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.93/1.54 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha33( X, Y ), alpha65( X
% 0.93/1.54 , Y ) }.
% 0.93/1.54 { ! alpha33( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! alpha65( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! alpha65( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! alpha65( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha65( X, Y ) }.
% 0.93/1.54 { ! alpha33( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! alpha33( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha33( X, Y ) }.
% 0.93/1.54 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha34( X, Y ),
% 0.93/1.54 alpha66( X, Y ) }.
% 0.93/1.54 { ! alpha34( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.54 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! alpha66( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.93/1.54 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.93/1.54 { ! alpha66( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! alpha66( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha66( X, Y ) }.
% 0.93/1.54 { ! alpha34( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! alpha34( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha34( X, Y ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.93/1.54 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.93/1.54 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.93/1.54 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.93/1.54 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.93/1.54 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.93/1.54 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.93/1.54 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.93/1.54 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.93/1.54 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.93/1.54 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.93/1.54 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.93/1.54 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.93/1.54 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.93/1.54 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) }.
% 0.93/1.54 { ! v_y____ = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.93/1.54 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.93/1.54 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ) ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) = v_z }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.93/1.54 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.93/1.54 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.93/1.54 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.93/1.54 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.93/1.54 .
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.93/1.54 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.93/1.54 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.54 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_Nat_Onat ), X ), Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.93/1.54 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.93/1.54 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.93/1.54 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.93/1.54 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.93/1.54 { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 tc_RealDef_Oreal, X ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.93/1.54 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_RealDef_Oreal ) }.
% 0.93/1.54 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 0.93/1.54 tc_Complex_Ocomplex, X ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.93/1.54 }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.93/1.54 ) }.
% 0.93/1.54 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.93/1.54 tc_Complex_Ocomplex ) }.
% 0.93/1.54 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.93/1.54 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.93/1.54 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.93/1.54 ), T = Y }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.93/1.54 ), Z = X }.
% 0.93/1.54 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.93/1.54 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.93/1.54 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.93/1.54 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.93/1.54 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.93/1.54 Z, X ) ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.93/1.54 ) }.
% 0.93/1.54 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.93/1.54 ) }.
% 0.93/1.54 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.93/1.54 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_Complex_Ocomplex ) }.
% 0.93/1.54 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.93/1.54 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.93/1.54 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.93/1.54 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.93/1.54 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.93/1.54 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.93/1.54 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.93/1.54 , Z, X ) ) }.
% 0.93/1.54 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.93/1.54 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.93/1.54 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.93/1.54 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), X ) ), c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), T ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.54 tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.93/1.54 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.93/1.54 { v_z = c_Complex_Ocomplex_OComplex( skol9, skol10 ) }.
% 0.93/1.54 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.93/1.54 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.93/1.54 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.93/1.54 { c_Transcendental_Oarctan( X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.93/1.54 ( tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal
% 0.93/1.54 , c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), c_Transcendental_Oarctan
% 0.93/1.54 ( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.93/1.54 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.93/1.54 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP(
% 0.93/1.54 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.93/1.54 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.54 c_Int_OPls ) ) ) ) ) ) ) ) ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.54 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.54 { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.93/1.54 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.54 { c_Transcendental_Oarctan( c_Groups_Ouminus__class_Ouminus(
% 0.93/1.54 tc_RealDef_Oreal, X ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.54 tc_RealDef_Oreal, c_Transcendental_Oarctan( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.93/1.54 c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.93/1.54 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 0.93/1.54 ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 0.93/1.54 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.93/1.54 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 Y, T ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 T, Y ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 T, Y ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 Y, Z ), T = Y }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 Y, Z ) }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 T, Y ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 T, Y ) }.
% 0.93/1.54 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.93/1.54 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.93/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.93/1.54 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) }.
% 0.93/1.54 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.93/1.54 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.54 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.54 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.93/1.54 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.54 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.93/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.54 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.54 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.93/1.54 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.54 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.54 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.54 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.93/1.54 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.54 , T ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.54 , T, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.54 , Y, T ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.54 , T, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.93/1.54 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.93/1.54 ( X, T, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.54 , Y, Z ) ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.54 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.93/1.54 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.93/1.54 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.93/1.54 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.54 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.93/1.54 ) }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.93/1.54 ( X ) }.
% 0.93/1.54 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Y ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.93/1.54 ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.54 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.93/1.54 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.93/1.54 = Y }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.54 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.93/1.54 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.54 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.54 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.93/1.54 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.54 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.93/1.54 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.93/1.54 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.93/1.54 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.54 ( X, Y ), Z ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.54 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.54 ( X, Z ), Y ) }.
% 0.93/1.54 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.54 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.54 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.93/1.54 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.55 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 Z, Y ) ) = Y }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.55 Y ) ) = Y }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.93/1.55 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.93/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.93/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.93/1.55 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.93/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.93/1.55 ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 Z, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 Y, Z ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.55 .
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.93/1.55 .
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.55 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.93/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.93/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.93/1.55 ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.55 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.93/1.55 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.55 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.93/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.93/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.93/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.93/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.93/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.93/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.93/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.93/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.93/1.55 , Y, T ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.93/1.55 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.93/1.55 ( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.93/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.93/1.55 , Z, Y ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.93/1.55 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.93/1.55 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.55 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.55 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.93/1.55 ( X, Y ), Y ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.93/1.55 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.93/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.55 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 , Y ) }.
% 0.93/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.93/1.55 , Y ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.55 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.93/1.55 Z ) = Y }.
% 0.93/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.55 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.93/1.55 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.93/1.55 ( X, Y ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.93/1.55 X ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.93/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.93/1.55 X, Y ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.93/1.55 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.93/1.55 , Y ) ) }.
% 0.93/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.93/1.55 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.93/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.93/1.55 X, Z, Y ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.93/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.93/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.93/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.93/1.55 ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.93/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.93/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.93/1.55 ) ) }.
% 0.93/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.93/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.93/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.93/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.93/1.55 c_Complex_Oii ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.93/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.93/1.55 c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.93/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.93/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.93/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.93/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.93/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.93/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.93/1.55 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.93/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.93/1.55 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.93/1.55 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.93/1.55 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 0.93/1.55 X ) }.
% 0.93/1.55 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.93/1.55 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.93/1.55 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.93/1.55 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.55 tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.93/1.55 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.93/1.55 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.93/1.55 { class_Power_Opower( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.93/1.55 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.93/1.55 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.93/1.55 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.93/1.55 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.55 tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.93/1.55 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.55 tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.93/1.55 .
% 0.93/1.55 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.93/1.55 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.93/1.55 tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.93/1.55 { ! c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.93/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_x ),
% 0.93/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.93/1.55 c_Int_OPls ) ) ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.93/1.55 c_Int_OBit0( c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = hAPP( hAPP
% 0.93/1.55 ( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.93/1.55 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, v_x,
% 0.93/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.93/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) ), c_Int_Onumber__class_Onumber__of(
% 0.93/1.55 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.93/1.55
% 0.93/1.55 *** allocated 15000 integers for clauses
% 0.93/1.55 *** allocated 22500 integers for clauses
% 0.93/1.55 *** allocated 33750 integers for clauses
% 0.93/1.55 *** allocated 50625 integers for clauses
% 0.93/1.55 *** allocated 75937 integers for clauses
% 0.93/1.55 *** allocated 113905 integers for clauses
% 0.93/1.55 percentage equality = 0.254420, percentage horn = 0.902579
% 0.93/1.55 This is a problem with some equality
% 0.93/1.55
% 0.93/1.55
% 0.93/1.55
% 0.93/1.55 Options Used:
% 0.93/1.55
% 0.93/1.55 useres = 1
% 0.93/1.55 useparamod = 1
% 0.93/1.55 useeqrefl = 1
% 0.93/1.55 useeqfact = 1
% 0.93/1.55 usefactor = 1
% 0.93/1.55 usesimpsplitting = 0
% 0.93/1.55 usesimpdemod = 5
% 0.93/1.55 usesimpres = 3
% 0.93/1.55
% 0.93/1.55 resimpinuse = 1000
% 0.93/1.55 resimpclauses = 20000
% 0.93/1.55 substype = eqrewr
% 0.93/1.55 backwardsubs = 1
% 0.93/1.55 selectoldest = 5
% 0.93/1.55
% 0.93/1.55 litorderings [0] = split
% 0.93/1.55 litorderings [1] = extend the termordering, first sorting on arguments
% 0.93/1.55
% 0.93/1.55 termordering = kbo
% 0.93/1.55
% 0.93/1.55 litapriori = 0
% 0.93/1.55 termapriori = 1
% 0.93/1.55 litaposteriori = 0
% 0.93/1.55 termaposteriori = 0
% 0.93/1.55 demodaposteriori = 0
% 0.93/1.55 ordereqreflfact = 0
% 0.93/1.55
% 0.93/1.55 litselect = negord
% 0.93/1.55
% 0.93/1.55 maxweight = 15
% 0.93/1.55 maxdepth = 30000
% 0.93/1.55 maxlength = 115
% 0.93/1.55 maxnrvars = 195
% 0.93/1.55 excuselevel = 1
% 0.93/1.55 increasemaxweight = 1
% 0.93/1.55
% 0.93/1.55 maxselected = 10000000
% 0.93/1.55 maxnrclauses = 10000000
% 0.93/1.55
% 0.93/1.55 showgenerated = 0
% 0.93/1.55 showkept = 0
% 0.93/1.55 showselected = 0
% 0.93/1.55 showdeleted = 0
% 0.93/1.55 showresimp = 1
% 0.93/1.55 showstatus = 2000
% 0.93/1.55
% 0.93/1.55 prologoutput = 0
% 0.93/1.55 nrgoals = 5000000
% 0.93/1.55 totalproof = 1
% 0.93/1.55
% 0.93/1.55 Symbols occurring in the translation:
% 0.93/1.55
% 0.93/1.55 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.93/1.55 . [1, 2] (w:1, o:180, a:1, s:1, b:0),
% 0.93/1.55 ! [4, 1] (w:0, o:103, a:1, s:1, b:0),
% 0.93/1.55 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.55 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.93/1.55 hAPP [38, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.93/1.55 class_Fields_Ofield [41, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.93/1.55 class_Int_Onumber__ring [42, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.93/1.55 c_Int_OPls [43, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.93/1.55 c_Int_OBit1 [44, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.93/1.55 c_Int_Onumber__class_Onumber__of [45, 2] (w:1, o:205, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 c_Rings_Oinverse__class_Odivide [46, 3] (w:1, o:223, a:1, s:1, b:0),
% 0.93/1.55
% 0.93/1.55 class_Fields_Ofield__inverse__zero [50, 1] (w:1, o:112, a:1, s:1, b:0
% 0.93/1.55 ),
% 0.93/1.55 c_Power_Opower__class_Opower [51, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.93/1.55 c_Int_OBit0 [52, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.93/1.55 tc_RealDef_Oreal [57, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.93/1.55 c_Groups_Otimes__class_Otimes [58, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.93/1.55 tc_Nat_Onat [59, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.93/1.55 class_Groups_Omonoid__mult [62, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.93/1.55 class_Int_Onumber [63, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.93/1.55 tc_Int_Oint [65, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.93/1.55 class_Groups_Ocomm__monoid__mult [67, 1] (w:1, o:121, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 class_Int_Oring__char__0 [72, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Ocomm__semiring__1 [75, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.93/1.55 c_Groups_Oplus__class_Oplus [77, 3] (w:1, o:224, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Odivision__ring [79, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.93/1.55 c_Nat_OSuc [81, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oring__1__no__zero__divisors [83, 1] (w:1, o:128, a:1, s:
% 0.93/1.55 1, b:0),
% 0.93/1.55 c_Groups_Ozero__class_Ozero [84, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Osemiring__1 [85, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.93/1.55 c_Groups_Oone__class_Oone [86, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.93/1.55 class_Power_Opower [87, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Osemiring__0 [88, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Odivision__ring__inverse__zero [89, 1] (w:1, o:138, a:1
% 0.93/1.55 , s:1, b:0),
% 0.93/1.55 class_Groups_Olinordered__ab__group__add [92, 1] (w:1, o:118, a:1, s:
% 0.93/1.55 1, b:0),
% 0.93/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [97
% 0.93/1.55 , 1] (w:1, o:159, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Ozero__neq__one [98, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__ring__strict [99, 1] (w:1, o:140, a:1, s:1
% 0.93/1.55 , b:0),
% 0.93/1.55 class_Rings_Omult__zero [101, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Ono__zero__divisors [102, 1] (w:1, o:150, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 class_Rings_Osemiring [104, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Ocomm__semiring [105, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oring__no__zero__divisors [108, 1] (w:1, o:130, a:1, s:1
% 0.93/1.55 , b:0),
% 0.93/1.55 class_Rings_Olinordered__idom [110, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.93/1.55 c_Orderings_Oord__class_Oless__eq [115, 3] (w:1, o:225, a:1, s:1, b:0
% 0.93/1.55 ),
% 0.93/1.55 c_Orderings_Oord__class_Oless [116, 3] (w:1, o:226, a:1, s:1, b:0),
% 0.93/1.55 c_Int_OMin [117, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.93/1.55 c_Power_Opower_Opower [118, 3] (w:1, o:227, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oring__1 [119, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.93/1.55 c_Groups_Ouminus__class_Ouminus [120, 2] (w:1, o:206, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 c_Groups_Ominus__class_Ominus [121, 3] (w:1, o:228, a:1, s:1, b:0),
% 0.93/1.55 v_y____ [122, 0] (w:1, o:79, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Ocomm__ring__1 [129, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.93/1.55 class_Orderings_Olinorder [131, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__semidom [132, 1] (w:1, o:143, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 class_Rings_Oordered__ring [136, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__semiring__strict [137, 1] (w:1, o:144, a:1
% 0.93/1.55 , s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__semiring [138, 1] (w:1, o:145, a:1, s:1, b:0
% 0.93/1.55 ),
% 0.93/1.55 class_Fields_Olinordered__field [139, 1] (w:1, o:116, a:1, s:1, b:0)
% 0.93/1.55 ,
% 0.93/1.55 class_Groups_Oab__group__add [144, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oring [145, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oidom [146, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.93/1.55 class_Groups_Ogroup__add [147, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.93/1.55 class_Fields_Olinordered__field__inverse__zero [148, 1] (w:1, o:117
% 0.93/1.55 , a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__semiring__1__strict [149, 1] (w:1, o:146, a:
% 0.93/1.55 1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__comm__semiring__strict [150, 1] (w:1, o:147
% 0.93/1.55 , a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__ring [151, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Oordered__cancel__semiring [152, 1] (w:1, o:154, a:1, s:1
% 0.93/1.55 , b:0),
% 0.93/1.55 class_Rings_Oordered__semiring [153, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.93/1.55
% 0.93/1.55 class_Rings_Oordered__comm__semiring [154, 1] (w:1, o:156, a:1, s:1
% 0.93/1.55 , b:0),
% 0.93/1.55 class_RealVector_Oreal__field [157, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.93/1.55 class_Rings_Olinordered__semiring__1 [158, 1] (w:1, o:148, a:1, s:1
% 0.93/1.55 , b:0),
% 0.93/1.55 c_NthRoot_Osqrt [160, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.93/1.55 hBOOL [163, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.93/1.55 tc_Complex_Ocomplex [180, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.93/1.65 v_z [181, 0] (w:1, o:100, a:1, s:1, b:0),
% 0.93/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [182, 1] (w:1, o:
% 0.93/1.65 114, a:1, s:1, b:0),
% 0.93/1.65 v_x____ [184, 0] (w:1, o:77, a:1, s:1, b:0),
% 0.93/1.65 c_Complex_Ocomplex_OComplex [185, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.93/1.65 c_Complex_Ocomplex_Ocomplex__size [193, 1] (w:1, o:164, a:1, s:1, b:0
% 0.93/1.65 ),
% 0.93/1.65 c_Transcendental_Oarctan [194, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Oordered__comm__monoid__add [195, 1] (w:1, o:166, a:1
% 0.93/1.65 , s:1, b:0),
% 0.93/1.65 class_Groups_Ozero [196, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Oab__semigroup__mult [197, 1] (w:1, o:168, a:1, s:1, b:0
% 0.93/1.65 ),
% 0.93/1.65 class_Groups_Ocancel__semigroup__add [198, 1] (w:1, o:169, a:1, s:1
% 0.93/1.65 , b:0),
% 0.93/1.65 class_Groups_Ocancel__ab__semigroup__add [199, 1] (w:1, o:170, a:1
% 0.93/1.65 , s:1, b:0),
% 0.93/1.65 class_Groups_Oab__semigroup__add [200, 1] (w:1, o:171, a:1, s:1, b:0)
% 0.93/1.65 ,
% 0.93/1.65 class_Groups_Oone [201, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Ocomm__monoid__add [202, 1] (w:1, o:173, a:1, s:1, b:0)
% 0.93/1.65 ,
% 0.93/1.65 class_Groups_Omonoid__add [203, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [204, 1] (w:1, o:
% 0.93/1.65 175, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Oordered__ab__semigroup__add [205, 1] (w:1, o:176, a:1
% 0.93/1.65 , s:1, b:0),
% 0.93/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [206, 1] (w:1, o:
% 0.93/1.65 177, a:1, s:1, b:0),
% 0.93/1.65 class_Groups_Oordered__ab__group__add [207, 1] (w:1, o:178, a:1, s:1
% 0.93/1.65 , b:0),
% 0.93/1.65 c_Complex_Oii [208, 0] (w:1, o:102, a:1, s:1, b:0),
% 0.93/1.65 class_RealVector_Oreal__normed__algebra [209, 1] (w:1, o:158, a:1, s:
% 0.93/1.65 1, b:0),
% 0.93/1.65 v_x [210, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.93/1.65 alpha1 [211, 3] (w:1, o:229, a:1, s:1, b:1),
% 0.93/1.65 alpha2 [212, 3] (w:1, o:240, a:1, s:1, b:1),
% 0.93/1.65 alpha3 [213, 3] (w:1, o:251, a:1, s:1, b:1),
% 0.93/1.65 alpha4 [214, 3] (w:1, o:254, a:1, s:1, b:1),
% 0.93/1.65 alpha5 [215, 3] (w:1, o:255, a:1, s:1, b:1),
% 0.93/1.65 alpha6 [216, 3] (w:1, o:262, a:1, s:1, b:1),
% 0.93/1.65 alpha7 [217, 2] (w:1, o:210, a:1, s:1, b:1),
% 0.93/1.65 alpha8 [218, 2] (w:1, o:211, a:1, s:1, b:1),
% 0.93/1.65 alpha9 [219, 2] (w:1, o:212, a:1, s:1, b:1),
% 0.93/1.65 alpha10 [220, 3] (w:1, o:230, a:1, s:1, b:1),
% 0.93/1.65 alpha11 [221, 3] (w:1, o:233, a:1, s:1, b:1),
% 0.93/1.65 alpha12 [222, 3] (w:1, o:234, a:1, s:1, b:1),
% 0.93/1.65 alpha13 [223, 3] (w:1, o:235, a:1, s:1, b:1),
% 0.93/1.65 alpha14 [224, 3] (w:1, o:236, a:1, s:1, b:1),
% 0.93/1.65 alpha15 [225, 3] (w:1, o:237, a:1, s:1, b:1),
% 0.93/1.65 alpha16 [226, 4] (w:1, o:267, a:1, s:1, b:1),
% 0.93/1.65 alpha17 [227, 4] (w:1, o:268, a:1, s:1, b:1),
% 0.93/1.65 alpha18 [228, 3] (w:1, o:238, a:1, s:1, b:1),
% 0.93/1.65 alpha19 [229, 3] (w:1, o:239, a:1, s:1, b:1),
% 0.93/1.65 alpha20 [230, 3] (w:1, o:241, a:1, s:1, b:1),
% 0.93/1.65 alpha21 [231, 3] (w:1, o:242, a:1, s:1, b:1),
% 0.93/1.65 alpha22 [232, 3] (w:1, o:243, a:1, s:1, b:1),
% 0.93/1.65 alpha23 [233, 3] (w:1, o:244, a:1, s:1, b:1),
% 0.93/1.65 alpha24 [234, 3] (w:1, o:245, a:1, s:1, b:1),
% 0.93/1.65 alpha25 [235, 3] (w:1, o:246, a:1, s:1, b:1),
% 0.93/1.65 alpha26 [236, 3] (w:1, o:247, a:1, s:1, b:1),
% 0.93/1.65 alpha27 [237, 3] (w:1, o:248, a:1, s:1, b:1),
% 0.93/1.65 alpha28 [238, 3] (w:1, o:249, a:1, s:1, b:1),
% 0.93/1.65 alpha29 [239, 3] (w:1, o:250, a:1, s:1, b:1),
% 0.93/1.65 alpha30 [240, 2] (w:1, o:213, a:1, s:1, b:1),
% 0.93/1.65 alpha31 [241, 3] (w:1, o:252, a:1, s:1, b:1),
% 0.93/1.65 alpha32 [242, 3] (w:1, o:253, a:1, s:1, b:1),
% 0.93/1.65 alpha33 [243, 2] (w:1, o:214, a:1, s:1, b:1),
% 0.93/1.65 alpha34 [244, 2] (w:1, o:215, a:1, s:1, b:1),
% 0.93/1.65 alpha35 [245, 4] (w:1, o:269, a:1, s:1, b:1),
% 0.93/1.65 alpha36 [246, 4] (w:1, o:270, a:1, s:1, b:1),
% 0.93/1.65 alpha37 [247, 4] (w:1, o:271, a:1, s:1, b:1),
% 0.93/1.65 alpha38 [248, 4] (w:1, o:272, a:1, s:1, b:1),
% 0.93/1.65 alpha39 [249, 4] (w:1, o:273, a:1, s:1, b:1),
% 0.93/1.65 alpha40 [250, 4] (w:1, o:274, a:1, s:1, b:1),
% 0.93/1.65 alpha41 [251, 2] (w:1, o:216, a:1, s:1, b:1),
% 0.93/1.65 alpha42 [252, 2] (w:1, o:217, a:1, s:1, b:1),
% 0.93/1.65 alpha43 [253, 4] (w:1, o:275, a:1, s:1, b:1),
% 0.93/1.65 alpha44 [254, 4] (w:1, o:276, a:1, s:1, b:1),
% 0.93/1.65 alpha45 [255, 4] (w:1, o:277, a:1, s:1, b:1),
% 35.37/35.79 alpha46 [256, 4] (w:1, o:278, a:1, s:1, b:1),
% 35.37/35.79 alpha47 [257, 4] (w:1, o:279, a:1, s:1, b:1),
% 35.37/35.79 alpha48 [258, 4] (w:1, o:280, a:1, s:1, b:1),
% 35.37/35.79 alpha49 [259, 4] (w:1, o:281, a:1, s:1, b:1),
% 35.37/35.79 alpha50 [260, 4] (w:1, o:282, a:1, s:1, b:1),
% 35.37/35.79 alpha51 [261, 3] (w:1, o:256, a:1, s:1, b:1),
% 35.37/35.79 alpha52 [262, 3] (w:1, o:257, a:1, s:1, b:1),
% 35.37/35.79 alpha53 [263, 3] (w:1, o:258, a:1, s:1, b:1),
% 35.37/35.79 alpha54 [264, 3] (w:1, o:259, a:1, s:1, b:1),
% 35.37/35.79 alpha55 [265, 3] (w:1, o:260, a:1, s:1, b:1),
% 35.37/35.79 alpha56 [266, 3] (w:1, o:261, a:1, s:1, b:1),
% 35.37/35.79 alpha57 [267, 4] (w:1, o:283, a:1, s:1, b:1),
% 35.37/35.79 alpha58 [268, 4] (w:1, o:284, a:1, s:1, b:1),
% 35.37/35.79 alpha59 [269, 4] (w:1, o:285, a:1, s:1, b:1),
% 35.37/35.79 alpha60 [270, 4] (w:1, o:286, a:1, s:1, b:1),
% 35.37/35.79 alpha61 [271, 4] (w:1, o:287, a:1, s:1, b:1),
% 35.37/35.79 alpha62 [272, 4] (w:1, o:288, a:1, s:1, b:1),
% 35.37/35.79 alpha63 [273, 3] (w:1, o:263, a:1, s:1, b:1),
% 35.37/35.79 alpha64 [274, 3] (w:1, o:264, a:1, s:1, b:1),
% 35.37/35.79 alpha65 [275, 2] (w:1, o:208, a:1, s:1, b:1),
% 35.37/35.79 alpha66 [276, 2] (w:1, o:209, a:1, s:1, b:1),
% 35.37/35.79 alpha67 [277, 4] (w:1, o:289, a:1, s:1, b:1),
% 35.37/35.79 alpha68 [278, 4] (w:1, o:290, a:1, s:1, b:1),
% 35.37/35.79 alpha69 [279, 4] (w:1, o:291, a:1, s:1, b:1),
% 35.37/35.79 alpha70 [280, 4] (w:1, o:292, a:1, s:1, b:1),
% 35.37/35.79 alpha71 [281, 4] (w:1, o:293, a:1, s:1, b:1),
% 35.37/35.79 alpha72 [282, 4] (w:1, o:294, a:1, s:1, b:1),
% 35.37/35.79 alpha73 [283, 4] (w:1, o:295, a:1, s:1, b:1),
% 35.37/35.79 alpha74 [284, 4] (w:1, o:296, a:1, s:1, b:1),
% 35.37/35.79 alpha75 [285, 4] (w:1, o:297, a:1, s:1, b:1),
% 35.37/35.79 alpha76 [286, 4] (w:1, o:298, a:1, s:1, b:1),
% 35.37/35.79 alpha77 [287, 4] (w:1, o:299, a:1, s:1, b:1),
% 35.37/35.79 alpha78 [288, 4] (w:1, o:300, a:1, s:1, b:1),
% 35.37/35.79 alpha79 [289, 4] (w:1, o:301, a:1, s:1, b:1),
% 35.37/35.79 alpha80 [290, 4] (w:1, o:302, a:1, s:1, b:1),
% 35.37/35.79 alpha81 [291, 4] (w:1, o:303, a:1, s:1, b:1),
% 35.37/35.79 alpha82 [292, 4] (w:1, o:304, a:1, s:1, b:1),
% 35.37/35.79 alpha83 [293, 4] (w:1, o:305, a:1, s:1, b:1),
% 35.37/35.79 alpha84 [294, 4] (w:1, o:306, a:1, s:1, b:1),
% 35.37/35.79 alpha85 [295, 4] (w:1, o:307, a:1, s:1, b:1),
% 35.37/35.79 alpha86 [296, 4] (w:1, o:308, a:1, s:1, b:1),
% 35.37/35.79 alpha87 [297, 4] (w:1, o:309, a:1, s:1, b:1),
% 35.37/35.79 alpha88 [298, 4] (w:1, o:310, a:1, s:1, b:1),
% 35.37/35.79 alpha89 [299, 4] (w:1, o:311, a:1, s:1, b:1),
% 35.37/35.79 alpha90 [300, 4] (w:1, o:312, a:1, s:1, b:1),
% 35.37/35.79 alpha91 [301, 4] (w:1, o:313, a:1, s:1, b:1),
% 35.37/35.79 alpha92 [302, 4] (w:1, o:314, a:1, s:1, b:1),
% 35.37/35.79 alpha93 [303, 4] (w:1, o:315, a:1, s:1, b:1),
% 35.37/35.79 alpha94 [304, 4] (w:1, o:316, a:1, s:1, b:1),
% 35.37/35.79 alpha95 [305, 4] (w:1, o:317, a:1, s:1, b:1),
% 35.37/35.79 alpha96 [306, 4] (w:1, o:318, a:1, s:1, b:1),
% 35.37/35.79 alpha97 [307, 4] (w:1, o:319, a:1, s:1, b:1),
% 35.37/35.79 alpha98 [308, 4] (w:1, o:320, a:1, s:1, b:1),
% 35.37/35.79 alpha99 [309, 4] (w:1, o:321, a:1, s:1, b:1),
% 35.37/35.79 alpha100 [310, 4] (w:1, o:322, a:1, s:1, b:1),
% 35.37/35.79 alpha101 [311, 4] (w:1, o:323, a:1, s:1, b:1),
% 35.37/35.79 alpha102 [312, 4] (w:1, o:324, a:1, s:1, b:1),
% 35.37/35.79 alpha103 [313, 3] (w:1, o:231, a:1, s:1, b:1),
% 35.37/35.79 alpha104 [314, 3] (w:1, o:232, a:1, s:1, b:1),
% 35.37/35.79 skol1 [315, 2] (w:1, o:218, a:1, s:1, b:1),
% 35.37/35.79 skol2 [316, 2] (w:1, o:219, a:1, s:1, b:1),
% 35.37/35.79 skol3 [317, 2] (w:1, o:220, a:1, s:1, b:1),
% 35.37/35.79 skol4 [318, 2] (w:1, o:221, a:1, s:1, b:1),
% 35.37/35.79 skol5 [319, 1] (w:1, o:179, a:1, s:1, b:1),
% 35.37/35.79 skol6 [320, 3] (w:1, o:265, a:1, s:1, b:1),
% 35.37/35.79 skol7 [321, 3] (w:1, o:266, a:1, s:1, b:1),
% 35.37/35.79 skol8 [322, 2] (w:1, o:222, a:1, s:1, b:1),
% 35.37/35.79 skol9 [323, 0] (w:1, o:43, a:1, s:1, b:1),
% 35.37/35.79 skol10 [324, 0] (w:1, o:44, a:1, s:1, b:1).
% 35.37/35.79
% 35.37/35.79
% 35.37/35.79 Starting Search:
% 35.37/35.79
% 35.37/35.79 *** allocated 170857 integers for clauses
% 35.37/35.79 Resimplifying inuse:
% 35.37/35.79 Done
% 35.37/35.79
% 35.37/35.79
% 35.37/35.79 Intermediate Status:
% 35.37/35.79 Generated: 2860
% 35.37/35.79 Kept: 2012
% 35.37/35.79 Inuse: 25
% 35.37/35.79 Deleted: 1
% 35.37/35.79 Deletedinuse: 0
% 35.37/35.79
% 35.37/35.79 *** allocated 256285 integers for clauses
% 35.37/35.79 Resimplifying inuse:
% 35.37/35.79 Done
% 35.37/35.79
% 35.37/35.79 *** allocated 170857 integers for termspace/termends
% 35.37/35.79 *** allocated 384427 integers for clauses
% 35.37/35.79 Resimplifying inuse:
% 35.37/35.79 Done
% 35.37/35.79
% 35.37/35.79
% 35.37/35.79 Intermediate Status:
% 35.37/35.79 Generated: 7903
% 35.37/35.79 Kept: 4017
% 88.63/89.04 Inuse: 176
% 88.63/89.04 Deleted: 14
% 88.63/89.04 Deletedinuse: 2
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 256285 integers for termspace/termends
% 88.63/89.04 *** allocated 576640 integers for clauses
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 12486
% 88.63/89.04 Kept: 6017
% 88.63/89.04 Inuse: 269
% 88.63/89.04 Deleted: 26
% 88.63/89.04 Deletedinuse: 2
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 864960 integers for clauses
% 88.63/89.04 *** allocated 384427 integers for termspace/termends
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 21882
% 88.63/89.04 Kept: 9157
% 88.63/89.04 Inuse: 327
% 88.63/89.04 Deleted: 31
% 88.63/89.04 Deletedinuse: 2
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 35096
% 88.63/89.04 Kept: 11520
% 88.63/89.04 Inuse: 361
% 88.63/89.04 Deleted: 32
% 88.63/89.04 Deletedinuse: 2
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 576640 integers for termspace/termends
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 42276
% 88.63/89.04 Kept: 13573
% 88.63/89.04 Inuse: 411
% 88.63/89.04 Deleted: 32
% 88.63/89.04 Deletedinuse: 2
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 1297440 integers for clauses
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 64300
% 88.63/89.04 Kept: 16884
% 88.63/89.04 Inuse: 445
% 88.63/89.04 Deleted: 41
% 88.63/89.04 Deletedinuse: 10
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 864960 integers for termspace/termends
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 81051
% 88.63/89.04 Kept: 19773
% 88.63/89.04 Inuse: 495
% 88.63/89.04 Deleted: 41
% 88.63/89.04 Deletedinuse: 10
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying clauses:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 93099
% 88.63/89.04 Kept: 21917
% 88.63/89.04 Inuse: 510
% 88.63/89.04 Deleted: 712
% 88.63/89.04 Deletedinuse: 10
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 1946160 integers for clauses
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 111780
% 88.63/89.04 Kept: 24473
% 88.63/89.04 Inuse: 555
% 88.63/89.04 Deleted: 712
% 88.63/89.04 Deletedinuse: 10
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 1297440 integers for termspace/termends
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 122144
% 88.63/89.04 Kept: 27014
% 88.63/89.04 Inuse: 570
% 88.63/89.04 Deleted: 713
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 132637
% 88.63/89.04 Kept: 29302
% 88.63/89.04 Inuse: 624
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 147686
% 88.63/89.04 Kept: 31901
% 88.63/89.04 Inuse: 644
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 182902
% 88.63/89.04 Kept: 33913
% 88.63/89.04 Inuse: 654
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 202170
% 88.63/89.04 Kept: 35932
% 88.63/89.04 Inuse: 679
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 *** allocated 2919240 integers for clauses
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 *** allocated 1946160 integers for termspace/termends
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 216985
% 88.63/89.04 Kept: 38329
% 88.63/89.04 Inuse: 689
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 223390
% 88.63/89.04 Kept: 40786
% 88.63/89.04 Inuse: 704
% 88.63/89.04 Deleted: 714
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying clauses:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 230649
% 88.63/89.04 Kept: 43180
% 88.63/89.04 Inuse: 729
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 244621
% 88.63/89.04 Kept: 45291
% 88.63/89.04 Inuse: 744
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 251816
% 88.63/89.04 Kept: 48353
% 88.63/89.04 Inuse: 749
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 258340
% 88.63/89.04 Kept: 50462
% 88.63/89.04 Inuse: 779
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 271091
% 88.63/89.04 Kept: 53463
% 88.63/89.04 Inuse: 824
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 88.63/89.04 Done
% 88.63/89.04
% 88.63/89.04
% 88.63/89.04 Intermediate Status:
% 88.63/89.04 Generated: 281165
% 88.63/89.04 Kept: 55732
% 88.63/89.04 Inuse: 874
% 88.63/89.04 Deleted: 1105
% 88.63/89.04 Deletedinuse: 11
% 88.63/89.04
% 88.63/89.04 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 290751
% 189.95/190.37 Kept: 58162
% 189.95/190.37 Inuse: 894
% 189.95/190.37 Deleted: 1105
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 *** allocated 4378860 integers for clauses
% 189.95/190.37 *** allocated 2919240 integers for termspace/termends
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 307852
% 189.95/190.37 Kept: 60906
% 189.95/190.37 Inuse: 924
% 189.95/190.37 Deleted: 1105
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying clauses:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 313274
% 189.95/190.37 Kept: 63012
% 189.95/190.37 Inuse: 944
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 330108
% 189.95/190.37 Kept: 65698
% 189.95/190.37 Inuse: 969
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 335571
% 189.95/190.37 Kept: 67819
% 189.95/190.37 Inuse: 989
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 346239
% 189.95/190.37 Kept: 70564
% 189.95/190.37 Inuse: 1014
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 355209
% 189.95/190.37 Kept: 73229
% 189.95/190.37 Inuse: 1044
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 364101
% 189.95/190.37 Kept: 75319
% 189.95/190.37 Inuse: 1074
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 372621
% 189.95/190.37 Kept: 77409
% 189.95/190.37 Inuse: 1094
% 189.95/190.37 Deleted: 1187
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 380682
% 189.95/190.37 Kept: 79497
% 189.95/190.37 Inuse: 1138
% 189.95/190.37 Deleted: 1188
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying clauses:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 392772
% 189.95/190.37 Kept: 82763
% 189.95/190.37 Inuse: 1168
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 398613
% 189.95/190.37 Kept: 84767
% 189.95/190.37 Inuse: 1198
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 404961
% 189.95/190.37 Kept: 86899
% 189.95/190.37 Inuse: 1233
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 *** allocated 4378860 integers for termspace/termends
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 411677
% 189.95/190.37 Kept: 89061
% 189.95/190.37 Inuse: 1278
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 416944
% 189.95/190.37 Kept: 91210
% 189.95/190.37 Inuse: 1318
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 *** allocated 6568290 integers for clauses
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 423240
% 189.95/190.37 Kept: 93337
% 189.95/190.37 Inuse: 1358
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 429366
% 189.95/190.37 Kept: 95617
% 189.95/190.37 Inuse: 1383
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 438905
% 189.95/190.37 Kept: 97951
% 189.95/190.37 Inuse: 1393
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 445192
% 189.95/190.37 Kept: 99972
% 189.95/190.37 Inuse: 1403
% 189.95/190.37 Deleted: 1283
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying clauses:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 453946
% 189.95/190.37 Kept: 102237
% 189.95/190.37 Inuse: 1428
% 189.95/190.37 Deleted: 1430
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 460230
% 189.95/190.37 Kept: 104406
% 189.95/190.37 Inuse: 1473
% 189.95/190.37 Deleted: 1430
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 468873
% 189.95/190.37 Kept: 106463
% 189.95/190.37 Inuse: 1488
% 189.95/190.37 Deleted: 1430
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37
% 189.95/190.37 Intermediate Status:
% 189.95/190.37 Generated: 478569
% 189.95/190.37 Kept: 109020
% 189.95/190.37 Inuse: 1508
% 189.95/190.37 Deleted: 1430
% 189.95/190.37 Deletedinuse: 11
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 189.95/190.37 Done
% 189.95/190.37
% 189.95/190.37 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 483966
% 284.55/284.97 Kept: 111796
% 284.55/284.97 Inuse: 1523
% 284.55/284.97 Deleted: 1430
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 492819
% 284.55/284.97 Kept: 113904
% 284.55/284.97 Inuse: 1537
% 284.55/284.97 Deleted: 1431
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 498336
% 284.55/284.97 Kept: 116323
% 284.55/284.97 Inuse: 1551
% 284.55/284.97 Deleted: 1432
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 503674
% 284.55/284.97 Kept: 118629
% 284.55/284.97 Inuse: 1571
% 284.55/284.97 Deleted: 1432
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 511377
% 284.55/284.97 Kept: 120935
% 284.55/284.97 Inuse: 1586
% 284.55/284.97 Deleted: 1432
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying clauses:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 519347
% 284.55/284.97 Kept: 122951
% 284.55/284.97 Inuse: 1601
% 284.55/284.97 Deleted: 1621
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 525111
% 284.55/284.97 Kept: 124983
% 284.55/284.97 Inuse: 1627
% 284.55/284.97 Deleted: 1621
% 284.55/284.97 Deletedinuse: 11
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 533160
% 284.55/284.97 Kept: 127025
% 284.55/284.97 Inuse: 1652
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 *** allocated 6568290 integers for termspace/termends
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 543365
% 284.55/284.97 Kept: 129054
% 284.55/284.97 Inuse: 1673
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 558943
% 284.55/284.97 Kept: 131085
% 284.55/284.97 Inuse: 1677
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 566643
% 284.55/284.97 Kept: 133102
% 284.55/284.97 Inuse: 1693
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 575972
% 284.55/284.97 Kept: 135296
% 284.55/284.97 Inuse: 1716
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 584569
% 284.55/284.97 Kept: 137324
% 284.55/284.97 Inuse: 1740
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 591558
% 284.55/284.97 Kept: 139340
% 284.55/284.97 Inuse: 1766
% 284.55/284.97 Deleted: 1622
% 284.55/284.97 Deletedinuse: 12
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 599103
% 284.55/284.97 Kept: 141483
% 284.55/284.97 Inuse: 1785
% 284.55/284.97 Deleted: 1624
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 *** allocated 9852435 integers for clauses
% 284.55/284.97 Resimplifying clauses:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 635364
% 284.55/284.97 Kept: 147049
% 284.55/284.97 Inuse: 1800
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 646113
% 284.55/284.97 Kept: 149068
% 284.55/284.97 Inuse: 1816
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 659777
% 284.55/284.97 Kept: 152334
% 284.55/284.97 Inuse: 1840
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 672586
% 284.55/284.97 Kept: 155198
% 284.55/284.97 Inuse: 1860
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 681263
% 284.55/284.97 Kept: 157202
% 284.55/284.97 Inuse: 1880
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 690274
% 284.55/284.97 Kept: 159409
% 284.55/284.97 Inuse: 1920
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 703325
% 284.55/284.97 Kept: 162777
% 284.55/284.97 Inuse: 1945
% 284.55/284.97 Deleted: 2430
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying clauses:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 711887
% 284.55/284.97 Kept: 164795
% 284.55/284.97 Inuse: 1959
% 284.55/284.97 Deleted: 2737
% 284.55/284.97 Deletedinuse: 13
% 284.55/284.97
% 284.55/284.97 Resimplifying inuse:
% 284.55/284.97 Done
% 284.55/284.97
% 284.55/284.97
% 284.55/284.97 Intermediate Status:
% 284.55/284.97 Generated: 718492
% 284.55/284.97 Kept: 166831
% 284.55/284.97 Inuse: 1990
% 284.55/284.97 Deleted: 2737
% 284.55/284.97 Deletedinuse: 13Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------