TSTP Solution File: SWW291+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW291+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 23:21:52 EDT 2022
% Result : Timeout 300.07s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW291+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 5 17:38:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.87/1.49 *** allocated 10000 integers for termspace/termends
% 0.87/1.49 *** allocated 10000 integers for clauses
% 0.87/1.49 *** allocated 10000 integers for justifications
% 0.87/1.49 *** allocated 15000 integers for termspace/termends
% 0.87/1.49 *** allocated 22500 integers for termspace/termends
% 0.87/1.49 *** allocated 33750 integers for termspace/termends
% 0.87/1.49 Bliksem 1.12
% 0.87/1.49
% 0.87/1.49
% 0.87/1.49 Automatic Strategy Selection
% 0.87/1.49
% 0.87/1.49 *** allocated 50625 integers for termspace/termends
% 0.87/1.49 *** allocated 75937 integers for termspace/termends
% 0.87/1.49 *** allocated 113905 integers for termspace/termends
% 0.87/1.49 *** allocated 170857 integers for termspace/termends
% 0.87/1.49
% 0.87/1.49 Clauses:
% 0.87/1.49
% 0.87/1.49 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.87/1.49 { ! v_a = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.49 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ) ), v_p ), v_u____ ) = v_r }.
% 0.87/1.49 { v_p_H = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ) ), v_p ), v_t____ ) }.
% 0.87/1.49 { v_r = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ) ), v_p ), v_u____ ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.87/1.49 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.87/1.49 { v_r = c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ), c_Polynomial_Osmult( tc_Complex_Ocomplex, v_a, v_q
% 0.87/1.49 ), v_p_H ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.49 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.87/1.49 ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.87/1.49 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.87/1.49 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.87/1.49 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.87/1.49 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.87/1.49 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.87/1.49 { c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 0.87/1.49 , c_Polynomial_Osmult( tc_Complex_Ocomplex, v_a, v_q ), v_p_H ) = v_r }.
% 0.87/1.49 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p
% 0.87/1.49 , v_r ) }.
% 0.87/1.49 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), v_p
% 0.87/1.49 , v_p_H ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.87/1.49 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.87/1.49 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.49 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.87/1.49 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.49 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.87/1.49 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.87/1.49 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.87/1.49 Z ) ), U ), T ) = Y }.
% 0.87/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.87/1.49 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ) }.
% 0.87/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.87/1.49 W ) ), U ), Y ) }.
% 0.87/1.49 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.49 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.87/1.49 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.87/1.49 ( X ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.87/1.49 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.87/1.49 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.87/1.49 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.87/1.49 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.87/1.49 ), U = Z, T = Y }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.87/1.49 ) ), T ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.87/1.49 ) ), Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.49 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.49 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.87/1.49 ), ! U = T }.
% 0.87/1.49 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.87/1.49 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.87/1.49 ), ! Z = Y }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { v_p_H = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ) ), v_p ), skol2 ) }.
% 0.87/1.49 { v_r = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ) ), v_p ), skol3 ) }.
% 0.87/1.49 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.87/1.49 v_p, v_q ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.87/1.49 tc_Complex_Ocomplex ), v_p, v_r ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.49 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.87/1.49 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.87/1.49 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 Z, T ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.87/1.49 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.87/1.49 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.87/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! T =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 0.87/1.49 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), T ), hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Z ), X ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), T =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.87/1.49 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 0.87/1.49 , X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.87/1.49 ), Y, c_Polynomial_Osmult( tc_Complex_Ocomplex, Z, X ) ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.87/1.49 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.87/1.49 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.87/1.49 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.87/1.49 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.87/1.49 X, T, Z ), Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.87/1.49 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.87/1.49 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha1( X
% 0.87/1.49 , Y, T ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha37( X
% 0.87/1.49 , Y, Z, T ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha37( X, Y, Z, T )
% 0.87/1.49 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.87/1.49 ( X, T, Z ), Y ) }.
% 0.87/1.49 { ! alpha37( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.87/1.49 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 0.87/1.49 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha37( X
% 0.87/1.49 , Y, Z, T ) }.
% 0.87/1.49 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.87/1.49 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.87/1.49 , Y, Z ) }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.87/1.49 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.87/1.49 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.87/1.49 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha38( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha2( X, Y, T ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha38( X, Y, Z, T ), !
% 0.87/1.49 alpha2( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.49 { ! alpha38( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.87/1.49 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha38( X, Y, Z, T ) }.
% 0.87/1.49 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha38(
% 0.87/1.49 X, Y, Z, T ) }.
% 0.87/1.49 { ! alpha2( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { Y = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.87/1.49 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha2( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha39( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha3( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha39( X, Y, Z, T ), !
% 0.87/1.49 alpha3( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.87/1.49 { ! alpha39( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.87/1.49 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha39( X, Y, Z, T ) }.
% 0.87/1.49 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha39(
% 0.87/1.49 X, Y, Z, T ) }.
% 0.87/1.49 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.87/1.49 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.87/1.49 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.87/1.49 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.87/1.49 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.87/1.49 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.87/1.49 hAPP( Z, skol4( U, W, Z ) ) ) }.
% 0.87/1.49 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.87/1.49 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol4( X
% 0.87/1.49 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.87/1.49 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.87/1.49 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.87/1.49 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol15( X,
% 0.87/1.49 Y, Z ) ) ) ) }.
% 0.87/1.49 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.87/1.49 Z ) ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.49 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.49 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.87/1.49 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__field( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.87/1.49 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__field( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.49 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__field( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.49 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.49 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.87/1.49 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.87/1.49 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.87/1.49 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.87/1.49 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.87/1.49 = Y }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.87/1.49 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.87/1.49 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 T, Y ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 T, Y ) }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Y, Z ), T = Y }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Y, Z ) }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 T, Y ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 T, Y ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Y, T ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.87/1.49 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.87/1.49 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.49 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.87/1.49 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.87/1.49 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.87/1.49 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.87/1.49 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.87/1.49 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.87/1.49 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.87/1.49 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.87/1.49 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.87/1.49 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.87/1.49 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.87/1.49 ), Y ) }.
% 0.87/1.49 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.87/1.49 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.87/1.49 hAPP( Z, Y ) ) }.
% 0.87/1.49 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.87/1.49 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.87/1.49 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.87/1.49 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.87/1.49 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.49 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.49 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.49 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.87/1.49 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.87/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.87/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.87/1.49 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.87/1.49 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.87/1.49 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.87/1.49 Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.87/1.49 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 0.87/1.49 , Z ), alpha40( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha40( X, Y, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), alpha40( X, Y, Z ) }.
% 0.87/1.49 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ), alpha5( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha41( X, Y, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ), Y ), alpha41( X, Y, Z ) }.
% 0.87/1.49 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.87/1.49 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.87/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Y, Z ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 Z, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ) }.
% 0.87/1.49 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.87/1.49 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.87/1.49 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oone__class_Oone( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha6( X, Y, Z ), alpha42
% 0.87/1.49 ( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha6( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), alpha42( X, Y, Z ) }.
% 0.87/1.49 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ), alpha43
% 0.87/1.49 ( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ), Y ), alpha43( X, Y, Z ) }.
% 0.87/1.49 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.87/1.49 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.87/1.49 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y
% 0.87/1.49 , X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.87/1.49 ), Y, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.87/1.49 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.87/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.87/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.87/1.49 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.87/1.49 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.49 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.87/1.49 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.87/1.49 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.87/1.49 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.87/1.49 , Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.87/1.49 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.87/1.49 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.87/1.49 c_Polynomial_OpCons( X, T,
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.87/1.49 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.87/1.49 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.87/1.49 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.87/1.49 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , T, Y ), Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! Z = Y }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.87/1.49 ( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.49 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.49 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.49 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.87/1.49 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.87/1.49 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! Y = Z }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! Z = Y }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.87/1.49 , ! Z = Y }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 Y ), ! Z = Y }.
% 0.87/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 Z ), ! Z = Y }.
% 0.87/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.49 , T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , T, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , Y, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , T, Y ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, T, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , Y, Z ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.87/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.87/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.87/1.49 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha8( X, Y, Z, T ),
% 0.87/1.49 alpha44( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha44( X, Y, Z, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.49 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha44( X, Y, Z, T ) }.
% 0.87/1.49 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.87/1.49 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha8( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha9( X, Y, Z, T ),
% 0.87/1.49 alpha45( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha45( X, Y, Z, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha45( X, Y, Z, T ) }.
% 0.87/1.49 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha9( X, Y, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.87/1.49 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.49 , Y, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.87/1.49 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( X ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.87/1.49 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.87/1.49 .
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.87/1.49 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.87/1.49 ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , Y, Z ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.49 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , Y, Z ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.87/1.49 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ), alpha46( X,
% 0.87/1.49 Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha10( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.49 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), alpha46( X, Y, Z ) }.
% 0.87/1.49 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), alpha10( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha11( X, Y, Z ), alpha47
% 0.87/1.49 ( X, Y, Z ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.49 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.49 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), alpha47( X, Y, Z ) }.
% 0.87/1.49 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.49 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.49 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.49 ), alpha11( X, Y, Z ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.87/1.49 ( tc_Polynomial_Opoly( X ) ),
% 0.87/1.49 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.87/1.49 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.87/1.49 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.49 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.49 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.87/1.49 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.87/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.49 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.49 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.49 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.49 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.49 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.87/1.50 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.87/1.50 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.87/1.50 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.87/1.50 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.87/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( X, Z, W ) ), U ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.87/1.50 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.87/1.50 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 X, W, Z ) ), U ), T ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), Z ), U ), Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.50 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.50 Z, Y ) ), alpha69( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 0.87/1.50 , T ), ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.50 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), alpha82( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha69( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha82( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha82( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha82( X, Y, Z, T ), alpha12( X, Y, T ) }.
% 0.87/1.50 { ! alpha95( X, Y, Z, T ), ! alpha12( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha95( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha95( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 alpha48( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha48( X, Y, Z, T )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha12( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha12( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Z ), Y ), alpha70( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 0.87/1.50 , T ), ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.87/1.50 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), alpha83( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.50 , alpha70( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha83( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha83( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha83( X, Y, Z, T ), alpha13( X, Y, Z ) }.
% 0.87/1.50 { ! alpha96( X, Y, Z, T ), ! alpha13( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha96( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha96( X, Y, Z, T )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.50 alpha49( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha49( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha13( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha13( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.50 Z, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.50 Z, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.50 Z, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.87/1.50 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.87/1.50 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.87/1.50 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.87/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.87/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.87/1.50 hAPP( Y, U ) ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.87/1.50 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.87/1.50 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.87/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.87/1.50 hAPP( Y, U ) ) }.
% 0.87/1.50 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, Z, Y ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, Y, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.87/1.50 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.87/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.87/1.50 hAPP( Y, U ) ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.87/1.50 ( Z, skol5( X, Y, Z ) ), hAPP( Y, skol5( X, Y, Z ) ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha50( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha71( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha50( X, Y, Z
% 0.87/1.50 , T ), ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.50 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), alpha84( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha71( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha84( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha84( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha84( X, Y, Z, T ), alpha14( X, Y, T ) }.
% 0.87/1.50 { ! alpha97( X, Y, Z, T ), ! alpha14( X, Y, T ), alpha84( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha97( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha97( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha50( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 alpha50( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha50( X, Y, Z, T )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha14( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), alpha14( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , T, Z ), Y ), alpha51( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , T, Z ), Y ), alpha72( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha51( X, Y, Z
% 0.87/1.50 , T ), ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.87/1.50 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), alpha85( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.50 , alpha72( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha85( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha85( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha85( X, Y, Z, T ), alpha15( X, Y, Z ) }.
% 0.87/1.50 { ! alpha98( X, Y, Z, T ), ! alpha15( X, Y, Z ), alpha85( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha98( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha98( X, Y, Z, T )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.50 alpha51( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha51( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha15( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Y ), alpha15( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , T, Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , T, Y ), Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.87/1.50 alpha16( X, Y, Z ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.87/1.50 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! alpha16( X, Y, Z ),
% 0.87/1.50 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.87/1.50 { ! alpha16( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.50 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.50 alpha16( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), skol6
% 0.87/1.50 ( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, skol6( X, T, U ),
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), skol6( X, Y, Z ) ), Z ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ), skol7( X, T, U ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 Y, skol7( X, Y, Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ), Y ), alpha52( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ), Y ), alpha73( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha52( X, Y, Z, T ), ! alpha73( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.87/1.50 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.87/1.50 { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ) ), alpha86( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha73( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha86( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha86( X, Y, Z, T ), alpha99( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha86( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 0.87/1.50 { ! alpha99( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha86( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha99( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), alpha99( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ), T ), alpha99( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha52( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ) ), alpha52( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha17( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Y ), alpha17( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha53( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha74( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha53( X, Y, Z, T ), ! alpha74( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.87/1.50 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), alpha87( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.50 , alpha74( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha87( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha87( X, Y, Z, T ), alpha100( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha87( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 0.87/1.50 { ! alpha100( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha87( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha100( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha100( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ), Z ), T ), alpha100( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.50 alpha53( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ), Z ) ), alpha53( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha18( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha18( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha75( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha54( X, Y, Z, T ), ! alpha75( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.50 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), alpha88( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha75( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha88( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha88( X, Y, Z, T ), alpha101( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha88( X, Y, Z, T ), alpha19( X, Y, T ) }.
% 0.87/1.50 { ! alpha101( X, Y, Z, T ), ! alpha19( X, Y, T ), alpha88( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha101( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha101( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Y ) ), alpha101( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 alpha54( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Y ), Z ), alpha54( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha19( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) ), alpha55( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) ), alpha76( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha55( X, Y, Z, T ), ! alpha76( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless__eq( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) ) }.
% 0.87/1.50 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ) ), alpha89( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha76( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha89( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha89( X, Y, Z, T ), alpha102( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha89( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.87/1.50 { ! alpha102( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha89( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha102( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), alpha102( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) ), alpha102( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha55( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), Z ), alpha55( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), alpha20( X, Y, Z ) }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.87/1.50 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.87/1.50 .
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.87/1.50 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.87/1.50 }.
% 0.87/1.50 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.87/1.50 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.87/1.50 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.87/1.50 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.87/1.50 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.87/1.50 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Z, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.87/1.50 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.87/1.50 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.87/1.50 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.87/1.50 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.87/1.50 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.87/1.50 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ) = Y, alpha56( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ) = Y, alpha21( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 alpha56( X, Y, Z, T ), ! alpha21( X, Y, Z ),
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ) = Y }.
% 0.87/1.50 { ! alpha56( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ) }.
% 0.87/1.50 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ), alpha56( X, Y, Z, T ) }.
% 0.87/1.50 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha56( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha21( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.50 .
% 0.87/1.50 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ), alpha21( X, Y, Z ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha21( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), alpha57( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), alpha22( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 alpha57( X, Y, Z, T ), ! alpha22( X, Y, Z ),
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.87/1.50 { ! alpha57( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.87/1.50 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha57( X, Y, Z, T ) }.
% 0.87/1.50 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha57( X, Y, Z, T ) }
% 0.87/1.50 .
% 0.87/1.50 { ! alpha22( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) }.
% 0.87/1.50 { Z = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 0.87/1.50 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ), alpha22( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha58( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha23( X, Y, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 alpha58( X, Y, Z, T ), ! alpha23( X, Y, T ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.50 { ! alpha58( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X
% 0.87/1.50 , T ) ), Y ) = Z }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha58( X, Y, Z, T ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) = Z, alpha58( X, Y, Z, T
% 0.87/1.50 ) }.
% 0.87/1.50 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) }.
% 0.87/1.50 { Y = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 0.87/1.50 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ), alpha23( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.87/1.50 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), alpha59( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.87/1.50 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), alpha24( X, Y, T ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.87/1.50 alpha59( X, Y, Z, T ), ! alpha24( X, Y, T ), T =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) }.
% 0.87/1.50 { ! alpha59( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) = Z }.
% 0.87/1.50 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ), alpha59( X, Y, Z, T ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z, alpha59( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha24( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.50 .
% 0.87/1.50 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ), alpha24( X, Y, Z ) }.
% 0.87/1.50 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ), Y ), alpha60( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Z ) ), Y ), alpha77( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha60( X, Y, Z, T ), ! alpha77( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.87/1.50 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.87/1.50 { ! alpha77( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ) ), alpha90( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha77( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha90( X, Y, Z, T ), alpha77( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha90( X, Y, Z, T ), alpha103( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha90( X, Y, Z, T ), alpha25( X, Y, Z ) }.
% 0.87/1.50 { ! alpha103( X, Y, Z, T ), ! alpha25( X, Y, Z ), alpha90( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha103( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), alpha103( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ), T ), alpha103( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha60( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Z ) ) ), alpha60( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha25( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha78( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha61( X, Y, Z, T ), ! alpha78( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.87/1.50 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! alpha78( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), alpha91( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.87/1.50 , alpha78( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha91( X, Y, Z, T ), alpha78( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha91( X, Y, Z, T ), alpha104( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha91( X, Y, Z, T ), alpha26( X, Y, Z ) }.
% 0.87/1.50 { ! alpha104( X, Y, Z, T ), ! alpha26( X, Y, Z ), alpha91( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha104( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha104( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ), Z ), T ), alpha104( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.87/1.50 alpha61( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ), Z ) ), alpha61( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha26( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha26( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha62( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.87/1.50 ( X, Z, Y ) ), alpha79( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha62( X, Y, Z, T ), ! alpha79( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.50 { ! alpha79( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), alpha92( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.87/1.50 , alpha79( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha92( X, Y, Z, T ), alpha79( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha92( X, Y, Z, T ), alpha105( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha92( X, Y, Z, T ), alpha27( X, Y, T ) }.
% 0.87/1.50 { ! alpha105( X, Y, Z, T ), ! alpha27( X, Y, T ), alpha92( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha105( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 alpha105( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Y ) ), alpha105( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 alpha62( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 T ) ), Y ), Z ), alpha62( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha27( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) ), alpha63( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.87/1.50 X, Y ) ) ), alpha80( X, Y, Z, T ) }.
% 0.87/1.50 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.87/1.50 class_Int_Onumber( X ), ! alpha63( X, Y, Z, T ), ! alpha80( X, Y, Z, T )
% 0.87/1.50 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.87/1.50 { ! alpha80( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ) ), alpha93( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha80( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha93( X, Y, Z, T ), alpha80( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha93( X, Y, Z, T ), alpha106( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha93( X, Y, Z, T ), alpha28( X, Y, T ) }.
% 0.87/1.50 { ! alpha106( X, Y, Z, T ), ! alpha28( X, Y, T ), alpha93( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha106( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ), c_Groups_Ozero__class_Ozero( X ) ), alpha106( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ) ), alpha106( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha63( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), Z ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha63( X, Y, Z, T ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.87/1.50 ( X, Y ) ), Z ), alpha63( X, Y, Z, T ) }.
% 0.87/1.50 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha28( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.87/1.50 , alpha28( X, Y, Z ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Int_Osucc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.87/1.50 { X = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.87/1.50 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Complex_Ocomplex ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.87/1.50 tc_Complex_Ocomplex ) ) ) ) ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.87/1.50 }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.87/1.50 }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Int_Oint ) ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), X ) = X }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ) ) = X }.
% 0.87/1.50 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.87/1.50 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.87/1.50 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.87/1.50 .
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.87/1.50 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 0.87/1.50 ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.50 tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 0.87/1.50 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.87/1.50 , Z ), X ) ), T ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, U, T ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.87/1.50 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.87/1.50 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.87/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.87/1.50 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.87/1.50 ) ) }.
% 0.87/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.87/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.87/1.50 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.87/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.87/1.50 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.50 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.50 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.87/1.50 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.87/1.50 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.87/1.50 { c_Int_Osucc( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.87/1.50 = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) ) }.
% 0.87/1.50 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.87/1.50 ( X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.87/1.50 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.87/1.50 ( X ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.87/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.87/1.50 ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.50 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) = hAPP(
% 0.87/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ), X ) }.
% 0.87/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.87/1.50 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.50 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.87/1.50 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.87/1.50 { Y = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.87/1.50 ( tc_Complex_Ocomplex ) ) ) ), X ) }.
% 0.87/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 0.87/1.50 ( tc_Complex_Ocomplex ) ) ) ), X ) = Y }.
% 0.87/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.87/1.50 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.87/1.50 tc_Complex_Ocomplex ) ) ) ), X ) = hAPP( c_Polynomial_Opoly(
% 0.87/1.50 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 0.87/1.50 tc_Complex_Ocomplex ) ) ), X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.87/1.50 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.87/1.50 , Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.87/1.50 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.87/1.50 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.87/1.50 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.87/1.50 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.87/1.50 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.87/1.50 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.87/1.50 Y ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.50 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.87/1.50 tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.87/1.50 ) ), X ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.87/1.50 ), X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.87/1.50 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.87/1.50 , Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.87/1.50 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.87/1.50 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.87/1.50 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.87/1.50 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.87/1.50 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.87/1.50 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.87/1.50 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Int_Oint ) }.
% 0.87/1.50 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Int_Oint ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.87/1.50 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, X, Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Int_Oint ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.87/1.50 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.87/1.50 }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.87/1.50 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.87/1.50 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.87/1.50 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Int_Oint ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.87/1.50 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.87/1.50 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.87/1.50 , Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.87/1.50 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Int_Oint, X, Y ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol8( Z, Y ) ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.87/1.50 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Int_Oint, skol8( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.87/1.50 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.87/1.50 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.87/1.50 , Z ), X ) ) ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.87/1.50 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.87/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ), Z ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Z ), Y ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.87/1.50 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.87/1.50 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ) ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 Y ) ) = Y }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 Z, Y ) ) = Y }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.87/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 0.87/1.50 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.87/1.50 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.87/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.87/1.50 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.87/1.50 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.87/1.50 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ), Z = Y }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) }.
% 0.87/1.50 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.87/1.50 ) ) }.
% 0.87/1.50 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.87/1.50 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.50 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ), Y ) }.
% 0.87/1.50 { ! class_RealVector_Oreal__normed__field( X ),
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.87/1.50 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 Y ) ) }.
% 0.87/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Int_Oint, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.87/1.50 , Z, Y ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.87/1.50 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.87/1.50 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 = Y }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.87/1.50 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 = Y }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ), Y ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.50 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 , Y ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.87/1.50 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.87/1.50 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.87/1.50 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.87/1.50 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Z ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.87/1.50 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.87/1.50 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 Z ) = Y }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 X, Y ) }.
% 0.87/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.87/1.50 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.87/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.50 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.87/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.87/1.50 ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.87/1.50 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.87/1.50 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Y ) ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.87/1.50 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.87/1.50 X, Z, Y ) }.
% 0.87/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.87/1.50 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.87/1.50 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.87/1.50 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.87/1.50 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), Y ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.87/1.50 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.87/1.50 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.87/1.50 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.87/1.50 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.87/1.50 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Int_Oint, X, Y ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.87/1.50 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.87/1.50 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 0.87/1.50 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.87/1.50 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.87/1.50 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.87/1.50 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 0.87/1.50 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.87/1.50 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.87/1.50 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.87/1.50 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.50 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.87/1.50 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.87/1.50 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 0.87/1.50 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 0.87/1.50 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.87/1.50 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.87/1.50 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.87/1.50 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.87/1.50 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.87/1.50 , Y ), X ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ) }.
% 0.87/1.50 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ) ) = Y }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.87/1.50 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.87/1.50 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.87/1.50 , X ) }.
% 0.87/1.50 { alpha108( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.87/1.50 { alpha108( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 0.87/1.50 hAPP( X, Y ), Z ) ) }.
% 0.87/1.50 { ! alpha108( X, Y, Z ), alpha109( X, Y, Z ), Z = Y }.
% 0.87/1.50 { ! alpha108( X, Y, Z ), alpha109( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ),
% 0.87/1.50 Z ) ) }.
% 0.87/1.50 { ! alpha109( X, Y, Z ), alpha108( X, Y, Z ) }.
% 0.87/1.50 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha108( X, Y, Z ) }.
% 0.87/1.50 { ! alpha109( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha109( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.87/1.50 X, Y ), Z ) ), alpha109( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.87/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.87/1.50 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.87/1.50 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.87/1.50 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.87/1.50 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.87/1.50 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Z, Y ), X ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.87/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.87/1.50 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.87/1.50 ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.87/1.50 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.87/1.50 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.87/1.50 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.87/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.87/1.50 .
% 0.87/1.50 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.87/1.50 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.87/1.50 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.87/1.50 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.87/1.50 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.87/1.50 .
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ) ) = X }.
% 0.87/1.50 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), X ) = X }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.87/1.50 .
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.87/1.50 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.87/1.50 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.87/1.50 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.87/1.50 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.87/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.87/1.50 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.87/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.87/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 Y ), X ) ) }.
% 0.87/1.50 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.87/1.50 , ! alpha29( X, Y, Z ) }.
% 0.87/1.50 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.87/1.50 , ! alpha64( X, Y, Z ) }.
% 0.87/1.50 { alpha29( X, Y, Z ), alpha64( X, Y, Z ), hBOOL( hAPP( Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.87/1.50 { ! alpha64( X, Y, Z ), ! hBOOL( hAPP( Z, skol10( T, U, Z ) ) ) }.
% 0.87/1.50 { ! alpha64( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.87/1.50 skol10( X, Y, Z ) ) }.
% 0.87/1.50 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.87/1.50 ) ), alpha64( X, Y, Z ) }.
% 0.87/1.50 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.87/1.50 }.
% 0.87/1.50 { ! alpha29( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ) ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha29( X, Y, Z ) }.
% 0.87/1.50 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.87/1.50 , alpha30( X, Y, Z ) }.
% 0.87/1.50 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.87/1.50 , alpha65( X, Y, Z ) }.
% 0.87/1.50 { ! alpha30( X, Y, Z ), ! alpha65( X, Y, Z ), hBOOL( hAPP( Z,
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.87/1.50 { ! alpha65( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.87/1.50 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.87/1.50 { ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ), alpha65( X, Y, Z ) }.
% 0.87/1.50 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol11( X, Y, Z ) ),
% 0.87/1.50 alpha65( X, Y, Z ) }.
% 0.87/1.50 { ! alpha30( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.87/1.50 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.87/1.50 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha30( X, Y, Z ) }
% 0.87/1.50 .
% 0.87/1.50 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha30
% 0.87/1.50 ( X, Y, Z ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.50 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.87/1.50 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.87/1.50 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.87/1.50 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.87/1.50 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.87/1.50 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.50 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.50 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.87/1.50 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.50 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.87/1.50 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.87/1.50 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.87/1.50 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.87/1.50 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.87/1.50 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.50 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.50 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.87/1.50 ), X ) ) }.
% 0.87/1.50 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha31( X, Y ), Y = X }
% 0.87/1.50 .
% 0.87/1.50 { ! alpha31( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! alpha31( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! alpha31( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), alpha31( X, Y ) }.
% 0.87/1.50 { ! alpha32( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! alpha32( X, Y ), ! Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha32( X, Y ) }
% 0.87/1.50 .
% 0.87/1.50 { ! alpha32( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! alpha32( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), alpha32( X, Y ) }.
% 0.87/1.50 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.87/1.50 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.87/1.50 , Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.87/1.50 Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Y, Z ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.87/1.50 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.50 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.87/1.50 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.87/1.50 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.87/1.50 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.87/1.50 ) }.
% 0.87/1.50 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.87/1.50 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.87/1.50 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.87/1.50 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.50 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.87/1.50 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.87/1.50 ( tc_Nat_Onat ) ) ) ) }.
% 0.87/1.50 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.87/1.50 ( X ) }.
% 0.87/1.50 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.87/1.50 = c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.50 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.50 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.87/1.50 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.87/1.50 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.87/1.50 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.87/1.50 tc_Nat_Onat, Y, X ) }.
% 0.87/1.50 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.50 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.50 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.87/1.50 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.87/1.50 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.87/1.51 X ) ) }.
% 0.87/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.87/1.51 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.87/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.87/1.51 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.87/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.87/1.51 tc_Nat_Onat ) ) = Y }.
% 0.87/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.87/1.51 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.51 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.51 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.87/1.51 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.87/1.51 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.87/1.51 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.87/1.51 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.87/1.51 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.87/1.51 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.87/1.51 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.87/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.87/1.51 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.87/1.51 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.87/1.51 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.87/1.51 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.87/1.51 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.87/1.51 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.87/1.51 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.87/1.51 ), T ), U ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.51 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.51 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.87/1.51 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.51 tc_Nat_Onat ), X ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.87/1.51 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.87/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.87/1.51 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.87/1.51 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.87/1.51 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.51 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.51 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.87/1.51 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.87/1.51 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.51 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.87/1.51 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.87/1.51 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.51 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.87/1.51 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.87/1.51 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.87/1.51 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.87/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.87/1.51 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.87/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.87/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.87/1.51 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.87/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.87/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.87/1.51 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.87/1.51 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.87/1.51 ( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.87/1.51 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.87/1.51 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.87/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.87/1.51 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.87/1.51 c_Groups_Oone__class_Oone( X ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.87/1.51 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.87/1.51 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.87/1.51 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.87/1.51 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ), Y ) }.
% 0.87/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.87/1.51 ), X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) ) }.
% 0.87/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.87/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.87/1.51 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.87/1.51 ) }.
% 0.87/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Nat_Onat, Z, X ) }.
% 0.87/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.87/1.51 tc_Nat_Onat ), X ) }.
% 0.87/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.87/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.87/1.51 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.87/1.51 ) }.
% 0.87/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Int_Oint, Z, X ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.87/1.51 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.87/1.51 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.87/1.51 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.87/1.51 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.87/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.87/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.87/1.51 Y ) ) ), Y ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.87/1.51 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.87/1.51 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.87/1.51 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.87/1.51 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.87/1.51 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.87/1.51 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.87/1.51 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.87/1.51 Y ) ) ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.87/1.51 X ) ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.87/1.51 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.87/1.51 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.87/1.51 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.87/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.87/1.51 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.87/1.51 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.51 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.87/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.87/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.87/1.51 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.87/1.51 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.87/1.51 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.87/1.51 { ! c_Nat_OSuc( X ) = X }.
% 0.87/1.51 { ! X = c_Nat_OSuc( X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.87/1.51 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.87/1.51 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.87/1.51 .
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.87/1.51 .
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.87/1.51 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.87/1.51 X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.87/1.51 }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.51 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.87/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.87/1.51 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.87/1.51 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.87/1.51 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.87/1.51 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.87/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.87/1.51 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.51 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.51 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.87/1.51 .
% 0.87/1.51 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.87/1.51 ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.87/1.51 , c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.87/1.51 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.87/1.51 }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.87/1.51 c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.87/1.51 ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.51 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.87/1.51 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.87/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.87/1.51 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.87/1.51 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.87/1.51 ), X ) ) }.
% 0.87/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.87/1.51 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.87/1.51 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.87/1.51 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.87/1.51 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.87/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.87/1.51 ), X ) ) }.
% 0.87/1.51 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.87/1.51 .
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.87/1.51 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) ) }.
% 0.87/1.51 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.87/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.87/1.51 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha33( X, Y ),
% 0.87/1.51 alpha66( X, Y ) }.
% 0.87/1.51 { ! alpha33( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.87/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! alpha66( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.87/1.51 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.87/1.51 { ! alpha66( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! alpha66( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha66( X, Y ) }.
% 0.87/1.51 { ! alpha33( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! alpha33( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha33( X, Y ) }.
% 0.87/1.51 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha34( X, Y ), alpha67( X
% 0.87/1.51 , Y ) }.
% 0.87/1.51 { ! alpha34( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! alpha67( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! alpha67( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! alpha67( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha67( X, Y ) }.
% 0.87/1.51 { ! alpha34( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.87/1.51 tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! alpha34( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha34( X, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha35( X, Y ) }.
% 0.87/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.87/1.51 c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! alpha35( X, Y ), Y = c_Nat_OSuc( skol13( Z, Y ) ) }.
% 0.87/1.51 { ! alpha35( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( X
% 0.87/1.51 , Y ), X ) }.
% 0.87/1.51 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.87/1.51 ), alpha35( X, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol14( X ) ) }.
% 0.87/1.51 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.87/1.51 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.87/1.51 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.87/1.51 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.87/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.87/1.51 X ), Y ), Z = Y }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.51 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.87/1.51 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.87/1.51 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.87/1.51 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.87/1.51 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.87/1.51 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.87/1.51 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.87/1.51 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.87/1.51 ) ) = X }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.87/1.51 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.87/1.51 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.87/1.51 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.87/1.51 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.87/1.51 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.87/1.51 c_Groups_Oone__class_Oone( X ) ) }.
% 0.87/1.51 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.87/1.51 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.87/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.87/1.51 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.87/1.51 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.87/1.51 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.87/1.51 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.87/1.51 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.87/1.51 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.87/1.51 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.87/1.51 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.87/1.51 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.87/1.51 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.87/1.51 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 0.87/1.51 ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.87/1.51 tc_Nat_Onat ), X ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) )
% 0.87/1.51 , c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( Y ) ), X ) }
% 0.87/1.51 .
% 0.87/1.51 { c_Nat__Numeral_Oneg( X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 0.87/1.51 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! c_Nat__Numeral_Oneg( X
% 0.87/1.51 ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X
% 0.87/1.51 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Numeral_Oneg( X ) }
% 0.87/1.51 .
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.87/1.51 c_Int_OBit0( X ) ) ), c_Nat__Numeral_Oneg(
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 0.87/1.51 ), c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.87/1.51 c_Int_OBit0( X ) ) ) }.
% 0.87/1.51 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.87/1.51 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.87/1.51 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.87/1.51 ) ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 0.87/1.51 ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), alpha36( X, Y ) }.
% 0.87/1.51 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), alpha68( X, Y ) }.
% 0.87/1.51 { ! alpha36( X, Y ), ! alpha68( X, Y ), c_Int_Onumber__class_Onumber__of(
% 0.87/1.51 tc_Nat_Onat, Y ) = c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.87/1.51 { ! alpha68( X, Y ), c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of
% 0.87/1.51 ( tc_Int_Oint, Y ) ), alpha81( X, Y ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 0.87/1.51 ), alpha68( X, Y ) }.
% 0.87/1.51 { ! alpha81( X, Y ), alpha68( X, Y ) }.
% 0.87/1.51 { ! alpha81( X, Y ), alpha94( X, Y ) }.
% 0.87/1.51 { ! alpha81( X, Y ), alpha107( X, Y ) }.
% 0.87/1.51 { ! alpha94( X, Y ), ! alpha107( X, Y ), alpha81( X, Y ) }.
% 0.87/1.51 { ! alpha107( X, Y ), c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of
% 0.87/1.51 ( tc_Int_Oint, X ) ), Y = X }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 0.87/1.51 ), alpha107( X, Y ) }.
% 0.87/1.51 { ! Y = X, alpha107( X, Y ) }.
% 0.87/1.51 { ! alpha94( X, Y ), ! c_Nat__Numeral_Oneg(
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 0.87/1.51 , alpha94( X, Y ) }.
% 0.87/1.51 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) =
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha94( X, Y ) }.
% 0.87/1.51 { ! alpha36( X, Y ), ! c_Nat__Numeral_Oneg(
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) )
% 0.87/1.51 , alpha36( X, Y ) }.
% 0.87/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.87/1.51 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha36( X, Y ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z )
% 0.87/1.51 ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z ) )
% 0.87/1.51 , ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y
% 0.87/1.51 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ), X ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z ) )
% 0.87/1.51 , c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 0.87/1.51 ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) }.
% 0.87/1.51 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 0.87/1.51 ), c_Nat_OSuc( c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.87/1.51 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 0.87/1.51 , c_Nat_OSuc( c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.87/1.51 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.87/1.51 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.87/1.51 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.87/1.51 ( tc_fun( Y, X ) ) }.
% 0.87/1.51 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.87/1.51 ) ) }.
% 0.87/1.51 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.87/1.51 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.87/1.51 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.87/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.87/1.51 tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.87/1.51 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.87/1.51 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.87/1.51 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.87/1.51 { class_Power_Opower( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oplus( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.87/1.51 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.87/1.51 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.87/1.51 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.87/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.87/1.51 tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oplus( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.87/1.51 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.87/1.51 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.87/1.51 tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Oplus( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ),
% 0.87/1.51 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.87/1.51 ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.87/1.51 X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.87/1.51 ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.87/1.51 }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.87/1.51 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ),
% 0.87/1.51 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.87/1.51 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.87/1.51 ( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.87/1.51 ( tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.87/1.51 }.
% 0.87/1.51 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oplus(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.87/1.51 ) ) }.
% 0.87/1.51 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.87/1.51 .
% 0.87/1.51 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 0.87/1.51 ( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.87/1.51 tc_Polynomial_Opoly( X ) ) }.
% 0.87/1.51 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.87/1.51 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.87/1.51 { ! v_q = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly(
% 0.87/1.51 tc_Complex_Ocomplex ) ), v_p ), c_Polynomial_Osmult( tc_Complex_Ocomplex
% 0.87/1.51 , c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex,
% 0.87/1.51 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), v_a ),
% 0.87/1.51 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( tc_Complex_Ocomplex ),
% 0.87/1.51 v_u____, v_t____ ) ) ) }.
% 0.87/1.51
% 0.87/1.51 *** allocated 15000 integers for clauses
% 0.87/1.51 *** allocated 22500 integers for clauses
% 0.87/1.51 *** allocated 33750 integers for clauses
% 0.87/1.51 *** allocated 50625 integers for clauses
% 0.87/1.51 *** allocated 75937 integers for clauses
% 0.87/1.51 *** allocated 113905 integers for clauses
% 0.87/1.51 percentage equality = 0.226751, percentage horn = 0.887012
% 0.87/1.51 This is a problem with some equality
% 0.87/1.51
% 0.87/1.51
% 0.87/1.51
% 0.87/1.51 Options Used:
% 0.87/1.51
% 0.87/1.51 useres = 1
% 0.87/1.51 useparamod = 1
% 0.87/1.51 useeqrefl = 1
% 0.87/1.51 useeqfact = 1
% 0.87/1.51 usefactor = 1
% 0.87/1.51 usesimpsplitting = 0
% 0.87/1.51 usesimpdemod = 5
% 0.87/1.51 usesimpres = 3
% 0.87/1.51
% 0.87/1.51 resimpinuse = 1000
% 0.87/1.51 resimpclauses = 20000
% 0.87/1.51 substype = eqrewr
% 0.87/1.51 backwardsubs = 1
% 0.87/1.51 selectoldest = 5
% 0.87/1.51
% 0.87/1.51 litorderings [0] = split
% 0.87/1.51 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.51
% 0.87/1.51 termordering = kbo
% 0.87/1.51
% 0.87/1.51 litapriori = 0
% 0.87/1.51 termapriori = 1
% 0.87/1.51 litaposteriori = 0
% 0.87/1.51 termaposteriori = 0
% 0.87/1.51 demodaposteriori = 0
% 0.87/1.51 ordereqreflfact = 0
% 0.87/1.51
% 0.87/1.51 litselect = negord
% 0.87/1.51
% 0.87/1.51 maxweight = 15
% 0.87/1.51 maxdepth = 30000
% 0.87/1.51 maxlength = 115
% 0.87/1.51 maxnrvars = 195
% 0.87/1.51 excuselevel = 1
% 0.87/1.51 increasemaxweight = 1
% 0.87/1.51
% 0.87/1.51 maxselected = 10000000
% 0.87/1.51 maxnrclauses = 10000000
% 0.87/1.51
% 0.87/1.51 showgenerated = 0
% 0.87/1.51 showkept = 0
% 0.87/1.51 showselected = 0
% 0.87/1.51 showdeleted = 0
% 0.87/1.51 showresimp = 1
% 0.87/1.51 showstatus = 2000
% 0.87/1.51
% 0.87/1.51 prologoutput = 0
% 0.87/1.51 nrgoals = 5000000
% 0.87/1.51 totalproof = 1
% 0.87/1.51
% 0.87/1.51 Symbols occurring in the translation:
% 0.87/1.51
% 0.87/1.51 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.51 . [1, 2] (w:1, o:196, a:1, s:1, b:0),
% 0.87/1.51 ! [4, 1] (w:0, o:109, a:1, s:1, b:0),
% 0.87/1.51 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.51 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.51 hAPP [38, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.87/1.51 v_a [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.87/1.51 tc_Complex_Ocomplex [40, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.87/1.51 tc_Polynomial_Opoly [42, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Otimes__class_Otimes [43, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.87/1.51 v_p [44, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.87/1.51 v_u____ [45, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.87/1.51 v_r [46, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.87/1.51 v_p_H [47, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.87/1.51 v_t____ [48, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ocomm__semiring__0 [53, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Oplus__class_Oplus [54, 3] (w:1, o:246, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_Osmult [55, 3] (w:1, o:249, a:1, s:1, b:0),
% 0.87/1.51 v_q [56, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Ominus__class_Ominus [57, 3] (w:1, o:250, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ocomm__semiring__1 [59, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Oone__class_Oone [60, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Odivision__ring [63, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.87/1.51 c_Rings_Oinverse__class_Odivide [64, 3] (w:1, o:251, a:1, s:1, b:0),
% 0.87/1.51
% 0.87/1.51 c_Rings_Odvd__class_Odvd [65, 3] (w:1, o:252, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Oidom [68, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ocomm__ring [69, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ono__zero__divisors [71, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.87/1.51
% 0.87/1.51 class_Rings_Oring__no__zero__divisors [73, 1] (w:1, o:137, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Rings_Omult__zero [74, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.87/1.51 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [75
% 0.87/1.51 , 1] (w:1, o:153, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ozero__neq__one [76, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Odivision__ring__inverse__zero [77, 1] (w:1, o:139, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 class_Rings_Oring [81, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Osemiring [92, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ocomm__semiring [93, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.87/1.51 class_RealVector_Oreal__field [100, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.87/1.51 class_Fields_Ofield [102, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.87/1.51 class_Fields_Ofield__inverse__zero [103, 1] (w:1, o:155, a:1, s:1, b:
% 0.87/1.51 0),
% 0.87/1.51 class_Rings_Odvd [105, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Ocomm__ring__1 [106, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Ocomm__monoid__add [108, 1] (w:1, o:158, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Groups_Oab__group__add [109, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Oring__1 [113, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Osemiring__0 [116, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.87/1.51 hBOOL [117, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.87/1.51 class_RealVector_Oreal__normed__algebra [118, 1] (w:1, o:147, a:1, s:
% 0.87/1.51 1, b:0),
% 0.87/1.51 class_Rings_Olinordered__ring__strict [119, 1] (w:1, o:126, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_RealVector_Oreal__normed__field [121, 1] (w:1, o:148, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Groups_Ogroup__add [125, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Ocomm__monoid__mult [126, 1] (w:1, o:162, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Groups_Omonoid__mult [127, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Ozero [128, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Oab__semigroup__mult [129, 1] (w:1, o:166, a:1, s:1, b:0
% 0.87/1.51 ),
% 0.87/1.51 class_Groups_Oab__semigroup__add [130, 1] (w:1, o:167, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Groups_Ocancel__semigroup__add [131, 1] (w:1, o:168, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Groups_Ocancel__ab__semigroup__add [132, 1] (w:1, o:169, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 class_Groups_Oone [133, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Omonoid__add [134, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Olinordered__ab__group__add [135, 1] (w:1, o:163, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 c_Polynomial_Opoly__rec [137, 5] (w:1, o:363, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_OpCons [138, 3] (w:1, o:254, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__semiring__1 [141, 1] (w:1, o:128, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 c_Orderings_Oord__class_Oless__eq [142, 3] (w:1, o:247, a:1, s:1, b:0
% 0.87/1.51 ),
% 0.87/1.51 class_Groups_Ominus [145, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.87/1.51 tc_fun [146, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.87/1.51 class_Lattices_Oab__semigroup__idem__mult [147, 1] (w:1, o:173, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 c_fequal [148, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.87/1.51 c_If [149, 4] (w:1, o:303, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Oordered__ab__semigroup__add__imp__le [150, 1] (w:1, o:
% 0.87/1.51 174, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Oordered__ab__semigroup__add [151, 1] (w:1, o:175, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 class_Groups_Oordered__ab__group__add [152, 1] (w:1, o:176, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Rings_Olinordered__ring [153, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Oordered__cancel__semiring [154, 1] (w:1, o:149, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Rings_Oordered__ring [155, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Oordered__semiring [156, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.87/1.51
% 0.87/1.51 class_Rings_Oordered__comm__semiring [157, 1] (w:1, o:152, a:1, s:1
% 0.87/1.51 , b:0),
% 0.87/1.51 class_Groups_Oordered__comm__monoid__add [158, 1] (w:1, o:177, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__semidom [159, 1] (w:1, o:129, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Fields_Olinordered__field__inverse__zero [160, 1] (w:1, o:156
% 0.87/1.51 , a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__idom [161, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_Opcompose [162, 3] (w:1, o:255, a:1, s:1, b:0),
% 0.87/1.51 class_Orderings_Opreorder [163, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.87/1.51 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [164, 3] (w:
% 0.87/1.51 1, o:245, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__semiring__1__strict [165, 1] (w:1, o:131, a:
% 0.87/1.51 1, s:1, b:0),
% 0.87/1.51 c_Orderings_Oord__class_Oless [166, 3] (w:1, o:248, a:1, s:1, b:0),
% 0.87/1.51 class_Fields_Olinordered__field [167, 1] (w:1, o:157, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Orderings_Olinorder [168, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.87/1.51 class_Orderings_Oorder [169, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.87/1.51 class_Orderings_Oord [170, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.87/1.51 class_Groups_Oordered__cancel__ab__semigroup__add [171, 1] (w:1, o:
% 0.87/1.51 182, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__comm__semiring__strict [172, 1] (w:1, o:132
% 0.87/1.51 , a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__semiring__strict [173, 1] (w:1, o:133, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 class_Rings_Olinordered__semiring [176, 1] (w:1, o:134, a:1, s:1, b:0
% 0.87/1.51 ),
% 0.87/1.51 c_Polynomial_Opos__poly [177, 2] (w:1, o:228, a:1, s:1, b:0),
% 0.87/1.51 class_Int_Onumber [180, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.87/1.51 c_Int_Onumber__class_Onumber__of [181, 2] (w:1, o:229, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Int_Onumber__ring [182, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.87/1.51 class_Int_Oring__char__0 [183, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.87/1.51 tc_Int_Oint [184, 0] (w:1, o:91, a:1, s:1, b:0),
% 0.87/1.51 c_Int_Osucc [186, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.87/1.51 c_Int_OBit0 [187, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_Opoly [188, 2] (w:1, o:230, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_Osynthetic__div [204, 3] (w:1, o:256, a:1, s:1, b:0),
% 0.87/1.51 c_Groups_Ouminus__class_Ouminus [205, 2] (w:1, o:231, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 c_Nat__Transfer_Otsub [206, 2] (w:1, o:232, a:1, s:1, b:0),
% 0.87/1.51 c_Polynomial_Oorder [207, 3] (w:1, o:253, a:1, s:1, b:0),
% 0.87/1.51 tc_Nat_Onat [208, 0] (w:1, o:99, a:1, s:1, b:0),
% 0.87/1.51 class_Lattices_Oboolean__algebra [209, 1] (w:1, o:188, a:1, s:1, b:0)
% 0.87/1.51 ,
% 0.87/1.51 class_Groups_Ouminus [210, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.87/1.51 class_Rings_Oring__1__no__zero__divisors [211, 1] (w:1, o:142, a:1
% 0.87/1.51 , s:1, b:0),
% 0.87/1.51 c_Power_Opower__class_Opower [212, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.87/1.51 class_Power_Opower [218, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.87/1.51 c_Nat_OSuc [221, 1] (w:1, o:192, a:1, s:1, b:0),
% 2.86/3.22 c_Power_Opower_Opower [228, 3] (w:1, o:257, a:1, s:1, b:0),
% 2.86/3.22 c_Nat__Numeral_Oneg [229, 1] (w:1, o:193, a:1, s:1, b:0),
% 2.86/3.22 class_Groups_Ocancel__comm__monoid__add [236, 1] (w:1, o:194, a:1, s:
% 2.86/3.22 1, b:0),
% 2.86/3.22 class_Groups_Oplus [238, 1] (w:1, o:195, a:1, s:1, b:0),
% 2.86/3.22 tc_HOL_Obool [239, 0] (w:1, o:90, a:1, s:1, b:0),
% 2.86/3.22 alpha1 [240, 3] (w:1, o:258, a:1, s:1, b:1),
% 2.86/3.22 alpha2 [241, 3] (w:1, o:271, a:1, s:1, b:1),
% 2.86/3.22 alpha3 [242, 3] (w:1, o:282, a:1, s:1, b:1),
% 2.86/3.22 alpha4 [243, 3] (w:1, o:284, a:1, s:1, b:1),
% 2.86/3.22 alpha5 [244, 3] (w:1, o:291, a:1, s:1, b:1),
% 2.86/3.22 alpha6 [245, 3] (w:1, o:292, a:1, s:1, b:1),
% 2.86/3.22 alpha7 [246, 3] (w:1, o:295, a:1, s:1, b:1),
% 2.86/3.22 alpha8 [247, 4] (w:1, o:314, a:1, s:1, b:1),
% 2.86/3.22 alpha9 [248, 4] (w:1, o:324, a:1, s:1, b:1),
% 2.86/3.22 alpha10 [249, 3] (w:1, o:259, a:1, s:1, b:1),
% 2.86/3.22 alpha11 [250, 3] (w:1, o:262, a:1, s:1, b:1),
% 2.86/3.22 alpha12 [251, 3] (w:1, o:263, a:1, s:1, b:1),
% 2.86/3.22 alpha13 [252, 3] (w:1, o:264, a:1, s:1, b:1),
% 2.86/3.22 alpha14 [253, 3] (w:1, o:265, a:1, s:1, b:1),
% 2.86/3.22 alpha15 [254, 3] (w:1, o:266, a:1, s:1, b:1),
% 2.86/3.22 alpha16 [255, 3] (w:1, o:267, a:1, s:1, b:1),
% 2.86/3.22 alpha17 [256, 3] (w:1, o:268, a:1, s:1, b:1),
% 2.86/3.22 alpha18 [257, 3] (w:1, o:269, a:1, s:1, b:1),
% 2.86/3.22 alpha19 [258, 3] (w:1, o:270, a:1, s:1, b:1),
% 2.86/3.22 alpha20 [259, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.86/3.22 alpha21 [260, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.86/3.22 alpha22 [261, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.86/3.22 alpha23 [262, 3] (w:1, o:275, a:1, s:1, b:1),
% 2.86/3.22 alpha24 [263, 3] (w:1, o:276, a:1, s:1, b:1),
% 2.86/3.22 alpha25 [264, 3] (w:1, o:277, a:1, s:1, b:1),
% 2.86/3.22 alpha26 [265, 3] (w:1, o:278, a:1, s:1, b:1),
% 2.86/3.22 alpha27 [266, 3] (w:1, o:279, a:1, s:1, b:1),
% 2.86/3.22 alpha28 [267, 3] (w:1, o:280, a:1, s:1, b:1),
% 2.86/3.22 alpha29 [268, 3] (w:1, o:281, a:1, s:1, b:1),
% 2.86/3.22 alpha30 [269, 3] (w:1, o:283, a:1, s:1, b:1),
% 2.86/3.22 alpha31 [270, 2] (w:1, o:233, a:1, s:1, b:1),
% 2.86/3.22 alpha32 [271, 2] (w:1, o:234, a:1, s:1, b:1),
% 2.86/3.22 alpha33 [272, 2] (w:1, o:235, a:1, s:1, b:1),
% 2.86/3.22 alpha34 [273, 2] (w:1, o:236, a:1, s:1, b:1),
% 2.86/3.22 alpha35 [274, 2] (w:1, o:237, a:1, s:1, b:1),
% 2.86/3.22 alpha36 [275, 2] (w:1, o:238, a:1, s:1, b:1),
% 2.86/3.22 alpha37 [276, 4] (w:1, o:325, a:1, s:1, b:1),
% 2.86/3.22 alpha38 [277, 4] (w:1, o:326, a:1, s:1, b:1),
% 2.86/3.22 alpha39 [278, 4] (w:1, o:327, a:1, s:1, b:1),
% 2.86/3.22 alpha40 [279, 3] (w:1, o:285, a:1, s:1, b:1),
% 2.86/3.22 alpha41 [280, 3] (w:1, o:286, a:1, s:1, b:1),
% 2.86/3.22 alpha42 [281, 3] (w:1, o:287, a:1, s:1, b:1),
% 2.86/3.22 alpha43 [282, 3] (w:1, o:288, a:1, s:1, b:1),
% 2.86/3.22 alpha44 [283, 4] (w:1, o:328, a:1, s:1, b:1),
% 2.86/3.22 alpha45 [284, 4] (w:1, o:329, a:1, s:1, b:1),
% 2.86/3.22 alpha46 [285, 3] (w:1, o:289, a:1, s:1, b:1),
% 2.86/3.22 alpha47 [286, 3] (w:1, o:290, a:1, s:1, b:1),
% 2.86/3.22 alpha48 [287, 4] (w:1, o:330, a:1, s:1, b:1),
% 2.86/3.22 alpha49 [288, 4] (w:1, o:331, a:1, s:1, b:1),
% 2.86/3.22 alpha50 [289, 4] (w:1, o:332, a:1, s:1, b:1),
% 2.86/3.22 alpha51 [290, 4] (w:1, o:333, a:1, s:1, b:1),
% 2.86/3.22 alpha52 [291, 4] (w:1, o:334, a:1, s:1, b:1),
% 2.86/3.22 alpha53 [292, 4] (w:1, o:335, a:1, s:1, b:1),
% 2.86/3.22 alpha54 [293, 4] (w:1, o:336, a:1, s:1, b:1),
% 2.86/3.22 alpha55 [294, 4] (w:1, o:337, a:1, s:1, b:1),
% 2.86/3.22 alpha56 [295, 4] (w:1, o:338, a:1, s:1, b:1),
% 2.86/3.22 alpha57 [296, 4] (w:1, o:339, a:1, s:1, b:1),
% 2.86/3.22 alpha58 [297, 4] (w:1, o:340, a:1, s:1, b:1),
% 2.86/3.22 alpha59 [298, 4] (w:1, o:341, a:1, s:1, b:1),
% 2.86/3.22 alpha60 [299, 4] (w:1, o:342, a:1, s:1, b:1),
% 2.86/3.22 alpha61 [300, 4] (w:1, o:343, a:1, s:1, b:1),
% 2.86/3.22 alpha62 [301, 4] (w:1, o:344, a:1, s:1, b:1),
% 2.86/3.22 alpha63 [302, 4] (w:1, o:345, a:1, s:1, b:1),
% 2.86/3.22 alpha64 [303, 3] (w:1, o:293, a:1, s:1, b:1),
% 2.86/3.22 alpha65 [304, 3] (w:1, o:294, a:1, s:1, b:1),
% 2.86/3.22 alpha66 [305, 2] (w:1, o:239, a:1, s:1, b:1),
% 2.86/3.22 alpha67 [306, 2] (w:1, o:240, a:1, s:1, b:1),
% 2.86/3.22 alpha68 [307, 2] (w:1, o:241, a:1, s:1, b:1),
% 2.86/3.22 alpha69 [308, 4] (w:1, o:346, a:1, s:1, b:1),
% 2.86/3.22 alpha70 [309, 4] (w:1, o:304, a:1, s:1, b:1),
% 2.86/3.22 alpha71 [310, 4] (w:1, o:305, a:1, s:1, b:1),
% 37.68/38.03 alpha72 [311, 4] (w:1, o:306, a:1, s:1, b:1),
% 37.68/38.03 alpha73 [312, 4] (w:1, o:307, a:1, s:1, b:1),
% 37.68/38.03 alpha74 [313, 4] (w:1, o:308, a:1, s:1, b:1),
% 37.68/38.03 alpha75 [314, 4] (w:1, o:309, a:1, s:1, b:1),
% 37.68/38.03 alpha76 [315, 4] (w:1, o:310, a:1, s:1, b:1),
% 37.68/38.03 alpha77 [316, 4] (w:1, o:311, a:1, s:1, b:1),
% 37.68/38.03 alpha78 [317, 4] (w:1, o:312, a:1, s:1, b:1),
% 37.68/38.03 alpha79 [318, 4] (w:1, o:313, a:1, s:1, b:1),
% 37.68/38.03 alpha80 [319, 4] (w:1, o:315, a:1, s:1, b:1),
% 37.68/38.03 alpha81 [320, 2] (w:1, o:242, a:1, s:1, b:1),
% 37.68/38.03 alpha82 [321, 4] (w:1, o:316, a:1, s:1, b:1),
% 37.68/38.03 alpha83 [322, 4] (w:1, o:317, a:1, s:1, b:1),
% 37.68/38.03 alpha84 [323, 4] (w:1, o:318, a:1, s:1, b:1),
% 37.68/38.03 alpha85 [324, 4] (w:1, o:319, a:1, s:1, b:1),
% 37.68/38.03 alpha86 [325, 4] (w:1, o:320, a:1, s:1, b:1),
% 37.68/38.03 alpha87 [326, 4] (w:1, o:321, a:1, s:1, b:1),
% 37.68/38.03 alpha88 [327, 4] (w:1, o:322, a:1, s:1, b:1),
% 37.68/38.03 alpha89 [328, 4] (w:1, o:323, a:1, s:1, b:1),
% 37.68/38.03 alpha90 [329, 4] (w:1, o:347, a:1, s:1, b:1),
% 37.68/38.03 alpha91 [330, 4] (w:1, o:348, a:1, s:1, b:1),
% 37.68/38.03 alpha92 [331, 4] (w:1, o:349, a:1, s:1, b:1),
% 37.68/38.03 alpha93 [332, 4] (w:1, o:350, a:1, s:1, b:1),
% 37.68/38.03 alpha94 [333, 2] (w:1, o:243, a:1, s:1, b:1),
% 37.68/38.03 alpha95 [334, 4] (w:1, o:351, a:1, s:1, b:1),
% 37.68/38.03 alpha96 [335, 4] (w:1, o:352, a:1, s:1, b:1),
% 37.68/38.03 alpha97 [336, 4] (w:1, o:353, a:1, s:1, b:1),
% 37.68/38.03 alpha98 [337, 4] (w:1, o:354, a:1, s:1, b:1),
% 37.68/38.03 alpha99 [338, 4] (w:1, o:355, a:1, s:1, b:1),
% 37.68/38.03 alpha100 [339, 4] (w:1, o:356, a:1, s:1, b:1),
% 37.68/38.03 alpha101 [340, 4] (w:1, o:357, a:1, s:1, b:1),
% 37.68/38.03 alpha102 [341, 4] (w:1, o:358, a:1, s:1, b:1),
% 37.68/38.03 alpha103 [342, 4] (w:1, o:359, a:1, s:1, b:1),
% 37.68/38.03 alpha104 [343, 4] (w:1, o:360, a:1, s:1, b:1),
% 37.68/38.03 alpha105 [344, 4] (w:1, o:361, a:1, s:1, b:1),
% 37.68/38.03 alpha106 [345, 4] (w:1, o:362, a:1, s:1, b:1),
% 37.68/38.03 alpha107 [346, 2] (w:1, o:244, a:1, s:1, b:1),
% 37.68/38.03 alpha108 [347, 3] (w:1, o:260, a:1, s:1, b:1),
% 37.68/38.03 alpha109 [348, 3] (w:1, o:261, a:1, s:1, b:1),
% 37.68/38.03 skol1 [349, 2] (w:1, o:221, a:1, s:1, b:1),
% 37.68/38.03 skol2 [350, 0] (w:1, o:14, a:1, s:1, b:1),
% 37.68/38.03 skol3 [351, 0] (w:1, o:15, a:1, s:1, b:1),
% 37.68/38.03 skol4 [352, 3] (w:1, o:296, a:1, s:1, b:1),
% 37.68/38.03 skol5 [353, 3] (w:1, o:297, a:1, s:1, b:1),
% 37.68/38.03 skol6 [354, 3] (w:1, o:298, a:1, s:1, b:1),
% 37.68/38.03 skol7 [355, 3] (w:1, o:299, a:1, s:1, b:1),
% 37.68/38.03 skol8 [356, 2] (w:1, o:222, a:1, s:1, b:1),
% 37.68/38.03 skol9 [357, 2] (w:1, o:223, a:1, s:1, b:1),
% 37.68/38.03 skol10 [358, 3] (w:1, o:300, a:1, s:1, b:1),
% 37.68/38.03 skol11 [359, 3] (w:1, o:301, a:1, s:1, b:1),
% 37.68/38.03 skol12 [360, 2] (w:1, o:224, a:1, s:1, b:1),
% 37.68/38.03 skol13 [361, 2] (w:1, o:225, a:1, s:1, b:1),
% 37.68/38.03 skol14 [362, 1] (w:1, o:115, a:1, s:1, b:1),
% 37.68/38.03 skol15 [363, 3] (w:1, o:302, a:1, s:1, b:1).
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Starting Search:
% 37.68/38.03
% 37.68/38.03 *** allocated 170857 integers for clauses
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 2786
% 37.68/38.03 Kept: 2007
% 37.68/38.03 Inuse: 6
% 37.68/38.03 Deleted: 0
% 37.68/38.03 Deletedinuse: 0
% 37.68/38.03
% 37.68/38.03 *** allocated 256285 integers for clauses
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 10527
% 37.68/38.03 Kept: 4007
% 37.68/38.03 Inuse: 152
% 37.68/38.03 Deleted: 1
% 37.68/38.03 Deletedinuse: 0
% 37.68/38.03
% 37.68/38.03 *** allocated 384427 integers for clauses
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03 *** allocated 256285 integers for termspace/termends
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 21958
% 37.68/38.03 Kept: 6213
% 37.68/38.03 Inuse: 215
% 37.68/38.03 Deleted: 1
% 37.68/38.03 Deletedinuse: 0
% 37.68/38.03
% 37.68/38.03 *** allocated 576640 integers for clauses
% 37.68/38.03 *** allocated 384427 integers for termspace/termends
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 38805
% 37.68/38.03 Kept: 9314
% 37.68/38.03 Inuse: 230
% 37.68/38.03 Deleted: 1
% 37.68/38.03 Deletedinuse: 0
% 37.68/38.03
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03 *** allocated 864960 integers for clauses
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 46786
% 37.68/38.03 Kept: 11337
% 37.68/38.03 Inuse: 275
% 37.68/38.03 Deleted: 4
% 37.68/38.03 Deletedinuse: 0
% 37.68/38.03
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03 *** allocated 576640 integers for termspace/termends
% 37.68/38.03 Resimplifying inuse:
% 37.68/38.03 Done
% 37.68/38.03
% 37.68/38.03
% 37.68/38.03 Intermediate Status:
% 37.68/38.03 Generated: 64276
% 37.68/38.03 Kept: 13354
% 91.51/91.96 Inuse: 315
% 91.51/91.96 Deleted: 5
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 74837
% 91.51/91.96 Kept: 15476
% 91.51/91.96 Inuse: 366
% 91.51/91.96 Deleted: 5
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 *** allocated 1297440 integers for clauses
% 91.51/91.96 *** allocated 864960 integers for termspace/termends
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 94980
% 91.51/91.96 Kept: 18140
% 91.51/91.96 Inuse: 386
% 91.51/91.96 Deleted: 5
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 115203
% 91.51/91.96 Kept: 20343
% 91.51/91.96 Inuse: 396
% 91.51/91.96 Deleted: 5
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying clauses:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 *** allocated 1297440 integers for termspace/termends
% 91.51/91.96 *** allocated 1946160 integers for clauses
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 127958
% 91.51/91.96 Kept: 22832
% 91.51/91.96 Inuse: 411
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 136785
% 91.51/91.96 Kept: 24843
% 91.51/91.96 Inuse: 458
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 144483
% 91.51/91.96 Kept: 26852
% 91.51/91.96 Inuse: 511
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 153286
% 91.51/91.96 Kept: 29112
% 91.51/91.96 Inuse: 546
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 160729
% 91.51/91.96 Kept: 31114
% 91.51/91.96 Inuse: 569
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 171415
% 91.51/91.96 Kept: 33824
% 91.51/91.96 Inuse: 581
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 *** allocated 1946160 integers for termspace/termends
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 176444
% 91.51/91.96 Kept: 35873
% 91.51/91.96 Inuse: 601
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 *** allocated 2919240 integers for clauses
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 183200
% 91.51/91.96 Kept: 38685
% 91.51/91.96 Inuse: 616
% 91.51/91.96 Deleted: 186
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying clauses:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 188275
% 91.51/91.96 Kept: 40800
% 91.51/91.96 Inuse: 636
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 204822
% 91.51/91.96 Kept: 43600
% 91.51/91.96 Inuse: 656
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 212827
% 91.51/91.96 Kept: 46852
% 91.51/91.96 Inuse: 671
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 217424
% 91.51/91.96 Kept: 48871
% 91.51/91.96 Inuse: 687
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 235386
% 91.51/91.96 Kept: 51868
% 91.51/91.96 Inuse: 701
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 244094
% 91.51/91.96 Kept: 55566
% 91.51/91.96 Inuse: 716
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 248117
% 91.51/91.96 Kept: 57583
% 91.51/91.96 Inuse: 726
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 302752
% 91.51/91.96 Kept: 60642
% 91.51/91.96 Inuse: 746
% 91.51/91.96 Deleted: 278
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying clauses:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 *** allocated 4378860 integers for clauses
% 91.51/91.96 *** allocated 2919240 integers for termspace/termends
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 310463
% 91.51/91.96 Kept: 62665
% 91.51/91.96 Inuse: 765
% 91.51/91.96 Deleted: 300
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 317575
% 91.51/91.96 Kept: 65086
% 91.51/91.96 Inuse: 781
% 91.51/91.96 Deleted: 300
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 331632
% 91.51/91.96 Kept: 68069
% 91.51/91.96 Inuse: 791
% 91.51/91.96 Deleted: 300
% 91.51/91.96 Deletedinuse: 0
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96 Resimplifying inuse:
% 91.51/91.96 Done
% 91.51/91.96
% 91.51/91.96
% 91.51/91.96 Intermediate Status:
% 91.51/91.96 Generated: 342333
% 91.51/91.96 Kept: 70138
% 91.51/91.96 Inuse: 816
% 183.10/183.48 Deleted: 300
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 350425
% 183.10/183.48 Kept: 72147
% 183.10/183.48 Inuse: 855
% 183.10/183.48 Deleted: 300
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 357422
% 183.10/183.48 Kept: 74148
% 183.10/183.48 Inuse: 887
% 183.10/183.48 Deleted: 300
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 364161
% 183.10/183.48 Kept: 78226
% 183.10/183.48 Inuse: 891
% 183.10/183.48 Deleted: 300
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 368958
% 183.10/183.48 Kept: 80516
% 183.10/183.48 Inuse: 896
% 183.10/183.48 Deleted: 300
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying clauses:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 380050
% 183.10/183.48 Kept: 83028
% 183.10/183.48 Inuse: 911
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 390059
% 183.10/183.48 Kept: 85180
% 183.10/183.48 Inuse: 921
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 400005
% 183.10/183.48 Kept: 87246
% 183.10/183.48 Inuse: 931
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 404278
% 183.10/183.48 Kept: 89521
% 183.10/183.48 Inuse: 936
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 412556
% 183.10/183.48 Kept: 92064
% 183.10/183.48 Inuse: 951
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 *** allocated 6568290 integers for clauses
% 183.10/183.48 *** allocated 4378860 integers for termspace/termends
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 423493
% 183.10/183.48 Kept: 97244
% 183.10/183.48 Inuse: 971
% 183.10/183.48 Deleted: 378
% 183.10/183.48 Deletedinuse: 0
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 431848
% 183.10/183.48 Kept: 99578
% 183.10/183.48 Inuse: 991
% 183.10/183.48 Deleted: 382
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying clauses:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 442575
% 183.10/183.48 Kept: 101595
% 183.10/183.48 Inuse: 1010
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 459516
% 183.10/183.48 Kept: 105003
% 183.10/183.48 Inuse: 1016
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 467385
% 183.10/183.48 Kept: 107009
% 183.10/183.48 Inuse: 1040
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 473714
% 183.10/183.48 Kept: 109046
% 183.10/183.48 Inuse: 1066
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 486329
% 183.10/183.48 Kept: 112871
% 183.10/183.48 Inuse: 1081
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 494693
% 183.10/183.48 Kept: 114945
% 183.10/183.48 Inuse: 1089
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 504534
% 183.10/183.48 Kept: 116973
% 183.10/183.48 Inuse: 1105
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 511464
% 183.10/183.48 Kept: 118974
% 183.10/183.48 Inuse: 1120
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 519656
% 183.10/183.48 Kept: 121044
% 183.10/183.48 Inuse: 1142
% 183.10/183.48 Deleted: 538
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying clauses:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 527618
% 183.10/183.48 Kept: 123147
% 183.10/183.48 Inuse: 1161
% 183.10/183.48 Deleted: 562
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 536019
% 183.10/183.48 Kept: 125165
% 183.10/183.48 Inuse: 1183
% 183.10/183.48 Deleted: 562
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 545153
% 183.10/183.48 Kept: 127237
% 183.10/183.48 Inuse: 1205
% 183.10/183.48 Deleted: 562
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 553883
% 183.10/183.48 Kept: 129272
% 183.10/183.48 Inuse: 1219
% 183.10/183.48 Deleted: 562
% 183.10/183.48 Deletedinuse: 4
% 183.10/183.48
% 183.10/183.48 Resimplifying inuse:
% 183.10/183.48 Done
% 183.10/183.48
% 183.10/183.48
% 183.10/183.48 Intermediate Status:
% 183.10/183.48 Generated: 562336
% 183.10/183.48 Kept: 131539
% 183.10/183.48 InusCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------