TSTP Solution File: SWW254+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW254+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 23:21:36 EDT 2022
% Result : Timeout 300.07s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW254+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jun 5 10:39:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.94/1.55 *** allocated 10000 integers for termspace/termends
% 0.94/1.55 *** allocated 10000 integers for clauses
% 0.94/1.55 *** allocated 10000 integers for justifications
% 0.94/1.55 *** allocated 15000 integers for termspace/termends
% 0.94/1.55 *** allocated 22500 integers for termspace/termends
% 0.94/1.55 *** allocated 33750 integers for termspace/termends
% 0.94/1.55 Bliksem 1.12
% 0.94/1.55
% 0.94/1.55
% 0.94/1.55 Automatic Strategy Selection
% 0.94/1.55
% 0.94/1.55 *** allocated 50625 integers for termspace/termends
% 0.94/1.55 *** allocated 75937 integers for termspace/termends
% 0.94/1.55 *** allocated 113905 integers for termspace/termends
% 0.94/1.55
% 0.94/1.55 Clauses:
% 0.94/1.55
% 0.94/1.55 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.94/1.55 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.55 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.55 tc_Complex_Ocomplex, v_p ) ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.55 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.55 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.55 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.55 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.55 ( X, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.94/1.55 class_RealVector_Oreal__normed__field( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.94/1.55 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.55 ( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.94/1.55 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.94/1.55 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha1( X, Y, Z ), alpha27
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha1( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha27( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), alpha27( X, Y, Z ) }.
% 0.94/1.55 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), alpha1( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.94/1.55 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ), alpha28( X, Y
% 0.94/1.55 , Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha2( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha28( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), alpha28( X, Y, Z ) }.
% 0.94/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), alpha2( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Y, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.55 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.55 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.94/1.55 X, T ) = hAPP( X, U ) }.
% 0.94/1.55 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol51( X ) ),
% 0.94/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.94/1.55 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), v_w____ ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), v_w____ ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.94/1.55 tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.94/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.55 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 0.94/1.55 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.94/1.55 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.94/1.55 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.94/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.94/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.94/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.94/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.94/1.55 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.55 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.94/1.55 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.94/1.55 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 X, Y ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.94/1.55 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.55 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.94/1.55 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha3( X, Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha29( X,
% 0.94/1.55 Y ) }.
% 0.94/1.55 { ! alpha3( X, Y ), ! alpha29( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.94/1.55 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha29( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha29( X, Y ) }.
% 0.94/1.55 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha3( X, Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha3( X, Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.94/1.55 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha4( X, Y, Z ), alpha30
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha4( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha30( X, Y, Z ) }.
% 0.94/1.55 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ), alpha31
% 0.94/1.55 ( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha5( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ), Y ), alpha31( X, Y, Z ) }.
% 0.94/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.94/1.55 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.55 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ) ) }.
% 0.94/1.55 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.94/1.55 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.94/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.55 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.55 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.94/1.55 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), skol3 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 0.94/1.55 skol52 ) }.
% 0.94/1.55 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol4 ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.94/1.55 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.94/1.55 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.94/1.55 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.94/1.55 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.94/1.55 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 0.94/1.55 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.94/1.55 , Y ) }.
% 0.94/1.55 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.55 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.94/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.55 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.55 ), ! U = T }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.94/1.55 ), ! Z = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 T, Y ), Z = Y }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 T, Y ) }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Y, Z ), T = Y }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.94/1.55 ) ), Z ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.94/1.55 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.55 ), U = Z, T = Y }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 T, Y ), Z = Y }.
% 0.94/1.55 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 T, Y ), Z = Y }.
% 0.94/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Y, T ), Z = Y }.
% 0.94/1.55 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.94/1.55 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.94/1.55 ) ), T ), Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.94/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.94/1.55 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.94/1.55 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.55 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.55 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.55 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, Z, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , T, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.55 = Y }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.94/1.55 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.94/1.55 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.94/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.55 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.94/1.55 ( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.94/1.55 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.55 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.94/1.55 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.55 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.94/1.55 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.94/1.55 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.94/1.55 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.94/1.55 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.94/1.55 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.55 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.55 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.94/1.55 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Z, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.55 .
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.94/1.55 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.94/1.55 , Y, T ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.55 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.55 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.94/1.55 }.
% 0.94/1.55 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.94/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.94/1.55 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.94/1.55 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.55 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.94/1.55 ), Y ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.94/1.55 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.94/1.55 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.94/1.55 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.94/1.55 ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.55 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.55 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.55 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.94/1.55 ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha6( X, Y
% 0.94/1.55 , Z ), alpha32( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.55 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha32( X, Y, Z ) }.
% 0.94/1.55 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ), alpha7( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z ),
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ), Y ), alpha33( X, Y, Z ) }.
% 0.94/1.55 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.55 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ) }.
% 0.94/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.55 ( X ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha8( X, Y, Z, T ),
% 0.94/1.56 alpha34( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha34( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.94/1.56 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha8( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha9( X, Y, Z, T ),
% 0.94/1.56 alpha35( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha35( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.94/1.56 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha9( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.94/1.56 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha36( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha10( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha36( X, Y, Z, T ), !
% 0.94/1.56 alpha10( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.94/1.56 { ! alpha36( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 0.94/1.56 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha36(
% 0.94/1.56 X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha37( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha11( X, Y, T ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha37( X, Y, Z, T ), !
% 0.94/1.56 alpha11( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.94/1.56 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha37(
% 0.94/1.56 X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha11( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { Y = c_Groups_Ozero__class_Ozero( X ), alpha11( X, Y, Z ) }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha11( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.94/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.94/1.56 , Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), !
% 0.94/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.56 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.94/1.56 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Z ), Y ), alpha38( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.56 Z ), Y ), alpha51( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 0.94/1.56 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.94/1.56 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), alpha61( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , alpha51( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha61( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha61( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha61( X, Y, Z, T ), alpha12( X, Y, Z ) }.
% 0.94/1.56 { ! alpha71( X, Y, Z, T ), ! alpha12( X, Y, Z ), alpha61( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha71( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 alpha71( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha71( X, Y, Z, T )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 alpha38( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha38( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , alpha12( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.94/1.56 , alpha12( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 Z, Y ) ), alpha39( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 Z, Y ) ), alpha52( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.94/1.56 , T ), ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.56 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha62( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.94/1.56 , alpha52( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha62( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha62( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha62( X, Y, Z, T ), alpha13( X, Y, T ) }.
% 0.94/1.56 { ! alpha72( X, Y, Z, T ), ! alpha13( X, Y, T ), alpha62( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha72( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 alpha72( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha72( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 alpha39( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha39( X, Y, Z, T )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , alpha13( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , alpha13( X, Y, Z ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.56 hAPP( Y, U ) ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.94/1.56 ( Z, skol5( X, Y, Z ) ), hAPP( Y, skol5( X, Y, Z ) ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.56 hAPP( Y, U ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.94/1.56 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.94/1.56 hAPP( Y, U ) ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.94/1.56 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! Y = Z }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! Z = Y }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 Z ), ! Z = Y }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 Y ) }.
% 0.94/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Z ), Y ), alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.94/1.56 , T, Z ), Y ), alpha53( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.94/1.56 , T ), ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.94/1.56 { ! alpha53( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), alpha63( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.94/1.56 , alpha53( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha63( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha63( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha63( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 0.94/1.56 { ! alpha73( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha63( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha73( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 alpha73( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha73( X, Y, Z, T )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.94/1.56 alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha40( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , alpha14( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Y ), alpha14( X, Y, Z ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ), alpha41( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 0.94/1.56 , T ), ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.94/1.56 { ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha64( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.94/1.56 , alpha54( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha64( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha64( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha64( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 0.94/1.56 { ! alpha74( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha64( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha74( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.94/1.56 alpha74( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha74( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.94/1.56 alpha41( X, Y, Z, T ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha41( X, Y, Z, T )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.94/1.56 , alpha15( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), alpha15( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.94/1.56 ( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.94/1.56 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.94/1.56 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.94/1.56 , ! Z = Y }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.94/1.56 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.56 skol6 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.56 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol6 ), X ) = hAPP(
% 0.94/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 0.94/1.56 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.56 tc_Complex_Ocomplex, v_pa____ ) ),
% 0.94/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.94/1.56 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.94/1.56 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol7( X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, Y, X ) = hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.56 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.94/1.56 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.94/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.94/1.56 ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.94/1.56 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.94/1.56 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.94/1.56 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.94/1.56 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.94/1.56 .
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.94/1.56 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) = X }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { alpha85( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.56 { alpha85( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.94/1.56 ( X, Y ), Z ) ) }.
% 0.94/1.56 { ! alpha85( X, Y, Z ), alpha89( X, Y, Z ), Z = Y }.
% 0.94/1.56 { ! alpha85( X, Y, Z ), alpha89( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! alpha89( X, Y, Z ), alpha85( X, Y, Z ) }.
% 0.94/1.56 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha85( X, Y, Z ) }.
% 0.94/1.56 { ! alpha89( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.94/1.56 }.
% 0.94/1.56 { ! alpha89( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.94/1.56 X, Y ), Z ) ), alpha89( X, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.94/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.94/1.56 , X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.94/1.56 ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.56 ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 Y ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.56 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.94/1.56 skol8 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.94/1.56 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.94/1.56 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol8 ), X ) = hAPP(
% 0.94/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.94/1.56 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.94/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) }.
% 0.94/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) }.
% 0.94/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.94/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.94/1.56 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.56 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 0.94/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.94/1.56 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.94/1.56 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.94/1.56 .
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_Nat_Onat, skol15( X, Y ), skol53( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 hAPP( Y, skol53( X, Y ) ), hAPP( Y, skol15( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.56 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol16( X, Y ) ) }.
% 0.94/1.56 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.56 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( Z, Y
% 0.94/1.56 ), Y ) }.
% 0.94/1.56 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.56 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.94/1.56 skol17( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.94/1.56 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.94/1.56 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.94/1.56 , skol17( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.94/1.56 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol18( X, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol19( X ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol20( X, Y ) ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 skol22( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, skol22( X, T, U ),
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), skol22( X, Y, Z ) ), Z ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol23( X, Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol54( X, Y, Z ) ) ), Z ),
% 0.94/1.56 c_SEQ_OBseq( X, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_Nat_Onat, skol24( X, Y ), skol55( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.94/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 hAPP( Y, skol24( X, Y ) ), hAPP( Y, skol55( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.56 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.56 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.56 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.94/1.56 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.56 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.94/1.56 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.56 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol25( X, Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.56 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.56 , c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.56 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.56 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.94/1.56 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.94/1.56 Y = X }.
% 0.94/1.56 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.94/1.56 , X ) }.
% 0.94/1.56 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.94/1.56 ( tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.94/1.56 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.94/1.56 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.94/1.56 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.94/1.56 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.94/1.56 c_RComplete_Onatfloor( X ) = Y }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.94/1.56 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.94/1.56 ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.56 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.94/1.56 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatceiling( Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.94/1.56 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_RealDef_Oreal ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.94/1.56 , X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.94/1.56 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.94/1.56 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.94/1.56 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.94/1.56 c_RComplete_Onatfloor( X ), Y ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol26( X, Y, Z ) ) ), Y ),
% 0.94/1.56 c_SEQ_OBseq( X, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.94/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) ) = Y }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.94/1.56 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.94/1.56 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.94/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.94/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.56 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.56 alpha16( X, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.56 alpha42( X, Y, Z ) }.
% 0.94/1.56 { ! alpha16( X, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha42( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 alpha55( X, Y, Z ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha42( X, Y, Z ) }.
% 0.94/1.56 { ! alpha55( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.94/1.56 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.94/1.56 ), alpha65( X, Y, Z, T ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol27( X, T, U ), X ),
% 0.94/1.56 alpha55( X, Y, Z ) }.
% 0.94/1.56 { ! alpha65( X, Y, Z, skol27( X, Y, Z ) ), alpha55( X, Y, Z ) }.
% 0.94/1.56 { ! alpha65( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.56 hBOOL( hAPP( Z, U ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol28( U, W, Z, V0 ) ) ), alpha65( X, Y, Z, T ) }.
% 0.94/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol28( X, Y, Z, T ) )
% 0.94/1.56 , T ), alpha65( X, Y, Z, T ) }.
% 0.94/1.56 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.94/1.56 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.56 ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.94/1.56 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.56 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.56 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.94/1.56 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.94/1.56 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.56 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.56 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.94/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( X ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.94/1.56 = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.94/1.56 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.94/1.56 ) ), Y ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ) ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.94/1.56 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.94/1.56 .
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.94/1.56 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.94/1.56 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.94/1.56 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.94/1.56 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.94/1.56 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.94/1.56 }.
% 0.94/1.56 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.94/1.56 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.94/1.56 ) ), Z ) }.
% 0.94/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.94/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.94/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.94/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.94/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.94/1.56 ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.94/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.94/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.94/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.56 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.94/1.56 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.94/1.56 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.94/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.94/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.94/1.56 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.94/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.94/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.94/1.56 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.94/1.56 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol29( X, Y ) ), Y
% 0.94/1.56 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.94/1.56 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.94/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), Y ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.94/1.56 ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha17( X, Z ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.56 alpha43( X, Y, Z ) }.
% 0.94/1.56 { ! alpha17( X, Z ), ! alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.56 { ! alpha43( X, Y, Z ), alpha56( X, Y, Z ) }.
% 0.94/1.56 { ! alpha43( X, Y, Z ), alpha66( X, Y, Z ) }.
% 0.94/1.56 { ! alpha56( X, Y, Z ), ! alpha66( X, Y, Z ), alpha43( X, Y, Z ) }.
% 0.94/1.56 { ! alpha66( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha75( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha66( X, Y, Z ) }.
% 0.94/1.56 { ! alpha75( X, Y, Z ), alpha66( X, Y, Z ) }.
% 0.94/1.56 { ! alpha75( X, Y, Z ), ! alpha79( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol30( T, U, Z ) ) ), alpha75( X, Y, Z ) }.
% 0.94/1.56 { alpha79( X, Y, skol30( X, Y, Z ) ), alpha75( X, Y, Z ) }.
% 0.94/1.56 { ! alpha79( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 skol31( X, T, U ) ) }.
% 0.94/1.56 { ! alpha79( X, Y, Z ), alpha83( X, Y, Z, skol31( X, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha83( X, Y, Z
% 0.94/1.56 , T ), alpha79( X, Y, Z ) }.
% 0.94/1.56 { ! alpha83( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha83( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha83( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { ! alpha56( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha67( X, Y, Z ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ), alpha56( X, Y, Z ) }.
% 0.94/1.56 { ! alpha67( X, Y, Z ), alpha56( X, Y, Z ) }.
% 0.94/1.56 { ! alpha67( X, Y, Z ), ! alpha76( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Z, skol32( T, U, Z ) ) ), alpha67( X, Y, Z ) }.
% 0.94/1.56 { alpha76( X, Y, skol32( X, Y, Z ) ), alpha67( X, Y, Z ) }.
% 0.94/1.56 { ! alpha76( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol33( T, U, W ) ) }.
% 0.94/1.56 { ! alpha76( X, Y, Z ), alpha80( X, Y, Z, skol33( X, Y, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha80( X, Y, Z, T )
% 0.94/1.56 , alpha76( X, Y, Z ) }.
% 0.94/1.56 { ! alpha80( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.94/1.56 ) }.
% 0.94/1.56 { ! alpha80( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha80( X,
% 0.94/1.56 Y, Z, T ) }.
% 0.94/1.56 { ! alpha17( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha17( X, Y ) }.
% 0.94/1.56 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha17
% 0.94/1.56 ( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.94/1.56 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha86( X,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, T, Z ) = Y }.
% 0.94/1.56 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha86( X,
% 0.94/1.56 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, T, Z ) = Y }.
% 0.94/1.56 { ! alpha86( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! alpha86( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha86( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.94/1.56 , alpha86( X, Y ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.94/1.56 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.94/1.56 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.94/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.94/1.56 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.94/1.56 ( X ), T, Z ), Y ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.94/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 0.94/1.56 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 0.94/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.94/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.94/1.56 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.94/1.56 X, Z ), Y ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.94/1.56 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol34( X, Y ) ), X ) =
% 0.94/1.56 Y }.
% 0.94/1.56 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y ) }.
% 0.94/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! alpha18( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! alpha18( X, Y ), alpha44( X, Y ), alpha57( X, Y ) }.
% 0.94/1.56 { ! alpha44( X, Y ), alpha18( X, Y ) }.
% 0.94/1.56 { ! alpha57( X, Y ), alpha18( X, Y ) }.
% 0.94/1.56 { ! alpha57( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! alpha57( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha57( X, Y ) }.
% 0.94/1.56 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha44( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.94/1.56 , Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.94/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.94/1.56 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.56 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.94/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.94/1.56 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.94/1.56 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.94/1.56 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.94/1.56 ( tc_Int_Oint ) }.
% 0.94/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ) = X }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ) ) = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.94/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.94/1.56 .
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.94/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.94/1.56 = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) ) }.
% 0.94/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.94/1.56 }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.56 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.56 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.94/1.56 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.94/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.94/1.56 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.94/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.94/1.56 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.94/1.56 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.56 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.94/1.56 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.94/1.56 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.94/1.56 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.94/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.56 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.94/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.94/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.94/1.56 tc_Int_Oint ) ) }.
% 0.94/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.94/1.56 tc_Int_Oint ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol35( Z, T ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol35( X, Y ) ), X ) =
% 0.94/1.56 Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.94/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.94/1.56 skol35( X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.94/1.56 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.94/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.94/1.56 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.94/1.56 tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), c_Transcendental_Oln( Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.94/1.56 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), X ) }.
% 0.94/1.56 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.56 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.94/1.56 tc_RealDef_Oreal, X, Y ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.56 ( X ), c_Transcendental_Oln( Y ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.94/1.56 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.94/1.56 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.94/1.56 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ) }.
% 0.94/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.94/1.56 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.94/1.57 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.94/1.57 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.94/1.57 ) ), ! alpha19( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), alpha19( X, Y, skol36( X, Y, Z ), skol56( X, Y, Z )
% 0.94/1.57 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol36( X, Y, Z ) ), skol56
% 0.94/1.57 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.94/1.57 { ! alpha19( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha45( X, Y, Z, T )
% 0.94/1.57 , alpha19( X, Y, Z, T ) }.
% 0.94/1.57 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.57 .
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha45( X,
% 0.94/1.57 Y, Z, T ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ) ) = X }.
% 0.94/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol37( X, Y ) ) }.
% 0.94/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.94/1.57 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol38( X, Y ) ) }.
% 0.94/1.57 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.94/1.57 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.94/1.57 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.94/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.94/1.57 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.94/1.57 ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.94/1.57 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 T, Y ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.94/1.57 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 T, Z ), Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.94/1.57 ), Z ), Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.94/1.57 , Y ) ), Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, Y, Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, Z, Y ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, X, Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.94/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.94/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.94/1.57 X, Z, Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.94/1.57 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.94/1.57 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.94/1.57 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.94/1.57 ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.94/1.57 , Y ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.94/1.57 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.94/1.57 ), Y ) ) = Z }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.94/1.57 , Z ) ) = Y }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.94/1.57 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.94/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.57 alpha20( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.57 alpha46( X, Y, Z ) }.
% 0.94/1.57 { ! alpha20( X, Y, Z ), ! alpha46( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha46( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 alpha58( X, Y, Z ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha46( X, Y, Z ) }.
% 0.94/1.57 { ! alpha58( X, Y, Z ), alpha46( X, Y, Z ) }.
% 0.94/1.57 { ! alpha58( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.94/1.57 ), alpha68( X, Y, Z, T ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( X, T, U ), X ),
% 0.94/1.57 alpha58( X, Y, Z ) }.
% 0.94/1.57 { ! alpha68( X, Y, Z, skol39( X, Y, Z ) ), alpha58( X, Y, Z ) }.
% 0.94/1.57 { ! alpha68( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.94/1.57 hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol40( X, Y, T ) ), T
% 0.94/1.57 ), alpha68( X, Y, Z, T ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, T ) ), alpha68( X, Y, Z, T ) }.
% 0.94/1.57 { ! alpha20( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha20( X, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.94/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.94/1.57 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.94/1.57 }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.57 alpha21( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.94/1.57 alpha47( X, Y, Z ) }.
% 0.94/1.57 { ! alpha21( X, Y, Z ), ! alpha47( X, Y, Z ), hBOOL( hAPP( Z,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha47( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.94/1.57 { ! alpha47( X, Y, Z ), alpha69( X, Y, Z ) }.
% 0.94/1.57 { ! alpha59( X, Y, Z ), ! alpha69( X, Y, Z ), alpha47( X, Y, Z ) }.
% 0.94/1.57 { ! alpha69( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha77( X, Y, Z ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha69( X, Y, Z ) }.
% 0.94/1.57 { ! alpha77( X, Y, Z ), alpha69( X, Y, Z ) }.
% 0.94/1.57 { ! alpha77( X, Y, Z ), ! alpha81( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, skol41( T, U, Z ) ) ), alpha77( X, Y, Z ) }.
% 0.94/1.57 { alpha81( X, Y, skol41( X, Y, Z ) ), alpha77( X, Y, Z ) }.
% 0.94/1.57 { ! alpha81( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.94/1.57 }.
% 0.94/1.57 { ! alpha81( X, Y, Z ), alpha84( X, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha84( X, Y, Z
% 0.94/1.57 ), alpha81( X, Y, Z ) }.
% 0.94/1.57 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! alpha84( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol42( X, Y,
% 0.94/1.57 Z ) ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha84( X,
% 0.94/1.57 Y, Z ) }.
% 0.94/1.57 { ! alpha59( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha70( X, Y, Z ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), X ), alpha59( X, Y, Z ) }.
% 0.94/1.57 { ! alpha70( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.94/1.57 { ! alpha70( X, Y, Z ), ! alpha78( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, skol43( T, U, Z ) ) ), alpha70( X, Y, Z ) }.
% 0.94/1.57 { alpha78( X, Y, skol43( X, Y, Z ) ), alpha70( X, Y, Z ) }.
% 0.94/1.57 { ! alpha78( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.94/1.57 { ! alpha78( X, Y, Z ), alpha82( X, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha82( X, Y, Z ),
% 0.94/1.57 alpha78( X, Y, Z ) }.
% 0.94/1.57 { ! alpha82( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.94/1.57 }.
% 0.94/1.57 { ! alpha82( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol44( X, Y,
% 0.94/1.57 Z ) ), Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha82( X,
% 0.94/1.57 Y, Z ) }.
% 0.94/1.57 { ! alpha21( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.94/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha21( X, Y, Z ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha21( X, Y, Z ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.94/1.57 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.94/1.57 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha87( X,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Z, Y ) = X }.
% 0.94/1.57 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha87( X,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Z, Y ) = X }.
% 0.94/1.57 { ! alpha87( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.94/1.57 { ! alpha87( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha87( X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.94/1.57 , alpha87( X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 0.94/1.57 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X, Y, skol45( X, Y
% 0.94/1.57 , Z ), skol57( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.94/1.57 skol45( X, Y, Z ) ), skol57( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.94/1.57 ) }.
% 0.94/1.57 { ! alpha22( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha48( X, Y, Z
% 0.94/1.57 , T ), alpha22( X, Y, Z, T ) }.
% 0.94/1.57 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.94/1.57 { ! alpha48( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.94/1.57 .
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha48( X,
% 0.94/1.57 Y, Z, T ) }.
% 0.94/1.57 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.94/1.57 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.94/1.57 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.94/1.57 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.94/1.57 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.94/1.57 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.94/1.57 ), T, Z ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol46( U, W, V0, T )
% 0.94/1.57 ), c_SEQ_OBseq( X, Y ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol46( X, Y, Z, T ) ) ), Z
% 0.94/1.57 ), c_SEQ_OBseq( X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 0.94/1.57 , X ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.57 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.94/1.57 X ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.94/1.57 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.94/1.57 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.94/1.57 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.94/1.57 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.94/1.57 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( X, Z, Y ) = T }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.94/1.57 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.94/1.57 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.94/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.94/1.57 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.94/1.57 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.94/1.57 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.94/1.57 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.94/1.57 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.94/1.57 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.57 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.57 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.57 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.94/1.57 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.94/1.57 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.57 ), T ), U ), Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.57 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.94/1.57 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.94/1.57 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.94/1.57 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.94/1.57 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.94/1.57 X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 Z, T ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.94/1.57 , Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.94/1.57 Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! alpha23( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! alpha23( X, Y ), ! Y = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha23( X, Y ) }
% 0.94/1.57 .
% 0.94/1.57 { ! alpha23( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! alpha23( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), alpha23( X, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha24( X, Y ), Y = X }
% 0.94/1.57 .
% 0.94/1.57 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! alpha24( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 0.94/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.94/1.57 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.94/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.94/1.57 ( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.94/1.57 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.57 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.94/1.57 hAPP( Z, skol47( U, W, Z ) ) ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.94/1.57 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol47( X
% 0.94/1.57 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.94/1.57 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.94/1.57 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol58( X,
% 0.94/1.57 Y, Z ) ) ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, Z, X ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.94/1.57 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.94/1.57 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Int_Oint, Z, X ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.94/1.57 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.94/1.57 , Z ), X ) ), T ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, U, T ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.94/1.57 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.94/1.57 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.94/1.57 ) ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.94/1.57 X, T, Z ), Y ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.94/1.57 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.94/1.57 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.94/1.57 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.94/1.57 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha25( X
% 0.94/1.57 , Y, T ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha49( X
% 0.94/1.57 , Y, Z, T ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), ! alpha25( X, Y, T ), ! alpha49( X, Y, Z, T )
% 0.94/1.57 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 0.94/1.57 ( X, T, Z ), Y ) }.
% 0.94/1.57 { ! alpha49( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.94/1.57 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha49( X, Y, Z, T ) }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha49( X
% 0.94/1.57 , Y, Z, T ) }.
% 0.94/1.57 { ! alpha25( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { Z = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z ) }.
% 0.94/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha25( X
% 0.94/1.57 , Y, Z ) }.
% 0.94/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ) ) }.
% 0.94/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.94/1.57 tc_Nat_Onat ), X ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ), Y ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.94/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.94/1.57 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.94/1.57 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol48( Z, Y ) ) ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.94/1.57 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.94/1.57 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.94/1.57 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.94/1.57 tc_Int_Oint, skol48( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.94/1.57 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.94/1.57 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.94/1.57 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ), !
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ), Z =
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), skol49( X, Y, Z ) ) )
% 0.94/1.57 }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 0.94/1.57 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.94/1.57 alpha26( X, Z ), alpha50( X, Y, Z ) }.
% 0.94/1.57 { ! alpha26( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha50( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.94/1.57 tc_Nat_Onat, Y, X ) ) ) }.
% 0.94/1.57 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol50( X
% 0.94/1.57 , Y, T ) ), Y ) }.
% 0.94/1.57 { ! alpha50( X, Y, Z ), alpha60( X, Y, Z, skol50( X, Y, Z ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha60( X
% 0.94/1.57 , Y, Z, T ), alpha50( X, Y, Z ) }.
% 0.94/1.57 { ! alpha60( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.94/1.57 ( T ) ) ) }.
% 0.94/1.57 { ! alpha60( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.94/1.57 hBOOL( hAPP( Z, T ) ), alpha60( X, Y, Z, T ) }.
% 0.94/1.57 { ! alpha26( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! alpha26( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ) ) ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha26( X, Y ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.94/1.57 X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.94/1.57 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.94/1.57 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.94/1.57 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 0.94/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.94/1.57 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.94/1.57 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 0.94/1.57 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.94/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.94/1.57 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.57 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.94/1.57 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.94/1.57 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.94/1.57 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.94/1.57 , U ), Z ) }.
% 0.94/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.94/1.57 Y ) ), Y ) }.
% 0.94/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.94/1.57 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.57 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.94/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.94/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.94/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.94/1.57 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.57 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.94/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 0.94/1.57 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.94/1.57 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.94/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.57 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.94/1.57 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.94/1.57 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.94/1.57 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.94/1.57 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.94/1.57 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.94/1.57 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.94/1.57 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.94/1.57 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.94/1.57 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.94/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.94/1.57 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.94/1.57 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.94/1.57 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.57 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.57 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.94/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.57 tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.94/1.57 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.94/1.57 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.94/1.57 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.94/1.57 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.94/1.57 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.94/1.57 { class_Power_Opower( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.94/1.57 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.94/1.57 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.94/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.57 tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.94/1.57 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.94/1.57 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.94/1.57 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.94/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.57 tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.94/1.57 .
% 0.94/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.94/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.57 tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ),
% 0.94/1.57 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.94/1.57 ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.94/1.57 X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.94/1.57 ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.57 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ),
% 0.94/1.57 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.94/1.57 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.94/1.57 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.94/1.57 ( tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.94/1.57 ( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.94/1.57 }.
% 0.94/1.57 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.94/1.57 .
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.94/1.57 tc_Polynomial_Opoly( X ) ) }.
% 0.94/1.57 { alpha88, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.94/1.57 { alpha88, ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! alpha88, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.94/1.57 { ! alpha88, ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.94/1.57 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.94/1.57 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.94/1.57 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) ),
% 0.94/1.57 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.94/1.57 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.94/1.57 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ), alpha88 }.
% 0.94/1.57
% 0.94/1.57 *** allocated 15000 integers for clauses
% 0.94/1.57 *** allocated 22500 integers for clauses
% 0.94/1.57 *** allocated 33750 integers for clauses
% 0.94/1.57 *** allocated 50625 integers for clauses
% 0.94/1.57 *** allocated 75937 integers for clauses
% 0.94/1.57 *** allocated 113905 integers for clauses
% 0.94/1.57 percentage equality = 0.217433, percentage horn = 0.880499
% 0.94/1.57 This is a problem with some equality
% 0.94/1.57
% 0.94/1.57
% 0.94/1.57
% 0.94/1.57 Options Used:
% 0.94/1.57
% 0.94/1.57 useres = 1
% 0.94/1.57 useparamod = 1
% 0.94/1.57 useeqrefl = 1
% 0.94/1.57 useeqfact = 1
% 0.94/1.57 usefactor = 1
% 0.94/1.57 usesimpsplitting = 0
% 0.94/1.57 usesimpdemod = 5
% 0.94/1.57 usesimpres = 3
% 0.94/1.57
% 0.94/1.57 resimpinuse = 1000
% 0.94/1.57 resimpclauses = 20000
% 0.94/1.57 substype = eqrewr
% 0.94/1.57 backwardsubs = 1
% 0.94/1.57 selectoldest = 5
% 0.94/1.57
% 0.94/1.57 litorderings [0] = split
% 0.94/1.57 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.57
% 0.94/1.57 termordering = kbo
% 0.94/1.57
% 0.94/1.57 litapriori = 0
% 0.94/1.57 termapriori = 1
% 0.94/1.57 litaposteriori = 0
% 0.94/1.57 termaposteriori = 0
% 0.94/1.57 demodaposteriori = 0
% 0.94/1.57 ordereqreflfact = 0
% 0.94/1.57
% 0.94/1.57 litselect = negord
% 0.94/1.57
% 0.94/1.57 maxweight = 15
% 0.94/1.57 maxdepth = 30000
% 0.94/1.57 maxlength = 115
% 0.94/1.57 maxnrvars = 195
% 0.94/1.57 excuselevel = 1
% 0.94/1.57 increasemaxweight = 1
% 0.94/1.57
% 0.94/1.57 maxselected = 10000000
% 0.94/1.57 maxnrclauses = 10000000
% 0.94/1.57
% 0.94/1.57 showgenerated = 0
% 0.94/1.57 showkept = 0
% 0.94/1.57 showselected = 0
% 0.94/1.57 showdeleted = 0
% 0.94/1.57 showresimp = 1
% 0.94/1.57 showstatus = 2000
% 0.94/1.57
% 0.94/1.57 prologoutput = 0
% 0.94/1.57 nrgoals = 5000000
% 0.94/1.57 totalproof = 1
% 0.94/1.57
% 0.94/1.57 Symbols occurring in the translation:
% 0.94/1.57
% 0.94/1.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.57 . [1, 2] (w:1, o:198, a:1, s:1, b:0),
% 0.94/1.57 ! [4, 1] (w:0, o:113, a:1, s:1, b:0),
% 0.94/1.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.57 hAPP [38, 2] (w:1, o:222, a:1, s:1, b:0),
% 0.94/1.57 tc_Complex_Ocomplex [39, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.94/1.57 v_q____ [40, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.94/1.57 c_Polynomial_Opoly [41, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.94/1.57 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.94/1.57 v_p [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [44, 3] (w:1, o:
% 0.94/1.57 269, a:1, s:1, b:0),
% 0.94/1.57 class_RealVector_Oreal__normed__field [48, 1] (w:1, o:119, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 c_Rings_Oinverse__class_Odivide [49, 3] (w:1, o:270, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 c_RealVector_Onorm__class_Onorm [50, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 tc_RealDef_Oreal [51, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.94/1.57 class_Fields_Ofield__inverse__zero [52, 1] (w:1, o:120, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 class_RealVector_Oreal__normed__algebra__1 [53, 1] (w:1, o:121, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 c_Groups_Oone__class_Oone [54, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.94/1.57 class_RealVector_Oreal__normed__vector [56, 1] (w:1, o:123, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 c_Orderings_Oord__class_Oless [57, 3] (w:1, o:271, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Odivision__ring__inverse__zero [58, 1] (w:1, o:129, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Rings_Odivision__ring [59, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.94/1.57 class_Fields_Olinordered__field__inverse__zero [62, 1] (w:1, o:131
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 class_Fields_Olinordered__field [65, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 v_pa____ [66, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__idom [69, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ozero__neq__one [70, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__semidom [71, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Rings_Ocomm__semiring__1 [73, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.94/1.57 tc_Polynomial_Opoly [74, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ocomm__semiring__0 [75, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.94/1.57 c_Rings_Oinverse__class_Oinverse [76, 2] (w:1, o:225, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 c_Polynomial_Osmult [77, 3] (w:1, o:273, a:1, s:1, b:0),
% 0.94/1.57 v_w____ [78, 0] (w:1, o:43, a:1, s:1, b:0),
% 0.94/1.57 c_Groups_Osgn__class_Osgn [79, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.94/1.57 v_c____ [80, 0] (w:1, o:44, a:1, s:1, b:0),
% 0.94/1.57 c_Orderings_Oord__class_Oless__eq [82, 3] (w:1, o:272, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Int_Oring__char__0 [84, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Oidom [85, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.94/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [87, 2] (w:1, o:226
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 c_Groups_Oplus__class_Oplus [88, 3] (w:1, o:274, a:1, s:1, b:0),
% 0.94/1.57 class_RealVector_Oreal__normed__div__algebra [94, 1] (w:1, o:146, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 c_Groups_Otimes__class_Otimes [98, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.94/1.57 class_Fields_Ofield [100, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.94/1.57 class_Orderings_Opreorder [101, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Osgn__if [102, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.94/1.57 c_Polynomial_Oorder [103, 3] (w:1, o:275, a:1, s:1, b:0),
% 0.94/1.57 tc_Nat_Onat [104, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.94/1.57 class_Orderings_Olinorder [105, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.94/1.57 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.94/1.57 108, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Oab__semigroup__add [114, 1] (w:1, o:172, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Groups_Oab__semigroup__mult [115, 1] (w:1, o:173, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 class_Groups_Ocancel__semigroup__add [117, 1] (w:1, o:174, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Groups_Ocancel__ab__semigroup__add [120, 1] (w:1, o:175, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Rings_Osemiring [122, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.94/1.57 class_RealVector_Oreal__normed__algebra [124, 1] (w:1, o:157, a:1, s:
% 0.94/1.57 1, b:0),
% 0.94/1.57 class_Rings_Ocomm__semiring [126, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Ocomm__monoid__add [130, 1] (w:1, o:176, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Groups_Omonoid__add [131, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Olinordered__ab__group__add [132, 1] (w:1, o:177, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Groups_Oordered__ab__semigroup__add__imp__le [133, 1] (w:1, o:
% 0.94/1.57 179, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Oordered__ab__semigroup__add [134, 1] (w:1, o:180, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Groups_Oordered__cancel__ab__semigroup__add [135, 1] (w:1, o:
% 0.94/1.57 181, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Ocomm__monoid__mult [136, 1] (w:1, o:182, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Groups_Omonoid__mult [137, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ono__zero__divisors [139, 1] (w:1, o:164, a:1, s:1, b:0)
% 0.94/1.57 ,
% 0.94/1.57 class_Rings_Oring__no__zero__divisors [140, 1] (w:1, o:154, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Rings_Omult__zero [141, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Oordered__comm__monoid__add [142, 1] (w:1, o:184, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__semiring__1 [145, 1] (w:1, o:158, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Rings_Olinordered__semiring__1__strict [146, 1] (w:1, o:159, a:
% 0.94/1.57 1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__ring [147, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__ring__strict [148, 1] (w:1, o:136, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Rings_Oordered__cancel__semiring [149, 1] (w:1, o:165, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Rings_Oordered__ring [150, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Oordered__semiring [151, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.94/1.57
% 0.94/1.57 class_Rings_Oordered__comm__semiring [152, 1] (w:1, o:168, a:1, s:1
% 0.94/1.57 , b:0),
% 0.94/1.57 class_Rings_Olinordered__comm__semiring__strict [153, 1] (w:1, o:160
% 0.94/1.57 , a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__semiring__strict [154, 1] (w:1, o:161, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Groups_Ozero [156, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Olinordered__semiring [157, 1] (w:1, o:162, a:1, s:1, b:0
% 0.94/1.57 ),
% 0.94/1.57 class_Orderings_Oord [158, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.94/1.57 tc_fun [159, 2] (w:1, o:251, a:1, s:1, b:0),
% 0.94/1.57 class_Orderings_Oorder [160, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Oone [161, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.94/1.57 hBOOL [173, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.94/1.57 c_SEQ_Odecseq [183, 2] (w:1, o:253, a:1, s:1, b:0),
% 0.94/1.57 c_SEQ_OBseq [186, 2] (w:1, o:254, a:1, s:1, b:0),
% 0.94/1.57 c_SEQ_Oincseq [187, 2] (w:1, o:255, a:1, s:1, b:0),
% 0.94/1.57 c_RComplete_Onatceiling [188, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.94/1.57 c_RComplete_Onatfloor [189, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.94/1.57 c_RealDef_Oreal [190, 2] (w:1, o:252, a:1, s:1, b:0),
% 0.94/1.57 c_Divides_Odiv__class_Odiv [191, 3] (w:1, o:276, a:1, s:1, b:0),
% 0.94/1.57 c_Power_Opower__class_Opower [193, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.94/1.57 tc_Int_Oint [195, 0] (w:1, o:104, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Oring__1__no__zero__divisors [196, 1] (w:1, o:155, a:1
% 0.94/1.57 , s:1, b:0),
% 0.94/1.57 class_Divides_Osemiring__div [197, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.94/1.57 class_Power_Opower [198, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Osemiring__0 [199, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.94/1.57 c_Power_Opower_Opower [201, 3] (w:1, o:277, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ocomm__ring__1 [209, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.94/1.57 c_Polynomial_Omonom [210, 3] (w:1, o:278, a:1, s:1, b:0),
% 0.94/1.57 c_Complex_Orcis [211, 2] (w:1, o:256, a:1, s:1, b:0),
% 0.94/1.57 c_Transcendental_Oln [218, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.94/1.57 c_Divides_Odiv__class_Omod [219, 3] (w:1, o:279, a:1, s:1, b:0),
% 0.94/1.57 c_Complex_Oexpi [221, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.94/1.57 c_Rings_Odvd__class_Odvd [223, 3] (w:1, o:280, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Odvd [224, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.94/1.57 c_Groups_Ominus__class_Ominus [227, 3] (w:1, o:281, a:1, s:1, b:0),
% 0.94/1.57 c_Nat_OSuc [228, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.94/1.57 class_Rings_Ocomm__ring [230, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.94/1.57 class_Divides_Oring__div [231, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.94/1.57 class_Groups_Ocancel__comm__monoid__add [233, 1] (w:1, o:197, a:1, s:
% 0.94/1.57 1, b:0),
% 0.94/1.57 tc_HOL_Obool [235, 0] (w:1, o:103, a:1, s:1, b:0),
% 0.94/1.57 alpha1 [236, 3] (w:1, o:282, a:1, s:1, b:1),
% 0.94/1.57 alpha2 [237, 3] (w:1, o:289, a:1, s:1, b:1),
% 0.94/1.57 alpha3 [238, 2] (w:1, o:261, a:1, s:1, b:1),
% 0.94/1.57 alpha4 [239, 3] (w:1, o:294, a:1, s:1, b:1),
% 0.94/1.57 alpha5 [240, 3] (w:1, o:299, a:1, s:1, b:1),
% 0.94/1.57 alpha6 [241, 3] (w:1, o:305, a:1, s:1, b:1),
% 0.94/1.57 alpha7 [242, 3] (w:1, o:309, a:1, s:1, b:1),
% 0.94/1.57 alpha8 [243, 4] (w:1, o:353, a:1, s:1, b:1),
% 0.94/1.57 alpha9 [244, 4] (w:1, o:356, a:1, s:1, b:1),
% 0.94/1.57 alpha10 [245, 3] (w:1, o:283, a:1, s:1, b:1),
% 0.94/1.57 alpha11 [246, 3] (w:1, o:284, a:1, s:1, b:1),
% 0.94/1.57 alpha12 [247, 3] (w:1, o:285, a:1, s:1, b:1),
% 0.94/1.57 alpha13 [248, 3] (w:1, o:286, a:1, s:1, b:1),
% 0.94/1.57 alpha14 [249, 3] (w:1, o:287, a:1, s:1, b:1),
% 0.94/1.57 alpha15 [250, 3] (w:1, o:288, a:1, s:1, b:1),
% 0.94/1.57 alpha16 [251, 2] (w:1, o:262, a:1, s:1, b:1),
% 0.94/1.57 alpha17 [252, 2] (w:1, o:263, a:1, s:1, b:1),
% 0.94/1.57 alpha18 [253, 2] (w:1, o:264, a:1, s:1, b:1),
% 0.94/1.57 alpha19 [254, 4] (w:1, o:357, a:1, s:1, b:1),
% 0.94/1.57 alpha20 [255, 3] (w:1, o:310, a:1, s:1, b:1),
% 0.94/1.57 alpha21 [256, 3] (w:1, o:311, a:1, s:1, b:1),
% 0.94/1.57 alpha22 [257, 4] (w:1, o:358, a:1, s:1, b:1),
% 1.84/2.22 alpha23 [258, 2] (w:1, o:257, a:1, s:1, b:1),
% 1.84/2.22 alpha24 [259, 2] (w:1, o:258, a:1, s:1, b:1),
% 1.84/2.22 alpha25 [260, 3] (w:1, o:312, a:1, s:1, b:1),
% 1.84/2.22 alpha26 [261, 2] (w:1, o:259, a:1, s:1, b:1),
% 1.84/2.22 alpha27 [262, 3] (w:1, o:313, a:1, s:1, b:1),
% 1.84/2.22 alpha28 [263, 3] (w:1, o:314, a:1, s:1, b:1),
% 1.84/2.22 alpha29 [264, 2] (w:1, o:260, a:1, s:1, b:1),
% 1.84/2.22 alpha30 [265, 3] (w:1, o:290, a:1, s:1, b:1),
% 1.84/2.22 alpha31 [266, 3] (w:1, o:291, a:1, s:1, b:1),
% 1.84/2.22 alpha32 [267, 3] (w:1, o:292, a:1, s:1, b:1),
% 1.84/2.22 alpha33 [268, 3] (w:1, o:293, a:1, s:1, b:1),
% 1.84/2.22 alpha34 [269, 4] (w:1, o:359, a:1, s:1, b:1),
% 1.84/2.22 alpha35 [270, 4] (w:1, o:360, a:1, s:1, b:1),
% 1.84/2.22 alpha36 [271, 4] (w:1, o:361, a:1, s:1, b:1),
% 1.84/2.22 alpha37 [272, 4] (w:1, o:362, a:1, s:1, b:1),
% 1.84/2.22 alpha38 [273, 4] (w:1, o:363, a:1, s:1, b:1),
% 1.84/2.22 alpha39 [274, 4] (w:1, o:364, a:1, s:1, b:1),
% 1.84/2.22 alpha40 [275, 4] (w:1, o:365, a:1, s:1, b:1),
% 1.84/2.22 alpha41 [276, 4] (w:1, o:366, a:1, s:1, b:1),
% 1.84/2.22 alpha42 [277, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.84/2.22 alpha43 [278, 3] (w:1, o:296, a:1, s:1, b:1),
% 1.84/2.22 alpha44 [279, 2] (w:1, o:265, a:1, s:1, b:1),
% 1.84/2.22 alpha45 [280, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.84/2.22 alpha46 [281, 3] (w:1, o:297, a:1, s:1, b:1),
% 1.84/2.22 alpha47 [282, 3] (w:1, o:298, a:1, s:1, b:1),
% 1.84/2.22 alpha48 [283, 4] (w:1, o:368, a:1, s:1, b:1),
% 1.84/2.22 alpha49 [284, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.84/2.22 alpha50 [285, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.84/2.22 alpha51 [286, 4] (w:1, o:370, a:1, s:1, b:1),
% 1.84/2.22 alpha52 [287, 4] (w:1, o:371, a:1, s:1, b:1),
% 1.84/2.22 alpha53 [288, 4] (w:1, o:372, a:1, s:1, b:1),
% 1.84/2.22 alpha54 [289, 4] (w:1, o:373, a:1, s:1, b:1),
% 1.84/2.22 alpha55 [290, 3] (w:1, o:301, a:1, s:1, b:1),
% 1.84/2.22 alpha56 [291, 3] (w:1, o:302, a:1, s:1, b:1),
% 1.84/2.22 alpha57 [292, 2] (w:1, o:266, a:1, s:1, b:1),
% 1.84/2.22 alpha58 [293, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.84/2.22 alpha59 [294, 3] (w:1, o:304, a:1, s:1, b:1),
% 1.84/2.22 alpha60 [295, 4] (w:1, o:374, a:1, s:1, b:1),
% 1.84/2.22 alpha61 [296, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.84/2.22 alpha62 [297, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.84/2.22 alpha63 [298, 4] (w:1, o:377, a:1, s:1, b:1),
% 1.84/2.22 alpha64 [299, 4] (w:1, o:378, a:1, s:1, b:1),
% 1.84/2.22 alpha65 [300, 4] (w:1, o:379, a:1, s:1, b:1),
% 1.84/2.22 alpha66 [301, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.84/2.22 alpha67 [302, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.84/2.22 alpha68 [303, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.84/2.22 alpha69 [304, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.84/2.22 alpha70 [305, 3] (w:1, o:315, a:1, s:1, b:1),
% 1.84/2.22 alpha71 [306, 4] (w:1, o:349, a:1, s:1, b:1),
% 1.84/2.22 alpha72 [307, 4] (w:1, o:350, a:1, s:1, b:1),
% 1.84/2.22 alpha73 [308, 4] (w:1, o:351, a:1, s:1, b:1),
% 1.84/2.22 alpha74 [309, 4] (w:1, o:352, a:1, s:1, b:1),
% 1.84/2.22 alpha75 [310, 3] (w:1, o:316, a:1, s:1, b:1),
% 1.84/2.22 alpha76 [311, 3] (w:1, o:317, a:1, s:1, b:1),
% 1.84/2.22 alpha77 [312, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.84/2.22 alpha78 [313, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.84/2.22 alpha79 [314, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.84/2.22 alpha80 [315, 4] (w:1, o:354, a:1, s:1, b:1),
% 1.84/2.22 alpha81 [316, 3] (w:1, o:321, a:1, s:1, b:1),
% 1.84/2.22 alpha82 [317, 3] (w:1, o:322, a:1, s:1, b:1),
% 1.84/2.22 alpha83 [318, 4] (w:1, o:355, a:1, s:1, b:1),
% 1.84/2.22 alpha84 [319, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.84/2.22 alpha85 [320, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.84/2.22 alpha86 [321, 2] (w:1, o:267, a:1, s:1, b:1),
% 1.84/2.22 alpha87 [322, 2] (w:1, o:268, a:1, s:1, b:1),
% 1.84/2.22 alpha88 [323, 0] (w:1, o:112, a:1, s:1, b:1),
% 1.84/2.22 alpha89 [324, 3] (w:1, o:325, a:1, s:1, b:1),
% 1.84/2.22 skol1 [325, 2] (w:1, o:228, a:1, s:1, b:1),
% 1.84/2.22 skol2 [326, 1] (w:1, o:140, a:1, s:1, b:1),
% 1.84/2.22 skol3 [327, 0] (w:1, o:12, a:1, s:1, b:1),
% 1.84/2.22 skol4 [328, 0] (w:1, o:13, a:1, s:1, b:1),
% 1.84/2.22 skol5 [329, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.84/2.22 skol6 [330, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.84/2.22 skol7 [331, 1] (w:1, o:141, a:1, s:1, b:1),
% 1.84/2.22 skol8 [332, 0] (w:1, o:16, a:1, s:1, b:1),
% 1.84/2.22 skol9 [333, 2] (w:1, o:229, a:1, s:1, b:1),
% 1.84/2.22 skol10 [334, 1] (w:1, o:138, a:1, s:1, b:1),
% 1.84/2.22 skol11 [335, 2] (w:1, o:230, a:1, s:1, b:1),
% 12.27/12.62 skol12 [336, 2] (w:1, o:231, a:1, s:1, b:1),
% 12.27/12.62 skol13 [337, 2] (w:1, o:232, a:1, s:1, b:1),
% 12.27/12.62 skol14 [338, 2] (w:1, o:233, a:1, s:1, b:1),
% 12.27/12.62 skol15 [339, 2] (w:1, o:234, a:1, s:1, b:1),
% 12.27/12.62 skol16 [340, 2] (w:1, o:235, a:1, s:1, b:1),
% 12.27/12.62 skol17 [341, 2] (w:1, o:236, a:1, s:1, b:1),
% 12.27/12.62 skol18 [342, 2] (w:1, o:237, a:1, s:1, b:1),
% 12.27/12.62 skol19 [343, 1] (w:1, o:139, a:1, s:1, b:1),
% 12.27/12.62 skol20 [344, 2] (w:1, o:238, a:1, s:1, b:1),
% 12.27/12.62 skol21 [345, 2] (w:1, o:239, a:1, s:1, b:1),
% 12.27/12.62 skol22 [346, 3] (w:1, o:335, a:1, s:1, b:1),
% 12.27/12.62 skol23 [347, 2] (w:1, o:240, a:1, s:1, b:1),
% 12.27/12.62 skol24 [348, 2] (w:1, o:241, a:1, s:1, b:1),
% 12.27/12.62 skol25 [349, 2] (w:1, o:242, a:1, s:1, b:1),
% 12.27/12.62 skol26 [350, 3] (w:1, o:336, a:1, s:1, b:1),
% 12.27/12.62 skol27 [351, 3] (w:1, o:337, a:1, s:1, b:1),
% 12.27/12.62 skol28 [352, 4] (w:1, o:381, a:1, s:1, b:1),
% 12.27/12.62 skol29 [353, 2] (w:1, o:243, a:1, s:1, b:1),
% 12.27/12.62 skol30 [354, 3] (w:1, o:338, a:1, s:1, b:1),
% 12.27/12.62 skol31 [355, 3] (w:1, o:339, a:1, s:1, b:1),
% 12.27/12.62 skol32 [356, 3] (w:1, o:340, a:1, s:1, b:1),
% 12.27/12.62 skol33 [357, 3] (w:1, o:341, a:1, s:1, b:1),
% 12.27/12.62 skol34 [358, 2] (w:1, o:244, a:1, s:1, b:1),
% 12.27/12.62 skol35 [359, 2] (w:1, o:245, a:1, s:1, b:1),
% 12.27/12.62 skol36 [360, 3] (w:1, o:342, a:1, s:1, b:1),
% 12.27/12.62 skol37 [361, 2] (w:1, o:246, a:1, s:1, b:1),
% 12.27/12.62 skol38 [362, 2] (w:1, o:247, a:1, s:1, b:1),
% 12.27/12.62 skol39 [363, 3] (w:1, o:343, a:1, s:1, b:1),
% 12.27/12.62 skol40 [364, 3] (w:1, o:326, a:1, s:1, b:1),
% 12.27/12.62 skol41 [365, 3] (w:1, o:327, a:1, s:1, b:1),
% 12.27/12.62 skol42 [366, 3] (w:1, o:328, a:1, s:1, b:1),
% 12.27/12.62 skol43 [367, 3] (w:1, o:329, a:1, s:1, b:1),
% 12.27/12.62 skol44 [368, 3] (w:1, o:330, a:1, s:1, b:1),
% 12.27/12.62 skol45 [369, 3] (w:1, o:331, a:1, s:1, b:1),
% 12.27/12.62 skol46 [370, 4] (w:1, o:382, a:1, s:1, b:1),
% 12.27/12.62 skol47 [371, 3] (w:1, o:332, a:1, s:1, b:1),
% 12.27/12.62 skol48 [372, 2] (w:1, o:248, a:1, s:1, b:1),
% 12.27/12.62 skol49 [373, 3] (w:1, o:333, a:1, s:1, b:1),
% 12.27/12.62 skol50 [374, 3] (w:1, o:344, a:1, s:1, b:1),
% 12.27/12.62 skol51 [375, 1] (w:1, o:142, a:1, s:1, b:1),
% 12.27/12.62 skol52 [376, 0] (w:1, o:14, a:1, s:1, b:1),
% 12.27/12.62 skol53 [377, 2] (w:1, o:249, a:1, s:1, b:1),
% 12.27/12.62 skol54 [378, 3] (w:1, o:345, a:1, s:1, b:1),
% 12.27/12.62 skol55 [379, 2] (w:1, o:250, a:1, s:1, b:1),
% 12.27/12.62 skol56 [380, 3] (w:1, o:346, a:1, s:1, b:1),
% 12.27/12.62 skol57 [381, 3] (w:1, o:347, a:1, s:1, b:1),
% 12.27/12.62 skol58 [382, 3] (w:1, o:348, a:1, s:1, b:1).
% 12.27/12.62
% 12.27/12.62
% 12.27/12.62 Starting Search:
% 12.27/12.62
% 12.27/12.62 *** allocated 170857 integers for clauses
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 2891
% 12.27/12.62 Kept: 2057
% 12.27/12.62 Inuse: 0
% 12.27/12.62 Deleted: 0
% 12.27/12.62 Deletedinuse: 0
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 *** allocated 256285 integers for clauses
% 12.27/12.62 *** allocated 170857 integers for termspace/termends
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 6984
% 12.27/12.62 Kept: 4063
% 12.27/12.62 Inuse: 150
% 12.27/12.62 Deleted: 2
% 12.27/12.62 Deletedinuse: 0
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 *** allocated 384427 integers for clauses
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 *** allocated 256285 integers for termspace/termends
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 11104
% 12.27/12.62 Kept: 6139
% 12.27/12.62 Inuse: 254
% 12.27/12.62 Deleted: 2
% 12.27/12.62 Deletedinuse: 0
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 *** allocated 576640 integers for clauses
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 16194
% 12.27/12.62 Kept: 8153
% 12.27/12.62 Inuse: 337
% 12.27/12.62 Deleted: 15
% 12.27/12.62 Deletedinuse: 6
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 22342
% 12.27/12.62 Kept: 10167
% 12.27/12.62 Inuse: 387
% 12.27/12.62 Deleted: 17
% 12.27/12.62 Deletedinuse: 6
% 12.27/12.62
% 12.27/12.62 *** allocated 384427 integers for termspace/termends
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 *** allocated 864960 integers for clauses
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 28897
% 12.27/12.62 Kept: 12214
% 12.27/12.62 Inuse: 430
% 12.27/12.62 Deleted: 17
% 12.27/12.62 Deletedinuse: 6
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 33344
% 12.27/12.62 Kept: 14475
% 12.27/12.62 Inuse: 460
% 12.27/12.62 Deleted: 17
% 12.27/12.62 Deletedinuse: 6
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 12.27/12.62
% 12.27/12.62
% 12.27/12.62 Intermediate Status:
% 12.27/12.62 Generated: 38678
% 12.27/12.62 Kept: 16508
% 12.27/12.62 Inuse: 494
% 12.27/12.62 Deleted: 17
% 12.27/12.62 Deletedinuse: 6
% 12.27/12.62
% 12.27/12.62 Resimplifying inuse:
% 12.27/12.62 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 576640 integers for termspace/termends
% 54.48/54.81 *** allocated 1297440 integers for clauses
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 42685
% 54.48/54.81 Kept: 18523
% 54.48/54.81 Inuse: 523
% 54.48/54.81 Deleted: 17
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 47012
% 54.48/54.81 Kept: 20753
% 54.48/54.81 Inuse: 535
% 54.48/54.81 Deleted: 17
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying clauses:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 66481
% 54.48/54.81 Kept: 23199
% 54.48/54.81 Inuse: 550
% 54.48/54.81 Deleted: 184
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 70779
% 54.48/54.81 Kept: 25230
% 54.48/54.81 Inuse: 574
% 54.48/54.81 Deleted: 184
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 864960 integers for termspace/termends
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 75016
% 54.48/54.81 Kept: 27236
% 54.48/54.81 Inuse: 593
% 54.48/54.81 Deleted: 184
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 1946160 integers for clauses
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 79595
% 54.48/54.81 Kept: 29276
% 54.48/54.81 Inuse: 630
% 54.48/54.81 Deleted: 184
% 54.48/54.81 Deletedinuse: 6
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 84701
% 54.48/54.81 Kept: 31312
% 54.48/54.81 Inuse: 675
% 54.48/54.81 Deleted: 186
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 90120
% 54.48/54.81 Kept: 33323
% 54.48/54.81 Inuse: 701
% 54.48/54.81 Deleted: 186
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 96069
% 54.48/54.81 Kept: 35469
% 54.48/54.81 Inuse: 725
% 54.48/54.81 Deleted: 186
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 101421
% 54.48/54.81 Kept: 37495
% 54.48/54.81 Inuse: 761
% 54.48/54.81 Deleted: 186
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 107496
% 54.48/54.81 Kept: 39533
% 54.48/54.81 Inuse: 800
% 54.48/54.81 Deleted: 186
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying clauses:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 1297440 integers for termspace/termends
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 113967
% 54.48/54.81 Kept: 41713
% 54.48/54.81 Inuse: 840
% 54.48/54.81 Deleted: 309
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 2919240 integers for clauses
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 120321
% 54.48/54.81 Kept: 43724
% 54.48/54.81 Inuse: 874
% 54.48/54.81 Deleted: 309
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 126224
% 54.48/54.81 Kept: 45745
% 54.48/54.81 Inuse: 904
% 54.48/54.81 Deleted: 309
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 133611
% 54.48/54.81 Kept: 47784
% 54.48/54.81 Inuse: 928
% 54.48/54.81 Deleted: 309
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 137276
% 54.48/54.81 Kept: 50080
% 54.48/54.81 Inuse: 930
% 54.48/54.81 Deleted: 309
% 54.48/54.81 Deletedinuse: 8
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 144317
% 54.48/54.81 Kept: 52082
% 54.48/54.81 Inuse: 936
% 54.48/54.81 Deleted: 310
% 54.48/54.81 Deletedinuse: 9
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 152159
% 54.48/54.81 Kept: 54096
% 54.48/54.81 Inuse: 974
% 54.48/54.81 Deleted: 310
% 54.48/54.81 Deletedinuse: 9
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 176092
% 54.48/54.81 Kept: 57490
% 54.48/54.81 Inuse: 1010
% 54.48/54.81 Deleted: 310
% 54.48/54.81 Deletedinuse: 9
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 1946160 integers for termspace/termends
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 202721
% 54.48/54.81 Kept: 60747
% 54.48/54.81 Inuse: 1040
% 54.48/54.81 Deleted: 310
% 54.48/54.81 Deletedinuse: 9
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying clauses:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 220145
% 54.48/54.81 Kept: 64225
% 54.48/54.81 Inuse: 1080
% 54.48/54.81 Deleted: 402
% 54.48/54.81 Deletedinuse: 10
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81 *** allocated 4378860 integers for clauses
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 229962
% 54.48/54.81 Kept: 66256
% 54.48/54.81 Inuse: 1095
% 54.48/54.81 Deleted: 402
% 54.48/54.81 Deletedinuse: 10
% 54.48/54.81
% 54.48/54.81 Resimplifying inuse:
% 54.48/54.81 Done
% 54.48/54.81
% 54.48/54.81
% 54.48/54.81 Intermediate Status:
% 54.48/54.81 Generated: 243284
% 54.48/54.81 Kept: 68429
% 54.48/54.81 Inuse: 1120
% 177.35/177.69 Deleted: 402
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 253863
% 177.35/177.69 Kept: 72474
% 177.35/177.69 Inuse: 1150
% 177.35/177.69 Deleted: 402
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 261418
% 177.35/177.69 Kept: 75188
% 177.35/177.69 Inuse: 1175
% 177.35/177.69 Deleted: 402
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 267325
% 177.35/177.69 Kept: 77227
% 177.35/177.69 Inuse: 1220
% 177.35/177.69 Deleted: 402
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 273338
% 177.35/177.69 Kept: 79227
% 177.35/177.69 Inuse: 1259
% 177.35/177.69 Deleted: 402
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying clauses:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 279343
% 177.35/177.69 Kept: 81263
% 177.35/177.69 Inuse: 1284
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 *** allocated 2919240 integers for termspace/termends
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 307559
% 177.35/177.69 Kept: 85431
% 177.35/177.69 Inuse: 1315
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 320510
% 177.35/177.69 Kept: 88277
% 177.35/177.69 Inuse: 1325
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 333208
% 177.35/177.69 Kept: 90284
% 177.35/177.69 Inuse: 1342
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 357950
% 177.35/177.69 Kept: 94618
% 177.35/177.69 Inuse: 1365
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 376077
% 177.35/177.69 Kept: 97021
% 177.35/177.69 Inuse: 1370
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 *** allocated 6568290 integers for clauses
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 387225
% 177.35/177.69 Kept: 99182
% 177.35/177.69 Inuse: 1405
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 396621
% 177.35/177.69 Kept: 101316
% 177.35/177.69 Inuse: 1435
% 177.35/177.69 Deleted: 523
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying clauses:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 413666
% 177.35/177.69 Kept: 104550
% 177.35/177.69 Inuse: 1450
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 423849
% 177.35/177.69 Kept: 106622
% 177.35/177.69 Inuse: 1480
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 432467
% 177.35/177.69 Kept: 108725
% 177.35/177.69 Inuse: 1510
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 *** allocated 4378860 integers for termspace/termends
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 445673
% 177.35/177.69 Kept: 111061
% 177.35/177.69 Inuse: 1535
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 454083
% 177.35/177.69 Kept: 113143
% 177.35/177.69 Inuse: 1555
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 461298
% 177.35/177.69 Kept: 115161
% 177.35/177.69 Inuse: 1583
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 468279
% 177.35/177.69 Kept: 117324
% 177.35/177.69 Inuse: 1620
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 475202
% 177.35/177.69 Kept: 119466
% 177.35/177.69 Inuse: 1655
% 177.35/177.69 Deleted: 612
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying clauses:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 483315
% 177.35/177.69 Kept: 121481
% 177.35/177.69 Inuse: 1682
% 177.35/177.69 Deleted: 740
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 492172
% 177.35/177.69 Kept: 123752
% 177.35/177.69 Inuse: 1700
% 177.35/177.69 Deleted: 740
% 177.35/177.69 Deletedinuse: 10
% 177.35/177.69
% 177.35/177.69 Resimplifying inuse:
% 177.35/177.69 Done
% 177.35/177.69
% 177.35/177.69
% 177.35/177.69 Intermediate Status:
% 177.35/177.69 Generated: 503024
% 177.35/177.69 Kept: 125794
% 177.35/177.69 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------