TSTP Solution File: SWW219+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW219+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:19 EDT 2022
% Result : Timeout 300.02s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW219+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : bliksem %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % DateTime : Sun Jun 5 22:21:28 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.98/1.58 *** allocated 10000 integers for termspace/termends
% 0.98/1.58 *** allocated 10000 integers for clauses
% 0.98/1.58 *** allocated 10000 integers for justifications
% 0.98/1.58 *** allocated 15000 integers for termspace/termends
% 0.98/1.58 *** allocated 22500 integers for termspace/termends
% 0.98/1.58 *** allocated 33750 integers for termspace/termends
% 0.98/1.58 Bliksem 1.12
% 0.98/1.58
% 0.98/1.58
% 0.98/1.58 Automatic Strategy Selection
% 0.98/1.58
% 0.98/1.58 *** allocated 50625 integers for termspace/termends
% 0.98/1.58 *** allocated 75937 integers for termspace/termends
% 0.98/1.58 *** allocated 113905 integers for termspace/termends
% 0.98/1.58
% 0.98/1.58 Clauses:
% 0.98/1.58
% 0.98/1.58 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ), !
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ) =
% 0.98/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.98/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ) ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( skol2, X ) )
% 0.98/1.58 , v_r ) }.
% 0.98/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), hAPP( skol2, X ) ) ),
% 0.98/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.58 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) ) ) }.
% 0.98/1.59 { ! alpha1( Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y )
% 0.98/1.59 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, v_s____ ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, v_s____ ), alpha1(
% 0.98/1.59 skol3( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, v_s____ ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol3( X ) ) }.
% 0.98/1.59 { ! alpha1( X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol4( Y ) ), v_r )
% 0.98/1.59 }.
% 0.98/1.59 { ! alpha1( X ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP
% 0.98/1.59 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol4( X ) ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), alpha1( X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol5( Y ) ), v_r )
% 0.98/1.59 }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol5( X ) ) ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol6( Y ) ), v_r )
% 0.98/1.59 }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol6( X ) ) ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) ) ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol7( Y ) ), v_r )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol7( X ) ) ) ) ), X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol8( Y ) ), v_r )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol8( X ) ) ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol9 ), v_r ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol9 ) ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol10 ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), v_r ) }.
% 0.98/1.59 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) ) }.
% 0.98/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.98/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.59 ( X, Y ) ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.59 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.98/1.59 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ), alpha29
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha2( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ), Y ), alpha29( X, Y, Z ) }.
% 0.98/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha3( X, Y, Z ), alpha30
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha3( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha30( X, Y, Z ) }.
% 0.98/1.59 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Z ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Y, Z ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Y, Z ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.59 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ), alpha31( X, Y
% 0.98/1.59 , Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha4( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), alpha31( X, Y, Z ) }.
% 0.98/1.59 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), alpha4( X, Y, Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha5( X, Y, Z ), alpha32
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha5( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), alpha32( X, Y, Z ) }.
% 0.98/1.59 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), alpha5( X, Y, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.98/1.59 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.98/1.59 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.98/1.59 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha6( X, Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha33( X,
% 0.98/1.59 Y ) }.
% 0.98/1.59 { ! alpha6( X, Y ), ! alpha33( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.59 { ! alpha33( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha33( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha33( X, Y ) }.
% 0.98/1.59 { ! alpha6( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha6( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha6( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.98/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.98/1.59 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.59 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.59 ( X, Y ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.98/1.59 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.98/1.59 Y = X }.
% 0.98/1.59 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.98/1.59 , X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.59 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.98/1.59 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.59 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.59 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.59 class_RealVector_Oreal__normed__field( X ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.59 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.59 ( X, Y ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), v_r ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol11 ) ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol12( X, Y, Z ) ) ), Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( skol66( X, Y ) ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol84( T, U ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol84( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol13( X, Y, Z ) ) ), Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( skol67( X, Y ) ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol81( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol85( T, U ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol81( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol85( X, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ) }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ), T = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, T ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.59 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_RealDef_Oreal ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.59 , X ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.59 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, T, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , Y, T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , T, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ), Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Z ), Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.98/1.59 Y ) ) = Y }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) = Y }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 0.98/1.59 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ), Y ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.59 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.98/1.59 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , Y, T ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ), Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.59 Z ) = Y }.
% 0.98/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.59 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.98/1.59 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 0.98/1.59 ( X ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.59 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) ) }.
% 0.98/1.59 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! alpha7( Y ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y )
% 0.98/1.59 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol15 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol15 ), alpha7(
% 0.98/1.59 skol68( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol15 ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, skol68( X ) ) }.
% 0.98/1.59 { ! alpha7( X ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol16( Y ) ), v_r
% 0.98/1.59 ) }.
% 0.98/1.59 { ! alpha7( X ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP
% 0.98/1.59 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol16( X ) ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ), v_r ), !
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), Y ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), alpha7( X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.59 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.59 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.59 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.59 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.98/1.59 c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.59 , c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.98/1.59 .
% 0.98/1.59 { alpha88( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.59 { alpha88( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.59 ( X, Y ), Z ) ) }.
% 0.98/1.59 { ! alpha88( X, Y, Z ), alpha91( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! alpha88( X, Y, Z ), alpha91( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! alpha91( X, Y, Z ), alpha88( X, Y, Z ) }.
% 0.98/1.59 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha88( X, Y, Z ) }.
% 0.98/1.59 { ! alpha91( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.59 }.
% 0.98/1.59 { ! alpha91( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.59 X, Y ), Z ) ), alpha91( X, Y, Z ) }.
% 0.98/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.59 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.59 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol17( X, Y ) ) }.
% 0.98/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), X ) = X }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.59 .
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.59 .
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.59 X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.59 }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol18( X ) ) }.
% 0.98/1.59 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol19( Z, Y ) ) }.
% 0.98/1.59 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol19( X,
% 0.98/1.59 Y ), X ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.59 ), alpha8( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha9( X, Y ), alpha34
% 0.98/1.59 ( X, Y ) }.
% 0.98/1.59 { ! alpha9( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! alpha34( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! alpha34( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! alpha34( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha34( X, Y ) }.
% 0.98/1.59 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.98/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha10( X, Y ), alpha35( X
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! alpha10( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! alpha35( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! alpha35( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! alpha35( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha35( X, Y ) }.
% 0.98/1.59 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.59 , X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.59 .
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.59 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol20 ), v_r ) }.
% 0.98/1.59 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), skol20 ) ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, skol69 ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.98/1.59 ( Z, skol21( X, Y, Z ) ), hAPP( Y, skol21( X, Y, Z ) ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.98/1.59 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.98/1.59 hAPP( Y, U ) ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 Z ), ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Y = Z }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.98/1.59 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.59 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.59 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! Z = Y }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.98/1.59 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.59 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.59 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), !
% 0.98/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.59 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ),
% 0.98/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol22( X, Y ) ) }.
% 0.98/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 tc_Nat_Onat, skol23( X, Y ), skol70( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 hAPP( Y, skol70( X, Y ) ), hAPP( Y, skol23( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.98/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.59 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.98/1.59 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.98/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ), Z = Y }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) }.
% 0.98/1.59 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.98/1.59 ) ) }.
% 0.98/1.59 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Z, T ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol24( X, Y ) ) }.
% 0.98/1.59 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.98/1.59 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.59 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.98/1.59 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.59 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.98/1.59 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_RComplete_Onatceiling( Y ), X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.59 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.59 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.59 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.59 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_RComplete_Onatceiling( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.98/1.59 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.98/1.59 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.98/1.59 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.98/1.59 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.98/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.59 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol25( Z, Y
% 0.98/1.59 ), Y ) }.
% 0.98/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.59 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.59 skol25( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.98/1.59 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.98/1.59 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.98/1.59 , skol25( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, skol26( X ) ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( skol26( X ) ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.98/1.59 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.98/1.59 c_RComplete_Onatfloor( X ) = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, X ) ) }.
% 0.98/1.59 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.98/1.59 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.98/1.59 }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.98/1.59 ), c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.59 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.98/1.59 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.59 , c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.98/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.98/1.59 , c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.98/1.59 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_RealDef_Oreal ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.59 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 0.98/1.59 c_RComplete_Onatfloor( X ), Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( skol27( X, Y ) ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol71( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Nat_OSuc( skol28( X, Y ) ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 0.98/1.59 .
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol29( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol73( X, Y, Z ) ) ), Z ),
% 0.98/1.59 c_SEQ_OBseq( X, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 tc_Nat_Onat, skol30( X, Y ), skol74( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.98/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 hAPP( Y, skol30( X, Y ) ), hAPP( Y, skol74( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.98/1.59 , Y ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.98/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.98/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.98/1.59 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.98/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.59 ( X ), Z, Y ) ) }.
% 0.98/1.59 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.59 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.59 ( X ), Z, Y ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.98/1.59 }.
% 0.98/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol31( Z, T ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y, skol75( X, Y ) ) )
% 0.98/1.59 ) ), skol31( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( Y, skol82( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, hAPP( Y
% 0.98/1.59 , T ) ) ) ), Z ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol32( Z, T ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( Y, Z ), c_Groups_Ouminus__class_Ouminus( X, skol76( X, Y ) ) ) ),
% 0.98/1.59 skol32( X, Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( Y, skol83( X, Y, Z, T ) ), c_Groups_Ouminus__class_Ouminus( X, T ) ) )
% 0.98/1.59 , Z ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol33( X, Y, Z ) ) ), Y ),
% 0.98/1.59 c_SEQ_OBseq( X, Z ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol34( Z, T ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol34( X, Y ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.98/1.59 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 0.98/1.59 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol35( U, W, V0, T )
% 0.98/1.59 ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z, T ) ) ), Z
% 0.98/1.59 ), c_SEQ_OBseq( X, Y ) }.
% 0.98/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.59 alpha11( X, Z ), alpha36( X, Y, Z ) }.
% 0.98/1.59 { ! alpha11( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.59 { ! alpha36( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.59 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol36( X
% 0.98/1.59 , Y, T ) ), Y ) }.
% 0.98/1.59 { ! alpha36( X, Y, Z ), alpha54( X, Y, Z, skol36( X, Y, Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha54( X
% 0.98/1.59 , Y, Z, T ), alpha36( X, Y, Z ) }.
% 0.98/1.59 { ! alpha54( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.98/1.59 ( T ) ) ) }.
% 0.98/1.59 { ! alpha54( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.98/1.59 hBOOL( hAPP( Z, T ) ), alpha54( X, Y, Z, T ) }.
% 0.98/1.59 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! alpha11( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 tc_Nat_Onat ) ) ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha11( X, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.98/1.59 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.98/1.59 .
% 0.98/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.59 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 0.98/1.59 ) ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 0.98/1.59 ), Y ) ) = Z }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.59 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 0.98/1.59 , Z ) ) = Y }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 0.98/1.59 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.59 ), ! U = T }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.59 ), ! Z = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.98/1.59 ) ), Z ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.59 ), U = Z, T = Y }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.59 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) ), Y ) }.
% 0.98/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.59 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.98/1.59 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.59 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.98/1.59 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.59 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.59 .
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.59 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.59 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.59 .
% 0.98/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 0.98/1.59 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.98/1.59 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.59 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.59 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.59 ) }.
% 0.98/1.59 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.98/1.59 = Y }.
% 0.98/1.59 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.98/1.59 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.98/1.59 ) ), T ), Y ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.59 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.98/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.98/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.59 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.98/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.59 , Y ), X ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ) }.
% 0.98/1.59 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.59 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.98/1.59 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.98/1.59 ), Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.59 , Y ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.59 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.98/1.59 X, Z, Y ) }.
% 0.98/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.98/1.59 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, Z, Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, Y, Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.59 , Y ) ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.59 ), Z ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.98/1.59 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.98/1.59 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Z ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.98/1.59 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.59 T, Y ), Z ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.98/1.59 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.98/1.59 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.98/1.59 ), Z ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.98/1.59 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.98/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol37( X, Y ) ) }.
% 0.98/1.59 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.98/1.59 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.59 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.98/1.59 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.98/1.59 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.98/1.59 , Y ) ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.59 alpha12( X, Y, Z ) }.
% 0.98/1.59 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.59 alpha37( X, Y, Z ) }.
% 0.98/1.59 { ! alpha12( X, Y, Z ), ! alpha37( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.59 { ! alpha37( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 alpha55( X, Y, Z ) }.
% 0.98/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha37( X, Y, Z ) }.
% 0.98/1.59 { ! alpha55( X, Y, Z ), alpha37( X, Y, Z ) }.
% 0.98/1.59 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.98/1.59 ), alpha64( X, Y, Z, T ) }.
% 0.98/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol38( X, T, U ), X ),
% 0.98/1.59 alpha55( X, Y, Z ) }.
% 0.98/1.59 { ! alpha64( X, Y, Z, skol38( X, Y, Z ) ), alpha55( X, Y, Z ) }.
% 0.98/1.59 { ! alpha64( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.59 hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.59 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol39( X, Y, T ) ), T
% 0.98/1.59 ), alpha64( X, Y, Z, T ) }.
% 0.98/1.59 { ! hBOOL( hAPP( Z, T ) ), alpha64( X, Y, Z, T ) }.
% 0.98/1.59 { ! alpha12( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.59 hBOOL( hAPP( Z, Y ) ) }.
% 0.98/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y, Z ) }.
% 0.98/1.59 { ! hBOOL( hAPP( Z, Y ) ), alpha12( X, Y, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.98/1.59 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.98/1.59 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.98/1.59 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.98/1.59 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) }.
% 0.98/1.59 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.59 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.59 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.59 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha13( X, Y
% 0.98/1.59 , Z ), alpha38( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha38( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha38( X, Y, Z ) }.
% 0.98/1.59 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha13( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ), alpha14( X, Y, Z ), alpha39( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha39( X, Y, Z ),
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ), Y ), alpha39( X, Y, Z ) }.
% 0.98/1.59 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.59 ( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha15( X, Y, Z, T ),
% 0.98/1.59 alpha40( X, Y, Z, T ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha40( X, Y, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.59 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha40( X, Y, Z, T ) }.
% 0.98/1.59 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.98/1.59 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha15( X, Y, Z, T ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha16( X, Y, Z, T ),
% 0.98/1.59 alpha41( X, Y, Z, T ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha41( X, Y, Z, T ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.59 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.59 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha41( X, Y, Z, T ) }.
% 0.98/1.59 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.59 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.98/1.59 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.59 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.98/1.59 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha16( X, Y, Z, T ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.98/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.59 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.98/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.98/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha42( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha17( X, Y, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha42( X, Y, Z, T ), !
% 0.98/1.60 alpha17( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha42( X, Y, Z, T ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha42(
% 0.98/1.60 X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha17( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { Y = c_Groups_Ozero__class_Ozero( X ), alpha17( X, Y, Z ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha17( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha43( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha18( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha43( X, Y, Z, T ), !
% 0.98/1.60 alpha18( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.98/1.60 { ! alpha43( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha43( X, Y, Z, T ) }.
% 0.98/1.60 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha43(
% 0.98/1.60 X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha18( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { Z = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha18( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.98/1.60 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.98/1.60 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.60 Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.60 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.60 ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.60 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.60 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.60 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.60 ), X ) ) }.
% 0.98/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.98/1.60 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), Y ), alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.98/1.60 Z ), Y ), alpha56( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.98/1.60 , T ), ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.60 { ! alpha56( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha65( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , alpha56( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha65( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha65( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha65( X, Y, Z, T ), alpha19( X, Y, Z ) }.
% 0.98/1.60 { ! alpha74( X, Y, Z, T ), ! alpha19( X, Y, Z ), alpha65( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha74( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha74( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha74( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha44( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha44( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha19( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha19( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ), alpha45( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 Z, Y ) ), alpha57( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha45( X, Y, Z
% 0.98/1.60 , T ), ! alpha57( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha57( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha66( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha57( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha66( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha66( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha66( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.98/1.60 { ! alpha75( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha66( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha75( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha75( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha75( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha45( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 alpha45( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha45( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha20( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha20( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.98/1.60 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.98/1.60 ), Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), Y ), alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.98/1.60 , T, Z ), Y ), alpha58( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 0.98/1.60 , T ), ! alpha58( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.98/1.60 { ! alpha58( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), alpha67( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.98/1.60 , alpha58( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha67( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha67( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha67( X, Y, Z, T ), alpha21( X, Y, Z ) }.
% 0.98/1.60 { ! alpha76( X, Y, Z, T ), ! alpha21( X, Y, Z ), alpha67( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha76( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha76( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha76( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha46( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.98/1.60 alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha46( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha21( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.98/1.60 , Y ), alpha21( X, Y, Z ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), alpha47( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, Z, Y ) ), alpha59( X, Y, Z, T ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 0.98/1.60 , T ), ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.98/1.60 { ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), alpha68( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.98/1.60 , alpha59( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha68( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha68( X, Y, Z, T ), alpha77( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha68( X, Y, Z, T ), alpha22( X, Y, T ) }.
% 0.98/1.60 { ! alpha77( X, Y, Z, T ), ! alpha22( X, Y, T ), alpha68( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha77( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 alpha77( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha77( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.98/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.98/1.60 alpha47( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha47( X, Y, Z, T )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.98/1.60 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.98/1.60 , alpha22( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) ), alpha22( X, Y, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.60 alpha23( X, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.98/1.60 alpha48( X, Y, Z ) }.
% 0.98/1.60 { ! alpha23( X, Z ), ! alpha48( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.60 { ! alpha48( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 alpha60( X, Y, Z ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha48( X, Y, Z ) }.
% 0.98/1.60 { ! alpha60( X, Y, Z ), alpha48( X, Y, Z ) }.
% 0.98/1.60 { ! alpha60( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.98/1.60 ), alpha69( X, Y, Z, T ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol40( X, T, U ), X ),
% 0.98/1.60 alpha60( X, Y, Z ) }.
% 0.98/1.60 { ! alpha69( X, Y, Z, skol40( X, Y, Z ) ), alpha60( X, Y, Z ) }.
% 0.98/1.60 { ! alpha69( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.98/1.60 hBOOL( hAPP( Z, U ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, skol41( U, W, Z, V0 ) ) ), alpha69( X, Y, Z, T ) }.
% 0.98/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol41( X, Y, Z, T ) )
% 0.98/1.60 , T ), alpha69( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha23( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha23( X, Y ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha23
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.98/1.60 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 0.98/1.60 ), T, Z ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), Z, Y ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.98/1.60 ( X ), T, Z ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.60 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.98/1.60 ( tc_Nat_Onat, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.98/1.60 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol42( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol42( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43( Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol43( X ) ) ) }.
% 0.98/1.60 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol44( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol44( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol45( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol45( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol46( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__field( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.98/1.60 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol46( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol47( Y ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol47( X ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol48( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol48( X, Y ) ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol49( Z, T ) ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol49( X, Y ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.60 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.98/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.60 skol50( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, skol50( X, T, U ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), skol50( X, Y, Z ) ), Z ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.60 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.60 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.60 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.60 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.60 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.98/1.60 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), Y ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.60 ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.98/1.60 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.60 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.60 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.60 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.60 ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.60 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.60 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.60 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.98/1.60 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.98/1.60 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.98/1.60 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( X ) }.
% 0.98/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.98/1.60 = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 0.98/1.60 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Nat_Onat ) ) = Y }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.60 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.60 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.60 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.60 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.98/1.60 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 0.98/1.60 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.60 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.60 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.60 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.98/1.60 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 0.98/1.60 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Y ), Z = Y }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.98/1.60 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.98/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.98/1.60 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.98/1.60 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.98/1.60 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.98/1.60 c_Groups_Oone__class_Oone( X ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.60 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.60 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.98/1.60 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.98/1.60 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.98/1.60 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol51( X, Y ) ), Y
% 0.98/1.60 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.98/1.60 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.98/1.60 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.98/1.60 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Z, Y ), X ) }.
% 0.98/1.60 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha89( X,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, T, Z ) = Y }.
% 0.98/1.60 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha89( X,
% 0.98/1.60 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, T, Z ) = Y }.
% 0.98/1.60 { ! alpha89( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! alpha89( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha89( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.98/1.60 , alpha89( X, Y ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.60 alpha24( X, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.60 alpha49( X, Y, Z ) }.
% 0.98/1.60 { ! alpha24( X, Z ), ! alpha49( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.60 { ! alpha49( X, Y, Z ), alpha61( X, Y, Z ) }.
% 0.98/1.60 { ! alpha49( X, Y, Z ), alpha70( X, Y, Z ) }.
% 0.98/1.60 { ! alpha61( X, Y, Z ), ! alpha70( X, Y, Z ), alpha49( X, Y, Z ) }.
% 0.98/1.60 { ! alpha70( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha78( X, Y, Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha70( X, Y, Z ) }.
% 0.98/1.60 { ! alpha78( X, Y, Z ), alpha70( X, Y, Z ) }.
% 0.98/1.60 { ! alpha78( X, Y, Z ), ! alpha82( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ), alpha78( X, Y, Z ) }.
% 0.98/1.60 { alpha82( X, Y, skol52( X, Y, Z ) ), alpha78( X, Y, Z ) }.
% 0.98/1.60 { ! alpha82( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 skol53( X, T, U ) ) }.
% 0.98/1.60 { ! alpha82( X, Y, Z ), alpha86( X, Y, Z, skol53( X, Y, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha86( X, Y, Z
% 0.98/1.60 , T ), alpha82( X, Y, Z ) }.
% 0.98/1.60 { ! alpha86( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! alpha86( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha86( X,
% 0.98/1.60 Y, Z, T ) }.
% 0.98/1.60 { ! alpha61( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha71( X, Y, Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ), alpha61( X, Y, Z ) }.
% 0.98/1.60 { ! alpha71( X, Y, Z ), alpha61( X, Y, Z ) }.
% 0.98/1.60 { ! alpha71( X, Y, Z ), ! alpha79( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, skol54( T, U, Z ) ) ), alpha71( X, Y, Z ) }.
% 0.98/1.60 { alpha79( X, Y, skol54( X, Y, Z ) ), alpha71( X, Y, Z ) }.
% 0.98/1.60 { ! alpha79( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol55( T, U, W ) ) }.
% 0.98/1.60 { ! alpha79( X, Y, Z ), alpha83( X, Y, Z, skol55( X, Y, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha83( X, Y, Z, T )
% 0.98/1.60 , alpha79( X, Y, Z ) }.
% 0.98/1.60 { ! alpha83( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! alpha83( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha83( X,
% 0.98/1.60 Y, Z, T ) }.
% 0.98/1.60 { ! alpha24( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.60 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha24( X, Y ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha24
% 0.98/1.60 ( X, Y ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.98/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.98/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.60 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.60 alpha25( X, Y, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.98/1.60 alpha50( X, Y, Z ) }.
% 0.98/1.60 { ! alpha25( X, Y, Z ), ! alpha50( X, Y, Z ), hBOOL( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.60 { ! alpha50( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.98/1.60 { ! alpha50( X, Y, Z ), alpha72( X, Y, Z ) }.
% 0.98/1.60 { ! alpha62( X, Y, Z ), ! alpha72( X, Y, Z ), alpha50( X, Y, Z ) }.
% 0.98/1.60 { ! alpha72( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha80( X, Y, Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha72( X, Y, Z ) }.
% 0.98/1.60 { ! alpha80( X, Y, Z ), alpha72( X, Y, Z ) }.
% 0.98/1.60 { ! alpha80( X, Y, Z ), ! alpha84( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, skol56( T, U, Z ) ) ), alpha80( X, Y, Z ) }.
% 0.98/1.60 { alpha84( X, Y, skol56( X, Y, Z ) ), alpha80( X, Y, Z ) }.
% 0.98/1.60 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha84( X, Y, Z ), alpha87( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha87( X, Y, Z
% 0.98/1.60 ), alpha84( X, Y, Z ) }.
% 0.98/1.60 { ! alpha87( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! alpha87( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol57( X, Y,
% 0.98/1.60 Z ) ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha87( X,
% 0.98/1.60 Y, Z ) }.
% 0.98/1.60 { ! alpha62( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha73( X, Y, Z ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ), alpha62( X, Y, Z ) }.
% 0.98/1.60 { ! alpha73( X, Y, Z ), alpha62( X, Y, Z ) }.
% 0.98/1.60 { ! alpha73( X, Y, Z ), ! alpha81( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, skol58( T, U, Z ) ) ), alpha73( X, Y, Z ) }.
% 0.98/1.60 { alpha81( X, Y, skol58( X, Y, Z ) ), alpha73( X, Y, Z ) }.
% 0.98/1.60 { ! alpha81( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.98/1.60 { ! alpha81( X, Y, Z ), alpha85( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha85( X, Y, Z ),
% 0.98/1.60 alpha81( X, Y, Z ) }.
% 0.98/1.60 { ! alpha85( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.98/1.60 }.
% 0.98/1.60 { ! alpha85( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.98/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol59( X, Y,
% 0.98/1.60 Z ) ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha85( X,
% 0.98/1.60 Y, Z ) }.
% 0.98/1.60 { ! alpha25( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.60 hBOOL( hAPP( Z, Y ) ) }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha25( X, Y, Z ) }.
% 0.98/1.60 { ! hBOOL( hAPP( Z, Y ) ), alpha25( X, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.98/1.60 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha90( X,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Z, Y ) = X }.
% 0.98/1.60 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha90( X,
% 0.98/1.60 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Z, Y ) = X }.
% 0.98/1.60 { ! alpha90( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! alpha90( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha90( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.98/1.60 , alpha90( X, Y ) }.
% 0.98/1.60 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol60( X, Y ) ) }.
% 0.98/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.98/1.60 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 0.98/1.60 ) ), ! alpha26( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), alpha26( X, Y, skol61( X, Y, Z ), skol77( X, Y, Z )
% 0.98/1.60 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 0.98/1.60 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol61( X, Y, Z ) ), skol77
% 0.98/1.60 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 0.98/1.60 { ! alpha26( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha51( X, Y, Z, T )
% 0.98/1.60 , alpha26( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha51( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! alpha51( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha51( X,
% 0.98/1.60 Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha27( X, Y, T,
% 0.98/1.60 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha27( X, Y, skol62( X, Y
% 0.98/1.60 , Z ), skol78( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 0.98/1.60 skol62( X, Y, Z ) ), skol78( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.98/1.60 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 0.98/1.60 ) }.
% 0.98/1.60 { ! alpha27( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha52( X, Y, Z
% 0.98/1.60 , T ), alpha27( X, Y, Z, T ) }.
% 0.98/1.60 { ! alpha52( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! alpha52( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha52( X,
% 0.98/1.60 Y, Z, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 0.98/1.60 ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.98/1.60 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.60 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.98/1.60 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.98/1.60 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.60 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol63( Z, T ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol63( X, Y ) ), X ) =
% 0.98/1.60 Y }.
% 0.98/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, X, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.98/1.60 }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.98/1.60 }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.98/1.60 = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ) }.
% 0.98/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.98/1.60 ( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ) ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.98/1.60 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.98/1.60 }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.98/1.60 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ) ) = X }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) = X }.
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.98/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha28( X, Y ) }.
% 0.98/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! alpha28( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! alpha28( X, Y ), alpha53( X, Y ), alpha63( X, Y ) }.
% 0.98/1.60 { ! alpha53( X, Y ), alpha28( X, Y ) }.
% 0.98/1.60 { ! alpha63( X, Y ), alpha28( X, Y ) }.
% 0.98/1.60 { ! alpha63( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! alpha63( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha63( X, Y ) }.
% 0.98/1.60 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha53( X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.98/1.60 , Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.98/1.60 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.98/1.60 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.98/1.60 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.98/1.60 ( tc_Int_Oint, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.98/1.60 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.98/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.98/1.60 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.98/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Int_Oint ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.98/1.60 tc_Int_Oint ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Int_Oint, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3div( X, Y ) =
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 0.98/1.60 ( tc_Int_Oint, X, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol64( Z, T ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol64( X, Y ) ), X ) =
% 0.98/1.60 Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.98/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.98/1.60 skol64( X, Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 W ) ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.60 Z ) ), U ), T ) = Y }.
% 0.98/1.60 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.98/1.60 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), Z ), U ), Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.98/1.60 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.60 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.98/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.98/1.60 Z ) ), Y ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.98/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.98/1.60 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.98/1.60 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.98/1.60 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.98/1.60 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.98/1.60 , U ), Z ) }.
% 0.98/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.98/1.60 Y ) ), Y ) }.
% 0.98/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.98/1.60 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.98/1.60 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, Y ), Y ) }.
% 0.98/1.60 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.98/1.60 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.98/1.60 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.98/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.98/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.60 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.98/1.60 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, Y ), X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.98/1.60 ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.98/1.60 ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.60 tc_Nat_Onat, Z, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.60 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.98/1.60 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.98/1.60 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.98/1.60 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.60 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.98/1.60 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.98/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.98/1.60 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.60 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.98/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.60 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.98/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.98/1.60 X, Z, Y ) }.
% 0.98/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.60 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.60 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.98/1.60 ( tc_fun( Y, X ) ) }.
% 0.98/1.60 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.98/1.60 ) ) }.
% 0.98/1.60 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.98/1.60 .
% 0.98/1.60 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.98/1.60 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.98/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.60 tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.98/1.60 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.98/1.60 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.98/1.60 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.98/1.60 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.98/1.60 { class_Power_Opower( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.98/1.60 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.98/1.60 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.98/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.60 tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.98/1.60 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.98/1.60 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.98/1.60 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.98/1.60 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.98/1.60 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.98/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.60 tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.98/1.60 .
% 0.98/1.60 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.98/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.60 tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.98/1.60 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ),
% 0.98/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ),
% 0.98/1.61 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.98/1.61 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.98/1.61 ( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.98/1.61 ( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( X, skol65( X
% 0.98/1.61 ) ) ), v_r ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.98/1.61 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.98/1.61 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), hAPP( X, skol79( X ) ) )
% 0.98/1.61 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_s____ ),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.98/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.98/1.61 tc_Nat_Onat, c_Nat_OSuc( skol79( X ) ) ) ) ) ), v_thesis____ }.
% 0.98/1.61 { ! v_thesis____ }.
% 0.98/1.61
% 0.98/1.61 *** allocated 15000 integers for clauses
% 0.98/1.61 *** allocated 22500 integers for clauses
% 0.98/1.61 *** allocated 33750 integers for clauses
% 0.98/1.61 *** allocated 50625 integers for clauses
% 0.98/1.61 *** allocated 75937 integers for clauses
% 0.98/1.61 *** allocated 113905 integers for clauses
% 0.98/1.61 percentage equality = 0.230918, percentage horn = 0.904000
% 0.98/1.61 This is a problem with some equality
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61 Options Used:
% 0.98/1.61
% 0.98/1.61 useres = 1
% 0.98/1.61 useparamod = 1
% 0.98/1.61 useeqrefl = 1
% 0.98/1.61 useeqfact = 1
% 0.98/1.61 usefactor = 1
% 0.98/1.61 usesimpsplitting = 0
% 0.98/1.61 usesimpdemod = 5
% 0.98/1.61 usesimpres = 3
% 0.98/1.61
% 0.98/1.61 resimpinuse = 1000
% 0.98/1.61 resimpclauses = 20000
% 0.98/1.61 substype = eqrewr
% 0.98/1.61 backwardsubs = 1
% 0.98/1.61 selectoldest = 5
% 0.98/1.61
% 0.98/1.61 litorderings [0] = split
% 0.98/1.61 litorderings [1] = extend the termordering, first sorting on arguments
% 0.98/1.61
% 0.98/1.61 termordering = kbo
% 0.98/1.61
% 0.98/1.61 litapriori = 0
% 0.98/1.61 termapriori = 1
% 0.98/1.61 litaposteriori = 0
% 0.98/1.61 termaposteriori = 0
% 0.98/1.61 demodaposteriori = 0
% 0.98/1.61 ordereqreflfact = 0
% 0.98/1.61
% 0.98/1.61 litselect = negord
% 0.98/1.61
% 0.98/1.61 maxweight = 15
% 0.98/1.61 maxdepth = 30000
% 0.98/1.61 maxlength = 115
% 0.98/1.61 maxnrvars = 195
% 0.98/1.61 excuselevel = 1
% 0.98/1.61 increasemaxweight = 1
% 0.98/1.61
% 0.98/1.61 maxselected = 10000000
% 0.98/1.61 maxnrclauses = 10000000
% 0.98/1.61
% 0.98/1.61 showgenerated = 0
% 0.98/1.61 showkept = 0
% 0.98/1.61 showselected = 0
% 0.98/1.61 showdeleted = 0
% 0.98/1.61 showresimp = 1
% 0.98/1.61 showstatus = 2000
% 0.98/1.61
% 0.98/1.61 prologoutput = 0
% 0.98/1.61 nrgoals = 5000000
% 0.98/1.61 totalproof = 1
% 0.98/1.61
% 0.98/1.61 Symbols occurring in the translation:
% 0.98/1.61
% 0.98/1.61 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.98/1.61 . [1, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.98/1.61 ! [4, 1] (w:0, o:119, a:1, s:1, b:0),
% 0.98/1.61 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.98/1.61 hAPP [38, 2] (w:1, o:243, a:1, s:1, b:0),
% 0.98/1.61 tc_RealDef_Oreal [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.98/1.61 v_r [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.98/1.61 c_Orderings_Oord__class_Oless__eq [42, 3] (w:1, o:305, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 tc_Complex_Ocomplex [45, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.98/1.61 c_RealVector_Onorm__class_Onorm [46, 2] (w:1, o:244, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 v_p [47, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Opoly [48, 2] (w:1, o:245, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ouminus__class_Ouminus [49, 2] (w:1, o:247, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 c_Groups_Oone__class_Oone [50, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.98/1.61 c_Orderings_Oord__class_Oless [51, 3] (w:1, o:306, a:1, s:1, b:0),
% 0.98/1.61 v_s____ [53, 0] (w:1, o:35, a:1, s:1, b:0),
% 0.98/1.61 tc_Nat_Onat [55, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.98/1.61 c_Nat_OSuc [56, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.98/1.61 c_RealDef_Oreal [57, 2] (w:1, o:248, a:1, s:1, b:0),
% 0.98/1.61 c_Rings_Oinverse__class_Odivide [58, 3] (w:1, o:307, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 c_Groups_Oplus__class_Oplus [59, 3] (w:1, o:308, a:1, s:1, b:0),
% 0.98/1.61 class_RealVector_Oreal__normed__vector [72, 1] (w:1, o:127, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Fields_Olinordered__field [75, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 class_RealVector_Oreal__normed__field [76, 1] (w:1, o:129, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Fields_Olinordered__field__inverse__zero [78, 1] (w:1, o:130
% 0.98/1.61 , a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ogroup__add [81, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.98/1.61 class_Fields_Ofield__inverse__zero [89, 1] (w:1, o:131, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_RealVector_Oreal__normed__algebra__1 [90, 1] (w:1, o:134, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__semidom [96, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Groups_Oordered__comm__monoid__add [97, 1] (w:1, o:138, a:1, s:
% 0.98/1.61 1, b:0),
% 0.98/1.61 class_Rings_Odivision__ring [98, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ozero [99, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__idom [100, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oab__semigroup__add [101, 1] (w:1, o:147, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Groups_Ocancel__semigroup__add [103, 1] (w:1, o:148, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Groups_Ocancel__ab__semigroup__add [104, 1] (w:1, o:149, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Groups_Oone [105, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Omonoid__add [106, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ocomm__monoid__add [107, 1] (w:1, o:153, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Groups_Olinordered__ab__group__add [108, 1] (w:1, o:151, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [109, 1] (w:1, o:
% 0.98/1.61 154, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__ab__semigroup__add [110, 1] (w:1, o:155, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__cancel__ab__semigroup__add [112, 1] (w:1, o:
% 0.98/1.61 156, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ozero__neq__one [113, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oordered__ab__group__add [114, 1] (w:1, o:158, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Odivision__ring__inverse__zero [115, 1] (w:1, o:159, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Groups_Oab__group__add [116, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.98/1.61 hBOOL [124, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Opreorder [130, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ocomm__ring [132, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.98/1.61 tc_Polynomial_Opoly [133, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ocomm__semiring__1 [134, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 class_Rings_Ocomm__semiring__0 [136, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 class_Orderings_Oord [137, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.98/1.61 tc_fun [138, 2] (w:1, o:283, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Olinorder [139, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.98/1.61 class_Orderings_Oorder [140, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.98/1.61 class_Int_Oring__char__0 [142, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oidom [143, 1] (w:1, o:182, a:1, s:1, b:0),
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [145, 2] (w:1, o:
% 0.98/1.61 246, a:1, s:1, b:0),
% 0.98/1.61 c_Polynomial_Oorder [146, 3] (w:1, o:309, a:1, s:1, b:0),
% 0.98/1.61 c_SEQ_Odecseq [148, 2] (w:1, o:284, a:1, s:1, b:0),
% 0.98/1.61 class_Lattices_Oboolean__algebra [149, 1] (w:1, o:184, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Groups_Ouminus [151, 1] (w:1, o:185, a:1, s:1, b:0),
% 0.98/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.98/1.61 152, 1] (w:1, o:205, a:1, s:1, b:0),
% 0.98/1.61 c_RComplete_Onatceiling [153, 1] (w:1, o:206, a:1, s:1, b:0),
% 0.98/1.61 c_RComplete_Onatfloor [154, 1] (w:1, o:207, a:1, s:1, b:0),
% 0.98/1.61 c_Divides_Odiv__class_Odiv [156, 3] (w:1, o:310, a:1, s:1, b:0),
% 0.98/1.61 c_SEQ_OBseq [157, 2] (w:1, o:285, a:1, s:1, b:0),
% 0.98/1.61 c_SEQ_Oincseq [158, 2] (w:1, o:286, a:1, s:1, b:0),
% 0.98/1.61 class_Divides_Osemiring__div [159, 1] (w:1, o:209, a:1, s:1, b:0),
% 0.98/1.61 class_Fields_Ofield [160, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.98/1.61 c_Divides_Odiv__class_Omod [162, 3] (w:1, o:311, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Otimes__class_Otimes [165, 1] (w:1, o:210, a:1, s:1, b:0),
% 0.98/1.61 class_RealVector_Oreal__normed__algebra [166, 1] (w:1, o:186, a:1, s:
% 0.98/1.61 1, b:0),
% 0.98/1.61 class_Rings_Oring [173, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Oab__semigroup__mult [175, 1] (w:1, o:211, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_RealVector_Oreal__normed__div__algebra [176, 1] (w:1, o:188, a:
% 0.98/1.61 1, s:1, b:0),
% 0.98/1.61 class_Groups_Omonoid__mult [177, 1] (w:1, o:212, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ocomm__monoid__mult [178, 1] (w:1, o:213, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Rings_Ocomm__semiring [179, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Osemiring [181, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Ono__zero__divisors [184, 1] (w:1, o:199, a:1, s:1, b:0)
% 0.98/1.61 ,
% 0.98/1.61 class_Rings_Oring__no__zero__divisors [185, 1] (w:1, o:189, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Omult__zero [186, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.98/1.61 class_Lattices_Oab__semigroup__idem__mult [187, 1] (w:1, o:183, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Divides_Oring__div [188, 1] (w:1, o:208, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__ring [189, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__ring__strict [190, 1] (w:1, o:136, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Oordered__cancel__semiring [191, 1] (w:1, o:200, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Oordered__ring [192, 1] (w:1, o:201, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oordered__semiring [193, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.98/1.61
% 0.98/1.61 class_Rings_Oordered__comm__semiring [194, 1] (w:1, o:203, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Olinordered__semiring__strict [195, 1] (w:1, o:193, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__comm__semiring__strict [196, 1] (w:1, o:194
% 0.98/1.61 , a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oring__1__no__zero__divisors [197, 1] (w:1, o:190, a:1
% 0.98/1.61 , s:1, b:0),
% 0.98/1.61 class_Rings_Ocomm__ring__1 [198, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Olinordered__semiring [199, 1] (w:1, o:195, a:1, s:1, b:0
% 0.98/1.61 ),
% 0.98/1.61 class_Rings_Olinordered__semiring__1 [202, 1] (w:1, o:196, a:1, s:1
% 0.98/1.61 , b:0),
% 0.98/1.61 class_Rings_Olinordered__semiring__1__strict [203, 1] (w:1, o:197, a:
% 0.98/1.61 1, s:1, b:0),
% 0.98/1.61 c_Power_Opower__class_Opower [209, 1] (w:1, o:214, a:1, s:1, b:0),
% 0.98/1.61 tc_Int_Oint [210, 0] (w:1, o:112, a:1, s:1, b:0),
% 0.98/1.61 class_Power_Opower [211, 1] (w:1, o:215, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Osemiring__0 [212, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.98/1.61 class_Rings_Oring__1 [213, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.98/1.61 c_Power_Opower_Opower [215, 3] (w:1, o:312, a:1, s:1, b:0),
% 0.98/1.61 c_Complex_Orcis [224, 2] (w:1, o:287, a:1, s:1, b:0),
% 0.98/1.61 c_SMT_Oz3mod [231, 2] (w:1, o:288, a:1, s:1, b:0),
% 0.98/1.61 c_SMT_Oz3div [232, 2] (w:1, o:289, a:1, s:1, b:0),
% 0.98/1.61 c_Groups_Ominus__class_Ominus [233, 3] (w:1, o:313, a:1, s:1, b:0),
% 0.98/1.61 class_Groups_Ocancel__comm__monoid__add [237, 1] (w:1, o:216, a:1, s:
% 0.98/1.61 1, b:0),
% 0.98/1.61 tc_HOL_Obool [239, 0] (w:1, o:111, a:1, s:1, b:0),
% 0.98/1.61 v_thesis____ [241, 0] (w:1, o:118, a:1, s:1, b:0),
% 0.98/1.61 alpha1 [242, 1] (w:1, o:217, a:1, s:1, b:1),
% 0.98/1.61 alpha2 [243, 3] (w:1, o:320, a:1, s:1, b:1),
% 0.98/1.61 alpha3 [244, 3] (w:1, o:326, a:1, s:1, b:1),
% 0.98/1.61 alpha4 [245, 3] (w:1, o:334, a:1, s:1, b:1),
% 0.98/1.61 alpha5 [246, 3] (w:1, o:337, a:1, s:1, b:1),
% 0.98/1.61 alpha6 [247, 2] (w:1, o:291, a:1, s:1, b:1),
% 0.98/1.61 alpha7 [248, 1] (w:1, o:218, a:1, s:1, b:1),
% 0.98/1.61 alpha8 [249, 2] (w:1, o:292, a:1, s:1, b:1),
% 0.98/1.61 alpha9 [250, 2] (w:1, o:294, a:1, s:1, b:1),
% 0.98/1.61 alpha10 [251, 2] (w:1, o:295, a:1, s:1, b:1),
% 0.98/1.61 alpha11 [252, 2] (w:1, o:296, a:1, s:1, b:1),
% 0.98/1.61 alpha12 [253, 3] (w:1, o:314, a:1, s:1, b:1),
% 0.98/1.61 alpha13 [254, 3] (w:1, o:315, a:1, s:1, b:1),
% 0.98/1.61 alpha14 [255, 3] (w:1, o:316, a:1, s:1, b:1),
% 0.98/1.61 alpha15 [256, 4] (w:1, o:383, a:1, s:1, b:1),
% 0.98/1.61 alpha16 [257, 4] (w:1, o:384, a:1, s:1, b:1),
% 0.98/1.61 alpha17 [258, 3] (w:1, o:317, a:1, s:1, b:1),
% 0.98/1.61 alpha18 [259, 3] (w:1, o:318, a:1, s:1, b:1),
% 0.98/1.61 alpha19 [260, 3] (w:1, o:319, a:1, s:1, b:1),
% 0.98/1.61 alpha20 [261, 3] (w:1, o:321, a:1, s:1, b:1),
% 0.98/1.61 alpha21 [262, 3] (w:1, o:322, a:1, s:1, b:1),
% 0.98/1.61 alpha22 [263, 3] (w:1, o:323, a:1, s:1, b:1),
% 0.98/1.61 alpha23 [264, 2] (w:1, o:297, a:1, s:1, b:1),
% 0.98/1.63 alpha24 [265, 2] (w:1, o:298, a:1, s:1, b:1),
% 0.98/1.63 alpha25 [266, 3] (w:1, o:324, a:1, s:1, b:1),
% 0.98/1.63 alpha26 [267, 4] (w:1, o:385, a:1, s:1, b:1),
% 0.98/1.63 alpha27 [268, 4] (w:1, o:386, a:1, s:1, b:1),
% 0.98/1.63 alpha28 [269, 2] (w:1, o:299, a:1, s:1, b:1),
% 0.98/1.63 alpha29 [270, 3] (w:1, o:325, a:1, s:1, b:1),
% 0.98/1.63 alpha30 [271, 3] (w:1, o:327, a:1, s:1, b:1),
% 0.98/1.63 alpha31 [272, 3] (w:1, o:328, a:1, s:1, b:1),
% 0.98/1.63 alpha32 [273, 3] (w:1, o:329, a:1, s:1, b:1),
% 0.98/1.63 alpha33 [274, 2] (w:1, o:300, a:1, s:1, b:1),
% 0.98/1.63 alpha34 [275, 2] (w:1, o:301, a:1, s:1, b:1),
% 0.98/1.63 alpha35 [276, 2] (w:1, o:302, a:1, s:1, b:1),
% 0.98/1.63 alpha36 [277, 3] (w:1, o:330, a:1, s:1, b:1),
% 0.98/1.63 alpha37 [278, 3] (w:1, o:331, a:1, s:1, b:1),
% 0.98/1.63 alpha38 [279, 3] (w:1, o:332, a:1, s:1, b:1),
% 0.98/1.63 alpha39 [280, 3] (w:1, o:333, a:1, s:1, b:1),
% 0.98/1.63 alpha40 [281, 4] (w:1, o:387, a:1, s:1, b:1),
% 0.98/1.63 alpha41 [282, 4] (w:1, o:388, a:1, s:1, b:1),
% 0.98/1.63 alpha42 [283, 4] (w:1, o:389, a:1, s:1, b:1),
% 0.98/1.63 alpha43 [284, 4] (w:1, o:390, a:1, s:1, b:1),
% 0.98/1.63 alpha44 [285, 4] (w:1, o:391, a:1, s:1, b:1),
% 0.98/1.63 alpha45 [286, 4] (w:1, o:392, a:1, s:1, b:1),
% 0.98/1.63 alpha46 [287, 4] (w:1, o:393, a:1, s:1, b:1),
% 0.98/1.63 alpha47 [288, 4] (w:1, o:394, a:1, s:1, b:1),
% 0.98/1.63 alpha48 [289, 3] (w:1, o:335, a:1, s:1, b:1),
% 0.98/1.63 alpha49 [290, 3] (w:1, o:336, a:1, s:1, b:1),
% 0.98/1.63 alpha50 [291, 3] (w:1, o:338, a:1, s:1, b:1),
% 0.98/1.63 alpha51 [292, 4] (w:1, o:395, a:1, s:1, b:1),
% 0.98/1.63 alpha52 [293, 4] (w:1, o:396, a:1, s:1, b:1),
% 0.98/1.63 alpha53 [294, 2] (w:1, o:290, a:1, s:1, b:1),
% 0.98/1.63 alpha54 [295, 4] (w:1, o:397, a:1, s:1, b:1),
% 0.98/1.63 alpha55 [296, 3] (w:1, o:339, a:1, s:1, b:1),
% 0.98/1.63 alpha56 [297, 4] (w:1, o:398, a:1, s:1, b:1),
% 0.98/1.63 alpha57 [298, 4] (w:1, o:399, a:1, s:1, b:1),
% 0.98/1.63 alpha58 [299, 4] (w:1, o:400, a:1, s:1, b:1),
% 0.98/1.63 alpha59 [300, 4] (w:1, o:401, a:1, s:1, b:1),
% 0.98/1.63 alpha60 [301, 3] (w:1, o:340, a:1, s:1, b:1),
% 0.98/1.63 alpha61 [302, 3] (w:1, o:341, a:1, s:1, b:1),
% 0.98/1.63 alpha62 [303, 3] (w:1, o:342, a:1, s:1, b:1),
% 0.98/1.63 alpha63 [304, 2] (w:1, o:303, a:1, s:1, b:1),
% 0.98/1.63 alpha64 [305, 4] (w:1, o:402, a:1, s:1, b:1),
% 0.98/1.63 alpha65 [306, 4] (w:1, o:403, a:1, s:1, b:1),
% 0.98/1.63 alpha66 [307, 4] (w:1, o:404, a:1, s:1, b:1),
% 0.98/1.63 alpha67 [308, 4] (w:1, o:405, a:1, s:1, b:1),
% 0.98/1.63 alpha68 [309, 4] (w:1, o:406, a:1, s:1, b:1),
% 0.98/1.63 alpha69 [310, 4] (w:1, o:407, a:1, s:1, b:1),
% 0.98/1.63 alpha70 [311, 3] (w:1, o:343, a:1, s:1, b:1),
% 0.98/1.63 alpha71 [312, 3] (w:1, o:344, a:1, s:1, b:1),
% 0.98/1.63 alpha72 [313, 3] (w:1, o:345, a:1, s:1, b:1),
% 0.98/1.63 alpha73 [314, 3] (w:1, o:346, a:1, s:1, b:1),
% 0.98/1.63 alpha74 [315, 4] (w:1, o:408, a:1, s:1, b:1),
% 0.98/1.63 alpha75 [316, 4] (w:1, o:409, a:1, s:1, b:1),
% 0.98/1.63 alpha76 [317, 4] (w:1, o:410, a:1, s:1, b:1),
% 0.98/1.63 alpha77 [318, 4] (w:1, o:411, a:1, s:1, b:1),
% 0.98/1.63 alpha78 [319, 3] (w:1, o:347, a:1, s:1, b:1),
% 0.98/1.63 alpha79 [320, 3] (w:1, o:348, a:1, s:1, b:1),
% 0.98/1.63 alpha80 [321, 3] (w:1, o:349, a:1, s:1, b:1),
% 0.98/1.63 alpha81 [322, 3] (w:1, o:350, a:1, s:1, b:1),
% 0.98/1.63 alpha82 [323, 3] (w:1, o:351, a:1, s:1, b:1),
% 0.98/1.63 alpha83 [324, 4] (w:1, o:412, a:1, s:1, b:1),
% 0.98/1.63 alpha84 [325, 3] (w:1, o:352, a:1, s:1, b:1),
% 0.98/1.63 alpha85 [326, 3] (w:1, o:353, a:1, s:1, b:1),
% 0.98/1.63 alpha86 [327, 4] (w:1, o:413, a:1, s:1, b:1),
% 0.98/1.63 alpha87 [328, 3] (w:1, o:354, a:1, s:1, b:1),
% 0.98/1.63 alpha88 [329, 3] (w:1, o:355, a:1, s:1, b:1),
% 0.98/1.63 alpha89 [330, 2] (w:1, o:293, a:1, s:1, b:1),
% 0.98/1.63 alpha90 [331, 2] (w:1, o:304, a:1, s:1, b:1),
% 0.98/1.63 alpha91 [332, 3] (w:1, o:356, a:1, s:1, b:1),
% 0.98/1.63 skol1 [333, 2] (w:1, o:249, a:1, s:1, b:1),
% 0.98/1.63 skol2 [334, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.98/1.63 skol3 [335, 1] (w:1, o:166, a:1, s:1, b:1),
% 0.98/1.63 skol4 [336, 1] (w:1, o:167, a:1, s:1, b:1),
% 0.98/1.63 skol5 [337, 1] (w:1, o:170, a:1, s:1, b:1),
% 0.98/1.63 skol6 [338, 1] (w:1, o:171, a:1, s:1, b:1),
% 0.98/1.63 skol7 [339, 1] (w:1, o:174, a:1, s:1, b:1),
% 0.98/1.63 skol8 [340, 1] (w:1, o:176, a:1, s:1, b:1),
% 0.98/1.63 skol9 [341, 0] (w:1, o:16, a:1, s:1, b:1),
% 5.04/5.40 skol10 [342, 0] (w:1, o:12, a:1, s:1, b:1),
% 5.04/5.40 skol11 [343, 0] (w:1, o:13, a:1, s:1, b:1),
% 5.04/5.40 skol12 [344, 3] (w:1, o:357, a:1, s:1, b:1),
% 5.04/5.40 skol13 [345, 3] (w:1, o:358, a:1, s:1, b:1),
% 5.04/5.40 skol14 [346, 2] (w:1, o:250, a:1, s:1, b:1),
% 5.04/5.40 skol15 [347, 0] (w:1, o:14, a:1, s:1, b:1),
% 5.04/5.40 skol16 [348, 1] (w:1, o:177, a:1, s:1, b:1),
% 5.04/5.40 skol17 [349, 2] (w:1, o:251, a:1, s:1, b:1),
% 5.04/5.40 skol18 [350, 1] (w:1, o:178, a:1, s:1, b:1),
% 5.04/5.40 skol19 [351, 2] (w:1, o:252, a:1, s:1, b:1),
% 5.04/5.40 skol20 [352, 0] (w:1, o:17, a:1, s:1, b:1),
% 5.04/5.40 skol21 [353, 3] (w:1, o:359, a:1, s:1, b:1),
% 5.04/5.40 skol22 [354, 2] (w:1, o:253, a:1, s:1, b:1),
% 5.04/5.40 skol23 [355, 2] (w:1, o:254, a:1, s:1, b:1),
% 5.04/5.40 skol24 [356, 2] (w:1, o:255, a:1, s:1, b:1),
% 5.04/5.40 skol25 [357, 2] (w:1, o:256, a:1, s:1, b:1),
% 5.04/5.40 skol26 [358, 1] (w:1, o:165, a:1, s:1, b:1),
% 5.04/5.40 skol27 [359, 2] (w:1, o:257, a:1, s:1, b:1),
% 5.04/5.40 skol28 [360, 2] (w:1, o:258, a:1, s:1, b:1),
% 5.04/5.40 skol29 [361, 2] (w:1, o:259, a:1, s:1, b:1),
% 5.04/5.40 skol30 [362, 2] (w:1, o:260, a:1, s:1, b:1),
% 5.04/5.40 skol31 [363, 2] (w:1, o:261, a:1, s:1, b:1),
% 5.04/5.40 skol32 [364, 2] (w:1, o:262, a:1, s:1, b:1),
% 5.04/5.40 skol33 [365, 3] (w:1, o:360, a:1, s:1, b:1),
% 5.04/5.40 skol34 [366, 2] (w:1, o:263, a:1, s:1, b:1),
% 5.04/5.40 skol35 [367, 4] (w:1, o:414, a:1, s:1, b:1),
% 5.04/5.40 skol36 [368, 3] (w:1, o:361, a:1, s:1, b:1),
% 5.04/5.40 skol37 [369, 2] (w:1, o:264, a:1, s:1, b:1),
% 5.04/5.40 skol38 [370, 3] (w:1, o:362, a:1, s:1, b:1),
% 5.04/5.40 skol39 [371, 3] (w:1, o:363, a:1, s:1, b:1),
% 5.04/5.40 skol40 [372, 3] (w:1, o:364, a:1, s:1, b:1),
% 5.04/5.40 skol41 [373, 4] (w:1, o:415, a:1, s:1, b:1),
% 5.04/5.40 skol42 [374, 2] (w:1, o:265, a:1, s:1, b:1),
% 5.04/5.40 skol43 [375, 1] (w:1, o:168, a:1, s:1, b:1),
% 5.04/5.40 skol44 [376, 2] (w:1, o:266, a:1, s:1, b:1),
% 5.04/5.40 skol45 [377, 2] (w:1, o:267, a:1, s:1, b:1),
% 5.04/5.40 skol46 [378, 2] (w:1, o:268, a:1, s:1, b:1),
% 5.04/5.40 skol47 [379, 1] (w:1, o:169, a:1, s:1, b:1),
% 5.04/5.40 skol48 [380, 2] (w:1, o:269, a:1, s:1, b:1),
% 5.04/5.40 skol49 [381, 2] (w:1, o:270, a:1, s:1, b:1),
% 5.04/5.40 skol50 [382, 3] (w:1, o:365, a:1, s:1, b:1),
% 5.04/5.40 skol51 [383, 2] (w:1, o:271, a:1, s:1, b:1),
% 5.04/5.40 skol52 [384, 3] (w:1, o:366, a:1, s:1, b:1),
% 5.04/5.40 skol53 [385, 3] (w:1, o:367, a:1, s:1, b:1),
% 5.04/5.40 skol54 [386, 3] (w:1, o:368, a:1, s:1, b:1),
% 5.04/5.40 skol55 [387, 3] (w:1, o:369, a:1, s:1, b:1),
% 5.04/5.40 skol56 [388, 3] (w:1, o:370, a:1, s:1, b:1),
% 5.04/5.40 skol57 [389, 3] (w:1, o:371, a:1, s:1, b:1),
% 5.04/5.40 skol58 [390, 3] (w:1, o:372, a:1, s:1, b:1),
% 5.04/5.40 skol59 [391, 3] (w:1, o:373, a:1, s:1, b:1),
% 5.04/5.40 skol60 [392, 2] (w:1, o:272, a:1, s:1, b:1),
% 5.04/5.40 skol61 [393, 3] (w:1, o:374, a:1, s:1, b:1),
% 5.04/5.40 skol62 [394, 3] (w:1, o:375, a:1, s:1, b:1),
% 5.04/5.40 skol63 [395, 2] (w:1, o:273, a:1, s:1, b:1),
% 5.04/5.40 skol64 [396, 2] (w:1, o:274, a:1, s:1, b:1),
% 5.04/5.40 skol65 [397, 1] (w:1, o:172, a:1, s:1, b:1),
% 5.04/5.40 skol66 [398, 2] (w:1, o:275, a:1, s:1, b:1),
% 5.04/5.40 skol67 [399, 2] (w:1, o:276, a:1, s:1, b:1),
% 5.04/5.40 skol68 [400, 1] (w:1, o:173, a:1, s:1, b:1),
% 5.04/5.40 skol69 [401, 0] (w:1, o:18, a:1, s:1, b:1),
% 5.04/5.40 skol70 [402, 2] (w:1, o:277, a:1, s:1, b:1),
% 5.04/5.40 skol71 [403, 3] (w:1, o:376, a:1, s:1, b:1),
% 5.04/5.40 skol72 [404, 3] (w:1, o:377, a:1, s:1, b:1),
% 5.04/5.40 skol73 [405, 3] (w:1, o:378, a:1, s:1, b:1),
% 5.04/5.40 skol74 [406, 2] (w:1, o:278, a:1, s:1, b:1),
% 5.04/5.40 skol75 [407, 2] (w:1, o:279, a:1, s:1, b:1),
% 5.04/5.40 skol76 [408, 2] (w:1, o:280, a:1, s:1, b:1),
% 5.04/5.40 skol77 [409, 3] (w:1, o:379, a:1, s:1, b:1),
% 5.04/5.40 skol78 [410, 3] (w:1, o:380, a:1, s:1, b:1),
% 5.04/5.40 skol79 [411, 1] (w:1, o:175, a:1, s:1, b:1),
% 5.04/5.40 skol80 [412, 3] (w:1, o:381, a:1, s:1, b:1),
% 5.04/5.40 skol81 [413, 3] (w:1, o:382, a:1, s:1, b:1),
% 5.04/5.40 skol82 [414, 4] (w:1, o:416, a:1, s:1, b:1),
% 5.04/5.40 skol83 [415, 4] (w:1, o:417, a:1, s:1, b:1),
% 5.04/5.40 skol84 [416, 2] (w:1, o:281, a:1, s:1, b:1),
% 5.04/5.40 skol85 [417, 2] (w:1, o:282, a:1, s:1, b:1).
% 5.04/5.40
% 5.04/5.40
% 5.04/5.40 Starting Search:
% 5.04/5.40
% 5.04/5.40 *** allocated 170857 integers for clauses
% 5.04/5.40
% 5.04/5.40 Intermediate Status:
% 5.04/5.40 Generated: 2745
% 5.04/5.40 Kept: 2042
% 5.04/5.40 Inuse: 0
% 5.04/5.40 Deleted: 0
% 28.35/28.69 Deletedinuse: 0
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 256285 integers for clauses
% 28.35/28.69 *** allocated 170857 integers for termspace/termends
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 384427 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 6502
% 28.35/28.69 Kept: 4315
% 28.35/28.69 Inuse: 207
% 28.35/28.69 Deleted: 5
% 28.35/28.69 Deletedinuse: 1
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 256285 integers for termspace/termends
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 576640 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 9535
% 28.35/28.69 Kept: 6323
% 28.35/28.69 Inuse: 344
% 28.35/28.69 Deleted: 5
% 28.35/28.69 Deletedinuse: 1
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 12552
% 28.35/28.69 Kept: 8324
% 28.35/28.69 Inuse: 487
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 384427 integers for termspace/termends
% 28.35/28.69 *** allocated 864960 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 15594
% 28.35/28.69 Kept: 10690
% 28.35/28.69 Inuse: 522
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 18815
% 28.35/28.69 Kept: 12694
% 28.35/28.69 Inuse: 557
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 22698
% 28.35/28.69 Kept: 14755
% 28.35/28.69 Inuse: 597
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 576640 integers for termspace/termends
% 28.35/28.69 *** allocated 1297440 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 29098
% 28.35/28.69 Kept: 17208
% 28.35/28.69 Inuse: 642
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 34858
% 28.35/28.69 Kept: 19225
% 28.35/28.69 Inuse: 667
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 38499
% 28.35/28.69 Kept: 21926
% 28.35/28.69 Inuse: 672
% 28.35/28.69 Deleted: 6
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying clauses:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 42018
% 28.35/28.69 Kept: 23945
% 28.35/28.69 Inuse: 726
% 28.35/28.69 Deleted: 313
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 864960 integers for termspace/termends
% 28.35/28.69 *** allocated 1946160 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 45736
% 28.35/28.69 Kept: 26098
% 28.35/28.69 Inuse: 767
% 28.35/28.69 Deleted: 313
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 49497
% 28.35/28.69 Kept: 28711
% 28.35/28.69 Inuse: 792
% 28.35/28.69 Deleted: 313
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 56559
% 28.35/28.69 Kept: 31016
% 28.35/28.69 Inuse: 811
% 28.35/28.69 Deleted: 314
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 63073
% 28.35/28.69 Kept: 33086
% 28.35/28.69 Inuse: 821
% 28.35/28.69 Deleted: 314
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 69933
% 28.35/28.69 Kept: 35194
% 28.35/28.69 Inuse: 831
% 28.35/28.69 Deleted: 314
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 76970
% 28.35/28.69 Kept: 37297
% 28.35/28.69 Inuse: 841
% 28.35/28.69 Deleted: 314
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 82587
% 28.35/28.69 Kept: 39730
% 28.35/28.69 Inuse: 855
% 28.35/28.69 Deleted: 315
% 28.35/28.69 Deletedinuse: 2
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 *** allocated 1297440 integers for termspace/termends
% 28.35/28.69 *** allocated 2919240 integers for clauses
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 89205
% 28.35/28.69 Kept: 41769
% 28.35/28.69 Inuse: 860
% 28.35/28.69 Deleted: 318
% 28.35/28.69 Deletedinuse: 5
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying clauses:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 93645
% 28.35/28.69 Kept: 44210
% 28.35/28.69 Inuse: 870
% 28.35/28.69 Deleted: 1110
% 28.35/28.69 Deletedinuse: 5
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 101472
% 28.35/28.69 Kept: 47764
% 28.35/28.69 Inuse: 905
% 28.35/28.69 Deleted: 1111
% 28.35/28.69 Deletedinuse: 6
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 106294
% 28.35/28.69 Kept: 49812
% 28.35/28.69 Inuse: 937
% 28.35/28.69 Deleted: 1111
% 28.35/28.69 Deletedinuse: 6
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 28.35/28.69
% 28.35/28.69
% 28.35/28.69 Intermediate Status:
% 28.35/28.69 Generated: 111094
% 28.35/28.69 Kept: 51833
% 28.35/28.69 Inuse: 966
% 28.35/28.69 Deleted: 1111
% 28.35/28.69 Deletedinuse: 6
% 28.35/28.69
% 28.35/28.69 Resimplifying inuse:
% 28.35/28.69 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 115846
% 105.50/105.93 Kept: 53858
% 105.50/105.93 Inuse: 996
% 105.50/105.93 Deleted: 1111
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 123899
% 105.50/105.93 Kept: 56136
% 105.50/105.93 Inuse: 1004
% 105.50/105.93 Deleted: 1111
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 126947
% 105.50/105.93 Kept: 58634
% 105.50/105.93 Inuse: 1005
% 105.50/105.93 Deleted: 1111
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 130822
% 105.50/105.93 Kept: 61189
% 105.50/105.93 Inuse: 1015
% 105.50/105.93 Deleted: 1111
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying clauses:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 136471
% 105.50/105.93 Kept: 63196
% 105.50/105.93 Inuse: 1067
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 *** allocated 4378860 integers for clauses
% 105.50/105.93 *** allocated 1946160 integers for termspace/termends
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 142686
% 105.50/105.93 Kept: 65287
% 105.50/105.93 Inuse: 1125
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 152894
% 105.50/105.93 Kept: 67721
% 105.50/105.93 Inuse: 1135
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 160414
% 105.50/105.93 Kept: 69870
% 105.50/105.93 Inuse: 1180
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 165972
% 105.50/105.93 Kept: 71915
% 105.50/105.93 Inuse: 1225
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 171405
% 105.50/105.93 Kept: 73974
% 105.50/105.93 Inuse: 1270
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 179636
% 105.50/105.93 Kept: 77823
% 105.50/105.93 Inuse: 1320
% 105.50/105.93 Deleted: 1380
% 105.50/105.93 Deletedinuse: 6
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 185479
% 105.50/105.93 Kept: 80507
% 105.50/105.93 Inuse: 1339
% 105.50/105.93 Deleted: 1383
% 105.50/105.93 Deletedinuse: 8
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 189475
% 105.50/105.93 Kept: 82707
% 105.50/105.93 Inuse: 1344
% 105.50/105.93 Deleted: 1383
% 105.50/105.93 Deletedinuse: 8
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying clauses:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 202694
% 105.50/105.93 Kept: 85979
% 105.50/105.93 Inuse: 1349
% 105.50/105.93 Deleted: 1888
% 105.50/105.93 Deletedinuse: 8
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 212332
% 105.50/105.93 Kept: 88496
% 105.50/105.93 Inuse: 1359
% 105.50/105.93 Deleted: 1888
% 105.50/105.93 Deletedinuse: 8
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 *** allocated 2919240 integers for termspace/termends
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 217498
% 105.50/105.93 Kept: 90509
% 105.50/105.93 Inuse: 1388
% 105.50/105.93 Deleted: 1889
% 105.50/105.93 Deletedinuse: 9
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 222840
% 105.50/105.93 Kept: 92578
% 105.50/105.93 Inuse: 1419
% 105.50/105.93 Deleted: 1890
% 105.50/105.93 Deletedinuse: 10
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 230384
% 105.50/105.93 Kept: 97123
% 105.50/105.93 Inuse: 1439
% 105.50/105.93 Deleted: 1890
% 105.50/105.93 Deletedinuse: 10
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 *** allocated 6568290 integers for clauses
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 240842
% 105.50/105.93 Kept: 99962
% 105.50/105.93 Inuse: 1444
% 105.50/105.93 Deleted: 1892
% 105.50/105.93 Deletedinuse: 12
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 254598
% 105.50/105.93 Kept: 103844
% 105.50/105.93 Inuse: 1464
% 105.50/105.93 Deleted: 1892
% 105.50/105.93 Deletedinuse: 12
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying clauses:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 260297
% 105.50/105.93 Kept: 106671
% 105.50/105.93 Inuse: 1479
% 105.50/105.93 Deleted: 2198
% 105.50/105.93 Deletedinuse: 12
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 272209
% 105.50/105.93 Kept: 113796
% 105.50/105.93 Inuse: 1510
% 105.50/105.93 Deleted: 2223
% 105.50/105.93 Deletedinuse: 33
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 279480
% 105.50/105.93 Kept: 118105
% 105.50/105.93 Inuse: 1536
% 105.50/105.93 Deleted: 2227
% 105.50/105.93 Deletedinuse: 33
% 105.50/105.93
% 105.50/105.93 Resimplifying inuse:
% 105.50/105.93 Done
% 105.50/105.93
% 105.50/105.93
% 105.50/105.93 Intermediate Status:
% 105.50/105.93 Generated: 289442
% 105.50/105.93 Kept: 124141
% 105.50/105.93 Inuse: 1546
% 105.50/105.93 Deleted: 2227
% 252.32/252.76 Deletedinuse: 33
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying clauses:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 302761
% 252.32/252.76 Kept: 127700
% 252.32/252.76 Inuse: 1561
% 252.32/252.76 Deleted: 3095
% 252.32/252.76 Deletedinuse: 33
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 310436
% 252.32/252.76 Kept: 131681
% 252.32/252.76 Inuse: 1576
% 252.32/252.76 Deleted: 3095
% 252.32/252.76 Deletedinuse: 33
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 318990
% 252.32/252.76 Kept: 133797
% 252.32/252.76 Inuse: 1606
% 252.32/252.76 Deleted: 3096
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 331233
% 252.32/252.76 Kept: 137245
% 252.32/252.76 Inuse: 1611
% 252.32/252.76 Deleted: 3096
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 345292
% 252.32/252.76 Kept: 141065
% 252.32/252.76 Inuse: 1621
% 252.32/252.76 Deleted: 3096
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 354155
% 252.32/252.76 Kept: 145290
% 252.32/252.76 Inuse: 1636
% 252.32/252.76 Deleted: 3096
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying clauses:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 *** allocated 4378860 integers for termspace/termends
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 360012
% 252.32/252.76 Kept: 148809
% 252.32/252.76 Inuse: 1641
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 368961
% 252.32/252.76 Kept: 150835
% 252.32/252.76 Inuse: 1671
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 *** allocated 9852435 integers for clauses
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 384572
% 252.32/252.76 Kept: 158180
% 252.32/252.76 Inuse: 1696
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 392351
% 252.32/252.76 Kept: 161231
% 252.32/252.76 Inuse: 1706
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 399839
% 252.32/252.76 Kept: 163248
% 252.32/252.76 Inuse: 1734
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 406916
% 252.32/252.76 Kept: 166692
% 252.32/252.76 Inuse: 1741
% 252.32/252.76 Deleted: 3245
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying clauses:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 413538
% 252.32/252.76 Kept: 168724
% 252.32/252.76 Inuse: 1772
% 252.32/252.76 Deleted: 3359
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 428342
% 252.32/252.76 Kept: 175792
% 252.32/252.76 Inuse: 1789
% 252.32/252.76 Deleted: 3359
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 436004
% 252.32/252.76 Kept: 179982
% 252.32/252.76 Inuse: 1799
% 252.32/252.76 Deleted: 3359
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 441416
% 252.32/252.76 Kept: 183600
% 252.32/252.76 Inuse: 1804
% 252.32/252.76 Deleted: 3359
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 446840
% 252.32/252.76 Kept: 187225
% 252.32/252.76 Inuse: 1809
% 252.32/252.76 Deleted: 3359
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying clauses:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 452301
% 252.32/252.76 Kept: 190868
% 252.32/252.76 Inuse: 1814
% 252.32/252.76 Deleted: 3453
% 252.32/252.76 Deletedinuse: 34
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 458972
% 252.32/252.76 Kept: 192933
% 252.32/252.76 Inuse: 1838
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 465215
% 252.32/252.76 Kept: 194988
% 252.32/252.76 Inuse: 1861
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 476420
% 252.32/252.76 Kept: 197290
% 252.32/252.76 Inuse: 1874
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 481820
% 252.32/252.76 Kept: 199495
% 252.32/252.76 Inuse: 1894
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 487466
% 252.32/252.76 Kept: 201519
% 252.32/252.76 Inuse: 1917
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 252.32/252.76
% 252.32/252.76
% 252.32/252.76 Intermediate Status:
% 252.32/252.76 Generated: 504773
% 252.32/252.76 Kept: 205967
% 252.32/252.76 Inuse: 1939
% 252.32/252.76 Deleted: 3454
% 252.32/252.76 Deletedinuse: 35
% 252.32/252.76
% 252.32/252.76 Resimplifying inuse:
% 252.32/252.76 Done
% 300.02/300.40 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------