TSTP Solution File: SWW286+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW286+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 23:21:50 EDT 2022
% Result : Timeout 300.01s 300.59s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW286+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 05:47:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.91/1.56 *** allocated 10000 integers for termspace/termends
% 0.91/1.56 *** allocated 10000 integers for clauses
% 0.91/1.56 *** allocated 10000 integers for justifications
% 0.91/1.56 *** allocated 15000 integers for termspace/termends
% 0.91/1.56 *** allocated 22500 integers for termspace/termends
% 0.91/1.56 *** allocated 33750 integers for termspace/termends
% 0.91/1.56 Bliksem 1.12
% 0.91/1.56
% 0.91/1.56
% 0.91/1.56 Automatic Strategy Selection
% 0.91/1.56
% 0.91/1.56 *** allocated 50625 integers for termspace/termends
% 0.91/1.56 *** allocated 75937 integers for termspace/termends
% 0.91/1.56 *** allocated 113905 integers for termspace/termends
% 0.91/1.56
% 0.91/1.56 Clauses:
% 0.91/1.56
% 0.91/1.56 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.91/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ) }.
% 0.91/1.56 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.56 { v_p = c_Polynomial_OpCons( tc_Complex_Ocomplex, v_k____,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.91/1.56 ) }.
% 0.91/1.56 { c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.91/1.56 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.91/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.91/1.56 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.91/1.56 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.91/1.56 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.91/1.56 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.91/1.56 ( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.91/1.56 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha24( X, Y, Z, T ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha1( X, Y, T ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha24( X, Y, Z, T ), !
% 0.91/1.56 alpha1( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.91/1.56 { ! alpha24( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.91/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z, T ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha24(
% 0.91/1.56 X, Y, Z, T ) }.
% 0.91/1.56 { ! alpha1( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { Y = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.91/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha25( X, Y, Z, T ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha2( X, Y, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha25( X, Y, Z, T ), !
% 0.91/1.56 alpha2( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.91/1.56 { ! alpha25( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.91/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.91/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 0.91/1.56 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha25(
% 0.91/1.56 X, Y, Z, T ) }.
% 0.91/1.56 { ! alpha2( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { Z = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) ) = Y }.
% 0.91/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.91/1.56 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.91/1.56 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.91/1.56 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( X ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.56 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.91/1.56 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.91/1.56 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.91/1.56 = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.91/1.56 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.91/1.56 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.91/1.56 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.91/1.56 { v_p = c_Polynomial_OpCons( tc_Complex_Ocomplex, skol2,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! skol2 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.91/1.56 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.91/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ), ! alpha3, c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.91/1.56 ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex, v_p ) ) ), alpha26
% 0.91/1.56 }.
% 0.91/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( tc_Complex_Ocomplex ), v_p, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.91/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree
% 0.91/1.56 ( tc_Complex_Ocomplex, v_p ) ) ), alpha3 }.
% 0.91/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ), ! alpha26, alpha3 }.
% 0.91/1.56 { ! alpha26, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ) }.
% 0.91/1.56 { ! alpha26, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ) }.
% 0.91/1.56 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.56 tc_Complex_Ocomplex ) ), ! v_q = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), alpha26 }.
% 0.91/1.56 { ! alpha3, ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.91/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol3 ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha3 }.
% 0.91/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), skol3 ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), alpha3 }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.91/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.91/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.91/1.56 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 Z, T ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.56 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.91/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.91/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.91/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.91/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.91/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.91/1.56 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.91/1.56 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.91/1.56 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.91/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.91/1.56 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.91/1.56 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.91/1.56 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.91/1.56 = Y }.
% 0.91/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol4( Z, Y ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.91/1.56 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.91/1.56 ), X ), T ) ) }.
% 0.91/1.56 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol4( X, Y ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.91/1.56 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.91/1.56 ), X ), Z ) ) }.
% 0.91/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.91/1.56 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.91/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.91/1.56 , Y ), X ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.91/1.56 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.91/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.91/1.56 .
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.91/1.56 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.91/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.91/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.91/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.91/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.56 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.56 X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.91/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.91/1.56 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.91/1.56 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.91/1.56 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.91/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.91/1.56 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.91/1.56 X, Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.91/1.56 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.91/1.56 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 X ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.91/1.56 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.91/1.56 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.91/1.56 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), !
% 0.91/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.91/1.56 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.91/1.56 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.91/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.91/1.56 ( X ) }.
% 0.91/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.91/1.56 , Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.91/1.56 Z, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.56 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha4( X, Y ), ! Y = X }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha4( X, Y ) }
% 0.91/1.56 .
% 0.91/1.56 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha5( X, Y ), Y = X }
% 0.91/1.56 .
% 0.91/1.56 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 0.91/1.56 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.91/1.56 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.91/1.56 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol5( X
% 0.91/1.56 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol5( X, Y, Z ) ), Z = Y
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.91/1.56 ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.91/1.56 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.91/1.56 c_Polynomial_Ocoeff( X, Y ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.91/1.56 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.91/1.56 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.56 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( X ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Y ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.56 = Y }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.91/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.91/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.91/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.91/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.91/1.56 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.91/1.56 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.91/1.56 , Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.91/1.56 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.91/1.56 , Z, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.91/1.56 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.91/1.56 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.91/1.56 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.91/1.56 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) = Z }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.91/1.56 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.91/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.91/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.91/1.56 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.91/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.91/1.56 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.91/1.56 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.91/1.56 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.91/1.56 Y ) ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.91/1.56 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.91/1.56 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.91/1.56 Y ) ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.91/1.56 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.91/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.91/1.56 tc_Nat_Onat ), X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, Z, X ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.91/1.56 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.91/1.56 ) }.
% 0.91/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 0.91/1.56 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.91/1.56 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.91/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Y, T ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 T, Y ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 T, Y ), Z = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.91/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Y, Z ), T = Y }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Y, Z ) }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 T, Y ), Z = Y }.
% 0.91/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 T, Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.91/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.91/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.91/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.91/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.91/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.91/1.56 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.91/1.56 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.91/1.56 { ! c_Nat_OSuc( X ) = X }.
% 0.91/1.56 { ! X = c_Nat_OSuc( X ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.91/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.91/1.56 ) ), T ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.91/1.56 ), U = Z, T = Y }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.91/1.56 ) ), Z ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.91/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.91/1.56 ), ! U = T }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.91/1.56 ), ! Z = Y }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 Z, Y ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 Y ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.91/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.91/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.56 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.91/1.56 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.91/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.56 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.91/1.56 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.91/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.91/1.56 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.91/1.56 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.91/1.56 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.91/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.56 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.91/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.91/1.56 ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.91/1.56 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.91/1.56 ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 X ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Y ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.56 Z ) = Y }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.91/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.56 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.91/1.56 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.56 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.91/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.91/1.56 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.91/1.56 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.91/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.91/1.56 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.91/1.56 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.91/1.56 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.91/1.56 .
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.91/1.56 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.91/1.56 .
% 0.91/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.91/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.91/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.91/1.56 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.91/1.56 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.91/1.56 ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Int_Oint, Z, X ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.91/1.56 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.91/1.56 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.91/1.56 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.91/1.56 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.56 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.91/1.56 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.91/1.56 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.91/1.56 hAPP( Z, skol6( U, W, Z ) ) ) }.
% 0.91/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.91/1.56 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol6( X
% 0.91/1.56 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.91/1.56 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.91/1.56 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol21( X,
% 0.91/1.56 Y, Z ) ) ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.91/1.56 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.91/1.56 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( X, Z ) }.
% 0.91/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.56 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.91/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, Y ), alpha57( X, Y, Z, T ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.91/1.56 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, Y ), alpha57( X, Y, Z, T ), ! hAPP(
% 0.91/1.56 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.91/1.56 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.91/1.56 .
% 0.91/1.56 { ! alpha57( X, Y, Z, T ), alpha59( X, Y, Z, T ), alpha55( X, Y, T ) }.
% 0.91/1.56 { ! alpha57( X, Y, Z, T ), alpha59( X, Y, Z, T ), ! hAPP(
% 0.91/1.56 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! alpha59( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 0.91/1.56 { ! alpha55( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.91/1.56 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.56 alpha57( X, Y, Z, T ) }.
% 0.91/1.56 { ! alpha59( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), Z, T ), alpha60( X, Y, Z, T ) }.
% 0.91/1.56 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha59( X, Y
% 0.91/1.56 , Z, T ) }.
% 0.91/1.56 { ! alpha60( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 0.91/1.56 { ! alpha60( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.91/1.56 ), skol7( X, Y, U, W ), Y ) }.
% 0.91/1.56 { ! alpha60( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.91/1.56 ), skol7( X, Y, U, T ), T ) }.
% 0.91/1.56 { ! alpha60( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.91/1.56 ( X ), skol7( X, Y, Z, T ), Z ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha60( X, Y
% 0.91/1.56 , Z, T ) }.
% 0.91/1.56 { ! alpha55( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! alpha55( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha55( X, Y, Z
% 0.91/1.56 ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.91/1.56 .
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.91/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.91/1.56 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.91/1.56 ) ) }.
% 0.91/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.91/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( tc_Nat_Onat ) ) = X }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ), X ) = X }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.91/1.56 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.91/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.91/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Z, Y ) ) }.
% 0.91/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha27( X
% 0.91/1.56 , Y ) }.
% 0.91/1.56 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! alpha27( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! alpha27( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! alpha27( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha27( X, Y ) }.
% 0.91/1.56 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 0.91/1.56 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha7( X, Y ), alpha28
% 0.91/1.56 ( X, Y ) }.
% 0.91/1.56 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha28( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! alpha28( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! alpha28( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha28( X, Y ) }.
% 0.91/1.56 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Nat_Onat ) ) }.
% 0.91/1.56 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.91/1.56 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.91/1.56 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.56 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.91/1.56 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.91/1.56 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Z ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.56 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.91/1.56 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.91/1.56 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.91/1.56 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.91/1.56 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.91/1.56 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.56 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.91/1.56 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.91/1.56 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.91/1.56 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.91/1.56 , Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.91/1.56 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.91/1.56 }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.91/1.56 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.91/1.56 ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.91/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.91/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.56 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.91/1.56 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.91/1.56 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.91/1.56 .
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.56 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.91/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.91/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.91/1.56 ( tc_Int_Oint ) ) = X }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.56 tc_Int_Oint ), X ) = X }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.91/1.56 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.91/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.56 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.56 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.91/1.56 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.56 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.91/1.56 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.91/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.91/1.56 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.91/1.56 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 0.91/1.56 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.91/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.91/1.56 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 0.91/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.91/1.56 ( tc_Int_Oint ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.91/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.91/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.91/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.91/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.91/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.91/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.91/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.91/1.56 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.91/1.56 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.91/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.91/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.91/1.57 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.91/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.91/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.91/1.57 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.57 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.91/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.91/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.91/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.91/1.57 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.91/1.57 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.91/1.57 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__field( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.91/1.57 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.57 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.91/1.57 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.91/1.57 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.91/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.91/1.57 Z ) ), U ), T ) = Y }.
% 0.91/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.91/1.57 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), U ), Y ) }.
% 0.91/1.57 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.57 W ) ), U ), Y ) }.
% 0.91/1.57 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), U ), Y ) }.
% 0.91/1.57 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.91/1.57 Z ) ), Y ) ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 X, Y ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.91/1.57 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.57 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.57 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.57 X, Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.91/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.91/1.57 Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.57 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.91/1.57 ), Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.91/1.57 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.91/1.57 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.91/1.57 X, T, Z ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.91/1.57 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.91/1.57 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.91/1.57 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) }.
% 0.91/1.57 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.91/1.57 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.91/1.57 }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.91/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.91/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.91/1.57 c_Polynomial_Odegree( X, Y ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.91/1.57 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha8( X
% 0.91/1.57 , Y, T ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha29( X
% 0.91/1.57 , Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! alpha8( X, Y, T ), ! alpha29( X, Y, Z, T )
% 0.91/1.57 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.91/1.57 ( X, T, Z ), Y ) }.
% 0.91/1.57 { ! alpha29( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.91/1.57 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha29( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha29( X
% 0.91/1.57 , Y, Z, T ) }.
% 0.91/1.57 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 0.91/1.57 , Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.91/1.57 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.91/1.57 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Nat_Onat ) ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Int_Oint, Y, X ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.91/1.57 , Z ), X ) ), T ) ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, U, T ) ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.91/1.57 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.91/1.57 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.91/1.57 ( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.91/1.57 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.91/1.57 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.91/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.91/1.57 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.57 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 0.91/1.57 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 0.91/1.57 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 0.91/1.57 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 0.91/1.57 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.57 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.91/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.91/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.91/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.91/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.91/1.57 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.91/1.57 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.91/1.57 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.91/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 0.91/1.57 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 0.91/1.57 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.91/1.57 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.91/1.57 c_Polynomial_OpCons( X, T,
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.91/1.57 , alpha43( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha43( X, Y, Z, T ),
% 0.91/1.57 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.91/1.57 { ! alpha43( X, Y, Z, T ), alpha9( X, Z, T ) }.
% 0.91/1.57 { ! alpha43( X, Y, Z, T ), alpha30( X, Y, T ) }.
% 0.91/1.57 { ! alpha9( X, Z, T ), ! alpha30( X, Y, T ), alpha43( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha30( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), alpha44( X, Y, Z ) }.
% 0.91/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha30( X
% 0.91/1.57 , Y, Z ) }.
% 0.91/1.57 { ! alpha44( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.91/1.57 { ! alpha44( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha44( X
% 0.91/1.57 , Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.91/1.57 ), c_Polynomial_Odegree( X, Z ) ), alpha44( X, Y, Z ) }.
% 0.91/1.57 { ! alpha9( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X, Y
% 0.91/1.57 , Z ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha9( X
% 0.91/1.57 , Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.91/1.57 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.91/1.57 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.57 X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.91/1.57 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.91/1.57 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.91/1.57 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.91/1.57 = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.91/1.57 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.57 , Y, Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.57 , T, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.57 , Y, T ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.57 , T, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.57 , T ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( X, Y ), Z ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.57 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( X, Z ), Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.57 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.91/1.57 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.91/1.57 }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.91/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.57 X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.91/1.57 .
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.91/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.91/1.57 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.91/1.57 , X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.91/1.57 , Y ) ) = Y }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.91/1.57 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.91/1.57 { alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.91/1.57 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.91/1.57 { alpha56( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.91/1.57 ( X, Y ), Z ) ) }.
% 0.91/1.57 { ! alpha56( X, Y, Z ), alpha58( X, Y, Z ), Z = Y }.
% 0.91/1.57 { ! alpha56( X, Y, Z ), alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.91/1.57 ) ) }.
% 0.91/1.57 { ! alpha58( X, Y, Z ), alpha56( X, Y, Z ) }.
% 0.91/1.57 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha56( X, Y, Z ) }.
% 0.91/1.57 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! alpha58( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.91/1.57 X, Y ), Z ) ), alpha58( X, Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.91/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.57 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.91/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.91/1.57 ) ), Y ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.91/1.57 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.91/1.57 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.57 = Y }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.91/1.57 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.91/1.57 X, Y ) ) = Y }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.91/1.57 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.57 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.91/1.57 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ) ), Z ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.91/1.57 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.91/1.57 , Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.91/1.57 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha10( X, Y, Z, T ),
% 0.91/1.57 alpha31( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha31( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.91/1.57 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha10( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha11( X, Y, Z, T ),
% 0.91/1.57 alpha32( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha32( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.57 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha11( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.57 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.57 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.57 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Y ) }.
% 0.91/1.57 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.57 , Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.91/1.57 , Y, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.91/1.57 , Y, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.91/1.57 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha33( X,
% 0.91/1.57 Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.91/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.91/1.57 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.57 ), alpha33( X, Y, Z ) }.
% 0.91/1.57 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.57 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 ), alpha12( X, Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha34
% 0.91/1.57 ( X, Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.57 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 ), alpha34( X, Y, Z ) }.
% 0.91/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.57 ), alpha13( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.91/1.57 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha14( X, Y ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { ! alpha14( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.57 c_Nat_OSuc( X ) ) }.
% 0.91/1.57 { ! alpha14( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 0.91/1.57 { ! alpha14( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X,
% 0.91/1.57 Y ), X ) }.
% 0.91/1.57 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.91/1.57 ), alpha14( X, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 0.91/1.57 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.91/1.57 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.91/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.91/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.57 Y ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Nat_Onat ), X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.91/1.57 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.91/1.57 ), X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.91/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.91/1.57 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.91/1.57 ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.91/1.57 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.91/1.57 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Polynomial_Opoly( X ) ),
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.91/1.57 c_Polynomial_Odegree( X, Z ) }.
% 0.91/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.91/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.91/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.91/1.57 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.91/1.57 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.91/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.91/1.57 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.91/1.57 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.91/1.57 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.91/1.57 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.91/1.57 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.91/1.57 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.91/1.57 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.57 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.91/1.57 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.91/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 X, W, Z ) ), U ), T ), Y ) }.
% 0.91/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), Z ), U ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( X, Z, W ) ), U ), Y ) ) }.
% 0.91/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.57 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Y ), Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Z ), Y ), alpha35( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.91/1.57 Z ), Y ), alpha45( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.91/1.57 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.91/1.57 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), alpha49( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.57 , alpha45( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha49( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha49( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha49( X, Y, Z, T ), alpha15( X, Y, Z ) }.
% 0.91/1.57 { ! alpha53( X, Y, Z, T ), ! alpha15( X, Y, Z ), alpha49( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 alpha53( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha53( X, Y, Z, T )
% 0.91/1.57 }.
% 0.91/1.57 { ! alpha35( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.57 alpha35( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha35( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , alpha15( X, Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.91/1.57 , alpha15( X, Y, Z ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ), alpha36( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.91/1.57 Z, Y ) ), alpha46( X, Y, Z, T ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.91/1.57 , T ), ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.91/1.57 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), alpha50( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.91/1.57 , alpha46( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha50( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha50( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha50( X, Y, Z, T ), alpha16( X, Y, T ) }.
% 0.91/1.57 { ! alpha54( X, Y, Z, T ), ! alpha16( X, Y, T ), alpha50( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 alpha54( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha54( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 alpha36( X, Y, Z, T ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha36( X, Y, Z, T )
% 0.91/1.57 }.
% 0.91/1.57 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , alpha16( X, Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.57 , alpha16( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.57 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.57 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.91/1.57 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.91/1.57 ) ) = X }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.57 , ! alpha17( X, Y, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.57 , ! alpha37( X, Y, Z ) }.
% 0.91/1.57 { alpha17( X, Y, Z ), alpha37( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.57 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 0.91/1.57 { ! alpha37( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.57 skol11( X, Y, Z ) ) }.
% 0.91/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.91/1.57 ) ), alpha37( X, Y, Z ) }.
% 0.91/1.57 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.91/1.57 }.
% 0.91/1.57 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.57 , alpha18( X, Y, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.57 , alpha38( X, Y, Z ) }.
% 0.91/1.57 { ! alpha18( X, Y, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.57 { ! alpha38( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha38( X, Y, Z ) }.
% 0.91/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 0.91/1.57 alpha38( X, Y, Z ) }.
% 0.91/1.57 { ! alpha18( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.91/1.57 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha18( X, Y, Z ) }
% 0.91/1.57 .
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha18
% 0.91/1.57 ( X, Y, Z ) }.
% 0.91/1.57 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.91/1.57 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.91/1.57 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.91/1.57 ( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.91/1.57 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.91/1.57 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.91/1.57 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.91/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.91/1.57 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.91/1.57 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.91/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.91/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.91/1.57 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), Y ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.91/1.57 ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.91/1.57 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 0.91/1.57 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 0.91/1.57 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Int_Oint, Z, Y ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Int_Oint, Z, X ), Y ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.57 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol13( X, Y ) ) }.
% 0.91/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.91/1.57 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol14( X, Y ) ) }.
% 0.91/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.91/1.57 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.91/1.57 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.91/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.91/1.57 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, Y ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.91/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Y, X ), X ) }.
% 0.91/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.91/1.57 = X }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ) ) ) }.
% 0.91/1.57 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.91/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.91/1.57 alpha19( X, Y, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.91/1.57 alpha39( X, Y, Z ) }.
% 0.91/1.57 { ! alpha19( X, Y, Z ), ! alpha39( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.57 { ! alpha39( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 alpha47( X, Y, Z ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha39( X, Y, Z ) }.
% 0.91/1.57 { ! alpha47( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.91/1.57 { ! alpha47( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.91/1.57 ), alpha51( X, Y, Z, T ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( X, T, U ), X ),
% 0.91/1.57 alpha47( X, Y, Z ) }.
% 0.91/1.57 { ! alpha51( X, Y, Z, skol15( X, Y, Z ) ), alpha47( X, Y, Z ) }.
% 0.91/1.57 { ! alpha51( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.91/1.57 hBOOL( hAPP( Z, T ) ) }.
% 0.91/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol16( X, Y, T ) ), T
% 0.91/1.57 ), alpha51( X, Y, Z, T ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, T ) ), alpha51( X, Y, Z, T ) }.
% 0.91/1.57 { ! alpha19( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha19( X, Y, Z ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.91/1.57 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.91/1.57 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.91/1.57 X, Z, Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.91/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.91/1.57 ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.91/1.57 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.91/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.91/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.91/1.57 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.91/1.57 ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.91/1.57 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 T, Y ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.91/1.57 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 T, Z ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.91/1.57 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.91/1.57 ), Z ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.91/1.57 , Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, Y, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, Z, Y ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.91/1.57 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.91/1.57 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.91/1.57 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.91/1.57 , U ), Z ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.91/1.57 Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.91/1.57 , Y ) ), Y ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.91/1.57 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.91/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.91/1.57 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.91/1.57 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.91/1.57 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.91/1.57 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.91/1.57 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.91/1.57 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.91/1.57 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.91/1.57 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 alpha20( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! alpha20( X, Y, Z ),
% 0.91/1.57 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.91/1.57 { ! alpha20( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.57 alpha20( X, Y, Z ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.91/1.57 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, Y ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.57 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, Y ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.91/1.57 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.91/1.57 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.91/1.57 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.91/1.57 , Z ) ) }.
% 0.91/1.57 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.91/1.57 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.91/1.57 , Z ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.91/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.91/1.57 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.91/1.57 }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.91/1.57 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.91/1.57 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.91/1.57 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.91/1.57 ( hAPP( c_Power_Opower__class_Opower( X ),
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.91/1.57 ), Z ), Y ) ) }.
% 0.91/1.57 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.57 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 0.91/1.57 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.91/1.57 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.91/1.57 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 0.91/1.57 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.91/1.57 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.91/1.57 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.91/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.91/1.57 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 0.91/1.57 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 0.91/1.57 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, Z, Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.57 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ) ) = X }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.91/1.57 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.57 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.91/1.57 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.91/1.57 , Y ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, X, Y ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Z, Y ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.57 tc_Int_Oint, X ) = X }.
% 0.91/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.91/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.91/1.57 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.91/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Int_Oint, X, Y ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.91/1.57 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.91/1.57 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.91/1.57 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.91/1.57 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.91/1.57 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( X, Z, Y ) = T }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.91/1.57 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.91/1.57 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.91/1.57 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.91/1.57 ), Y ) ) = Z }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.91/1.57 , Z ) ) = Y }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.91/1.57 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.91/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.57 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.91/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.91/1.57 ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.91/1.57 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.91/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.91/1.57 ( X, Z, Y ), T ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.91/1.57 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.91/1.57 ( X, Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.57 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 0.91/1.57 ( X ) ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.91/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.91/1.57 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), T, Z ), Y ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), Z, Y ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.91/1.57 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.91/1.57 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.91/1.57 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.91/1.57 .
% 0.91/1.57 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.91/1.57 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.91/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.91/1.57 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.57 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.57 }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.57 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.91/1.57 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.57 ) }.
% 0.91/1.57 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.91/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.91/1.57 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.91/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.91/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.91/1.57 ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 0.91/1.57 ( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 0.91/1.57 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 0.91/1.57 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 0.91/1.57 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.91/1.57 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.91/1.57 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.91/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.57 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.91/1.57 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.57 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.91/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.91/1.57 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.91/1.57 ), T, Z ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.91/1.57 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.91/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.91/1.57 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.57 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.91/1.57 alpha21( X, Z ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.91/1.57 alpha40( X, Y, Z ) }.
% 0.91/1.57 { ! alpha21( X, Z ), ! alpha40( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.57 { ! alpha40( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.57 alpha48( X, Y, Z ) }.
% 0.91/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha40( X, Y, Z ) }.
% 0.91/1.57 { ! alpha48( X, Y, Z ), alpha40( X, Y, Z ) }.
% 0.91/1.57 { ! alpha48( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.91/1.57 ), alpha52( X, Y, Z, T ) }.
% 0.91/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X, T, U ), X ),
% 0.91/1.57 alpha48( X, Y, Z ) }.
% 0.91/1.57 { ! alpha52( X, Y, Z, skol17( X, Y, Z ) ), alpha48( X, Y, Z ) }.
% 0.91/1.57 { ! alpha52( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.91/1.57 hBOOL( hAPP( Z, U ) ) }.
% 0.91/1.57 { ! hBOOL( hAPP( Z, skol18( U, W, Z, V0 ) ) ), alpha52( X, Y, Z, T ) }.
% 0.91/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.91/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y, Z, T ) )
% 0.91/1.58 , T ), alpha52( X, Y, Z, T ) }.
% 0.91/1.58 { ! alpha21( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.58 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha21( X, Y ) }.
% 0.91/1.58 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha21
% 0.91/1.58 ( X, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.58 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.58 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.58 tc_Polynomial_Opoly( X ), Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 0.91/1.58 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.58 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 0.91/1.58 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.58 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.91/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.91/1.58 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.58 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.91/1.58 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.91/1.58 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.58 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.58 c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.91/1.58 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.58 .
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.91/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.91/1.58 }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 0.91/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.91/1.58 }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.91/1.58 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.91/1.58 ) ), ! alpha22( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.58 ( tc_Int_Oint ), X ), alpha22( X, Y, skol19( X, Y, Z ), skol22( X, Y, Z )
% 0.91/1.58 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.91/1.58 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.58 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol19( X, Y, Z ) ), skol22
% 0.91/1.58 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.91/1.58 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.91/1.58 ) }.
% 0.91/1.58 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.91/1.58 { ! alpha22( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha41( X, Y, Z, T )
% 0.91/1.58 , alpha22( X, Y, Z, T ) }.
% 0.91/1.58 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.91/1.58 ) }.
% 0.91/1.58 { ! alpha41( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.91/1.58 .
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.91/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha41( X,
% 0.91/1.58 Y, Z, T ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.91/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha23( X, Y, T,
% 0.91/1.58 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha23( X, Y, skol20( X, Y
% 0.91/1.58 , Z ), skol23( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.91/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.91/1.58 skol20( X, Y, Z ) ), skol23( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.91/1.58 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.91/1.58 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.91/1.58 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.91/1.58 ) }.
% 0.91/1.58 { ! alpha23( X, Y, Z, T ), alpha42( X, Y, Z, T ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha42( X, Y, Z
% 0.91/1.58 , T ), alpha23( X, Y, Z, T ) }.
% 0.91/1.58 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.58 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.91/1.58 .
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.91/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha42( X,
% 0.91/1.58 Y, Z, T ) }.
% 0.91/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.91/1.58 tc_Int_Oint, X, Y ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.58 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.91/1.58 ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.91/1.58 ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.91/1.58 ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.58 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.91/1.58 ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.58 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.58 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.58 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.58 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.58 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.91/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.91/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.58 ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.58 ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.58 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.58 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.91/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 }.
% 0.91/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.91/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.91/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.91/1.58 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.91/1.58 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.91/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.58 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.91/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.91/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.91/1.58 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.91/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.91/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.91/1.58 { ! class_Fields_Olinordered__field( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.58 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.91/1.58 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.91/1.58 { ! class_Fields_Olinordered__field( X ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.58 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.58 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.58 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.91/1.58 X ) ) }.
% 0.91/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.91/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.91/1.58 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.91/1.58 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.91/1.58 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.91/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.91/1.58 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.58 tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.91/1.58 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.91/1.58 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.91/1.58 { class_Power_Opower( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.91/1.58 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.91/1.58 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.91/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.58 tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.91/1.58 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.58 tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.91/1.58 { ! class_Rings_Oidom( X ),
% 0.91/1.58 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.91/1.58 ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.91/1.58 X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.91/1.58 ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.91/1.58 .
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.91/1.58 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ),
% 0.91/1.58 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.91/1.58 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.91/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.91/1.58 ( tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.91/1.58 ( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.91/1.58 }.
% 0.91/1.58 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.91/1.58 ) ) }.
% 0.91/1.58 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.91/1.58 .
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.91/1.58 tc_Polynomial_Opoly( X ) ) }.
% 0.91/1.58 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.91/1.58 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.91/1.58 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly(
% 0.91/1.58 tc_Complex_Ocomplex ) ), v_q ), c_Polynomial_Odegree( tc_Complex_Ocomplex
% 0.91/1.58 , v_p ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.91/1.58 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ), v_p ), c_Polynomial_OpCons
% 0.91/1.58 ( tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(
% 0.91/1.58 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 0.91/1.58 v_k____ ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.91/1.58 tc_Complex_Ocomplex ) ) ) ) }.
% 0.91/1.58
% 0.91/1.58 *** allocated 15000 integers for clauses
% 0.91/1.58 *** allocated 22500 integers for clauses
% 0.91/1.58 *** allocated 33750 integers for clauses
% 0.91/1.58 *** allocated 50625 integers for clauses
% 0.91/1.58 *** allocated 75937 integers for clauses
% 0.91/1.58 *** allocated 113905 integers for clauses
% 0.91/1.58 percentage equality = 0.339391, percentage horn = 0.868746
% 0.91/1.58 This is a problem with some equality
% 0.91/1.58
% 0.91/1.58
% 0.91/1.58
% 0.91/1.58 Options Used:
% 0.91/1.58
% 0.91/1.58 useres = 1
% 0.91/1.58 useparamod = 1
% 0.91/1.58 useeqrefl = 1
% 0.91/1.58 useeqfact = 1
% 0.91/1.58 usefactor = 1
% 0.91/1.58 usesimpsplitting = 0
% 0.91/1.58 usesimpdemod = 5
% 0.91/1.58 usesimpres = 3
% 0.91/1.58
% 0.91/1.58 resimpinuse = 1000
% 0.91/1.58 resimpclauses = 20000
% 0.91/1.58 substype = eqrewr
% 0.91/1.58 backwardsubs = 1
% 0.91/1.58 selectoldest = 5
% 0.91/1.58
% 0.91/1.58 litorderings [0] = split
% 0.91/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 0.91/1.58
% 0.91/1.58 termordering = kbo
% 0.91/1.58
% 0.91/1.58 litapriori = 0
% 0.91/1.58 termapriori = 1
% 0.91/1.58 litaposteriori = 0
% 0.91/1.58 termaposteriori = 0
% 0.91/1.58 demodaposteriori = 0
% 0.91/1.58 ordereqreflfact = 0
% 0.91/1.58
% 0.91/1.58 litselect = negord
% 0.91/1.58
% 0.91/1.58 maxweight = 15
% 0.91/1.58 maxdepth = 30000
% 0.91/1.58 maxlength = 115
% 0.91/1.58 maxnrvars = 195
% 0.91/1.58 excuselevel = 1
% 0.91/1.58 increasemaxweight = 1
% 0.91/1.58
% 0.91/1.58 maxselected = 10000000
% 0.91/1.58 maxnrclauses = 10000000
% 0.91/1.58
% 0.91/1.58 showgenerated = 0
% 0.91/1.58 showkept = 0
% 0.91/1.58 showselected = 0
% 0.91/1.58 showdeleted = 0
% 0.91/1.58 showresimp = 1
% 0.91/1.58 showstatus = 2000
% 0.91/1.58
% 0.91/1.58 prologoutput = 0
% 0.91/1.58 nrgoals = 5000000
% 0.91/1.58 totalproof = 1
% 0.91/1.58
% 0.91/1.58 Symbols occurring in the translation:
% 0.91/1.58
% 0.91/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.91/1.58 . [1, 2] (w:1, o:173, a:1, s:1, b:0),
% 0.91/1.58 ! [4, 1] (w:0, o:98, a:1, s:1, b:0),
% 0.91/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.58 hAPP [38, 2] (w:1, o:197, a:1, s:1, b:0),
% 0.91/1.58 v_p [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.91/1.58 tc_Complex_Ocomplex [40, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.91/1.58 tc_Polynomial_Opoly [41, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.91/1.58 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.91/1.58 v_k____ [43, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_OpCons [44, 3] (w:1, o:225, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Odegree [45, 2] (w:1, o:199, a:1, s:1, b:0),
% 0.91/1.58 tc_Nat_Onat [46, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Ocomm__semiring__1 [50, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.91/1.58 c_Power_Opower__class_Opower [51, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.91/1.58 c_Groups_Oone__class_Oone [52, 1] (w:1, o:111, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Ozero [53, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.91/1.58 class_Fields_Ofield__inverse__zero [56, 1] (w:1, o:112, a:1, s:1, b:0
% 0.91/1.58 ),
% 0.91/1.58 c_Rings_Oinverse__class_Odivide [57, 3] (w:1, o:226, a:1, s:1, b:0),
% 0.91/1.58
% 0.91/1.58 class_Fields_Ofield [59, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Odivision__ring__inverse__zero [60, 1] (w:1, o:118, a:1
% 0.91/1.58 , s:1, b:0),
% 0.91/1.58 class_Rings_Odivision__ring [61, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.91/1.58 class_Power_Opower [63, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Osemiring__0 [64, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.91/1.58 c_Groups_Otimes__class_Otimes [66, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Omonoid__mult [68, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Ono__zero__divisors [70, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.91/1.58
% 0.91/1.58 class_Rings_Oring__no__zero__divisors [71, 1] (w:1, o:121, a:1, s:1
% 0.91/1.58 , b:0),
% 0.91/1.58 class_Rings_Omult__zero [72, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Ozero__neq__one [73, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Oring__1__no__zero__divisors [74, 1] (w:1, o:122, a:1, s:
% 0.91/1.58 1, b:0),
% 0.91/1.58 class_Groups_Ocomm__monoid__mult [76, 1] (w:1, o:139, a:1, s:1, b:0)
% 0.91/1.58 ,
% 0.91/1.58 class_Rings_Ocomm__semiring__0 [83, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Opoly [90, 2] (w:1, o:200, a:1, s:1, b:0),
% 0.91/1.58 c_Power_Opower_Opower [91, 3] (w:1, o:227, a:1, s:1, b:0),
% 0.91/1.58 v_q [92, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.91/1.58 c_Rings_Odvd__class_Odvd [93, 3] (w:1, o:228, a:1, s:1, b:0),
% 0.91/1.58 class_RealVector_Oreal__normed__field [94, 1] (w:1, o:140, a:1, s:1
% 0.91/1.58 , b:0),
% 0.91/1.58 class_Int_Oring__char__0 [95, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Oidom [96, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Odvd [99, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Oab__semigroup__mult [105, 1] (w:1, o:144, a:1, s:1, b:0
% 0.91/1.58 ),
% 0.91/1.58 class_Groups_Oone [107, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.91/1.58 class_RealVector_Oreal__normed__algebra [108, 1] (w:1, o:146, a:1, s:
% 0.91/1.58 1, b:0),
% 0.91/1.58 c_Polynomial_Oorder [109, 3] (w:1, o:224, a:1, s:1, b:0),
% 0.91/1.58 c_Groups_Ouminus__class_Ouminus [112, 2] (w:1, o:202, a:1, s:1, b:0)
% 0.91/1.58 ,
% 0.91/1.58 class_Rings_Ocomm__ring__1 [113, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Omonom [114, 3] (w:1, o:229, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Opoly__rec [116, 5] (w:1, o:304, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Osynthetic__div [117, 3] (w:1, o:230, a:1, s:1, b:0),
% 0.91/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [118, 2] (w:1, o:
% 0.91/1.58 201, a:1, s:1, b:0),
% 0.91/1.58 c_fequal [119, 2] (w:1, o:203, a:1, s:1, b:0),
% 0.91/1.58 c_If [120, 4] (w:1, o:276, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Ocoeff [121, 2] (w:1, o:198, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Oab__group__add [122, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Ocomm__ring [123, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Ogroup__add [125, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Olinordered__ab__group__add [126, 1] (w:1, o:127, a:1
% 0.91/1.58 , s:1, b:0),
% 0.91/1.58 class_Rings_Oring [128, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.91/1.58 class_Rings_Oring__1 [129, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.91/1.58 c_Nat_OSuc [130, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.91/1.58 c_Groups_Oplus__class_Oplus [131, 3] (w:1, o:232, a:1, s:1, b:0),
% 0.91/1.58 c_Polynomial_Opoly__gcd [132, 3] (w:1, o:233, a:1, s:1, b:0),
% 0.91/1.58 class_Groups_Ocomm__monoid__add [133, 1] (w:1, o:150, a:1, s:1, b:0)
% 0.91/1.60 ,
% 0.91/1.60 class_Groups_Ocancel__semigroup__add [134, 1] (w:1, o:151, a:1, s:1
% 0.91/1.60 , b:0),
% 0.91/1.60 class_Groups_Ocancel__ab__semigroup__add [135, 1] (w:1, o:152, a:1
% 0.91/1.60 , s:1, b:0),
% 0.91/1.60 class_Groups_Oab__semigroup__add [136, 1] (w:1, o:153, a:1, s:1, b:0)
% 0.91/1.60 ,
% 0.91/1.60 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.91/1.60 139, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.91/1.60 class_Groups_Omonoid__add [140, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.91/1.60 class_Rings_Osemiring [142, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.91/1.60 class_Rings_Ocomm__semiring [143, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.91/1.60 tc_Int_Oint [151, 0] (w:1, o:77, a:1, s:1, b:0),
% 0.91/1.60 hBOOL [154, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.91/1.60 c_Polynomial_Opcompose [155, 3] (w:1, o:234, a:1, s:1, b:0),
% 0.91/1.60 class_Rings_Olinordered__ring__strict [156, 1] (w:1, o:129, a:1, s:1
% 0.91/1.60 , b:0),
% 0.91/1.60 c_Polynomial_Osmult [161, 3] (w:1, o:235, a:1, s:1, b:0),
% 0.91/1.60 c_Groups_Ominus__class_Ominus [162, 3] (w:1, o:236, a:1, s:1, b:0),
% 0.91/1.60 class_RealVector_Oreal__field [169, 1] (w:1, o:155, a:1, s:1, b:0),
% 0.91/1.60 c_Polynomial_Opdivmod__rel [170, 5] (w:1, o:305, a:1, s:1, b:0),
% 0.91/1.60 c_Divides_Odiv__class_Omod [178, 3] (w:1, o:237, a:1, s:1, b:0),
% 0.91/1.60 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [179, 3] (w:
% 0.91/1.60 1, o:231, a:1, s:1, b:0),
% 0.91/1.60 c_Orderings_Oord__class_Oless [180, 3] (w:1, o:222, a:1, s:1, b:0),
% 0.91/1.60 c_Rings_Oinverse__class_Oinverse [181, 2] (w:1, o:204, a:1, s:1, b:0)
% 0.91/1.60 ,
% 0.91/1.60 class_Fields_Olinordered__field__inverse__zero [182, 1] (w:1, o:114
% 0.91/1.60 , a:1, s:1, b:0),
% 0.91/1.60 class_Fields_Olinordered__field [183, 1] (w:1, o:115, a:1, s:1, b:0)
% 0.91/1.60 ,
% 0.91/1.60 class_Rings_Olinordered__semidom [186, 1] (w:1, o:131, a:1, s:1, b:0)
% 0.91/1.60 ,
% 0.91/1.60 class_Groups_Oordered__ab__semigroup__add__imp__le [187, 1] (w:1, o:
% 0.91/1.60 163, a:1, s:1, b:0),
% 0.91/1.60 class_Groups_Oordered__cancel__ab__semigroup__add [188, 1] (w:1, o:
% 0.91/1.60 164, a:1, s:1, b:0),
% 0.91/1.60 class_Groups_Oordered__ab__group__add [189, 1] (w:1, o:165, a:1, s:1
% 0.91/1.60 , b:0),
% 0.91/1.60 class_Rings_Olinordered__idom [190, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.91/1.60 class_Rings_Olinordered__comm__semiring__strict [193, 1] (w:1, o:133
% 0.91/1.60 , a:1, s:1, b:0),
% 0.91/1.60 class_Rings_Olinordered__semiring__strict [194, 1] (w:1, o:134, a:1
% 0.91/1.60 , s:1, b:0),
% 0.91/1.60 class_Rings_Olinordered__ring [195, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.91/1.60 class_Groups_Oordered__comm__monoid__add [196, 1] (w:1, o:166, a:1
% 0.91/1.60 , s:1, b:0),
% 0.91/1.60 class_Rings_Oordered__ring [202, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.91/1.60 class_Divides_Osemiring__div [204, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.91/1.60 class_Divides_Oring__div [208, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.91/1.60 c_Polynomial_Opos__poly [209, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.91/1.60 c_Divides_Odiv__class_Odiv [210, 3] (w:1, o:238, a:1, s:1, b:0),
% 0.91/1.60 c_Groups_Oabs__class_Oabs [211, 2] (w:1, o:206, a:1, s:1, b:0),
% 0.91/1.60 class_Groups_Oordered__ab__group__add__abs [212, 1] (w:1, o:169, a:1
% 0.91/1.60 , s:1, b:0),
% 0.91/1.60 class_Groups_Oabs__if [213, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.91/1.60 c_Groups_Osgn__class_Osgn [214, 2] (w:1, o:207, a:1, s:1, b:0),
% 0.91/1.60 class_RealVector_Oreal__normed__vector [215, 1] (w:1, o:157, a:1, s:1
% 0.91/1.60 , b:0),
% 0.91/1.60 class_RealVector_Oreal__normed__algebra__1 [216, 1] (w:1, o:158, a:1
% 0.91/1.60 , s:1, b:0),
% 0.91/1.60 class_RealVector_Oreal__normed__div__algebra [217, 1] (w:1, o:159, a:
% 0.91/1.60 1, s:1, b:0),
% 0.91/1.60 class_Groups_Osgn__if [218, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.91/1.60 c_Orderings_Oord__class_Oless__eq [219, 3] (w:1, o:223, a:1, s:1, b:0
% 0.91/1.60 ),
% 0.91/1.60 class_Rings_Olinordered__semiring [220, 1] (w:1, o:135, a:1, s:1, b:0
% 0.91/1.60 ),
% 0.91/1.60 class_Groups_Ocancel__comm__monoid__add [222, 1] (w:1, o:172, a:1, s:
% 0.91/1.60 1, b:0),
% 0.91/1.60 alpha1 [223, 3] (w:1, o:239, a:1, s:1, b:1),
% 0.91/1.60 alpha2 [224, 3] (w:1, o:247, a:1, s:1, b:1),
% 0.91/1.60 alpha3 [225, 0] (w:1, o:97, a:1, s:1, b:1),
% 0.91/1.60 alpha4 [226, 2] (w:1, o:208, a:1, s:1, b:1),
% 0.91/1.60 alpha5 [227, 2] (w:1, o:209, a:1, s:1, b:1),
% 0.91/1.60 alpha6 [228, 2] (w:1, o:210, a:1, s:1, b:1),
% 0.91/1.60 alpha7 [229, 2] (w:1, o:211, a:1, s:1, b:1),
% 0.91/1.60 alpha8 [230, 3] (w:1, o:248, a:1, s:1, b:1),
% 18.36/18.73 alpha9 [231, 3] (w:1, o:249, a:1, s:1, b:1),
% 18.36/18.73 alpha10 [232, 4] (w:1, o:277, a:1, s:1, b:1),
% 18.36/18.73 alpha11 [233, 4] (w:1, o:278, a:1, s:1, b:1),
% 18.36/18.73 alpha12 [234, 3] (w:1, o:240, a:1, s:1, b:1),
% 18.36/18.73 alpha13 [235, 3] (w:1, o:241, a:1, s:1, b:1),
% 18.36/18.73 alpha14 [236, 2] (w:1, o:212, a:1, s:1, b:1),
% 18.36/18.73 alpha15 [237, 3] (w:1, o:242, a:1, s:1, b:1),
% 18.36/18.73 alpha16 [238, 3] (w:1, o:243, a:1, s:1, b:1),
% 18.36/18.73 alpha17 [239, 3] (w:1, o:244, a:1, s:1, b:1),
% 18.36/18.73 alpha18 [240, 3] (w:1, o:245, a:1, s:1, b:1),
% 18.36/18.73 alpha19 [241, 3] (w:1, o:246, a:1, s:1, b:1),
% 18.36/18.73 alpha20 [242, 3] (w:1, o:250, a:1, s:1, b:1),
% 18.36/18.73 alpha21 [243, 2] (w:1, o:213, a:1, s:1, b:1),
% 18.36/18.73 alpha22 [244, 4] (w:1, o:279, a:1, s:1, b:1),
% 18.36/18.73 alpha23 [245, 4] (w:1, o:280, a:1, s:1, b:1),
% 18.36/18.73 alpha24 [246, 4] (w:1, o:281, a:1, s:1, b:1),
% 18.36/18.73 alpha25 [247, 4] (w:1, o:282, a:1, s:1, b:1),
% 18.36/18.73 alpha26 [248, 0] (w:1, o:96, a:1, s:1, b:1),
% 18.36/18.73 alpha27 [249, 2] (w:1, o:214, a:1, s:1, b:1),
% 18.36/18.73 alpha28 [250, 2] (w:1, o:215, a:1, s:1, b:1),
% 18.36/18.73 alpha29 [251, 4] (w:1, o:283, a:1, s:1, b:1),
% 18.36/18.73 alpha30 [252, 3] (w:1, o:251, a:1, s:1, b:1),
% 18.36/18.73 alpha31 [253, 4] (w:1, o:284, a:1, s:1, b:1),
% 18.36/18.73 alpha32 [254, 4] (w:1, o:285, a:1, s:1, b:1),
% 18.36/18.73 alpha33 [255, 3] (w:1, o:252, a:1, s:1, b:1),
% 18.36/18.73 alpha34 [256, 3] (w:1, o:253, a:1, s:1, b:1),
% 18.36/18.73 alpha35 [257, 4] (w:1, o:286, a:1, s:1, b:1),
% 18.36/18.73 alpha36 [258, 4] (w:1, o:287, a:1, s:1, b:1),
% 18.36/18.73 alpha37 [259, 3] (w:1, o:254, a:1, s:1, b:1),
% 18.36/18.73 alpha38 [260, 3] (w:1, o:255, a:1, s:1, b:1),
% 18.36/18.73 alpha39 [261, 3] (w:1, o:256, a:1, s:1, b:1),
% 18.36/18.73 alpha40 [262, 3] (w:1, o:257, a:1, s:1, b:1),
% 18.36/18.73 alpha41 [263, 4] (w:1, o:288, a:1, s:1, b:1),
% 18.36/18.73 alpha42 [264, 4] (w:1, o:289, a:1, s:1, b:1),
% 18.36/18.73 alpha43 [265, 4] (w:1, o:290, a:1, s:1, b:1),
% 18.36/18.73 alpha44 [266, 3] (w:1, o:258, a:1, s:1, b:1),
% 18.36/18.73 alpha45 [267, 4] (w:1, o:291, a:1, s:1, b:1),
% 18.36/18.73 alpha46 [268, 4] (w:1, o:292, a:1, s:1, b:1),
% 18.36/18.73 alpha47 [269, 3] (w:1, o:259, a:1, s:1, b:1),
% 18.36/18.73 alpha48 [270, 3] (w:1, o:260, a:1, s:1, b:1),
% 18.36/18.73 alpha49 [271, 4] (w:1, o:293, a:1, s:1, b:1),
% 18.36/18.73 alpha50 [272, 4] (w:1, o:294, a:1, s:1, b:1),
% 18.36/18.73 alpha51 [273, 4] (w:1, o:295, a:1, s:1, b:1),
% 18.36/18.73 alpha52 [274, 4] (w:1, o:296, a:1, s:1, b:1),
% 18.36/18.73 alpha53 [275, 4] (w:1, o:297, a:1, s:1, b:1),
% 18.36/18.73 alpha54 [276, 4] (w:1, o:298, a:1, s:1, b:1),
% 18.36/18.73 alpha55 [277, 3] (w:1, o:261, a:1, s:1, b:1),
% 18.36/18.73 alpha56 [278, 3] (w:1, o:262, a:1, s:1, b:1),
% 18.36/18.73 alpha57 [279, 4] (w:1, o:299, a:1, s:1, b:1),
% 18.36/18.73 alpha58 [280, 3] (w:1, o:263, a:1, s:1, b:1),
% 18.36/18.73 alpha59 [281, 4] (w:1, o:300, a:1, s:1, b:1),
% 18.36/18.73 alpha60 [282, 4] (w:1, o:301, a:1, s:1, b:1),
% 18.36/18.73 skol1 [283, 2] (w:1, o:216, a:1, s:1, b:1),
% 18.36/18.73 skol2 [284, 0] (w:1, o:14, a:1, s:1, b:1),
% 18.36/18.73 skol3 [285, 0] (w:1, o:15, a:1, s:1, b:1),
% 18.36/18.73 skol4 [286, 2] (w:1, o:217, a:1, s:1, b:1),
% 18.36/18.73 skol5 [287, 3] (w:1, o:264, a:1, s:1, b:1),
% 18.36/18.73 skol6 [288, 3] (w:1, o:265, a:1, s:1, b:1),
% 18.36/18.73 skol7 [289, 4] (w:1, o:302, a:1, s:1, b:1),
% 18.36/18.73 skol8 [290, 1] (w:1, o:103, a:1, s:1, b:1),
% 18.36/18.73 skol9 [291, 2] (w:1, o:218, a:1, s:1, b:1),
% 18.36/18.73 skol10 [292, 2] (w:1, o:219, a:1, s:1, b:1),
% 18.36/18.73 skol11 [293, 3] (w:1, o:266, a:1, s:1, b:1),
% 18.36/18.73 skol12 [294, 3] (w:1, o:267, a:1, s:1, b:1),
% 18.36/18.73 skol13 [295, 2] (w:1, o:220, a:1, s:1, b:1),
% 18.36/18.73 skol14 [296, 2] (w:1, o:221, a:1, s:1, b:1),
% 18.36/18.73 skol15 [297, 3] (w:1, o:268, a:1, s:1, b:1),
% 18.36/18.73 skol16 [298, 3] (w:1, o:269, a:1, s:1, b:1),
% 18.36/18.73 skol17 [299, 3] (w:1, o:270, a:1, s:1, b:1),
% 18.36/18.73 skol18 [300, 4] (w:1, o:303, a:1, s:1, b:1),
% 18.36/18.73 skol19 [301, 3] (w:1, o:271, a:1, s:1, b:1),
% 18.36/18.73 skol20 [302, 3] (w:1, o:272, a:1, s:1, b:1),
% 18.36/18.73 skol21 [303, 3] (w:1, o:273, a:1, s:1, b:1),
% 18.36/18.73 skol22 [304, 3] (w:1, o:274, a:1, s:1, b:1),
% 18.36/18.73 skol23 [305, 3] (w:1, o:275, a:1, s:1, b:1).
% 18.36/18.73
% 18.36/18.73
% 18.36/18.73 Starting Search:
% 18.36/18.73
% 18.36/18.73 *** allocated 170857 integers for clauses
% 18.36/18.73 Resimplifying inuse:
% 18.36/18.73 Done
% 18.36/18.73
% 18.36/18.73
% 18.36/18.73 Intermediate Status:
% 18.36/18.73 Generated: 2945
% 18.36/18.73 Kept: 2019
% 18.36/18.73 Inuse: 44
% 90.63/91.00 Deleted: 2
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 *** allocated 256285 integers for clauses
% 90.63/91.00 *** allocated 170857 integers for termspace/termends
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 384427 integers for clauses
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 9554
% 90.63/91.00 Kept: 4352
% 90.63/91.00 Inuse: 118
% 90.63/91.00 Deleted: 3
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 256285 integers for termspace/termends
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 14709
% 90.63/91.00 Kept: 6469
% 90.63/91.00 Inuse: 163
% 90.63/91.00 Deleted: 3
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 576640 integers for clauses
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 18662
% 90.63/91.00 Kept: 8531
% 90.63/91.00 Inuse: 208
% 90.63/91.00 Deleted: 3
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 384427 integers for termspace/termends
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 27984
% 90.63/91.00 Kept: 10752
% 90.63/91.00 Inuse: 237
% 90.63/91.00 Deleted: 4
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 864960 integers for clauses
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 36698
% 90.63/91.00 Kept: 12758
% 90.63/91.00 Inuse: 268
% 90.63/91.00 Deleted: 4
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 576640 integers for termspace/termends
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 44658
% 90.63/91.00 Kept: 14787
% 90.63/91.00 Inuse: 289
% 90.63/91.00 Deleted: 5
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 49964
% 90.63/91.00 Kept: 16827
% 90.63/91.00 Inuse: 330
% 90.63/91.00 Deleted: 6
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 1297440 integers for clauses
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 59746
% 90.63/91.00 Kept: 18848
% 90.63/91.00 Inuse: 349
% 90.63/91.00 Deleted: 6
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying clauses:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 864960 integers for termspace/termends
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 96690
% 90.63/91.00 Kept: 21711
% 90.63/91.00 Inuse: 370
% 90.63/91.00 Deleted: 386
% 90.63/91.00 Deletedinuse: 0
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 103139
% 90.63/91.00 Kept: 23728
% 90.63/91.00 Inuse: 409
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 110573
% 90.63/91.00 Kept: 25755
% 90.63/91.00 Inuse: 439
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 115930
% 90.63/91.00 Kept: 27816
% 90.63/91.00 Inuse: 464
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 *** allocated 1946160 integers for clauses
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 121340
% 90.63/91.00 Kept: 29854
% 90.63/91.00 Inuse: 499
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 128496
% 90.63/91.00 Kept: 32021
% 90.63/91.00 Inuse: 519
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 1297440 integers for termspace/termends
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 136654
% 90.63/91.00 Kept: 34039
% 90.63/91.00 Inuse: 539
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 144138
% 90.63/91.00 Kept: 36295
% 90.63/91.00 Inuse: 559
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 157951
% 90.63/91.00 Kept: 39378
% 90.63/91.00 Inuse: 594
% 90.63/91.00 Deleted: 388
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying clauses:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 166363
% 90.63/91.00 Kept: 41388
% 90.63/91.00 Inuse: 620
% 90.63/91.00 Deleted: 494
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 2919240 integers for clauses
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 178476
% 90.63/91.00 Kept: 43417
% 90.63/91.00 Inuse: 638
% 90.63/91.00 Deleted: 494
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 198194
% 90.63/91.00 Kept: 46203
% 90.63/91.00 Inuse: 644
% 90.63/91.00 Deleted: 494
% 90.63/91.00 Deletedinuse: 1
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 Resimplifying inuse:
% 90.63/91.00 Done
% 90.63/91.00
% 90.63/91.00 *** allocated 1946160 integers for termspace/termends
% 90.63/91.00
% 90.63/91.00 Intermediate Status:
% 90.63/91.00 Generated: 210365
% 90.63/91.00 Kept: 49942
% 258.20/258.77 Inuse: 669
% 258.20/258.77 Deleted: 494
% 258.20/258.77 Deletedinuse: 1
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 215635
% 258.20/258.77 Kept: 52153
% 258.20/258.77 Inuse: 683
% 258.20/258.77 Deleted: 495
% 258.20/258.77 Deletedinuse: 1
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 239835
% 258.20/258.77 Kept: 54932
% 258.20/258.77 Inuse: 689
% 258.20/258.77 Deleted: 497
% 258.20/258.77 Deletedinuse: 3
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 262580
% 258.20/258.77 Kept: 56937
% 258.20/258.77 Inuse: 702
% 258.20/258.77 Deleted: 498
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 267996
% 258.20/258.77 Kept: 58976
% 258.20/258.77 Inuse: 708
% 258.20/258.77 Deleted: 498
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying clauses:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 278052
% 258.20/258.77 Kept: 61076
% 258.20/258.77 Inuse: 728
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 296951
% 258.20/258.77 Kept: 63356
% 258.20/258.77 Inuse: 743
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 305697
% 258.20/258.77 Kept: 65772
% 258.20/258.77 Inuse: 763
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 *** allocated 4378860 integers for clauses
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 312164
% 258.20/258.77 Kept: 67812
% 258.20/258.77 Inuse: 778
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 *** allocated 2919240 integers for termspace/termends
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 321327
% 258.20/258.77 Kept: 71254
% 258.20/258.77 Inuse: 803
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 334355
% 258.20/258.77 Kept: 74185
% 258.20/258.77 Inuse: 828
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 344689
% 258.20/258.77 Kept: 78727
% 258.20/258.77 Inuse: 853
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 353200
% 258.20/258.77 Kept: 82850
% 258.20/258.77 Inuse: 868
% 258.20/258.77 Deleted: 3332
% 258.20/258.77 Deletedinuse: 4
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying clauses:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 367761
% 258.20/258.77 Kept: 85908
% 258.20/258.77 Inuse: 903
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 381689
% 258.20/258.77 Kept: 88559
% 258.20/258.77 Inuse: 918
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 392390
% 258.20/258.77 Kept: 91090
% 258.20/258.77 Inuse: 928
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 404084
% 258.20/258.77 Kept: 93253
% 258.20/258.77 Inuse: 943
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 412580
% 258.20/258.77 Kept: 95754
% 258.20/258.77 Inuse: 953
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 422054
% 258.20/258.77 Kept: 98034
% 258.20/258.77 Inuse: 958
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 *** allocated 6568290 integers for clauses
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 431050
% 258.20/258.77 Kept: 101143
% 258.20/258.77 Inuse: 973
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 437596
% 258.20/258.77 Kept: 103772
% 258.20/258.77 Inuse: 983
% 258.20/258.77 Deleted: 3413
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying clauses:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 469087
% 258.20/258.77 Kept: 107640
% 258.20/258.77 Inuse: 1003
% 258.20/258.77 Deleted: 3415
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 479478
% 258.20/258.77 Kept: 109662
% 258.20/258.77 Inuse: 1025
% 258.20/258.77 Deleted: 3415
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 *** allocated 4378860 integers for termspace/termends
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 490541
% 258.20/258.77 Kept: 111806
% 258.20/258.77 Inuse: 1063
% 258.20/258.77 Deleted: 3415
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 258.20/258.77 Intermediate Status:
% 258.20/258.77 Generated: 508049
% 258.20/258.77 Kept: 114636
% 258.20/258.77 Inuse: 1073
% 258.20/258.77 Deleted: 3415
% 258.20/258.77 Deletedinuse: 7
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77 Resimplifying inuse:
% 258.20/258.77 Done
% 258.20/258.77
% 258.20/258.77
% 300.01/300.59 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------