TSTP Solution File: SWW270+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW270+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:43 EDT 2022
% Result : Timeout 300.03s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW270+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jun 5 22:28:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.92/1.51 *** allocated 10000 integers for termspace/termends
% 0.92/1.51 *** allocated 10000 integers for clauses
% 0.92/1.51 *** allocated 10000 integers for justifications
% 0.92/1.51 *** allocated 15000 integers for termspace/termends
% 0.92/1.51 *** allocated 22500 integers for termspace/termends
% 0.92/1.51 *** allocated 33750 integers for termspace/termends
% 0.92/1.51 Bliksem 1.12
% 0.92/1.51
% 0.92/1.51
% 0.92/1.51 Automatic Strategy Selection
% 0.92/1.51
% 0.92/1.51 *** allocated 50625 integers for termspace/termends
% 0.92/1.51 *** allocated 75937 integers for termspace/termends
% 0.92/1.51 *** allocated 113905 integers for termspace/termends
% 0.92/1.51
% 0.92/1.51 Clauses:
% 0.92/1.51
% 0.92/1.51 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ),
% 0.92/1.51 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ) ), v_m____ ) }.
% 0.92/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.92/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ), X ) ), v_m____ ) }.
% 0.92/1.51 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.92/1.51 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.92/1.51 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ), hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ),
% 0.92/1.51 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ) ) ) =
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_d____ ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.92/1.51 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ),
% 0.92/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.51 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.92/1.51 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.51 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 0.92/1.51 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_RealVector_Oof__real
% 0.92/1.51 ( X, Z ) ), c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.51 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.51 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.51 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.92/1.51 { ! c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) =
% 0.92/1.51 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_x____ ) }.
% 0.92/1.51 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.92/1.51 , Y ) }.
% 0.92/1.51 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.92/1.51 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.92/1.51 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.92/1.51 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.92/1.51 ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol2( X ) ) ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Y ) ) ) }.
% 0.92/1.51 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.92/1.51 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol3( X, Y ) ) ),
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ) ) }.
% 0.92/1.51 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.92/1.51 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.92/1.51 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.92/1.51 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.92/1.51 { ! v_d____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.51 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_x____,
% 0.92/1.51 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.51 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 0.92/1.51 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_x____,
% 0.92/1.51 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.51 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_d____ ), v_m____
% 0.92/1.51 ) ) }.
% 0.92/1.51 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.51 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.51 tc_Complex_Ocomplex, v_d____, v_ds____ ) ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 Y ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 Z ), ! Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.92/1.52 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! Z = Y }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! Z = Y }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! Y = Z }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.92/1.52 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.92/1.52 , ! Z = Y }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.52 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.52 hAPP( Y, U ) ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.92/1.52 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.52 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.52 hAPP( Y, U ) ) }.
% 0.92/1.52 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Z, Y ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.92/1.52 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.52 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.92/1.52 hAPP( Y, U ) ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.92/1.52 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 0.92/1.52 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 0.92/1.52 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_cs____ ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ), X ) ), skol5 ) }.
% 0.92/1.52 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.52 tc_Complex_Ocomplex, v_d____, v_ds____ ) ), c_RealVector_Oof__real(
% 0.92/1.52 tc_Complex_Ocomplex, v_x____ ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Complex_Ocomplex ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_d____ ), v_m____
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.92/1.52 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.92/1.52 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.92/1.52 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.92/1.52 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ) ) }.
% 0.92/1.52 { ! v_d____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 0.92/1.52 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_d____, v_ds____ ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.52 }.
% 0.92/1.52 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.52 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Complex_Ocomplex ) ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.92/1.52 c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) ), X ) }.
% 0.92/1.52 { ! skol6 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_ds____ =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ), skol6 ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), v_ds____ =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 0.92/1.52 }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), ! v_p =
% 0.92/1.52 c_Polynomial_OpCons( tc_Complex_Ocomplex, X, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) ) ) }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.92/1.52 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.92/1.52 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.92/1.52 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.92/1.52 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.92/1.52 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.52 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.92/1.52 ( X, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.52 class_RealVector_Oreal__field( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Z, Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_RealVector_Oof__real( X, Z ),
% 0.92/1.52 c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.92/1.52 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.92/1.52 ( X, Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Z, Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_RealVector_Oof__real( X, Z ),
% 0.92/1.52 c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.92/1.52 ( X ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.52 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.52 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha1( X, Y
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha26( X,
% 0.92/1.52 Y ) }.
% 0.92/1.52 { ! alpha1( X, Y ), ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.92/1.52 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha26( X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha26( X, Y ) }.
% 0.92/1.52 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha1( X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha1( X, Y ) }.
% 0.92/1.52 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.92/1.52 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.92/1.52 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, Z ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.92/1.52 }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.92/1.52 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.92/1.52 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.92/1.52 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.92/1.52 , Z ), alpha27( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 0.92/1.52 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ), alpha3( X, Y, Z ), alpha28( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ), Y ), alpha28( X, Y, Z ) }.
% 0.92/1.52 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 0.92/1.52 alpha29( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha29( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.92/1.52 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha5( X, Y, Z, T ),
% 0.92/1.52 alpha30( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha30( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha5( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7 ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_d____ ), v_m____
% 0.92/1.52 ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8 ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol8,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_d____ ), v_m____
% 0.92/1.52 ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol8,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! v_c____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.52 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), skol9 ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ), alpha31( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 0.92/1.52 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), alpha57( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.52 , alpha48( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha57( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha57( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha57( X, Y, Z, T ), alpha6( X, Y, T ) }.
% 0.92/1.52 { ! alpha67( X, Y, Z, T ), ! alpha6( X, Y, T ), alpha57( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha67( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 alpha67( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha67( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha31( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 alpha31( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha31( X, Y, Z, T )
% 0.92/1.52 }.
% 0.92/1.52 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , alpha6( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), alpha6( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Z ), Y ), alpha32( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Z ), Y ), alpha49( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.92/1.52 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.92/1.52 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ), alpha58( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , alpha49( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha58( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha58( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha58( X, Y, Z, T ), alpha7( X, Y, Z ) }.
% 0.92/1.52 { ! alpha68( X, Y, Z, T ), ! alpha7( X, Y, Z ), alpha58( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha68( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 alpha68( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha68( X, Y, Z, T )
% 0.92/1.52 }.
% 0.92/1.52 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.92/1.52 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.52 alpha32( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha32( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , alpha7( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Y ), alpha7( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ) }.
% 0.92/1.52 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.92/1.52 X, T ) = hAPP( X, U ) }.
% 0.92/1.52 { ! hAPP( X, skol10( X ) ) = hAPP( X, skol61( X ) ),
% 0.92/1.52 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.92/1.52 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha8( X, Y, Z ), alpha33
% 0.92/1.52 ( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha8( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), alpha33( X, Y, Z ) }.
% 0.92/1.52 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), alpha8( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha9( X, Y, Z ), alpha34
% 0.92/1.52 ( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha9( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ), Y ), alpha34( X, Y, Z ) }.
% 0.92/1.52 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), alpha9( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha10( X, Y, Z ), alpha35
% 0.92/1.52 ( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha10( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), alpha35( X, Y, Z ) }.
% 0.92/1.52 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), alpha10( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.92/1.52 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ), alpha36( X,
% 0.92/1.52 Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), alpha36( X, Y, Z ) }.
% 0.92/1.52 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), alpha11( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Y, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Y, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha37( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha12( X, Y, T ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha37( X, Y, Z, T ), !
% 0.92/1.52 alpha12( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.52 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha37(
% 0.92/1.52 X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha12( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { Y = c_Groups_Ozero__class_Ozero( X ), alpha12( X, Y, Z ) }.
% 0.92/1.52 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha12( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha38( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha13( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha38( X, Y, Z, T ), !
% 0.92/1.52 alpha13( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.92/1.52 { ! alpha38( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.92/1.52 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha38( X, Y, Z, T ) }.
% 0.92/1.52 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha38(
% 0.92/1.52 X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha13( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { Z = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.92/1.52 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.92/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.92/1.52 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 Z, Y ) ), alpha39( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 Z, Y ) ), alpha50( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.92/1.52 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), alpha59( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.52 , alpha50( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha59( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha59( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha59( X, Y, Z, T ), alpha14( X, Y, T ) }.
% 0.92/1.52 { ! alpha69( X, Y, Z, T ), ! alpha14( X, Y, T ), alpha59( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha69( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 alpha69( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha69( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 alpha39( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha39( X, Y, Z, T )
% 0.92/1.52 }.
% 0.92/1.52 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , alpha14( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , alpha14( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Z ), Y ), alpha40( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Z ), Y ), alpha51( X, Y, Z, T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.92/1.52 , T ), ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.92/1.52 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ), alpha60( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , alpha51( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha60( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha60( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha60( X, Y, Z, T ), alpha15( X, Y, Z ) }.
% 0.92/1.52 { ! alpha70( X, Y, Z, T ), ! alpha15( X, Y, Z ), alpha60( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha70( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 alpha70( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha70( X, Y, Z, T )
% 0.92/1.52 }.
% 0.92/1.52 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.52 alpha40( X, Y, Z, T ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha40( X, Y, Z, T ) }.
% 0.92/1.52 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , alpha15( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.92/1.52 , alpha15( X, Y, Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 Z, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.92/1.52 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.92/1.52 , T, Y ), Z ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, Z, Y ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ), X ) ), skol11 ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex
% 0.92/1.52 ) ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, skol12( X, Y
% 0.92/1.52 , Z ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, T ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.92/1.52 tc_Complex_Ocomplex, Y, X ) ), T ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol13( X ) ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.52 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol16( X, Y ) ) ) }.
% 0.92/1.52 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol17( Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol17( X ) ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol18( X ) ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.52 alpha16( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.52 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! alpha16( X, Y, Z ),
% 0.92/1.52 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.92/1.52 { ! alpha16( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.52 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.92/1.52 alpha16( X, Y, Z ) }.
% 0.92/1.52 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.52 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.52 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.92/1.52 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.92/1.52 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.92/1.52 = Y }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol19( X ) ) )
% 0.92/1.52 }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Z, T ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.92/1.52 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol20( X, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.92/1.52 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.92/1.52 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.52 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.92/1.52 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { alpha81( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.92/1.52 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.92/1.52 { alpha81( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.92/1.52 ( X, Y ), Z ) ) }.
% 0.92/1.52 { ! alpha81( X, Y, Z ), alpha84( X, Y, Z ), Z = Y }.
% 0.92/1.52 { ! alpha81( X, Y, Z ), alpha84( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! alpha84( X, Y, Z ), alpha81( X, Y, Z ) }.
% 0.92/1.52 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha81( X, Y, Z ) }.
% 0.92/1.52 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.92/1.52 }.
% 0.92/1.52 { ! alpha84( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.92/1.52 X, Y ), Z ) ), alpha84( X, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.92/1.52 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.92/1.52 .
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.92/1.52 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.92/1.52 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.52 Y ), X ) ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.92/1.52 ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.92/1.52 ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.92/1.52 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.92/1.52 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.92/1.52 .
% 0.92/1.52 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.92/1.52 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.92/1.52 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.92/1.52 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.92/1.52 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.92/1.52 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.92/1.52 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.92/1.52 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.92/1.52 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.52 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.52 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.52 tc_Nat_Onat ), X ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol22( X ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol23( X, Y ) ) ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_Nat_Onat ) }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_Nat_Onat ) }.
% 0.92/1.52 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.92/1.52 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.52 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.92/1.52 , Y ), X ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.92/1.52 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.92/1.52 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.92/1.52 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.92/1.52 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Z, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol24( X, Y ) ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 skol25( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, skol25( X, T, U ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.92/1.52 , Y ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), skol25( X, Y, Z ) ), Z ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.92/1.52 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.92/1.52 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol26( X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.52 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol27( X, Y ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol29( X ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol30( X, Y ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.92/1.52 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.92/1.52 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 0.92/1.52 , c_NthRoot_Oroot( Y, Z ) ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.52 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.52 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.52 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.52 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.52 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.52 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , T ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , Y, T ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, Z, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, T, Y ) }.
% 0.92/1.52 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , Y, Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.52 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.92/1.52 c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.92/1.52 c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.92/1.52 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.92/1.52 c_RealVector_Oof__real( X, c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, Y
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.92/1.52 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Y, T ), Z = Y }.
% 0.92/1.52 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 T, Y ), Z = Y }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 T, Y ), Z = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.52 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Y, Z ), T = Y }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Y, Z ) }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 T, Y ), Z = Y }.
% 0.92/1.52 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 T, Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.92/1.52 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.52 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.92/1.52 { c_NthRoot_Oroot( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.92/1.52 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.52 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.92/1.52 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.92/1.52 ( X, Y ) ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.92/1.52 ), ! U = T }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.92/1.52 ), ! Z = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.52 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.92/1.52 ) ), Z ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.92/1.52 ), U = Z, T = Y }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.52 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.52 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.92/1.52 ) ), T ), Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.52 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.52 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__field( X ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.92/1.52 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.92/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), X ) = X }.
% 0.92/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ) ) = X }.
% 0.92/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.92/1.52 , X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.52 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol31( X, Y ) ) }.
% 0.92/1.52 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol32( X, Y ) ) }.
% 0.92/1.52 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.52 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.52 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.92/1.52 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.52 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.92/1.52 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.52 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y )
% 0.92/1.52 , Z = Y }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! Z = Y, c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot
% 0.92/1.52 ( X, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( X,
% 0.92/1.52 c_NthRoot_Oroot( Y, Z ) ) = c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.52 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.92/1.52 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 Z, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.52 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.52 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , Y, T ) ) }.
% 0.92/1.52 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.92/1.52 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.92/1.52 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.92/1.52 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.92/1.52 tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.52 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.92/1.52 .
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, Z, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.92/1.52 ), c_NthRoot_Oroot( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.92/1.52 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 Z, Y ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot
% 0.92/1.52 ( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Oroot
% 0.92/1.52 ( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), c_NthRoot_Oroot( hAPP(
% 0.92/1.52 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 0.92/1.52 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_RealDef_Oreal ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_NthRoot_Oroot( X, Y ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.92/1.52 , c_NthRoot_Oroot( X, Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.92/1.52 }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Rings_Oinverse__class_Odivide
% 0.92/1.52 ( tc_RealDef_Oreal, Z, Y ) ) = c_Rings_Oinverse__class_Odivide(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z ), c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.92/1.52 ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.92/1.52 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.92/1.52 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.92/1.52 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.92/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.52 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.52 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.92/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.92/1.52 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.92/1.52 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.92/1.52 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.92/1.52 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.52 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.92/1.52 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.52 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.92/1.52 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.52 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.92/1.52 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.52 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.92/1.52 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.92/1.52 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.52 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.92/1.52 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.52 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 0.92/1.52 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.52 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }
% 0.92/1.52 .
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.52 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.92/1.52 , Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.92/1.52 Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_NthRoot_Oroot( X, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.92/1.52 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 Y, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.92/1.52 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.92/1.52 c_NthRoot_Oroot( X, Y ) ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone(
% 0.92/1.52 tc_RealDef_Oreal ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.92/1.52 , Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.52 tc_RealDef_Oreal, Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.92/1.52 Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 0.92/1.52 Z ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) )
% 0.92/1.52 }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_NthRoot_Oroot( X, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.92/1.52 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 Y, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.92/1.52 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Z ),
% 0.92/1.52 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 0.92/1.52 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.92/1.52 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.92/1.52 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.52 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.92/1.52 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.52 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.52 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.92/1.52 ), Y ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.52 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.52 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.52 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.52 ) }.
% 0.92/1.52 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 0.92/1.53 , c_NthRoot_Oroot( X, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot( X
% 0.92/1.53 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Z )
% 0.92/1.53 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.92/1.53 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), c_NthRoot_Oroot(
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 0.92/1.53 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.53 ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 0.92/1.53 Z ), c_NthRoot_Oroot( Y, Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.92/1.53 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.92/1.53 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.92/1.53 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.92/1.53 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.92/1.53 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.92/1.53 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.53 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) ) }.
% 0.92/1.53 { c_Groups_Osgn__class_Osgn( tc_Complex_Ocomplex, X ) =
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, X,
% 0.92/1.53 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.92/1.53 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.92/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.53 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.92/1.53 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.92/1.53 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.53 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol33( Z, Y
% 0.92/1.53 ), Y ) }.
% 0.92/1.53 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.53 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.92/1.53 skol33( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.92/1.53 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.92/1.53 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.92/1.53 , skol33( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.92/1.53 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.53 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.92/1.53 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.92/1.53 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.92/1.53 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.92/1.53 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.92/1.53 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.92/1.53 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.53 }.
% 0.92/1.53 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.92/1.53 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.92/1.53 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.92/1.53 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.92/1.53 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.92/1.53 , c_RComplete_Onatfloor( X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.92/1.53 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.92/1.53 , c_RComplete_Onatfloor( X ) ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_RealDef_Oreal ) ) ) }.
% 0.92/1.53 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.92/1.53 Y = X }.
% 0.92/1.53 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.92/1.53 , X ) }.
% 0.92/1.53 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_RComplete_Onatfloor( X ), Y ) }.
% 0.92/1.53 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.92/1.53 ( tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.92/1.53 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.92/1.53 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.92/1.53 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.92/1.53 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.92/1.53 c_RComplete_Onatfloor( X ) = Y }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.92/1.53 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.92/1.53 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.92/1.53 ), c_RComplete_Onatfloor( X ) ) }.
% 0.92/1.53 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.92/1.53 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_RComplete_Onatceiling( Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.92/1.53 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.92/1.53 tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_RealDef_Oreal ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.92/1.53 , X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.92/1.53 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_RComplete_Onatceiling( X ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.92/1.53 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.92/1.53 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.92/1.53 c_RComplete_Onatfloor( X ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 0.92/1.53 ), X ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.53 c_NthRoot_Oroot( X, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.92/1.53 tc_RealDef_Oreal ), Y ), X ) ) = Y }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ) ) = Y }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.92/1.53 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.92/1.53 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.92/1.53 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 0.92/1.53 = hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_RealVector_Oof__real(
% 0.92/1.53 X, Z ) ), Y ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.92/1.53 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, Z, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) ) = hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Z
% 0.92/1.53 ) ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) =
% 0.92/1.53 Z, c_NthRoot_Oroot( X, Z ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.92/1.53 c_NthRoot_Oroot( X, Y ) ), X ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.92/1.53 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.53 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.53 alpha17( X, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.53 alpha41( X, Y, Z ) }.
% 0.92/1.53 { ! alpha17( X, Z ), ! alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.53 { ! alpha41( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 alpha52( X, Y, Z ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha41( X, Y, Z ) }.
% 0.92/1.53 { ! alpha52( X, Y, Z ), alpha41( X, Y, Z ) }.
% 0.92/1.53 { ! alpha52( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.92/1.53 ), alpha61( X, Y, Z, T ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol34( X, T, U ), X ),
% 0.92/1.53 alpha52( X, Y, Z ) }.
% 0.92/1.53 { ! alpha61( X, Y, Z, skol34( X, Y, Z ) ), alpha52( X, Y, Z ) }.
% 0.92/1.53 { ! alpha61( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.92/1.53 hBOOL( hAPP( Z, U ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, skol35( U, W, Z, V0 ) ) ), alpha61( X, Y, Z, T ) }.
% 0.92/1.53 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol35( X, Y, Z, T ) )
% 0.92/1.53 , T ), alpha61( X, Y, Z, T ) }.
% 0.92/1.53 { ! alpha17( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha17( X, Y ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17
% 0.92/1.53 ( X, Y ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.92/1.53 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.92/1.53 ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.92/1.53 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.92/1.53 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.92/1.53 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.92/1.53 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ), X ) =
% 0.92/1.53 c_RealVector_Oof__real( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.92/1.53 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.92/1.53 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.92/1.53 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.92/1.53 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.92/1.53 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( X ) }.
% 0.92/1.53 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.92/1.53 = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.92/1.53 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.92/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.92/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ) ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Nat_Onat, Z, Y ), X ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.92/1.53 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.53 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.92/1.53 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.92/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.92/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.92/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.92/1.53 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ) }.
% 0.92/1.53 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.92/1.53 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.92/1.53 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.92/1.53 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.92/1.53 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.92/1.53 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.92/1.53 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.53 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.92/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.92/1.53 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.92/1.53 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.53 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.92/1.53 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.92/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.92/1.53 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.92/1.53 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.92/1.53 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.92/1.53 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.92/1.53 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.92/1.53 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.92/1.53 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.92/1.53 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.92/1.53 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.92/1.53 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.92/1.53 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.92/1.53 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.92/1.53 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.92/1.53 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol36( X, Y ) ), Y
% 0.92/1.53 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.92/1.53 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.92/1.53 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), Y ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.92/1.53 ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Z, Y ), X ) }.
% 0.92/1.53 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha82( X,
% 0.92/1.53 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, T, Z ) = Y }.
% 0.92/1.53 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha82( X,
% 0.92/1.53 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, T, Z ) = Y }.
% 0.92/1.53 { ! alpha82( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! alpha82( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha82( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.92/1.53 , alpha82( X, Y ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.92/1.53 alpha18( X, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.92/1.53 alpha42( X, Y, Z ) }.
% 0.92/1.53 { ! alpha18( X, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.92/1.53 { ! alpha42( X, Y, Z ), alpha53( X, Y, Z ) }.
% 0.92/1.53 { ! alpha42( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.92/1.53 { ! alpha53( X, Y, Z ), ! alpha62( X, Y, Z ), alpha42( X, Y, Z ) }.
% 0.92/1.53 { ! alpha62( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha71( X, Y, Z ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha62( X, Y, Z ) }.
% 0.92/1.53 { ! alpha71( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.92/1.53 { ! alpha71( X, Y, Z ), ! alpha75( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, skol37( T, U, Z ) ) ), alpha71( X, Y, Z ) }.
% 0.92/1.53 { alpha75( X, Y, skol37( X, Y, Z ) ), alpha71( X, Y, Z ) }.
% 0.92/1.53 { ! alpha75( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 skol38( X, T, U ) ) }.
% 0.92/1.53 { ! alpha75( X, Y, Z ), alpha79( X, Y, Z, skol38( X, Y, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha79( X, Y, Z
% 0.92/1.53 , T ), alpha75( X, Y, Z ) }.
% 0.92/1.53 { ! alpha79( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! alpha79( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha79( X,
% 0.92/1.53 Y, Z, T ) }.
% 0.92/1.53 { ! alpha53( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha63( X, Y, Z ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ), alpha53( X, Y, Z ) }.
% 0.92/1.53 { ! alpha63( X, Y, Z ), alpha53( X, Y, Z ) }.
% 0.92/1.53 { ! alpha63( X, Y, Z ), ! alpha72( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, skol39( T, U, Z ) ) ), alpha63( X, Y, Z ) }.
% 0.92/1.53 { alpha72( X, Y, skol39( X, Y, Z ) ), alpha63( X, Y, Z ) }.
% 0.92/1.53 { ! alpha72( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol40( T, U, W ) ) }.
% 0.92/1.53 { ! alpha72( X, Y, Z ), alpha76( X, Y, Z, skol40( X, Y, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha76( X, Y, Z, T )
% 0.92/1.53 , alpha72( X, Y, Z ) }.
% 0.92/1.53 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! alpha76( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha76( X,
% 0.92/1.53 Y, Z, T ) }.
% 0.92/1.53 { ! alpha18( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha18
% 0.92/1.53 ( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.92/1.53 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.92/1.53 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.92/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.92/1.53 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.92/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.92/1.53 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.92/1.53 ( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.92/1.53 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.92/1.53 ( X ), T, Z ), Y ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_Nat_Onat, skol41( X, Y ), skol62( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.53 hAPP( Y, skol62( X, Y ) ), hAPP( Y, skol41( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.92/1.53 , Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.92/1.53 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.92/1.53 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.92/1.53 X, Z ), Y ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.92/1.53 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, X, Y ), X ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha19( X, Y ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! alpha19( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! alpha19( X, Y ), alpha43( X, Y ), alpha54( X, Y ) }.
% 0.92/1.53 { ! alpha43( X, Y ), alpha19( X, Y ) }.
% 0.92/1.53 { ! alpha54( X, Y ), alpha19( X, Y ) }.
% 0.92/1.53 { ! alpha54( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! alpha54( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha54( X, Y ) }.
% 0.92/1.53 { ! alpha43( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! alpha43( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha43( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.92/1.53 , Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.92/1.53 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, X, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, X, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.92/1.53 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.92/1.53 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.92/1.53 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ) ) = X }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ) = X }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.92/1.53 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.92/1.53 }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.92/1.53 = X }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) ) }.
% 0.92/1.53 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.92/1.53 }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.92/1.53 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.92/1.53 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.92/1.53 ( tc_Int_Oint ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.53 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.92/1.53 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.92/1.53 { c_Complex_Orcis( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.92/1.53 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) }.
% 0.92/1.53 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.53 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.92/1.53 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.92/1.53 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.92/1.53 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.92/1.53 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.92/1.53 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, X, Y ) ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ) ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol42( Z, T ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol42( X, Y ) ), X ) =
% 0.92/1.53 Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.92/1.53 skol42( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43( Z, T ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol43( X, Y ) ), X ) =
% 0.92/1.53 Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.92/1.53 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha20( X, Y, T,
% 0.92/1.53 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha20( X, Y, skol44( X, Y
% 0.92/1.53 , Z ), skol63( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.92/1.53 skol44( X, Y, Z ) ), skol63( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.92/1.53 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.92/1.53 ) }.
% 0.92/1.53 { ! alpha20( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha44( X, Y, Z
% 0.92/1.53 , T ), alpha20( X, Y, Z, T ) }.
% 0.92/1.53 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! alpha44( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha44( X,
% 0.92/1.53 Y, Z, T ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ) ) = X }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.92/1.53 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol45( X, Y ) ) }.
% 0.92/1.53 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.92/1.53 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.53 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol46( X, Y ) ) }.
% 0.92/1.53 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.92/1.53 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.92/1.53 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.92/1.53 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, X, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.92/1.53 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.92/1.53 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.92/1.53 ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.92/1.53 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 T, Y ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.92/1.53 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 T, Z ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.53 ), Z ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.92/1.53 , Y ) ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, Y, Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, Z, Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.92/1.53 X, Z, Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.92/1.53 , Y ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.92/1.53 ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.92/1.53 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.92/1.53 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.92/1.53 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.92/1.53 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.92/1.53 , Z ) ) = Y }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.92/1.53 ), Y ) ) = Z }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.92/1.53 ) ) }.
% 0.92/1.53 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.92/1.53 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.53 alpha21( X, Y, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.92/1.53 alpha45( X, Y, Z ) }.
% 0.92/1.53 { ! alpha21( X, Y, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.92/1.53 { ! alpha45( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 alpha55( X, Y, Z ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha45( X, Y, Z ) }.
% 0.92/1.53 { ! alpha55( X, Y, Z ), alpha45( X, Y, Z ) }.
% 0.92/1.53 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.92/1.53 ), alpha64( X, Y, Z, T ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol47( X, T, U ), X ),
% 0.92/1.53 alpha55( X, Y, Z ) }.
% 0.92/1.53 { ! alpha64( X, Y, Z, skol47( X, Y, Z ) ), alpha55( X, Y, Z ) }.
% 0.92/1.53 { ! alpha64( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.92/1.53 hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.53 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol48( X, Y, T ) ), T
% 0.92/1.53 ), alpha64( X, Y, Z, T ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, T ) ), alpha64( X, Y, Z, T ) }.
% 0.92/1.53 { ! alpha21( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 hBOOL( hAPP( Z, Y ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha21( X, Y, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, Y ) ), alpha21( X, Y, Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.92/1.53 }.
% 0.92/1.53 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha83( X,
% 0.92/1.53 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Z, Y ) = X }.
% 0.92/1.53 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha83( X,
% 0.92/1.53 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Z, Y ) = X }.
% 0.92/1.53 { ! alpha83( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.92/1.53 { ! alpha83( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha83( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.92/1.53 , alpha83( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.92/1.53 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.92/1.53 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.92/1.53 alpha22( X, Y, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.92/1.53 alpha46( X, Y, Z ) }.
% 0.92/1.53 { ! alpha22( X, Y, Z ), ! alpha46( X, Y, Z ), hBOOL( hAPP( Z,
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.92/1.53 { ! alpha46( X, Y, Z ), alpha56( X, Y, Z ) }.
% 0.92/1.53 { ! alpha46( X, Y, Z ), alpha65( X, Y, Z ) }.
% 0.92/1.53 { ! alpha56( X, Y, Z ), ! alpha65( X, Y, Z ), alpha46( X, Y, Z ) }.
% 0.92/1.53 { ! alpha65( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha73( X, Y, Z ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha65( X, Y, Z ) }.
% 0.92/1.53 { ! alpha73( X, Y, Z ), alpha65( X, Y, Z ) }.
% 0.92/1.53 { ! alpha73( X, Y, Z ), ! alpha77( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, skol49( T, U, Z ) ) ), alpha73( X, Y, Z ) }.
% 0.92/1.53 { alpha77( X, Y, skol49( X, Y, Z ) ), alpha73( X, Y, Z ) }.
% 0.92/1.53 { ! alpha77( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.92/1.53 }.
% 0.92/1.53 { ! alpha77( X, Y, Z ), alpha80( X, Y, Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha80( X, Y, Z
% 0.92/1.53 ), alpha77( X, Y, Z ) }.
% 0.92/1.53 { ! alpha80( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.92/1.53 { ! alpha80( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol50( X, Y,
% 0.92/1.53 Z ) ), Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha80( X,
% 0.92/1.53 Y, Z ) }.
% 0.92/1.53 { ! alpha56( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha66( X, Y, Z ) }.
% 0.92/1.53 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ), alpha56( X, Y, Z ) }.
% 0.92/1.53 { ! alpha66( X, Y, Z ), alpha56( X, Y, Z ) }.
% 0.92/1.53 { ! alpha66( X, Y, Z ), ! alpha74( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha66( X, Y, Z ) }.
% 0.92/1.53 { alpha74( X, Y, skol51( X, Y, Z ) ), alpha66( X, Y, Z ) }.
% 0.92/1.53 { ! alpha74( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.92/1.53 { ! alpha74( X, Y, Z ), alpha78( X, Y, Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha78( X, Y, Z ),
% 0.92/1.53 alpha74( X, Y, Z ) }.
% 0.92/1.53 { ! alpha78( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.92/1.53 }.
% 0.92/1.53 { ! alpha78( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.92/1.53 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol52( X, Y,
% 0.92/1.53 Z ) ), Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha78( X,
% 0.92/1.53 Y, Z ) }.
% 0.92/1.53 { ! alpha22( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 hBOOL( hAPP( Z, Y ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha22( X, Y, Z ) }.
% 0.92/1.53 { ! hBOOL( hAPP( Z, Y ) ), alpha22( X, Y, Z ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.92/1.53 ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.92/1.53 ) ), ! alpha23( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), alpha23( X, Y, skol53( X, Y, Z ), skol64( X, Y, Z )
% 0.92/1.53 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol53( X, Y, Z ) ), skol64
% 0.92/1.53 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.92/1.53 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! alpha23( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.92/1.53 { ! alpha23( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha47( X, Y, Z, T )
% 0.92/1.53 , alpha23( X, Y, Z, T ) }.
% 0.92/1.53 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! alpha47( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.92/1.53 .
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha47( X,
% 0.92/1.53 Y, Z, T ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol54( Z, T ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol54( X, Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol65( X, Y, Z ) ) ), Z ),
% 0.92/1.53 c_SEQ_OBseq( X, Y ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.92/1.53 tc_Nat_Onat, skol55( X, Y ), skol66( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.92/1.53 hAPP( Y, skol55( X, Y ) ), hAPP( Y, skol66( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.92/1.53 , Y ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.92/1.53 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.92/1.53 ), T, Z ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol56( Z, T ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol56( X, Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol57( X, Y, Z ) ) ), Y ),
% 0.92/1.53 c_SEQ_OBseq( X, Z ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol58( U, W, V0, T )
% 0.92/1.53 ), c_SEQ_OBseq( X, Y ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol58( X, Y, Z, T ) ) ), Z
% 0.92/1.53 ), c_SEQ_OBseq( X, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 0.92/1.53 , X ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.92/1.53 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }
% 0.92/1.53 .
% 0.92/1.53 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.92/1.53 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 0.92/1.53 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.53 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 0.92/1.53 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.53 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 0.92/1.53 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 0.92/1.53 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.92/1.53 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.92/1.53 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 0.92/1.53 , Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 0.92/1.53 Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, Y, X ), Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! alpha24( X, Y ), ! Y = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha24( X, Y ) }
% 0.92/1.53 .
% 0.92/1.53 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! alpha24( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha25( X, Y ), Y = X }
% 0.92/1.53 .
% 0.92/1.53 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! alpha25( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! alpha25( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, Y ), alpha25( X, Y ) }.
% 0.92/1.53 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 Z, T ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.92/1.53 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.92/1.53 X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.92/1.53 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.92/1.53 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.92/1.53 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.92/1.53 ), T ), U ), Y ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.92/1.53 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.92/1.53 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.92/1.53 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.92/1.53 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.92/1.53 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.92/1.53 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.92/1.53 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.92/1.53 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 0.92/1.53 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 0.92/1.53 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 0.92/1.53 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.92/1.53 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.92/1.53 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.92/1.53 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.92/1.53 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.92/1.53 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.92/1.53 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.92/1.53 ( X, Z, Y ) = T }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.92/1.53 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.92/1.53 ( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.92/1.53 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.92/1.53 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.92/1.53 hAPP( Z, skol59( U, W, Z ) ) ) }.
% 0.92/1.53 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.92/1.53 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol59( X
% 0.92/1.53 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.92/1.53 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 0.92/1.53 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol67( X,
% 0.92/1.53 Y, Z ) ) ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 0.92/1.53 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.92/1.53 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Int_Oint, Y, X ), X = Y }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 0.92/1.53 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 0.92/1.53 ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.92/1.53 , Z ), X ) ), T ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, U, T ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.92/1.53 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 0.92/1.53 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Int_Oint, Z, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.92/1.53 ) }.
% 0.92/1.53 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ) ) }.
% 0.92/1.53 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Nat_Onat ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Nat_Onat ), Y ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 0.92/1.53 tc_Nat_Onat, Z, X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol60( Z, Y ) ) ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.92/1.53 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.92/1.53 tc_Int_Oint, skol60( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.92/1.53 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.92/1.53 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.92/1.53 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.92/1.53 ) ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.92/1.53 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 0.92/1.53 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.53 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.92/1.53 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.92/1.53 , Z, Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.92/1.53 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.92/1.53 , Y ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.92/1.53 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 0.92/1.53 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 0.92/1.53 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 0.92/1.53 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.92/1.53 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.92/1.53 , Z ) ) }.
% 0.92/1.53 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.92/1.53 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.92/1.53 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.92/1.53 , Z ) ) }.
% 0.92/1.53 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.92/1.53 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.53 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.92/1.53 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.92/1.53 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.92/1.53 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Int_Oint ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.92/1.53 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.92/1.53 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.92/1.53 tc_Int_Oint ) ) }.
% 0.92/1.53 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.92/1.53 ( tc_Nat_Onat ), X ), c_NthRoot_Oroot( X, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_RealDef_Oreal, Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.92/1.53 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.92/1.53 , Y ) ), Y ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.92/1.53 ( tc_Int_Oint, Y, X ) ) }.
% 0.92/1.53 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.92/1.53 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( tc_Int_Oint, Y ), X ) }.
% 0.92/1.53 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.92/1.53 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.92/1.53 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.92/1.53 ( X ), Z, Y ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.92/1.53 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.53 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.92/1.53 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.92/1.53 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.92/1.53 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.92/1.53 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.92/1.53 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.92/1.53 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.92/1.53 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( X, Y ) ) }.
% 0.92/1.53 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ) ), Y ) }.
% 0.92/1.53 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.92/1.53 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.92/1.53 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( X, Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.92/1.53 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.53 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.92/1.53 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.53 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.92/1.53 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.53 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.92/1.53 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.92/1.53 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.92/1.53 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.92/1.53 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.53 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.92/1.53 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.92/1.53 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.92/1.53 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.92/1.53 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.92/1.53 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.92/1.53 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.92/1.53 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.92/1.53 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.92/1.53 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.92/1.53 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.53 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.92/1.53 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.92/1.53 ) ) }.
% 0.92/1.53 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.92/1.53 .
% 0.92/1.53 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.92/1.53 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.53 tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.92/1.53 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.92/1.53 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.92/1.53 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.92/1.53 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.92/1.53 { class_Power_Opower( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.92/1.53 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.92/1.53 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.92/1.53 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.53 tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.92/1.53 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.92/1.53 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.92/1.53 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.92/1.53 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.53 tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.92/1.53 .
% 0.92/1.53 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.92/1.53 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.53 tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ),
% 0.92/1.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.92/1.53 ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.92/1.53 X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.92/1.53 ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.92/1.53 }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.53 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ),
% 0.92/1.53 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.92/1.53 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.92/1.53 ( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.92/1.53 ( tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.92/1.53 ( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.92/1.53 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.53 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.92/1.54 }.
% 0.92/1.54 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.92/1.54 ) ) }.
% 0.92/1.54 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.92/1.54 .
% 0.92/1.54 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.92/1.54 tc_Polynomial_Opoly( X ) ) }.
% 0.92/1.54 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.92/1.54 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.92/1.54 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.92/1.54 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.92/1.54 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.92/1.54 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ), hAPP(
% 0.92/1.54 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_ds____ ),
% 0.92/1.54 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_x____ ) ) ) ), hAPP( hAPP
% 0.92/1.54 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_x____ ), v_m____ )
% 0.92/1.54 ) }.
% 0.92/1.54
% 0.92/1.54 *** allocated 15000 integers for clauses
% 0.92/1.54 *** allocated 22500 integers for clauses
% 0.92/1.54 *** allocated 33750 integers for clauses
% 0.92/1.54 *** allocated 50625 integers for clauses
% 0.92/1.54 *** allocated 75937 integers for clauses
% 0.92/1.54 *** allocated 113905 integers for clauses
% 0.92/1.54 percentage equality = 0.215534, percentage horn = 0.893930
% 0.92/1.54 This is a problem with some equality
% 0.92/1.54
% 0.92/1.54
% 0.92/1.54
% 0.92/1.54 Options Used:
% 0.92/1.54
% 0.92/1.54 useres = 1
% 0.92/1.54 useparamod = 1
% 0.92/1.54 useeqrefl = 1
% 0.92/1.54 useeqfact = 1
% 0.92/1.54 usefactor = 1
% 0.92/1.54 usesimpsplitting = 0
% 0.92/1.54 usesimpdemod = 5
% 0.92/1.54 usesimpres = 3
% 0.92/1.54
% 0.92/1.54 resimpinuse = 1000
% 0.92/1.54 resimpclauses = 20000
% 0.92/1.54 substype = eqrewr
% 0.92/1.54 backwardsubs = 1
% 0.92/1.54 selectoldest = 5
% 0.92/1.54
% 0.92/1.54 litorderings [0] = split
% 0.92/1.54 litorderings [1] = extend the termordering, first sorting on arguments
% 0.92/1.54
% 0.92/1.54 termordering = kbo
% 0.92/1.54
% 0.92/1.54 litapriori = 0
% 0.92/1.54 termapriori = 1
% 0.92/1.54 litaposteriori = 0
% 0.92/1.54 termaposteriori = 0
% 0.92/1.54 demodaposteriori = 0
% 0.92/1.54 ordereqreflfact = 0
% 0.92/1.54
% 0.92/1.54 litselect = negord
% 0.92/1.54
% 0.92/1.54 maxweight = 15
% 0.92/1.54 maxdepth = 30000
% 0.92/1.54 maxlength = 115
% 0.92/1.54 maxnrvars = 195
% 0.92/1.54 excuselevel = 1
% 0.92/1.54 increasemaxweight = 1
% 0.92/1.54
% 0.92/1.54 maxselected = 10000000
% 0.92/1.54 maxnrclauses = 10000000
% 0.92/1.54
% 0.92/1.54 showgenerated = 0
% 0.92/1.54 showkept = 0
% 0.92/1.54 showselected = 0
% 0.92/1.54 showdeleted = 0
% 0.92/1.54 showresimp = 1
% 0.92/1.54 showstatus = 2000
% 0.92/1.54
% 0.92/1.54 prologoutput = 0
% 0.92/1.54 nrgoals = 5000000
% 0.92/1.54 totalproof = 1
% 0.92/1.54
% 0.92/1.54 Symbols occurring in the translation:
% 0.92/1.54
% 0.92/1.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.92/1.54 . [1, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.92/1.54 ! [4, 1] (w:0, o:116, a:1, s:1, b:0),
% 0.92/1.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.92/1.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.92/1.54 hAPP [38, 2] (w:1, o:234, a:1, s:1, b:0),
% 0.92/1.54 tc_RealDef_Oreal [39, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.92/1.54 tc_Complex_Ocomplex [40, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.92/1.54 v_ds____ [41, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.92/1.54 c_Polynomial_Opoly [42, 2] (w:1, o:235, a:1, s:1, b:0),
% 0.92/1.54 v_x____ [43, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.92/1.54 c_RealVector_Oof__real [44, 2] (w:1, o:237, a:1, s:1, b:0),
% 0.92/1.54 c_RealVector_Onorm__class_Onorm [45, 2] (w:1, o:236, a:1, s:1, b:0),
% 0.92/1.54
% 0.92/1.54 v_m____ [46, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.92/1.54 c_Orderings_Oord__class_Oless__eq [47, 3] (w:1, o:287, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 c_Groups_Oone__class_Oone [49, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.92/1.54 c_Groups_Otimes__class_Otimes [50, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.92/1.54 v_d____ [51, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.92/1.54 class_RealVector_Oreal__normed__algebra [55, 1] (w:1, o:123, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_RealVector_Oreal__algebra__1 [56, 1] (w:1, o:124, a:1, s:1, b:0
% 0.92/1.54 ),
% 0.92/1.54 class_RealVector_Oreal__normed__div__algebra [57, 1] (w:1, o:125, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 c_Groups_Ozero__class_Ozero [58, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.92/1.54 c_Orderings_Oord__class_Oless [59, 3] (w:1, o:288, a:1, s:1, b:0),
% 0.92/1.54 class_Orderings_Opreorder [60, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Ocomm__semiring__0 [63, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.92/1.54 tc_Polynomial_Opoly [64, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.92/1.54 class_Int_Oring__char__0 [70, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oidom [71, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.92/1.54 v_c____ [72, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.92/1.54 c_Rings_Oinverse__class_Odivide [73, 3] (w:1, o:289, a:1, s:1, b:0),
% 0.92/1.54
% 0.92/1.54 c_Polynomial_OpCons [74, 3] (w:1, o:291, a:1, s:1, b:0),
% 0.92/1.54 class_RealVector_Oreal__normed__vector [75, 1] (w:1, o:146, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_RealVector_Oreal__normed__algebra__1 [76, 1] (w:1, o:147, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Orderings_Olinorder [79, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Ocomm__semiring__1 [80, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.92/1.54 class_Orderings_Oorder [81, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.92/1.54 class_Orderings_Oord [85, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.92/1.54 tc_fun [89, 2] (w:1, o:265, a:1, s:1, b:0),
% 0.92/1.54 v_cs____ [90, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__idom [93, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__semiring__strict [94, 1] (w:1, o:153, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [95, 3] (w:1, o:
% 0.92/1.54 292, a:1, s:1, b:0),
% 0.92/1.54 v_p [97, 0] (w:1, o:71, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ozero [100, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.92/1.54 class_Fields_Ofield__inverse__zero [101, 1] (w:1, o:154, a:1, s:1, b:
% 0.92/1.54 0),
% 0.92/1.54 class_RealVector_Oreal__normed__field [102, 1] (w:1, o:159, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_RealVector_Oreal__field [103, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Odivision__ring__inverse__zero [104, 1] (w:1, o:162, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Rings_Odivision__ring [105, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Omult__zero [114, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oring__no__zero__divisors [115, 1] (w:1, o:170, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_Rings_Ono__zero__divisors [116, 1] (w:1, o:171, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Rings_Ozero__neq__one [117, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__ring [118, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__ring__strict [119, 1] (w:1, o:152, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_Rings_Oordered__cancel__semiring [120, 1] (w:1, o:173, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_Rings_Oordered__ring [121, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oordered__semiring [122, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.92/1.54
% 0.92/1.54 class_Rings_Oordered__comm__semiring [123, 1] (w:1, o:176, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_Rings_Olinordered__comm__semiring__strict [125, 1] (w:1, o:164
% 0.92/1.54 , a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__semidom [126, 1] (w:1, o:165, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Rings_Olinordered__semiring [129, 1] (w:1, o:166, a:1, s:1, b:0
% 0.92/1.54 ),
% 0.92/1.54 class_Fields_Olinordered__field__inverse__zero [131, 1] (w:1, o:155
% 0.92/1.54 , a:1, s:1, b:0),
% 0.92/1.54 class_Fields_Olinordered__field [132, 1] (w:1, o:156, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Fields_Ofield [135, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.92/1.54 c_Polynomial_Opos__poly [139, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.92/1.54 c_Polynomial_Oorder [140, 3] (w:1, o:290, a:1, s:1, b:0),
% 0.92/1.54 tc_Nat_Onat [141, 0] (w:1, o:94, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Omonoid__mult [142, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ocomm__monoid__mult [143, 1] (w:1, o:179, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Groups_Oab__semigroup__mult [148, 1] (w:1, o:180, a:1, s:1, b:0
% 0.92/1.54 ),
% 0.92/1.54 class_Groups_Oone [149, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.92/1.54 c_Polynomial_Opoly__rec [150, 5] (w:1, o:398, a:1, s:1, b:0),
% 0.92/1.54 hBOOL [155, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.92/1.54 c_fequal [158, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.92/1.54 c_If [159, 4] (w:1, o:365, a:1, s:1, b:0),
% 0.92/1.54 c_Groups_Osgn__class_Osgn [160, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__semiring__1__strict [163, 1] (w:1, o:167, a:
% 0.92/1.54 1, s:1, b:0),
% 0.92/1.54 c_Groups_Oplus__class_Oplus [164, 3] (w:1, o:293, a:1, s:1, b:0),
% 0.92/1.54 c_NthRoot_Oroot [166, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.92/1.54 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.92/1.54 167, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ocomm__monoid__add [168, 1] (w:1, o:190, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Groups_Omonoid__add [169, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Olinordered__ab__group__add [170, 1] (w:1, o:177, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Groups_Oordered__ab__semigroup__add__imp__le [171, 1] (w:1, o:
% 0.92/1.54 192, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Oordered__ab__semigroup__add [172, 1] (w:1, o:193, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Groups_Oordered__cancel__ab__semigroup__add [173, 1] (w:1, o:
% 0.92/1.54 194, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ocancel__semigroup__add [174, 1] (w:1, o:195, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 class_Groups_Ocancel__ab__semigroup__add [175, 1] (w:1, o:196, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Groups_Oab__semigroup__add [176, 1] (w:1, o:197, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Rings_Osemiring [183, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Ocomm__semiring [184, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Osgn__if [188, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Oordered__comm__monoid__add [189, 1] (w:1, o:199, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Rings_Olinordered__semiring__1 [190, 1] (w:1, o:168, a:1, s:1
% 0.92/1.54 , b:0),
% 0.92/1.54 c_Polynomial_Opcompose [193, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.92/1.54 c_RComplete_Onatceiling [195, 1] (w:1, o:200, a:1, s:1, b:0),
% 0.92/1.54 c_Complex_Oexpi [196, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.92/1.54 c_RComplete_Onatfloor [197, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.92/1.54 c_RealDef_Oreal [198, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.92/1.54 c_Divides_Odiv__class_Odiv [199, 3] (w:1, o:295, a:1, s:1, b:0),
% 0.92/1.54 c_Power_Opower__class_Opower [200, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.92/1.54 tc_Int_Oint [202, 0] (w:1, o:109, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oring__1__no__zero__divisors [203, 1] (w:1, o:183, a:1
% 0.92/1.54 , s:1, b:0),
% 0.92/1.54 class_Divides_Osemiring__div [204, 1] (w:1, o:205, a:1, s:1, b:0),
% 0.92/1.54 class_Power_Opower [205, 1] (w:1, o:206, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Osemiring__0 [206, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.92/1.54 c_Power_Opower_Opower [207, 3] (w:1, o:296, a:1, s:1, b:0),
% 0.92/1.54 c_SEQ_Odecseq [216, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Ocomm__ring__1 [217, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.92/1.54 c_Polynomial_Omonom [218, 3] (w:1, o:297, a:1, s:1, b:0),
% 0.92/1.54 c_Complex_Orcis [219, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.92/1.54 c_Divides_Odiv__class_Omod [225, 3] (w:1, o:298, a:1, s:1, b:0),
% 0.92/1.54 c_SEQ_OBseq [228, 2] (w:1, o:273, a:1, s:1, b:0),
% 0.92/1.54 c_SEQ_Oincseq [229, 2] (w:1, o:274, a:1, s:1, b:0),
% 0.92/1.54 c_Rings_Odvd__class_Odvd [232, 3] (w:1, o:299, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Odvd [233, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.92/1.54 c_Groups_Ouminus__class_Ouminus [236, 2] (w:1, o:275, a:1, s:1, b:0)
% 0.92/1.54 ,
% 0.92/1.54 class_Divides_Oring__div [237, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oring__1 [238, 1] (w:1, o:184, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Oring [239, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.92/1.54 class_Rings_Ocomm__ring [240, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Oab__group__add [241, 1] (w:1, o:207, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ogroup__add [242, 1] (w:1, o:208, a:1, s:1, b:0),
% 0.92/1.54 class_Groups_Ocancel__comm__monoid__add [244, 1] (w:1, o:209, a:1, s:
% 0.92/1.54 1, b:0),
% 0.92/1.54 tc_HOL_Obool [246, 0] (w:1, o:108, a:1, s:1, b:0),
% 0.92/1.54 alpha1 [248, 2] (w:1, o:276, a:1, s:1, b:1),
% 0.92/1.54 alpha2 [249, 3] (w:1, o:307, a:1, s:1, b:1),
% 0.92/1.54 alpha3 [250, 3] (w:1, o:312, a:1, s:1, b:1),
% 0.92/1.54 alpha4 [251, 4] (w:1, o:372, a:1, s:1, b:1),
% 0.92/1.54 alpha5 [252, 4] (w:1, o:378, a:1, s:1, b:1),
% 0.92/1.54 alpha6 [253, 3] (w:1, o:317, a:1, s:1, b:1),
% 0.92/1.54 alpha7 [254, 3] (w:1, o:322, a:1, s:1, b:1),
% 0.92/1.54 alpha8 [255, 3] (w:1, o:330, a:1, s:1, b:1),
% 0.92/1.54 alpha9 [256, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.35/1.72 alpha10 [257, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.35/1.72 alpha11 [258, 3] (w:1, o:301, a:1, s:1, b:1),
% 1.35/1.72 alpha12 [259, 3] (w:1, o:302, a:1, s:1, b:1),
% 1.35/1.72 alpha13 [260, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.35/1.72 alpha14 [261, 3] (w:1, o:304, a:1, s:1, b:1),
% 1.35/1.72 alpha15 [262, 3] (w:1, o:305, a:1, s:1, b:1),
% 1.35/1.72 alpha16 [263, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.35/1.72 alpha17 [264, 2] (w:1, o:277, a:1, s:1, b:1),
% 1.35/1.72 alpha18 [265, 2] (w:1, o:278, a:1, s:1, b:1),
% 1.35/1.72 alpha19 [266, 2] (w:1, o:279, a:1, s:1, b:1),
% 1.35/1.72 alpha20 [267, 4] (w:1, o:379, a:1, s:1, b:1),
% 1.35/1.72 alpha21 [268, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.35/1.72 alpha22 [269, 3] (w:1, o:309, a:1, s:1, b:1),
% 1.35/1.72 alpha23 [270, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.35/1.72 alpha24 [271, 2] (w:1, o:280, a:1, s:1, b:1),
% 1.35/1.72 alpha25 [272, 2] (w:1, o:281, a:1, s:1, b:1),
% 1.35/1.72 alpha26 [273, 2] (w:1, o:282, a:1, s:1, b:1),
% 1.35/1.72 alpha27 [274, 3] (w:1, o:310, a:1, s:1, b:1),
% 1.35/1.72 alpha28 [275, 3] (w:1, o:311, a:1, s:1, b:1),
% 1.35/1.72 alpha29 [276, 4] (w:1, o:381, a:1, s:1, b:1),
% 1.35/1.72 alpha30 [277, 4] (w:1, o:366, a:1, s:1, b:1),
% 1.35/1.72 alpha31 [278, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.35/1.72 alpha32 [279, 4] (w:1, o:368, a:1, s:1, b:1),
% 1.35/1.72 alpha33 [280, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.35/1.72 alpha34 [281, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.35/1.72 alpha35 [282, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.35/1.72 alpha36 [283, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.35/1.72 alpha37 [284, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.35/1.72 alpha38 [285, 4] (w:1, o:370, a:1, s:1, b:1),
% 1.35/1.72 alpha39 [286, 4] (w:1, o:371, a:1, s:1, b:1),
% 1.35/1.72 alpha40 [287, 4] (w:1, o:373, a:1, s:1, b:1),
% 1.35/1.72 alpha41 [288, 3] (w:1, o:339, a:1, s:1, b:1),
% 1.35/1.72 alpha42 [289, 3] (w:1, o:340, a:1, s:1, b:1),
% 1.35/1.72 alpha43 [290, 2] (w:1, o:283, a:1, s:1, b:1),
% 1.35/1.72 alpha44 [291, 4] (w:1, o:374, a:1, s:1, b:1),
% 1.35/1.72 alpha45 [292, 3] (w:1, o:341, a:1, s:1, b:1),
% 1.35/1.72 alpha46 [293, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.35/1.72 alpha47 [294, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.35/1.72 alpha48 [295, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.35/1.72 alpha49 [296, 4] (w:1, o:377, a:1, s:1, b:1),
% 1.35/1.72 alpha50 [297, 4] (w:1, o:382, a:1, s:1, b:1),
% 1.35/1.72 alpha51 [298, 4] (w:1, o:383, a:1, s:1, b:1),
% 1.35/1.72 alpha52 [299, 3] (w:1, o:313, a:1, s:1, b:1),
% 1.35/1.72 alpha53 [300, 3] (w:1, o:314, a:1, s:1, b:1),
% 1.35/1.72 alpha54 [301, 2] (w:1, o:284, a:1, s:1, b:1),
% 1.35/1.72 alpha55 [302, 3] (w:1, o:315, a:1, s:1, b:1),
% 1.35/1.72 alpha56 [303, 3] (w:1, o:316, a:1, s:1, b:1),
% 1.35/1.72 alpha57 [304, 4] (w:1, o:384, a:1, s:1, b:1),
% 1.35/1.72 alpha58 [305, 4] (w:1, o:385, a:1, s:1, b:1),
% 1.35/1.72 alpha59 [306, 4] (w:1, o:386, a:1, s:1, b:1),
% 1.35/1.72 alpha60 [307, 4] (w:1, o:387, a:1, s:1, b:1),
% 1.35/1.72 alpha61 [308, 4] (w:1, o:388, a:1, s:1, b:1),
% 1.35/1.72 alpha62 [309, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.35/1.72 alpha63 [310, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.35/1.72 alpha64 [311, 4] (w:1, o:389, a:1, s:1, b:1),
% 1.35/1.72 alpha65 [312, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.35/1.72 alpha66 [313, 3] (w:1, o:321, a:1, s:1, b:1),
% 1.35/1.72 alpha67 [314, 4] (w:1, o:390, a:1, s:1, b:1),
% 1.35/1.72 alpha68 [315, 4] (w:1, o:391, a:1, s:1, b:1),
% 1.35/1.72 alpha69 [316, 4] (w:1, o:392, a:1, s:1, b:1),
% 1.35/1.72 alpha70 [317, 4] (w:1, o:393, a:1, s:1, b:1),
% 1.35/1.72 alpha71 [318, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.35/1.72 alpha72 [319, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.35/1.72 alpha73 [320, 3] (w:1, o:325, a:1, s:1, b:1),
% 1.35/1.72 alpha74 [321, 3] (w:1, o:326, a:1, s:1, b:1),
% 1.35/1.72 alpha75 [322, 3] (w:1, o:327, a:1, s:1, b:1),
% 1.35/1.72 alpha76 [323, 4] (w:1, o:394, a:1, s:1, b:1),
% 1.35/1.72 alpha77 [324, 3] (w:1, o:328, a:1, s:1, b:1),
% 1.35/1.72 alpha78 [325, 3] (w:1, o:329, a:1, s:1, b:1),
% 1.35/1.72 alpha79 [326, 4] (w:1, o:395, a:1, s:1, b:1),
% 1.35/1.72 alpha80 [327, 3] (w:1, o:331, a:1, s:1, b:1),
% 1.35/1.72 alpha81 [328, 3] (w:1, o:332, a:1, s:1, b:1),
% 1.35/1.72 alpha82 [329, 2] (w:1, o:285, a:1, s:1, b:1),
% 1.35/1.72 alpha83 [330, 2] (w:1, o:286, a:1, s:1, b:1),
% 1.35/1.72 alpha84 [331, 3] (w:1, o:333, a:1, s:1, b:1),
% 1.35/1.72 skol1 [332, 2] (w:1, o:238, a:1, s:1, b:1),
% 1.35/1.72 skol2 [333, 1] (w:1, o:138, a:1, s:1, b:1),
% 1.35/1.72 skol3 [334, 2] (w:1, o:245, a:1, s:1, b:1),
% 16.64/17.05 skol4 [335, 3] (w:1, o:347, a:1, s:1, b:1),
% 16.64/17.05 skol5 [336, 0] (w:1, o:12, a:1, s:1, b:1),
% 16.64/17.05 skol6 [337, 0] (w:1, o:13, a:1, s:1, b:1),
% 16.64/17.05 skol7 [338, 0] (w:1, o:14, a:1, s:1, b:1),
% 16.64/17.05 skol8 [339, 0] (w:1, o:15, a:1, s:1, b:1),
% 16.64/17.05 skol9 [340, 0] (w:1, o:16, a:1, s:1, b:1),
% 16.64/17.05 skol10 [341, 1] (w:1, o:133, a:1, s:1, b:1),
% 16.64/17.05 skol11 [342, 0] (w:1, o:17, a:1, s:1, b:1),
% 16.64/17.05 skol12 [343, 3] (w:1, o:348, a:1, s:1, b:1),
% 16.64/17.05 skol13 [344, 1] (w:1, o:134, a:1, s:1, b:1),
% 16.64/17.05 skol14 [345, 2] (w:1, o:246, a:1, s:1, b:1),
% 16.64/17.05 skol15 [346, 2] (w:1, o:247, a:1, s:1, b:1),
% 16.64/17.05 skol16 [347, 2] (w:1, o:248, a:1, s:1, b:1),
% 16.64/17.05 skol17 [348, 1] (w:1, o:135, a:1, s:1, b:1),
% 16.64/17.05 skol18 [349, 1] (w:1, o:136, a:1, s:1, b:1),
% 16.64/17.05 skol19 [350, 1] (w:1, o:137, a:1, s:1, b:1),
% 16.64/17.05 skol20 [351, 2] (w:1, o:239, a:1, s:1, b:1),
% 16.64/17.05 skol21 [352, 2] (w:1, o:240, a:1, s:1, b:1),
% 16.64/17.05 skol22 [353, 1] (w:1, o:139, a:1, s:1, b:1),
% 16.64/17.05 skol23 [354, 2] (w:1, o:241, a:1, s:1, b:1),
% 16.64/17.05 skol24 [355, 2] (w:1, o:242, a:1, s:1, b:1),
% 16.64/17.05 skol25 [356, 3] (w:1, o:349, a:1, s:1, b:1),
% 16.64/17.05 skol26 [357, 1] (w:1, o:140, a:1, s:1, b:1),
% 16.64/17.05 skol27 [358, 2] (w:1, o:243, a:1, s:1, b:1),
% 16.64/17.05 skol28 [359, 2] (w:1, o:244, a:1, s:1, b:1),
% 16.64/17.05 skol29 [360, 1] (w:1, o:141, a:1, s:1, b:1),
% 16.64/17.05 skol30 [361, 2] (w:1, o:249, a:1, s:1, b:1),
% 16.64/17.05 skol31 [362, 2] (w:1, o:250, a:1, s:1, b:1),
% 16.64/17.05 skol32 [363, 2] (w:1, o:251, a:1, s:1, b:1),
% 16.64/17.05 skol33 [364, 2] (w:1, o:252, a:1, s:1, b:1),
% 16.64/17.05 skol34 [365, 3] (w:1, o:343, a:1, s:1, b:1),
% 16.64/17.05 skol35 [366, 4] (w:1, o:396, a:1, s:1, b:1),
% 16.64/17.05 skol36 [367, 2] (w:1, o:253, a:1, s:1, b:1),
% 16.64/17.05 skol37 [368, 3] (w:1, o:344, a:1, s:1, b:1),
% 16.64/17.05 skol38 [369, 3] (w:1, o:345, a:1, s:1, b:1),
% 16.64/17.05 skol39 [370, 3] (w:1, o:346, a:1, s:1, b:1),
% 16.64/17.05 skol40 [371, 3] (w:1, o:350, a:1, s:1, b:1),
% 16.64/17.05 skol41 [372, 2] (w:1, o:254, a:1, s:1, b:1),
% 16.64/17.05 skol42 [373, 2] (w:1, o:255, a:1, s:1, b:1),
% 16.64/17.05 skol43 [374, 2] (w:1, o:256, a:1, s:1, b:1),
% 16.64/17.05 skol44 [375, 3] (w:1, o:351, a:1, s:1, b:1),
% 16.64/17.05 skol45 [376, 2] (w:1, o:257, a:1, s:1, b:1),
% 16.64/17.05 skol46 [377, 2] (w:1, o:258, a:1, s:1, b:1),
% 16.64/17.05 skol47 [378, 3] (w:1, o:352, a:1, s:1, b:1),
% 16.64/17.05 skol48 [379, 3] (w:1, o:353, a:1, s:1, b:1),
% 16.64/17.05 skol49 [380, 3] (w:1, o:354, a:1, s:1, b:1),
% 16.64/17.05 skol50 [381, 3] (w:1, o:355, a:1, s:1, b:1),
% 16.64/17.05 skol51 [382, 3] (w:1, o:356, a:1, s:1, b:1),
% 16.64/17.05 skol52 [383, 3] (w:1, o:357, a:1, s:1, b:1),
% 16.64/17.05 skol53 [384, 3] (w:1, o:358, a:1, s:1, b:1),
% 16.64/17.05 skol54 [385, 2] (w:1, o:259, a:1, s:1, b:1),
% 16.64/17.05 skol55 [386, 2] (w:1, o:260, a:1, s:1, b:1),
% 16.64/17.05 skol56 [387, 2] (w:1, o:261, a:1, s:1, b:1),
% 16.64/17.05 skol57 [388, 3] (w:1, o:359, a:1, s:1, b:1),
% 16.64/17.05 skol58 [389, 4] (w:1, o:397, a:1, s:1, b:1),
% 16.64/17.05 skol59 [390, 3] (w:1, o:360, a:1, s:1, b:1),
% 16.64/17.05 skol60 [391, 2] (w:1, o:262, a:1, s:1, b:1),
% 16.64/17.05 skol61 [392, 1] (w:1, o:142, a:1, s:1, b:1),
% 16.64/17.05 skol62 [393, 2] (w:1, o:263, a:1, s:1, b:1),
% 16.64/17.05 skol63 [394, 3] (w:1, o:361, a:1, s:1, b:1),
% 16.64/17.05 skol64 [395, 3] (w:1, o:362, a:1, s:1, b:1),
% 16.64/17.05 skol65 [396, 3] (w:1, o:363, a:1, s:1, b:1),
% 16.64/17.05 skol66 [397, 2] (w:1, o:264, a:1, s:1, b:1),
% 16.64/17.05 skol67 [398, 3] (w:1, o:364, a:1, s:1, b:1).
% 16.64/17.05
% 16.64/17.05
% 16.64/17.05 Starting Search:
% 16.64/17.05
% 16.64/17.05 *** allocated 170857 integers for clauses
% 16.64/17.05
% 16.64/17.05 Intermediate Status:
% 16.64/17.05 Generated: 2779
% 16.64/17.05 Kept: 2036
% 16.64/17.05 Inuse: 0
% 16.64/17.05 Deleted: 0
% 16.64/17.05 Deletedinuse: 0
% 16.64/17.05
% 16.64/17.05 Resimplifying inuse:
% 16.64/17.05 Done
% 16.64/17.05
% 16.64/17.05 *** allocated 256285 integers for clauses
% 16.64/17.05 *** allocated 170857 integers for termspace/termends
% 16.64/17.05 Resimplifying inuse:
% 16.64/17.05 Done
% 16.64/17.05
% 16.64/17.05 *** allocated 384427 integers for clauses
% 16.64/17.05
% 16.64/17.05 Intermediate Status:
% 16.64/17.05 Generated: 7263
% 16.64/17.05 Kept: 4116
% 16.64/17.05 Inuse: 180
% 16.64/17.05 Deleted: 1
% 16.64/17.05 Deletedinuse: 0
% 16.64/17.05
% 16.64/17.05 Resimplifying inuse:
% 16.64/17.05 Done
% 16.64/17.05
% 16.64/17.05 Resimplifying inuse:
% 16.64/17.05 Done
% 16.64/17.05
% 16.64/17.05 *** allocated 256285 integers for termspace/termends
% 16.64/17.05
% 16.64/17.05 Intermediate Status:
% 16.64/17.05 Generated: 11391
% 16.64/17.05 Kept: 6706
% 16.64/17.05 Inuse: 270
% 16.64/17.05 Deleted: 1
% 16.64/17.05 Deletedinuse: 0
% 16.64/17.05
% 16.64/17.05 Resimplifying inuse:
% 16.64/17.05 Done
% 16.64/17.05
% 16.64/17.05 *** allocated 576640 integers for clauses
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 15864
% 43.06/43.43 Kept: 8725
% 43.06/43.43 Inuse: 334
% 43.06/43.43 Deleted: 2
% 43.06/43.43 Deletedinuse: 0
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 384427 integers for termspace/termends
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 20909
% 43.06/43.43 Kept: 10745
% 43.06/43.43 Inuse: 384
% 43.06/43.43 Deleted: 2
% 43.06/43.43 Deletedinuse: 0
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 864960 integers for clauses
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 25464
% 43.06/43.43 Kept: 12789
% 43.06/43.43 Inuse: 409
% 43.06/43.43 Deleted: 2
% 43.06/43.43 Deletedinuse: 0
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 29998
% 43.06/43.43 Kept: 14857
% 43.06/43.43 Inuse: 439
% 43.06/43.43 Deleted: 2
% 43.06/43.43 Deletedinuse: 0
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 576640 integers for termspace/termends
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 35029
% 43.06/43.43 Kept: 16917
% 43.06/43.43 Inuse: 474
% 43.06/43.43 Deleted: 2
% 43.06/43.43 Deletedinuse: 0
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 1297440 integers for clauses
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 38531
% 43.06/43.43 Kept: 18923
% 43.06/43.43 Inuse: 499
% 43.06/43.43 Deleted: 3
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying clauses:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 46772
% 43.06/43.43 Kept: 21584
% 43.06/43.43 Inuse: 524
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 51216
% 43.06/43.43 Kept: 23593
% 43.06/43.43 Inuse: 567
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 864960 integers for termspace/termends
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 57211
% 43.06/43.43 Kept: 26483
% 43.06/43.43 Inuse: 579
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 1946160 integers for clauses
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 68293
% 43.06/43.43 Kept: 30012
% 43.06/43.43 Inuse: 599
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 84931
% 43.06/43.43 Kept: 33888
% 43.06/43.43 Inuse: 609
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 91061
% 43.06/43.43 Kept: 36224
% 43.06/43.43 Inuse: 619
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 1297440 integers for termspace/termends
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 95380
% 43.06/43.43 Kept: 38237
% 43.06/43.43 Inuse: 637
% 43.06/43.43 Deleted: 257
% 43.06/43.43 Deletedinuse: 1
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 100778
% 43.06/43.43 Kept: 40394
% 43.06/43.43 Inuse: 684
% 43.06/43.43 Deleted: 259
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying clauses:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 107689
% 43.06/43.43 Kept: 42426
% 43.06/43.43 Inuse: 701
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 *** allocated 2919240 integers for clauses
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 114898
% 43.06/43.43 Kept: 44558
% 43.06/43.43 Inuse: 714
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 126535
% 43.06/43.43 Kept: 47131
% 43.06/43.43 Inuse: 729
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 139366
% 43.06/43.43 Kept: 49766
% 43.06/43.43 Inuse: 744
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 146399
% 43.06/43.43 Kept: 53603
% 43.06/43.43 Inuse: 764
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 162256
% 43.06/43.43 Kept: 55750
% 43.06/43.43 Inuse: 774
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 *** allocated 1946160 integers for termspace/termends
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 184907
% 43.06/43.43 Kept: 58853
% 43.06/43.43 Inuse: 784
% 43.06/43.43 Deleted: 359
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying clauses:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43
% 43.06/43.43 Intermediate Status:
% 43.06/43.43 Generated: 194331
% 43.06/43.43 Kept: 61039
% 43.06/43.43 Inuse: 799
% 43.06/43.43 Deleted: 443
% 43.06/43.43 Deletedinuse: 3
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 43.06/43.43
% 43.06/43.43 Resimplifying inuse:
% 43.06/43.43 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 198587
% 157.64/158.08 Kept: 63077
% 157.64/158.08 Inuse: 824
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 203340
% 157.64/158.08 Kept: 65107
% 157.64/158.08 Inuse: 856
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 *** allocated 4378860 integers for clauses
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 210135
% 157.64/158.08 Kept: 67410
% 157.64/158.08 Inuse: 894
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 218662
% 157.64/158.08 Kept: 69646
% 157.64/158.08 Inuse: 914
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 227697
% 157.64/158.08 Kept: 72056
% 157.64/158.08 Inuse: 934
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 240749
% 157.64/158.08 Kept: 74064
% 157.64/158.08 Inuse: 949
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 249059
% 157.64/158.08 Kept: 76309
% 157.64/158.08 Inuse: 969
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 *** allocated 2919240 integers for termspace/termends
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 257000
% 157.64/158.08 Kept: 78532
% 157.64/158.08 Inuse: 989
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 264623
% 157.64/158.08 Kept: 80578
% 157.64/158.08 Inuse: 1009
% 157.64/158.08 Deleted: 443
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying clauses:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 271649
% 157.64/158.08 Kept: 82600
% 157.64/158.08 Inuse: 1029
% 157.64/158.08 Deleted: 558
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 278522
% 157.64/158.08 Kept: 84782
% 157.64/158.08 Inuse: 1069
% 157.64/158.08 Deleted: 558
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 284595
% 157.64/158.08 Kept: 86804
% 157.64/158.08 Inuse: 1104
% 157.64/158.08 Deleted: 558
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 295294
% 157.64/158.08 Kept: 89610
% 157.64/158.08 Inuse: 1118
% 157.64/158.08 Deleted: 558
% 157.64/158.08 Deletedinuse: 3
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 302446
% 157.64/158.08 Kept: 91634
% 157.64/158.08 Inuse: 1149
% 157.64/158.08 Deleted: 559
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 309267
% 157.64/158.08 Kept: 93651
% 157.64/158.08 Inuse: 1173
% 157.64/158.08 Deleted: 559
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 317728
% 157.64/158.08 Kept: 95932
% 157.64/158.08 Inuse: 1189
% 157.64/158.08 Deleted: 559
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 325447
% 157.64/158.08 Kept: 97951
% 157.64/158.08 Inuse: 1208
% 157.64/158.08 Deleted: 559
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 330773
% 157.64/158.08 Kept: 99954
% 157.64/158.08 Inuse: 1230
% 157.64/158.08 Deleted: 559
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying clauses:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 336497
% 157.64/158.08 Kept: 101988
% 157.64/158.08 Inuse: 1284
% 157.64/158.08 Deleted: 799
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 *** allocated 6568290 integers for clauses
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 342015
% 157.64/158.08 Kept: 104084
% 157.64/158.08 Inuse: 1324
% 157.64/158.08 Deleted: 799
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 347758
% 157.64/158.08 Kept: 106308
% 157.64/158.08 Inuse: 1379
% 157.64/158.08 Deleted: 799
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 353044
% 157.64/158.08 Kept: 108610
% 157.64/158.08 Inuse: 1414
% 157.64/158.08 Deleted: 799
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08
% 157.64/158.08 Intermediate Status:
% 157.64/158.08 Generated: 358400
% 157.64/158.08 Kept: 110631
% 157.64/158.08 Inuse: 1441
% 157.64/158.08 Deleted: 799
% 157.64/158.08 Deletedinuse: 4
% 157.64/158.08
% 157.64/158.08 Resimplifying inuse:
% 157.64/158.08 Done
% 157.64/158.08
% 157.64/158.08 *** allocated 4378860 integers for termspace/tCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------