TSTP Solution File: SWW206+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW206+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 23:21:13 EDT 2022
% Result : Timeout 300.01s 300.57s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW206+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jun 4 22:32:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.99/1.67 *** allocated 10000 integers for termspace/termends
% 0.99/1.67 *** allocated 10000 integers for clauses
% 0.99/1.67 *** allocated 10000 integers for justifications
% 0.99/1.67 *** allocated 15000 integers for termspace/termends
% 0.99/1.67 *** allocated 22500 integers for termspace/termends
% 0.99/1.67 *** allocated 33750 integers for termspace/termends
% 0.99/1.67 Bliksem 1.12
% 0.99/1.67
% 0.99/1.67
% 0.99/1.67 Automatic Strategy Selection
% 0.99/1.67
% 0.99/1.67 *** allocated 50625 integers for termspace/termends
% 0.99/1.67 *** allocated 75937 integers for termspace/termends
% 0.99/1.67 *** allocated 113905 integers for termspace/termends
% 0.99/1.67
% 0.99/1.67 Clauses:
% 0.99/1.67
% 0.99/1.67 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.99/1.67 { c_SEQ_Osubseq( v_f____ ) }.
% 0.99/1.67 { c_SEQ_Osubseq( v_ga____ ) }.
% 0.99/1.67 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.99/1.67 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 0.99/1.67 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 0.99/1.67 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 0.99/1.67 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.99/1.67 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 0.99/1.67 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 0.99/1.67 { c_SEQ_Osubseq( skol2 ) }.
% 0.99/1.67 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.99/1.67 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 0.99/1.67 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 0.99/1.67 , tc_Nat_Onat, v_f____, skol2 ) ) ) ) }.
% 0.99/1.67 { c_SEQ_Oconvergent( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.99/1.67 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 0.99/1.67 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s, X ) ) )
% 0.99/1.67 , v_r ) ) }.
% 0.99/1.67 { c_SEQ_Osubseq( skol3 ) }.
% 0.99/1.67 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 0.99/1.67 , tc_Nat_Onat, c_Fun_Ocomp( tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat,
% 0.99/1.67 c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat,
% 0.99/1.67 c_Complex_OIm, v_s ), v_f____ ), skol3 ) ) }.
% 0.99/1.67 { c_Lim_OisUCont( tc_Complex_Ocomplex, tc_RealDef_Oreal, c_Complex_OIm ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.67 c_SEQ_OBseq( X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC(
% 0.99/1.67 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_Nat_Onat ), Z ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 0.99/1.67 ( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 0.99/1.67 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ) ) ),
% 0.99/1.67 c_SEQ_OBseq( X, Y ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 0.99/1.67 ( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.99/1.67 c_SEQ_OBseq( X, Y ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.67 c_SEQ_OBseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.99/1.67 c_SEQ_OBseq( X, Y ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, hAPP(
% 0.99/1.67 v_s, X ) ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal
% 0.99/1.67 ), v_r ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), v_r ) ) }.
% 0.99/1.67 { c_Lim_OisUCont( tc_Complex_Ocomplex, tc_RealDef_Oreal, c_Complex_ORe ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_RealVector_Ometric__space( X ), c_SEQ_Oconvergent( X, c_COMBK( X
% 0.99/1.67 , tc_Nat_Onat, Y ) ) }.
% 0.99/1.67 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.99/1.67 c_SEQ_Oconvergent( X, Y ) }.
% 0.99/1.67 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.99/1.67 c_SEQ_OCauchy( X, Y ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.67 c_Complex_ORe, X ) ), c_RealVector_Onorm__class_Onorm(
% 0.99/1.67 tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.67 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X,
% 0.99/1.67 c_COMBB( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.99/1.67 c_SEQ_Oconvergent( X, Y ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha1( X, Y ),
% 0.99/1.67 alpha9( X, Y ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! alpha1( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! alpha9( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 0.99/1.67 .
% 0.99/1.67 { ! alpha9( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol4( X, Y
% 0.99/1.67 ) ), skol59( X, Y ) ) ), alpha9( X, Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol59( X,
% 0.99/1.67 Y ) ) ), hAPP( Y, skol4( X, Y ) ) ) ), alpha9( X, Y ) }.
% 0.99/1.67 { ! alpha1( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol5( X, Y
% 0.99/1.67 ) ), skol60( X, Y ) ) ), alpha1( X, Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol5( X, Y
% 0.99/1.67 ) ) ), hAPP( Y, skol60( X, Y ) ) ) ), alpha1( X, Y ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X ) ) )
% 0.99/1.67 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X ) ) )
% 0.99/1.67 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_OIm, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_Complex_Ocomplex ), X ) ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_RealDef_Oreal ), hAPP( c_Complex_OIm, X ) ) }.
% 0.99/1.67 { hAPP( c_Complex_ORe, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_Complex_Ocomplex ), X ) ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, X ) ) }.
% 0.99/1.67 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.99/1.67 c_SEQ_Oconvergent( X, Y ) }.
% 0.99/1.67 { ! c_SEQ_OCauchy( tc_RealDef_Oreal, X ), c_SEQ_Oconvergent(
% 0.99/1.67 tc_RealDef_Oreal, X ) }.
% 0.99/1.67 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.99/1.67 c_SEQ_OCauchy( X, Y ) }.
% 0.99/1.67 { ! c_SEQ_OCauchy( tc_Complex_Ocomplex, X ), c_SEQ_OCauchy(
% 0.99/1.67 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.99/1.67 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Omonoseq( X, Y ),
% 0.99/1.67 c_SEQ_Omonoseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.67 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.99/1.67 c_SEQ_Osubseq( Z ), c_SEQ_OCauchy( X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 0.99/1.67 tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.67 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ), !
% 0.99/1.67 c_SEQ_Osubseq( Z ), c_SEQ_Oconvergent( X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 0.99/1.67 tc_Nat_Onat, Y, Z ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.67 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 0.99/1.67 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 0.99/1.67 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! c_SEQ_Omonoseq( tc_RealDef_Oreal
% 0.99/1.67 , X ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 0.99/1.67 { ! c_SEQ_OCauchy( tc_Complex_Ocomplex, X ), c_SEQ_OCauchy(
% 0.99/1.67 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.99/1.67 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 0.99/1.67 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 0.99/1.67 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 0.99/1.67 { ! Y = X, hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ) }.
% 0.99/1.67 { ! Y = X, hAPP( c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ) }.
% 0.99/1.67 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 0.99/1.67 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 0.99/1.67 { c_SEQ_Osubseq( skol6 ) }.
% 0.99/1.67 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 0.99/1.67 , tc_Nat_Onat, c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.99/1.67 tc_Nat_Onat, c_Complex_ORe, v_s ), skol6 ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ), c_Groups_Oabs__class_Oabs( X, Y ) = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), v_r ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) ) ), hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Oabs__class_Oabs( X
% 0.99/1.67 , Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ) ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_OIm, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { hAPP( c_Complex_ORe, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { hAPP( c_Complex_OIm, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.99/1.67 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP
% 0.99/1.67 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.99/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y )
% 0.99/1.67 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) }.
% 0.99/1.67 { ! X = hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 hAPP( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ), hBOOL
% 0.99/1.67 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.99/1.67 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), X ) ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 0.99/1.67 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_Nat_Onat, Y ), hAPP( X, Y ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 0.99/1.67 ), hAPP( c_Complex_ORe, X ) ) }.
% 0.99/1.67 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y )
% 0.99/1.67 ), hAPP( c_Complex_OIm, X ) ) }.
% 0.99/1.67 { hAPP( c_Complex_ORe, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) ) }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 0.99/1.67 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 0.99/1.67 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 0.99/1.67 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.99/1.67 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.67 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 0.99/1.67 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.99/1.67 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 0.99/1.67 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 0.99/1.67 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 0.99/1.67 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 0.99/1.67 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.67 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.67 , X ), Y ) ), Y = X }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.67 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_RealDef_Oreal, Y ), Z ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 0.99/1.67 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 0.99/1.67 ), Y ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.99/1.67 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 = Y }.
% 0.99/1.67 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 = Y }.
% 0.99/1.67 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 X ), Y ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.67 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.67 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.67 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 0.99/1.67 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.67 Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.99/1.67 ), c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y
% 0.99/1.67 ) ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.67 }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.67 , Y ) ) = c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) )
% 0.99/1.67 }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.99/1.67 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ), Y ) ), !
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 0.99/1.67 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), X ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.99/1.67 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.99/1.67 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) ) =
% 0.99/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( X ), Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) }.
% 0.99/1.67 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.67 , c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.99/1.67 , c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.67 { ! class_RealVector_Ometric__space( Y ), ! class_RealVector_Ometric__space
% 0.99/1.67 ( X ), ! c_Lim_OisUCont( X, Y, Z ), ! c_SEQ_OCauchy( X, T ),
% 0.99/1.67 c_SEQ_OCauchy( Y, c_COMBB( X, Y, tc_Nat_Onat, Z, T ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol7( X, Y, Z ) ) ), hAPP
% 0.99/1.67 ( Y, skol7( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 0.99/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.67 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 0.99/1.67 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.67 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 0.99/1.67 ), Y = X }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.67 ) }.
% 0.99/1.67 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.67 , X ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.67 .
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hAPP( W, hAPP( U, T ) ) = hAPP( Z, hAPP( Y, X ) ), hAPP( c_Fun_Ocomp(
% 0.99/1.67 V4, V3, V2, W, U ), T ) = hAPP( c_Fun_Ocomp( V1, V3, V0, Z, Y ), X ) }.
% 0.99/1.67 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol8
% 0.99/1.67 ( X, Y ) ) }.
% 0.99/1.67 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol9
% 0.99/1.67 ( X, Y ) ) }.
% 0.99/1.67 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol10( X, Y ) ), skol61
% 0.99/1.67 ( X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol61( X, Y ) ) ), hAPP(
% 0.99/1.67 Y, skol10( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 = Y }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 = Y }.
% 0.99/1.67 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.67 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.67 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 0.99/1.67 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 0.99/1.67 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), Y ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.67 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.67 , hAPP( Z, Y ) ) }.
% 0.99/1.67 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 0.99/1.67 , Y ) }.
% 0.99/1.67 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.67 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 0.99/1.67 , hAPP( Z, Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Odecseq( X, Y ),
% 0.99/1.67 c_SEQ_Oincseq( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! c_SEQ_Oincseq( X, c_COMBB
% 0.99/1.67 ( X, X, tc_Nat_Onat, c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 0.99/1.67 c_SEQ_Odecseq( X, Y ) }.
% 0.99/1.67 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol11( X ) ), skol62( X
% 0.99/1.67 ) ) ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 0.99/1.67 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, skol11( X )
% 0.99/1.67 ) ), hAPP( X, skol62( X ) ) ) ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X
% 0.99/1.67 ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol12( X, Y ) ), skol63
% 0.99/1.67 ( X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol12( X, Y ) ) ), hAPP(
% 0.99/1.67 Y, skol63( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.99/1.67 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol13( U, W, V0, T
% 0.99/1.67 ) ) ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol13( X, Y, Z, T ) ) ) ),
% 0.99/1.67 Z ) ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.67 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.67 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! class_Groups_Ozero( X ), !
% 0.99/1.67 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.67 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Polynomial_Opoly( X ) ),
% 0.99/1.67 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.67 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 }.
% 0.99/1.67 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.67 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.67 ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.99/1.67 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.99/1.67 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 0.99/1.67 ( X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.99/1.67 }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 0.99/1.67 , Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_OBseq(
% 0.99/1.67 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.99/1.67 , X ) ) }.
% 0.99/1.67 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.99/1.67 { hAPP( c_Fun_Ocomp( W, U, T, c_COMBK( U, W, Z ), Y ), X ) = Z }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Oconvergent(
% 0.99/1.67 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.99/1.67 , X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Omonoseq(
% 0.99/1.67 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 0.99/1.67 , X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.67 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.67 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.67 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.99/1.67 ) }.
% 0.99/1.67 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) =
% 0.99/1.67 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, X ) ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm
% 0.99/1.67 , X ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.99/1.67 ), T = Y }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.99/1.67 ), Z = X }.
% 0.99/1.67 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.99/1.67 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_Nat_Onat ) ) = Y }.
% 0.99/1.67 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.67 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra__1( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_ORe, c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 0.99/1.67 { hAPP( c_Complex_OIm, c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 0.99/1.67 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 0.99/1.67 ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { c_Complex_Ocomplex_OComplex( hAPP( c_Complex_ORe, X ), hAPP(
% 0.99/1.67 c_Complex_OIm, X ) ) = X }.
% 0.99/1.67 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.99/1.67 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.67 ) }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.67 ) }.
% 0.99/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.67 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Complex_Ocomplex ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 0.99/1.67 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.99/1.67 ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 0.99/1.67 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ),
% 0.99/1.67 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex( hAPP
% 0.99/1.67 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.67 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.67 }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.99/1.67 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 0.99/1.67 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.67 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.99/1.67 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.99/1.67 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.99/1.67 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.99/1.67 }.
% 0.99/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.67 ) }.
% 0.99/1.67 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.67 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_Complex_Ocomplex ) }.
% 0.99/1.67 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 0.99/1.67 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.99/1.67 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 0.99/1.67 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.99/1.67 { ! c_Fun_Ocomp( W, U, T, Z, Y ) = X, hAPP( Z, hAPP( Y, V0 ) ) = hAPP( X,
% 0.99/1.67 V0 ) }.
% 0.99/1.67 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.99/1.67 { c_Fun_Ocomp( V0, W, U, T, c_Fun_Ocomp( Z, V0, U, Y, X ) ) = c_Fun_Ocomp(
% 0.99/1.67 Z, W, U, c_Fun_Ocomp( V0, W, Z, T, Y ), X ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X )
% 0.99/1.67 = c_Complex_Ocomplex_OComplex( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.99/1.67 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 0.99/1.67 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.99/1.67 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 0.99/1.67 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) ) ) }.
% 0.99/1.67 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.67 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.67 ( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.99/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) =
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.67 ), Z ), Y ) ) }.
% 0.99/1.67 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.67 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( X ) }.
% 0.99/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.67 = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.67 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.67 ) }.
% 0.99/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_Nat_Onat ) ) = Y }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 0.99/1.67 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.67 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.67 .
% 0.99/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.67 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Nat_Onat ) }.
% 0.99/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.99/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.99/1.67 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.99/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.99/1.67 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_Nat_Onat ) }.
% 0.99/1.67 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.99/1.67 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.99/1.67 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.99/1.67 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.67 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.99/1.67 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.67 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.99/1.67 }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.67 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 0.99/1.67 ( X ) ), Y ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.99/1.67 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, X ) ) ) }.
% 0.99/1.67 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.99/1.67 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.67 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.99/1.67 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.99/1.67 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.99/1.67 Y = X }.
% 0.99/1.67 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.67 , X ) }.
% 0.99/1.67 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.99/1.67 c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.99/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.67 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.67 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.67 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.99/1.67 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 0.99/1.67 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 0.99/1.67 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.99/1.67 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, Y ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.67 ( tc_Nat_Onat, Y ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.67 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X )
% 0.99/1.67 ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 0.99/1.67 ) }.
% 0.99/1.67 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.99/1.67 ( tc_Nat_Onat, X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.67 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 0.99/1.67 X ) ), Y ) }.
% 0.99/1.67 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.99/1.67 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) ) }.
% 0.99/1.67 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.67 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.99/1.67 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.67 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.67 .
% 0.99/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.67 Y ) ), X ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.67 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.99/1.67 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_RealDef_Oreal, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), c_RealDef_Oreal
% 0.99/1.67 ( tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.67 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 0.99/1.67 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.67 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.99/1.67 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 0.99/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 0.99/1.67 c_RComplete_Onatfloor( X ) = Y }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y )
% 0.99/1.67 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, X ) ) ) }.
% 0.99/1.67 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.67 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), c_Groups_Oone__class_Oone(
% 0.99/1.67 tc_RealDef_Oreal ) ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_Ocnj, X ) = c_Complex_Ocomplex_OComplex( hAPP(
% 0.99/1.67 c_Complex_ORe, X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.67 tc_RealDef_Oreal ), hAPP( c_Complex_OIm, X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.99/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.99/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.67 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.99/1.67 }.
% 0.99/1.67 { ! hAPP( c_Complex_Ocnj, Y ) = hAPP( c_Complex_Ocnj, X ), Y = X }.
% 0.99/1.67 { ! Y = X, hAPP( c_Complex_Ocnj, Y ) = hAPP( c_Complex_Ocnj, X ) }.
% 0.99/1.67 { hAPP( c_Complex_Ocnj, hAPP( c_Complex_Ocnj, X ) ) = X }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.99/1.67 { c_Lim_OisUCont( tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Complex_Ocnj
% 0.99/1.67 ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.67 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.67 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, U ) ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.67 c_Groups_Oabs__class_Oabs( X, U ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha2( X, Y, Z, T ),
% 0.99/1.67 alpha10( X, Y, Z, T ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! alpha10( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.99/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! alpha10( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.67 ), T ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha10( X, Y, Z, T ) }.
% 0.99/1.67 { ! alpha2( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.67 { ! alpha2( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.99/1.67 ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha2( X, Y, Z, T ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha3( X, Y, Z, T ),
% 0.99/1.67 alpha11( X, Y, Z, T ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! alpha11( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 0.99/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! alpha11( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 0.99/1.67 ), Z ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha11( X, Y, Z, T ) }.
% 0.99/1.67 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 0.99/1.67 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 0.99/1.67 ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha3( X, Y, Z, T ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 0.99/1.67 ( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 0.99/1.67 { hAPP( c_Complex_Ocnj, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.67 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( c_Complex_Ocnj
% 0.99/1.67 , Y ) ), X ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.99/1.67 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.67 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.67 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.67 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.99/1.67 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.67 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 0.99/1.67 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 0.99/1.67 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 0.99/1.67 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 0.99/1.67 .
% 0.99/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 0.99/1.67 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.99/1.67 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.67 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 0.99/1.67 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.67 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.67 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.67 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.99/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.99/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.99/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.67 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.67 ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.99/1.67 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.67 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.67 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 0.99/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 0.99/1.67 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.99/1.68 = Y }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Z ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Y ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), Z ) ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.68 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.68 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.99/1.68 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.99/1.68 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 0.99/1.68 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 0.99/1.68 , X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.68 ), ! Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.68 X ) ), Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_RealDef_Oreal, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.68 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y )
% 0.99/1.68 , X ) ), Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 0.99/1.68 , X ) ) }.
% 0.99/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.68 , Y ), X ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( c_Complex_ORe, hAPP( c_Complex_Ocnj, X ) ) = hAPP( c_Complex_ORe, X
% 0.99/1.68 ) }.
% 0.99/1.68 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.68 c_Complex_Ocnj, X ) ) = c_RealVector_Onorm__class_Onorm(
% 0.99/1.68 tc_Complex_Ocomplex, X ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), hAPP( c_Complex_Ocnj
% 0.99/1.68 , Y ) ), hAPP( c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex )
% 0.99/1.68 ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.68 { ! hAPP( c_Complex_Ocnj, X ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Complex_Ocomplex ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.99/1.68 c_Complex_Ocnj, X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex )
% 0.99/1.68 }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) )
% 0.99/1.68 = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 0.99/1.68 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 tc_Complex_Ocomplex ), X ) ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 tc_Complex_Ocomplex ), hAPP( c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.68 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.68 ), c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun
% 0.99/1.68 ( X, X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.68 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 0.99/1.68 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.99/1.68 c_SEQ_OCauchy( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.99/1.68 c_SEQ_OCauchy( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X )
% 0.99/1.68 , tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), c_Lim_OisUCont( X, X,
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), c_Lim_OisUCont( X, X,
% 0.99/1.68 c_COMBC( X, X, X, c_Groups_Otimes__class_Otimes( X ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha4( X
% 0.99/1.68 , Y, Z ), alpha12( X, Y, Z ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! alpha12( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! alpha12( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), alpha12( X, Y, Z ) }.
% 0.99/1.68 { ! alpha4( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.68 { ! alpha4( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), alpha4( X, Y, Z ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), alpha5( X, Y, Z ), alpha13( X, Y, Z
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! alpha13( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! alpha13( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), alpha13( X, Y, Z ) }.
% 0.99/1.68 { ! alpha5( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.99/1.68 { ! alpha5( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), alpha5( X, Y, Z ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.99/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.99/1.68 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), Y ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Y ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 , Z ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 , Y ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 0.99/1.68 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 0.99/1.68 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ), ! Y = c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( X ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.99/1.68 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.99/1.68 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.99/1.68 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.68 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.68 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 , Y ) }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 X ), Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) ) }.
% 0.99/1.68 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 0.99/1.68 tc_Complex_Ocomplex, c_COMBB( tc_Complex_Ocomplex, tc_Complex_Ocomplex,
% 0.99/1.68 tc_Nat_Onat, c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! c_SEQ_OCauchy( tc_Complex_Ocomplex, X ), c_SEQ_OCauchy(
% 0.99/1.68 tc_Complex_Ocomplex, c_COMBB( tc_Complex_Ocomplex, tc_Complex_Ocomplex,
% 0.99/1.68 tc_Nat_Onat, c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_RealDef_Oreal ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 0.99/1.68 { hAPP( c_Complex_OIm, hAPP( c_Complex_Ocnj, X ) ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm
% 0.99/1.68 , X ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.99/1.68 c_Complex_Ocomplex_OComplex( Y, hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.68 tc_RealDef_Oreal ), X ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 0.99/1.68 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) = c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring__abs( X ), alpha17( X, Z ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , Y ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring__abs( X ), alpha17( X, Z ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.99/1.68 { ! alpha17( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.99/1.68 { ! alpha17( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 0.99/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ) ), alpha17( X, Y ) }.
% 0.99/1.68 { ! class_Groups_Oabs__if( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), c_Groups_Oabs__class_Oabs( X, Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.68 { ! class_Groups_Oabs__if( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.68 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) ), c_Groups_Oabs__class_Oabs
% 0.99/1.68 ( X, Y ) = Y }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), c_Groups_Oabs__class_Oabs( X, Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.68 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.68 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ), ! Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.68 = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 0.99/1.68 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ) ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP
% 0.99/1.68 ( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), Y ) ), X ) ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), X ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, T ) ) ) ), Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 0.99/1.68 = hAPP( c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone
% 0.99/1.68 ( X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), c_Groups_Osgn__class_Osgn( X, Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 ), c_Groups_Osgn__class_Osgn( X, Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), c_Groups_Osgn__class_Osgn( X,
% 0.99/1.68 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.68 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) ), Y ) ), c_Groups_Osgn__class_Osgn( X, Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol14( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol14( X, Y ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol64( X, Y, Z ) ) ) ), Z )
% 0.99/1.68 ), c_SEQ_OBseq( X, Y ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.99/1.68 .
% 0.99/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.68 { alpha18( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.68 { alpha18( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.99/1.68 ( X, Y ), Z ) ) }.
% 0.99/1.68 { ! alpha18( X, Y, Z ), alpha21( X, Y, Z ), Z = Y }.
% 0.99/1.68 { ! alpha18( X, Y, Z ), alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! alpha21( X, Y, Z ), alpha18( X, Y, Z ) }.
% 0.99/1.68 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha18( X, Y, Z ) }.
% 0.99/1.68 { ! alpha21( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.68 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.68 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha21( X, Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 X = Y }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.99/1.68 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 0.99/1.68 Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 0.99/1.68 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Nat_Onat, Z ), X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 0.99/1.68 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.68 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 0.99/1.68 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 0.99/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_Int_Oint, Y ) ), X ) ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.99/1.68 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 0.99/1.68 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.99/1.68 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.99/1.68 .
% 0.99/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.99/1.68 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.68 .
% 0.99/1.68 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.99/1.68 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 0.99/1.68 = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.68 , X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.99/1.68 , X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.99/1.68 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.68 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.68 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.99/1.68 , Y ), X ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Nat_Onat ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Nat_Onat ) }.
% 0.99/1.68 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.99/1.68 c_Complex_Ocnj, Y ) ), hAPP( c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! c_SEQ_Osubseq( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, Z ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( X ) ),
% 0.99/1.68 skol65( X ) ) ), c_SEQ_Osubseq( X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X,
% 0.99/1.68 skol15( X ) ) ), hAPP( X, skol65( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.68 Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.68 Y ), X ) ) ) }.
% 0.99/1.68 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.99/1.68 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 0.99/1.68 ) }.
% 0.99/1.68 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.99/1.68 ( tc_Nat_Onat, X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.68 , Y ), X ) ) ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.68 , Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.68 { c_Complex_Oexpi( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), c_Complex_Oexpi( Y
% 0.99/1.68 ) ), c_Complex_Oexpi( X ) ) }.
% 0.99/1.68 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_Complex_Ocomplex ), X ), hAPP( c_Complex_Ocnj, X ) ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.99/1.68 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal
% 0.99/1.68 ( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 0.99/1.68 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 0.99/1.68 ) ), hAPP( c_Complex_ORe, X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.99/1.68 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), Y ) ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol16( X, Y ) ), Y
% 0.99/1.68 ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.68 , Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.99/1.68 , Y ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( tc_Int_Oint ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), X ) ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), X ) ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 0.99/1.68 hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.68 ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.68 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.68 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 0.99/1.68 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.68 Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.68 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 0.99/1.68 ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), c_Groups_Oabs__class_Oabs
% 0.99/1.68 ( tc_Int_Oint, X ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint )
% 0.99/1.68 , X ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), c_Groups_Oabs__class_Oabs
% 0.99/1.68 ( tc_Int_Oint, X ) = X }.
% 0.99/1.68 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.68 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_Int_Oint, Y ) ), X ) ) ) }.
% 0.99/1.68 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 0.99/1.68 }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 0.99/1.68 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.68 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.99/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.99/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.99/1.68 .
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Int_Oint, Y ), U ) ) }.
% 0.99/1.68 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.99/1.68 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 0.99/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 0.99/1.68 ), Y = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.68 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 0.99/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.99/1.68 ( tc_Int_Oint, U ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 0.99/1.68 ( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.99/1.68 tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol17 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol17 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol18 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol18 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol19( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, Z ) ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), hAPP( Y, skol66( X, Y ) ) ) ) ) ),
% 0.99/1.68 skol19( X, Y ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, skol72( X, Y, Z, T ) ) ), hAPP
% 0.99/1.68 ( c_Groups_Ouminus__class_Ouminus( X ), hAPP( Y, T ) ) ) ) ), Z ) ),
% 0.99/1.68 c_SEQ_OBseq( X, Y ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol20( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, Z ) ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), skol67( X, Y ) ) ) ) ), skol20( X,
% 0.99/1.68 Y ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( Y, skol73( X, Y, Z, T ) ) ), hAPP
% 0.99/1.68 ( c_Groups_Ouminus__class_Ouminus( X ), T ) ) ) ), Z ) ), c_SEQ_OBseq( X
% 0.99/1.68 , Y ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol21 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol21 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol22 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol22 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.99/1.68 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol23 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.68 c_Complex_Ocnj, X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.68 , X ) ), skol23 ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol24( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol24( X, Y ) ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol25( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol26( Y ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol26( X ) ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol27 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 0.99/1.68 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol28 ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.99/1.68 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.99/1.68 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 0.99/1.68 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.99/1.68 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.68 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.99/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }
% 0.99/1.68 .
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol29 ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.68 c_Complex_Ocnj, X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.68 , X ) ), skol29 ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol30( X, Y, Z ) ) ) ), Y )
% 0.99/1.68 ), c_SEQ_OBseq( X, Z ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol31( Z, T ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol31( X, Y ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 0.99/1.68 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.99/1.68 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 0.99/1.68 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 0.99/1.68 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 0.99/1.68 ) ), hAPP( c_Complex_ORe, X ) ) ) ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.68 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.99/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.68 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.68 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.68 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.99/1.68 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.99/1.68 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.99/1.68 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.99/1.68 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.99/1.68 hAPP( Z, Y ) ) }.
% 0.99/1.68 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.99/1.68 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.99/1.68 hAPP( Z, Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, Y, Z ) ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal ), X ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) = Z }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), Y ) = Z }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.68 , Y ) ) = c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.68 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.99/1.68 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.99/1.68 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.99/1.68 ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.99/1.68 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.99/1.68 ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 0.99/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.68 , Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.99/1.68 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) = hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 W ) ), U ) ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ) ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.68 Z ) ), U ) ), T ) = Y }.
% 0.99/1.68 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) = Y, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( X, T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.68 , T, Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), U ), c_Groups_Ominus__class_Ominus( X
% 0.99/1.68 , T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.68 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.68 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.68 ( X, Y ) ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 W ) ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.68 Z ) ), U ) ), T ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.99/1.68 Z ) ), U ) ), T ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 W ) ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ) }.
% 0.99/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.99/1.68 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.68 ( X ), U ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) )
% 0.99/1.68 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z ) )
% 0.99/1.68 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Y
% 0.99/1.68 ) ) ) ) ) }.
% 0.99/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) ), T ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.99/1.68 ) ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.99/1.68 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.99/1.68 Y ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.99/1.68 Z ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.68 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 0.99/1.68 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), T ), X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.99/1.68 ( tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 0.99/1.68 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.68 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 0.99/1.68 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 0.99/1.68 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), alpha6( X, Y, Z
% 0.99/1.68 ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol32( Z, T ) ) ),
% 0.99/1.68 c_SEQ_OCauchy( X, Y ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! alpha6( X, Y, skol32( X
% 0.99/1.68 , Y ) ), c_SEQ_OCauchy( X, Y ) }.
% 0.99/1.68 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.68 tc_Nat_Onat, skol33( X, Y, Z ) ), T ) ), alpha14( X, Y, Z, skol33( X, Y,
% 0.99/1.68 Z ), T ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol68
% 0.99/1.68 ( U, W, V0, T ) ) ), alpha6( X, Y, Z ) }.
% 0.99/1.68 { ! alpha14( X, Y, Z, T, skol68( X, Y, Z, T ) ), alpha6( X, Y, Z ) }.
% 0.99/1.68 { ! alpha14( X, Y, Z, T, U ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), W ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 hAPP( Y, U ), hAPP( Y, W ) ) ) ), Z ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol34
% 0.99/1.68 ( W, V0, V1, T, V2 ) ) ), alpha14( X, Y, Z, T, U ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.99/1.68 hAPP( Y, U ), hAPP( Y, skol34( X, Y, Z, T, U ) ) ) ) ), Z ) ), alpha14( X
% 0.99/1.68 , Y, Z, T, U ) }.
% 0.99/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol35( X, Y, Z ) ), T )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol35
% 0.99/1.68 ( X, Y, Z ) ), U ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( X, hAPP( Y, T ), hAPP( Y, U ) ) ) ), Z ) )
% 0.99/1.68 }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.68 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.68 { hAPP( c_Complex_ORe, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.99/1.68 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ) ) }.
% 0.99/1.68 { hAPP( c_Complex_OIm, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.99/1.68 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.99/1.68 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.99/1.68 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.99/1.68 , Z, X ) ) }.
% 0.99/1.68 { hAPP( c_Complex_Ocnj, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex
% 0.99/1.68 , Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 0.99/1.68 c_Complex_Ocnj, Y ), hAPP( c_Complex_Ocnj, X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( tc_Nat_Onat, X, Y ) ), Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Y ) = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 0.99/1.68 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 0.99/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 0.99/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.68 Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) = X }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.99/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 0.99/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.99/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 0.99/1.68 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), hAPP(
% 0.99/1.68 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.68 , alpha7( X, Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.68 , alpha15( X, Y, Z ) }.
% 0.99/1.68 { ! alpha7( X, Y, Z ), ! alpha15( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.68 { ! alpha15( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, skol36( T, U, Z ) ) ), alpha15( X, Y, Z ) }.
% 0.99/1.68 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol36(
% 0.99/1.68 X, Y, Z ) ), alpha15( X, Y, Z ) }.
% 0.99/1.68 { ! alpha7( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ) ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 alpha7( X, Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha7
% 0.99/1.68 ( X, Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.68 , ! alpha8( X, Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.99/1.68 , ! alpha16( X, Y, Z ) }.
% 0.99/1.68 { alpha8( X, Y, Z ), alpha16( X, Y, Z ), hBOOL( hAPP( Z,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.99/1.68 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( Z, skol37( T, U, Z ) ) ) }.
% 0.99/1.68 { ! alpha16( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.68 tc_Nat_Onat ), X ), skol37( X, Y, Z ) ) }.
% 0.99/1.68 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 0.99/1.68 hBOOL( hAPP( Z, T ) ), alpha16( X, Y, Z ) }.
% 0.99/1.68 { ! alpha8( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.68 { ! alpha8( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8( X
% 0.99/1.68 , Y, Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.68 tc_Int_Oint, Y ), X ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Int_Oint ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z,
% 0.99/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) =
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }
% 0.99/1.68 .
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.99/1.68 }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 0.99/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 0.99/1.68 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 0.99/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 0.99/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.99/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatfloor(
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.68 c_RComplete_Onatfloor( X ), Y ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatceiling(
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.99/1.68 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.68 c_RComplete_Onatceiling( X ), Y ) }.
% 0.99/1.68 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.99/1.68 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.99/1.68 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.99/1.68 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.99/1.68 ), Z ), Y ) }.
% 0.99/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ) ), hAPP(
% 0.99/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( c_Complex_ORe, Y )
% 0.99/1.68 , hAPP( c_Complex_ORe, X ) ) ) ), c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 0.99/1.68 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) ) ) ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( tc_Int_Oint, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.99/1.68 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 0.99/1.68 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_Int_Oint, Z, Y ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X
% 0.99/1.68 ) ) ), Y ) ) }.
% 0.99/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 0.99/1.68 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) ) }.
% 0.99/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.68 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.99/1.68 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.99/1.68 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( X ) }.
% 0.99/1.68 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.99/1.68 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.99/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.99/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.99/1.68 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.99/1.68 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.68 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 0.99/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 0.99/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ), c_Complex_Oii )
% 0.99/1.68 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.99/1.69 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.69 { hAPP( c_Complex_ORe, c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 0.99/1.69 tc_RealDef_Oreal ) }.
% 0.99/1.69 { hAPP( c_Complex_OIm, c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 0.99/1.69 tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { hAPP( c_Complex_Ocnj, c_Complex_Oii ) = hAPP(
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), c_Complex_Oii ) }
% 0.99/1.69 .
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.69 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) = hAPP(
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex ), X ) }.
% 0.99/1.69 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 0.99/1.69 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.99/1.69 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.99/1.69 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.69 c_Complex_Ocomplex_OComplex( Y, X ) ), c_Complex_Oii ) =
% 0.99/1.69 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.69 tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.69 c_Complex_Oii ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.99/1.69 c_Complex_Ocomplex_OComplex( hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.99/1.69 tc_RealDef_Oreal ), X ), Y ) }.
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.99/1.69 c_Complex_Oii ), c_Complex_Oii ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 0.99/1.69 ( tc_Complex_Ocomplex ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex )
% 0.99/1.69 ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.99/1.69 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol38( X ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 0.99/1.69 tc_Nat_Onat, skol38( X ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), skol39( X, U
% 0.99/1.69 , W, T ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.99/1.69 V0 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.99/1.69 hAPP( Z, T ), hAPP( Z, skol39( X, Y, Z, T ) ) ) ) ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), U ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.69 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.69 tc_Int_Oint, X, Y ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.99/1.69 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.99/1.69 ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.99/1.69 , Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 0.99/1.69 ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.99/1.69 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.99/1.69 tc_Int_Oint, X, Y ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.99/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U, Z
% 0.99/1.69 ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 0.99/1.69 skol40( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 0.99/1.69 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.99/1.69 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.99/1.69 , T ), X ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, skol40( X, Y ), X ) ) ), !
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y, T
% 0.99/1.69 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, T, hAPP
% 0.99/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol41( T, U, W ) ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol41( X, Y
% 0.99/1.69 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_RealDef_Oreal, Y ), T ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol41( X, Y
% 0.99/1.69 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_RealDef_Oreal, T ), Z ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP( Y,
% 0.99/1.69 skol42( Z, Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL
% 0.99/1.69 ( hAPP( Y, U ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.69 ( tc_Int_Oint ), U ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP( Y,
% 0.99/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), skol42( X, Y ) )
% 0.99/1.69 , X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 0.99/1.69 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y,
% 0.99/1.69 T ) ), hBOOL( hAPP( Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.69 tc_Int_Oint ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.99/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.69 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 skol43( Z, Y ) ), Y ) ) }.
% 0.99/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.69 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Nat_Onat, Z ), skol43( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.99/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.99/1.69 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.69 tc_Nat_Onat ), skol43( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.99/1.69 ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol44( Z, T ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol44( X, Y ) ), X ) =
% 0.99/1.69 Y }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol45( Z, T ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol45( X, Y ) ), X ) =
% 0.99/1.69 Y }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.99/1.69 skol45( X, Y ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol46( Y ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol46( X ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol47( Z, T ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol47( X, Y ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol48( Z, T ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol48( X, Y ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.99/1.69 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.99/1.69 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.99/1.69 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 0.99/1.69 ), c_SEQ_Olim( X, c_COMBB( X, X, tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus( X ), c_SEQ_Olim( X, Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.69 ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ), hBOOL( hAPP
% 0.99/1.69 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln(
% 0.99/1.69 X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), !
% 0.99/1.69 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! X = Y,
% 0.99/1.69 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.69 ) ), X ) ) }.
% 0.99/1.69 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.99/1.69 ( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ), hBOOL(
% 0.99/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 0.99/1.69 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.99/1.69 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! X =
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.99/1.69 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.99/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.99/1.69 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.99/1.69 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 0.99/1.69 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 0.99/1.69 ( tc_RealDef_Oreal ), c_Transcendental_Oln( X ) ), c_Transcendental_Oln(
% 0.99/1.69 Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.99/1.69 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) ), X ) ) }.
% 0.99/1.69 { alpha19( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Z )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ),
% 0.99/1.69 hAPP( X, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Nat_Onat, skol49( T, Y, U ) ), Y ) ) }.
% 0.99/1.69 { alpha19( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Z )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ),
% 0.99/1.69 hAPP( X, Y ) ) ), hAPP( X, skol49( X, Y, Z ) ) = Z }.
% 0.99/1.69 { ! alpha19( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, skol50( Z, Y ) ), Y ) ) }.
% 0.99/1.69 { ! alpha19( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X, hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), skol50( X, Y ) ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol50( X, Y ) ) )
% 0.99/1.69 ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.69 tc_Int_Oint, hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.69 tc_Nat_Onat ), Z ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X
% 0.99/1.69 , Z ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), alpha19( X, Y
% 0.99/1.69 ) }.
% 0.99/1.69 { alpha20( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Z )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ),
% 0.99/1.69 hAPP( X, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Nat_Onat, skol51( T, Y, U ) ), Y ) ) }.
% 0.99/1.69 { alpha20( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Z )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ),
% 0.99/1.69 hAPP( X, Y ) ) ), hAPP( X, skol51( X, Y, Z ) ) = Z }.
% 0.99/1.69 { ! alpha20( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, skol52( Z, Y ) ), Y ) ) }.
% 0.99/1.69 { ! alpha20( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( X, hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), skol52( X, Y ) ),
% 0.99/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X, skol52( X, Y ) ) )
% 0.99/1.69 ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.99/1.69 tc_Int_Oint, hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 0.99/1.69 tc_Nat_Onat ), Z ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), hAPP( X
% 0.99/1.69 , Z ) ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), alpha20( X, Y
% 0.99/1.69 ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.99/1.69 c_Complex_Ocnj, X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.99/1.69 , X ) ), skol53 ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol54( T, U, W ) ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol54( X, Y
% 0.99/1.69 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 Y ), T ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 0.99/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 0.99/1.69 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol54( X, Y
% 0.99/1.69 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 T ), Z ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol55( X, Y, Z ) ) ) ), Z )
% 0.99/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 0.99/1.69 tc_Nat_Onat, c_Nat_OSuc( skol69( X, Y ) ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ) ),
% 0.99/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol76( T, U ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ) ),
% 0.99/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol76( X, Y ) ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol56( X, Y, Z ) ) ) ), Z )
% 0.99/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 0.99/1.69 tc_Nat_Onat, c_Nat_OSuc( skol70( X, Y ) ) ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ) ),
% 0.99/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol77( T, U ) ) ) }.
% 0.99/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ) ),
% 0.99/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.99/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol77( X, Y ) ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 0.99/1.69 ), c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.99/1.69 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), c_Nat_OSuc( X ) ) }
% 0.99/1.69 .
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.99/1.69 ( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.99/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.99/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.99/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.99/1.69 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, c_Nat_OSuc( Y ) ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X,
% 0.99/1.69 skol57( X ) ) ), hAPP( X, c_Nat_OSuc( skol57( X ) ) ) ) ), c_SEQ_Osubseq
% 0.99/1.69 ( X ) }.
% 0.99/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ) ) }.
% 0.99/1.69 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.99/1.69 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.99/1.69 ) ) }.
% 0.99/1.69 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.99/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.99/1.69 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.99/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, c_Nat_OSuc
% 0.99/1.69 ( Z ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y,
% 0.99/1.69 c_Nat_OSuc( T ) ) ), hAPP( Y, T ) ) ) }.
% 0.99/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol58( X, Y ) ) ), hAPP(
% 0.99/1.69 Y, c_Nat_OSuc( skol58( X, Y ) ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 0.99/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, c_Nat_OSuc( skol71( X, Y )
% 0.99/1.69 ) ) ), hAPP( Y, skol71( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 0.99/1.69 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 0.99/1.69 ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 0.99/1.69 , X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 0.99/1.69 ), Z ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 c_Nat_OSuc( Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) ), X = Y }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) ), Y = X }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 0.99/1.69 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.69 c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.69 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.69 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.99/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.99/1.69 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.99/1.69 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 0.99/1.69 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 0.99/1.69 ), c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) ) }.
% 0.99/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.69 c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 0.99/1.69 ( Y ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.69 c_Nat_OSuc( Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.99/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.99/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.99/1.69 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.69 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.99/1.69 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.99/1.69 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.99/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.99/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.99/1.69 { ! X = c_Nat_OSuc( X ) }.
% 0.99/1.69 { ! c_Nat_OSuc( X ) = X }.
% 0.99/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.69 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.99/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.99/1.69 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.69 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.99/1.69 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 0.99/1.69 , X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 0.99/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.69 ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.99/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.99/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 0.99/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.99/1.69 ) ), X ) ) ) }.
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.99/1.69 ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 0.99/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.99/1.69 ( X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 0.99/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 0.99/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.69 ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 0.99/1.69 , X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.99/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 0.99/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.99/1.69 ), X ) ) ) }.
% 0.99/1.69 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.99/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.99/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.99/1.69 Y ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.69 c_Nat_OSuc( Y ) ) ), X = Y }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 0.99/1.69 c_Nat_OSuc( Y ) ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 0.99/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.99/1.69 Y ) ), X ) ) }.
% 0.99/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.99/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 0.99/1.69 c_Nat_OSuc( X ) ) ) }.
% 0.99/1.69 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.69 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.99/1.69 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.99/1.69 ( tc_fun( Y, X ) ) }.
% 0.99/1.69 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.99/1.69 ) ) }.
% 0.99/1.69 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.99/1.69 .
% 0.99/1.69 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.99/1.69 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.99/1.69 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.99/1.69 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.69 tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.99/1.69 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.99/1.69 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.99/1.69 { class_Power_Opower( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.99/1.69 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.99/1.69 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.99/1.69 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.69 tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.99/1.69 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.99/1.69 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.69 tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.99/1.69 .
% 0.99/1.69 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_SEQ_Ocomplete__space( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.99/1.69 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.69 tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_RealVector_Ometric__space( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_SEQ_Ocomplete__space( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.99/1.69 { ! class_Rings_Oidom( X ),
% 0.99/1.69 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.99/1.69 ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.99/1.69 X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.99/1.69 ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.69 .
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.69 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ),
% 0.99/1.69 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.99/1.69 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.99/1.69 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.99/1.69 ( tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.99/1.69 ) ) }.
% 0.99/1.69 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.99/1.69 .
% 0.99/1.69 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.99/1.69 tc_Polynomial_Opoly( X ) ) }.
% 0.99/1.69 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 0.99/1.69 { hAPP( c_COMBB( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 0.99/1.69 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 0.99/1.69 { hAPP( c_COMBS( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), hAPP( Y, X ) )
% 0.99/1.69 }.
% 0.99/1.69 { ! c_SEQ_OBseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 0.99/1.69 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 0.99/1.69 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 0.99/1.69 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 0.99/1.69
% 0.99/1.69 *** allocated 15000 integers for clauses
% 0.99/1.69 *** allocated 22500 integers for clauses
% 0.99/1.69 *** allocated 33750 integers for clauses
% 0.99/1.69 *** allocated 50625 integers for clauses
% 0.99/1.69 *** allocated 75937 integers for clauses
% 0.99/1.69 percentage equality = 0.243010, percentage horn = 0.930111
% 0.99/1.69 This is a problem with some equality
% 0.99/1.69
% 0.99/1.69
% 0.99/1.69
% 0.99/1.69 Options Used:
% 0.99/1.69
% 0.99/1.69 useres = 1
% 0.99/1.69 useparamod = 1
% 0.99/1.69 useeqrefl = 1
% 0.99/1.69 useeqfact = 1
% 0.99/1.69 usefactor = 1
% 0.99/1.69 usesimpsplitting = 0
% 0.99/1.69 usesimpdemod = 5
% 0.99/1.69 usesimpres = 3
% 0.99/1.69
% 0.99/1.69 resimpinuse = 1000
% 0.99/1.69 resimpclauses = 20000
% 0.99/1.69 substype = eqrewr
% 0.99/1.69 backwardsubs = 1
% 0.99/1.69 selectoldest = 5
% 0.99/1.69
% 0.99/1.69 litorderings [0] = split
% 0.99/1.69 litorderings [1] = extend the termordering, first sorting on arguments
% 0.99/1.69
% 0.99/1.69 termordering = kbo
% 0.99/1.69
% 0.99/1.69 litapriori = 0
% 0.99/1.69 termapriori = 1
% 0.99/1.69 litaposteriori = 0
% 0.99/1.69 termaposteriori = 0
% 0.99/1.69 demodaposteriori = 0
% 0.99/1.69 ordereqreflfact = 0
% 0.99/1.69
% 0.99/1.69 litselect = negord
% 0.99/1.69
% 0.99/1.69 maxweight = 15
% 0.99/1.69 maxdepth = 30000
% 0.99/1.69 maxlength = 115
% 0.99/1.69 maxnrvars = 195
% 0.99/1.69 excuselevel = 1
% 0.99/1.69 increasemaxweight = 1
% 0.99/1.69
% 0.99/1.69 maxselected = 10000000
% 0.99/1.69 maxnrclauses = 10000000
% 0.99/1.69
% 0.99/1.69 showgenerated = 0
% 0.99/1.69 showkept = 0
% 0.99/1.69 showselected = 0
% 0.99/1.69 showdeleted = 0
% 0.99/1.69 showresimp = 1
% 0.99/1.69 showstatus = 2000
% 0.99/1.69
% 0.99/1.69 prologoutput = 0
% 0.99/1.69 nrgoals = 5000000
% 0.99/1.69 totalproof = 1
% 0.99/1.69
% 0.99/1.69 Symbols occurring in the translation:
% 0.99/1.69
% 0.99/1.69 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.99/1.69 . [1, 2] (w:1, o:241, a:1, s:1, b:0),
% 0.99/1.69 ! [4, 1] (w:0, o:146, a:1, s:1, b:0),
% 0.99/1.69 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.69 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.99/1.69 hAPP [38, 2] (w:1, o:265, a:1, s:1, b:0),
% 0.99/1.69 v_f____ [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Osubseq [40, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.99/1.69 v_ga____ [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.99/1.69 tc_RealDef_Oreal [42, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.99/1.69 tc_Complex_Ocomplex [43, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.99/1.69 tc_Nat_Onat [44, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_OIm [45, 0] (w:1, o:30, a:1, s:1, b:0),
% 0.99/1.69 v_s [46, 0] (w:1, o:32, a:1, s:1, b:0),
% 0.99/1.69 c_COMBB [47, 5] (w:1, o:367, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Omonoseq [48, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_ORe [49, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Oconvergent [51, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.99/1.69 c_RealVector_Onorm__class_Onorm [53, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 c_Orderings_Oord__class_Oless__eq [54, 2] (w:1, o:273, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 v_r [55, 0] (w:1, o:31, a:1, s:1, b:0),
% 0.99/1.69 hBOOL [56, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.99/1.69 c_Fun_Ocomp [58, 5] (w:1, o:368, a:1, s:1, b:0),
% 0.99/1.69 c_Lim_OisUCont [59, 3] (w:1, o:326, a:1, s:1, b:0),
% 0.99/1.69 class_RealVector_Oreal__normed__vector [63, 1] (w:1, o:155, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 c_SEQ_OBseq [64, 2] (w:1, o:274, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Oplus__class_Oplus [65, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.99/1.69 c_COMBC [66, 5] (w:1, o:369, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Ouminus__class_Ouminus [67, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 c_SEQ_OCauchy [68, 2] (w:1, o:275, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Oabs__class_Oabs [69, 2] (w:1, o:277, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Oone__class_Oone [70, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Ozero__class_Ozero [71, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.99/1.69 class_RealVector_Ometric__space [73, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 c_COMBK [74, 3] (w:1, o:327, a:1, s:1, b:0),
% 0.99/1.69 class_SEQ_Ocomplete__space [75, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.99/1.69 class_Orderings_Oorder [77, 1] (w:1, o:195, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Oordered__ab__group__add [80, 1] (w:1, o:196, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 tc_fun [82, 2] (w:1, o:314, a:1, s:1, b:0),
% 0.99/1.69 c_COMBS [83, 5] (w:1, o:370, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Oordered__ab__group__add__abs [88, 1] (w:1, o:197, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_RealVector_Oreal__normed__algebra__1 [91, 1] (w:1, o:162, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Ozero [96, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ocancel__semigroup__add [100, 1] (w:1, o:199, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 class_Groups_Ocancel__ab__semigroup__add [101, 1] (w:1, o:200, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Oab__semigroup__add [102, 1] (w:1, o:201, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Groups_Oone [103, 1] (w:1, o:202, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ogroup__add [104, 1] (w:1, o:203, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ocomm__monoid__add [108, 1] (w:1, o:204, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Groups_Omonoid__add [109, 1] (w:1, o:206, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Olinordered__ab__group__add [110, 1] (w:1, o:205, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Oordered__ab__semigroup__add__imp__le [111, 1] (w:1, o:
% 0.99/1.69 207, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Oordered__ab__semigroup__add [113, 1] (w:1, o:208, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Oab__group__add [114, 1] (w:1, o:209, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Oordered__comm__monoid__add [116, 1] (w:1, o:210, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__semidom [119, 1] (w:1, o:165, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Orderings_Opreorder [120, 1] (w:1, o:212, a:1, s:1, b:0),
% 0.99/1.69 class_Orderings_Oord [121, 1] (w:1, o:211, a:1, s:1, b:0),
% 0.99/1.69 class_Orderings_Olinorder [122, 1] (w:1, o:213, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Ozero__neq__one [130, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__idom [131, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Odecseq [134, 2] (w:1, o:315, a:1, s:1, b:0),
% 0.99/1.69 class_Lattices_Oboolean__algebra [135, 1] (w:1, o:215, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Rings_Ocomm__semiring__1 [136, 1] (w:1, o:171, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.99/1.69 137, 1] (w:1, o:216, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ouminus [139, 1] (w:1, o:217, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Oincseq [140, 2] (w:1, o:316, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Oexpi [141, 1] (w:1, o:218, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Osgn__class_Osgn [144, 2] (w:1, o:317, a:1, s:1, b:0),
% 0.99/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [146, 2] (w:1, o:
% 0.99/1.69 276, a:1, s:1, b:0),
% 0.99/1.69 tc_Polynomial_Opoly [147, 1] (w:1, o:227, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Osgn__if [148, 1] (w:1, o:228, a:1, s:1, b:0),
% 0.99/1.69 c_Power_Opower__class_Opower [149, 1] (w:1, o:229, a:1, s:1, b:0),
% 0.99/1.69 c_RComplete_Onatceiling [150, 1] (w:1, o:151, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Ocomplex_OComplex [151, 2] (w:1, o:318, a:1, s:1, b:0),
% 0.99/1.69 class_RealVector_Oreal__normed__div__algebra [152, 1] (w:1, o:172, a:
% 0.99/1.69 1, s:1, b:0),
% 0.99/1.69 c_Complex_Ocomplex_Ocomplex__size [164, 1] (w:1, o:230, a:1, s:1, b:0
% 0.99/1.69 ),
% 0.99/1.69 class_Power_Opower [165, 1] (w:1, o:231, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Osemiring__0 [166, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Oring__1__no__zero__divisors [167, 1] (w:1, o:173, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Omonoid__mult [168, 1] (w:1, o:232, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Omult__zero [169, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Ono__zero__divisors [170, 1] (w:1, o:184, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 c_Nat_Osize__class_Osize [171, 2] (w:1, o:271, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Ocomplex_Ocomplex__case [173, 3] (w:1, o:328, a:1, s:1, b:0
% 0.99/1.69 ),
% 0.99/1.69 c_Complex_Ocomplex_Ocomplex__rec [174, 3] (w:1, o:329, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 c_RComplete_Onatfloor [175, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.99/1.69 c_RealDef_Oreal [176, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.99/1.69 c_Orderings_Oord__class_Oless [177, 2] (w:1, o:319, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Otimes__class_Otimes [178, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Ocnj [179, 0] (w:1, o:114, a:1, s:1, b:0),
% 0.99/1.69 class_Lattices_Oab__semigroup__idem__mult [184, 1] (w:1, o:214, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Groups_Oab__semigroup__mult [188, 1] (w:1, o:233, a:1, s:1, b:0
% 0.99/1.69 ),
% 0.99/1.69 class_RealVector_Oreal__normed__algebra [190, 1] (w:1, o:185, a:1, s:
% 0.99/1.69 1, b:0),
% 0.99/1.69 class_Rings_Olinordered__ring [191, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__ring__strict [192, 1] (w:1, o:164, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 class_Rings_Olinordered__semiring__strict [193, 1] (w:1, o:178, a:1
% 0.99/1.69 , s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__comm__semiring__strict [194, 1] (w:1, o:179
% 0.99/1.69 , a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__semiring [196, 1] (w:1, o:180, a:1, s:1, b:0
% 0.99/1.69 ),
% 0.99/1.69 class_Rings_Oring__no__zero__divisors [197, 1] (w:1, o:174, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 class_Groups_Oordered__cancel__ab__semigroup__add [198, 1] (w:1, o:
% 0.99/1.69 234, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Ocomm__semiring [199, 1] (w:1, o:186, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Osemiring [201, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ocomm__monoid__mult [207, 1] (w:1, o:235, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Rings_Oring [208, 1] (w:1, o:175, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Oidom [209, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__semiring__1__strict [213, 1] (w:1, o:181, a:
% 0.99/1.69 1, s:1, b:0),
% 0.99/1.69 class_Rings_Oordered__cancel__semiring [214, 1] (w:1, o:189, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 class_Rings_Oordered__ring [215, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Oordered__semiring [216, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 class_Rings_Oordered__comm__semiring [217, 1] (w:1, o:193, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 class_Rings_Ocomm__ring__1 [218, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Oordered__ring__abs [220, 1] (w:1, o:191, a:1, s:1, b:0)
% 0.99/1.69 ,
% 0.99/1.69 class_Groups_Oabs__if [221, 1] (w:1, o:236, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Oring__1 [222, 1] (w:1, o:176, a:1, s:1, b:0),
% 0.99/1.69 class_Rings_Olinordered__semiring__1 [223, 1] (w:1, o:182, a:1, s:1
% 0.99/1.69 , b:0),
% 0.99/1.69 tc_Int_Oint [227, 0] (w:1, o:128, a:1, s:1, b:0),
% 0.99/1.69 c_Power_Opower_Opower [234, 3] (w:1, o:330, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Orcis [239, 2] (w:1, o:320, a:1, s:1, b:0),
% 0.99/1.69 c_Groups_Ominus__class_Ominus [242, 3] (w:1, o:331, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ominus [244, 1] (w:1, o:237, a:1, s:1, b:0),
% 0.99/1.69 c_Complex_Oii [252, 0] (w:1, o:137, a:1, s:1, b:0),
% 0.99/1.69 c_Nat__Transfer_Otsub [254, 2] (w:1, o:272, a:1, s:1, b:0),
% 0.99/1.69 c_Transcendental_Oln [258, 1] (w:1, o:238, a:1, s:1, b:0),
% 0.99/1.69 c_SEQ_Olim [259, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.99/1.69 c_Nat_OSuc [260, 1] (w:1, o:239, a:1, s:1, b:0),
% 0.99/1.69 class_Groups_Ocancel__comm__monoid__add [266, 1] (w:1, o:240, a:1, s:
% 0.99/1.69 1, b:0),
% 0.99/1.69 class_Rings_Ocomm__semiring__0 [267, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.99/1.69
% 0.99/1.69 class_Rings_Ocomm__ring [268, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.99/1.69 tc_HOL_Obool [270, 0] (w:1, o:127, a:1, s:1, b:0),
% 0.99/1.69 alpha1 [275, 2] (w:1, o:321, a:1, s:1, b:1),
% 0.99/1.69 alpha2 [276, 4] (w:1, o:360, a:1, s:1, b:1),
% 0.99/1.69 alpha3 [277, 4] (w:1, o:361, a:1, s:1, b:1),
% 0.99/1.69 alpha4 [278, 3] (w:1, o:332, a:1, s:1, b:1),
% 0.99/1.69 alpha5 [279, 3] (w:1, o:333, a:1, s:1, b:1),
% 0.99/1.69 alpha6 [280, 3] (w:1, o:334, a:1, s:1, b:1),
% 0.99/1.69 alpha7 [281, 3] (w:1, o:335, a:1, s:1, b:1),
% 0.99/1.69 alpha8 [282, 3] (w:1, o:336, a:1, s:1, b:1),
% 3.67/4.02 alpha9 [283, 2] (w:1, o:322, a:1, s:1, b:1),
% 3.67/4.02 alpha10 [284, 4] (w:1, o:358, a:1, s:1, b:1),
% 3.67/4.02 alpha11 [285, 4] (w:1, o:359, a:1, s:1, b:1),
% 3.67/4.02 alpha12 [286, 3] (w:1, o:337, a:1, s:1, b:1),
% 3.67/4.02 alpha13 [287, 3] (w:1, o:338, a:1, s:1, b:1),
% 3.67/4.02 alpha14 [288, 5] (w:1, o:371, a:1, s:1, b:1),
% 3.67/4.02 alpha15 [289, 3] (w:1, o:339, a:1, s:1, b:1),
% 3.67/4.02 alpha16 [290, 3] (w:1, o:340, a:1, s:1, b:1),
% 3.67/4.02 alpha17 [291, 2] (w:1, o:323, a:1, s:1, b:1),
% 3.67/4.02 alpha18 [292, 3] (w:1, o:341, a:1, s:1, b:1),
% 3.67/4.02 alpha19 [293, 2] (w:1, o:324, a:1, s:1, b:1),
% 3.67/4.02 alpha20 [294, 2] (w:1, o:325, a:1, s:1, b:1),
% 3.67/4.02 alpha21 [295, 3] (w:1, o:342, a:1, s:1, b:1),
% 3.67/4.02 skol1 [296, 2] (w:1, o:278, a:1, s:1, b:1),
% 3.67/4.02 skol2 [297, 0] (w:1, o:17, a:1, s:1, b:1),
% 3.67/4.02 skol3 [298, 0] (w:1, o:24, a:1, s:1, b:1),
% 3.67/4.02 skol4 [299, 2] (w:1, o:281, a:1, s:1, b:1),
% 3.67/4.02 skol5 [300, 2] (w:1, o:289, a:1, s:1, b:1),
% 3.67/4.02 skol6 [301, 0] (w:1, o:26, a:1, s:1, b:1),
% 3.67/4.02 skol7 [302, 3] (w:1, o:344, a:1, s:1, b:1),
% 3.67/4.02 skol8 [303, 2] (w:1, o:294, a:1, s:1, b:1),
% 3.67/4.02 skol9 [304, 2] (w:1, o:295, a:1, s:1, b:1),
% 3.67/4.02 skol10 [305, 2] (w:1, o:296, a:1, s:1, b:1),
% 3.67/4.02 skol11 [306, 1] (w:1, o:219, a:1, s:1, b:1),
% 3.67/4.02 skol12 [307, 2] (w:1, o:297, a:1, s:1, b:1),
% 3.67/4.02 skol13 [308, 4] (w:1, o:362, a:1, s:1, b:1),
% 3.67/4.02 skol14 [309, 2] (w:1, o:298, a:1, s:1, b:1),
% 3.67/4.02 skol15 [310, 1] (w:1, o:220, a:1, s:1, b:1),
% 3.67/4.02 skol16 [311, 2] (w:1, o:299, a:1, s:1, b:1),
% 3.67/4.02 skol17 [312, 0] (w:1, o:15, a:1, s:1, b:1),
% 3.67/4.02 skol18 [313, 0] (w:1, o:16, a:1, s:1, b:1),
% 3.67/4.02 skol19 [314, 2] (w:1, o:300, a:1, s:1, b:1),
% 3.67/4.02 skol20 [315, 2] (w:1, o:301, a:1, s:1, b:1),
% 3.67/4.02 skol21 [316, 0] (w:1, o:18, a:1, s:1, b:1),
% 3.67/4.02 skol22 [317, 0] (w:1, o:19, a:1, s:1, b:1),
% 3.67/4.02 skol23 [318, 0] (w:1, o:20, a:1, s:1, b:1),
% 3.67/4.02 skol24 [319, 2] (w:1, o:302, a:1, s:1, b:1),
% 3.67/4.02 skol25 [320, 2] (w:1, o:303, a:1, s:1, b:1),
% 3.67/4.02 skol26 [321, 1] (w:1, o:221, a:1, s:1, b:1),
% 3.67/4.02 skol27 [322, 0] (w:1, o:21, a:1, s:1, b:1),
% 3.67/4.02 skol28 [323, 0] (w:1, o:22, a:1, s:1, b:1),
% 3.67/4.02 skol29 [324, 0] (w:1, o:23, a:1, s:1, b:1),
% 3.67/4.02 skol30 [325, 3] (w:1, o:345, a:1, s:1, b:1),
% 3.67/4.02 skol31 [326, 2] (w:1, o:279, a:1, s:1, b:1),
% 3.67/4.02 skol32 [327, 2] (w:1, o:280, a:1, s:1, b:1),
% 3.67/4.02 skol33 [328, 3] (w:1, o:346, a:1, s:1, b:1),
% 3.67/4.02 skol34 [329, 5] (w:1, o:372, a:1, s:1, b:1),
% 3.67/4.02 skol35 [330, 3] (w:1, o:347, a:1, s:1, b:1),
% 3.67/4.02 skol36 [331, 3] (w:1, o:348, a:1, s:1, b:1),
% 3.67/4.02 skol37 [332, 3] (w:1, o:349, a:1, s:1, b:1),
% 3.67/4.02 skol38 [333, 1] (w:1, o:222, a:1, s:1, b:1),
% 3.67/4.02 skol39 [334, 4] (w:1, o:363, a:1, s:1, b:1),
% 3.67/4.02 skol40 [335, 2] (w:1, o:282, a:1, s:1, b:1),
% 3.67/4.02 skol41 [336, 3] (w:1, o:350, a:1, s:1, b:1),
% 3.67/4.02 skol42 [337, 2] (w:1, o:283, a:1, s:1, b:1),
% 3.67/4.02 skol43 [338, 2] (w:1, o:284, a:1, s:1, b:1),
% 3.67/4.02 skol44 [339, 2] (w:1, o:285, a:1, s:1, b:1),
% 3.67/4.02 skol45 [340, 2] (w:1, o:286, a:1, s:1, b:1),
% 3.67/4.02 skol46 [341, 1] (w:1, o:223, a:1, s:1, b:1),
% 3.67/4.02 skol47 [342, 2] (w:1, o:287, a:1, s:1, b:1),
% 3.67/4.02 skol48 [343, 2] (w:1, o:288, a:1, s:1, b:1),
% 3.67/4.02 skol49 [344, 3] (w:1, o:351, a:1, s:1, b:1),
% 3.67/4.02 skol50 [345, 2] (w:1, o:304, a:1, s:1, b:1),
% 3.67/4.02 skol51 [346, 3] (w:1, o:352, a:1, s:1, b:1),
% 3.67/4.02 skol52 [347, 2] (w:1, o:305, a:1, s:1, b:1),
% 3.67/4.02 skol53 [348, 0] (w:1, o:25, a:1, s:1, b:1),
% 3.67/4.02 skol54 [349, 3] (w:1, o:353, a:1, s:1, b:1),
% 3.67/4.02 skol55 [350, 3] (w:1, o:354, a:1, s:1, b:1),
% 3.67/4.02 skol56 [351, 3] (w:1, o:355, a:1, s:1, b:1),
% 3.67/4.02 skol57 [352, 1] (w:1, o:224, a:1, s:1, b:1),
% 3.67/4.02 skol58 [353, 2] (w:1, o:306, a:1, s:1, b:1),
% 3.67/4.02 skol59 [354, 2] (w:1, o:307, a:1, s:1, b:1),
% 3.67/4.02 skol60 [355, 2] (w:1, o:308, a:1, s:1, b:1),
% 3.67/4.02 skol61 [356, 2] (w:1, o:309, a:1, s:1, b:1),
% 3.67/4.02 skol62 [357, 1] (w:1, o:225, a:1, s:1, b:1),
% 3.67/4.02 skol63 [358, 2] (w:1, o:310, a:1, s:1, b:1),
% 3.67/4.02 skol64 [359, 3] (w:1, o:343, a:1, s:1, b:1),
% 3.67/4.02 skol65 [360, 1] (w:1, o:226, a:1, s:1, b:1),
% 21.61/21.99 skol66 [361, 2] (w:1, o:311, a:1, s:1, b:1),
% 21.61/21.99 skol67 [362, 2] (w:1, o:312, a:1, s:1, b:1),
% 21.61/21.99 skol68 [363, 4] (w:1, o:364, a:1, s:1, b:1),
% 21.61/21.99 skol69 [364, 2] (w:1, o:313, a:1, s:1, b:1),
% 21.61/21.99 skol70 [365, 2] (w:1, o:290, a:1, s:1, b:1),
% 21.61/21.99 skol71 [366, 2] (w:1, o:291, a:1, s:1, b:1),
% 21.61/21.99 skol72 [367, 4] (w:1, o:365, a:1, s:1, b:1),
% 21.61/21.99 skol73 [368, 4] (w:1, o:366, a:1, s:1, b:1),
% 21.61/21.99 skol74 [369, 3] (w:1, o:356, a:1, s:1, b:1),
% 21.61/21.99 skol75 [370, 3] (w:1, o:357, a:1, s:1, b:1),
% 21.61/21.99 skol76 [371, 2] (w:1, o:292, a:1, s:1, b:1),
% 21.61/21.99 skol77 [372, 2] (w:1, o:293, a:1, s:1, b:1).
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Starting Search:
% 21.61/21.99
% 21.61/21.99 *** allocated 113905 integers for clauses
% 21.61/21.99 *** allocated 170857 integers for clauses
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 2939
% 21.61/21.99 Kept: 2000
% 21.61/21.99 Inuse: 73
% 21.61/21.99 Deleted: 0
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 *** allocated 256285 integers for clauses
% 21.61/21.99 *** allocated 170857 integers for termspace/termends
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 384427 integers for clauses
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 8092
% 21.61/21.99 Kept: 4083
% 21.61/21.99 Inuse: 311
% 21.61/21.99 Deleted: 5
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 256285 integers for termspace/termends
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 576640 integers for clauses
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 12278
% 21.61/21.99 Kept: 6513
% 21.61/21.99 Inuse: 403
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 384427 integers for termspace/termends
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 20885
% 21.61/21.99 Kept: 8635
% 21.61/21.99 Inuse: 423
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 864960 integers for clauses
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 27601
% 21.61/21.99 Kept: 11073
% 21.61/21.99 Inuse: 458
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 34588
% 21.61/21.99 Kept: 13242
% 21.61/21.99 Inuse: 478
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 576640 integers for termspace/termends
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 1297440 integers for clauses
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 39958
% 21.61/21.99 Kept: 15269
% 21.61/21.99 Inuse: 528
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 46169
% 21.61/21.99 Kept: 18306
% 21.61/21.99 Inuse: 568
% 21.61/21.99 Deleted: 8
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying clauses:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 50104
% 21.61/21.99 Kept: 20455
% 21.61/21.99 Inuse: 593
% 21.61/21.99 Deleted: 213
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 864960 integers for termspace/termends
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 54960
% 21.61/21.99 Kept: 23157
% 21.61/21.99 Inuse: 623
% 21.61/21.99 Deleted: 213
% 21.61/21.99 Deletedinuse: 0
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 1946160 integers for clauses
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 58344
% 21.61/21.99 Kept: 25161
% 21.61/21.99 Inuse: 647
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 65415
% 21.61/21.99 Kept: 27284
% 21.61/21.99 Inuse: 708
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 73743
% 21.61/21.99 Kept: 29604
% 21.61/21.99 Inuse: 718
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 1297440 integers for termspace/termends
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 80603
% 21.61/21.99 Kept: 31721
% 21.61/21.99 Inuse: 758
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 87592
% 21.61/21.99 Kept: 34033
% 21.61/21.99 Inuse: 788
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 94552
% 21.61/21.99 Kept: 36088
% 21.61/21.99 Inuse: 818
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99
% 21.61/21.99 Intermediate Status:
% 21.61/21.99 Generated: 99559
% 21.61/21.99 Kept: 38120
% 21.61/21.99 Inuse: 833
% 21.61/21.99 Deleted: 215
% 21.61/21.99 Deletedinuse: 2
% 21.61/21.99
% 21.61/21.99 Resimplifying inuse:
% 21.61/21.99 Done
% 21.61/21.99
% 21.61/21.99 *** allocated 2919240 integers for clauses
% 21.61/21.99 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying clauses:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 108130
% 73.52/73.90 Kept: 40293
% 73.52/73.90 Inuse: 883
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 119413
% 73.52/73.90 Kept: 42649
% 73.52/73.90 Inuse: 908
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 127926
% 73.52/73.90 Kept: 44683
% 73.52/73.90 Inuse: 948
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 *** allocated 1946160 integers for termspace/termends
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 146656
% 73.52/73.90 Kept: 48433
% 73.52/73.90 Inuse: 967
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 164268
% 73.52/73.90 Kept: 51356
% 73.52/73.90 Inuse: 978
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 172798
% 73.52/73.90 Kept: 55194
% 73.52/73.90 Inuse: 1018
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 176876
% 73.52/73.90 Kept: 58124
% 73.52/73.90 Inuse: 1023
% 73.52/73.90 Deleted: 468
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 187068
% 73.52/73.90 Kept: 61108
% 73.52/73.90 Inuse: 1026
% 73.52/73.90 Deleted: 475
% 73.52/73.90 Deletedinuse: 2
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying clauses:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 *** allocated 4378860 integers for clauses
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 191343
% 73.52/73.90 Kept: 64102
% 73.52/73.90 Inuse: 1031
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 199447
% 73.52/73.90 Kept: 66314
% 73.52/73.90 Inuse: 1076
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 209338
% 73.52/73.90 Kept: 70617
% 73.52/73.90 Inuse: 1116
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 224586
% 73.52/73.90 Kept: 73914
% 73.52/73.90 Inuse: 1146
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 *** allocated 2919240 integers for termspace/termends
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 231470
% 73.52/73.90 Kept: 75942
% 73.52/73.90 Inuse: 1196
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 238952
% 73.52/73.90 Kept: 79326
% 73.52/73.90 Inuse: 1221
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 243500
% 73.52/73.90 Kept: 82658
% 73.52/73.90 Inuse: 1226
% 73.52/73.90 Deleted: 2722
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying clauses:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 249264
% 73.52/73.90 Kept: 86319
% 73.52/73.90 Inuse: 1241
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 256243
% 73.52/73.90 Kept: 90160
% 73.52/73.90 Inuse: 1261
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 265083
% 73.52/73.90 Kept: 92478
% 73.52/73.90 Inuse: 1306
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 *** allocated 6568290 integers for clauses
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 277326
% 73.52/73.90 Kept: 96007
% 73.52/73.90 Inuse: 1311
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 289572
% 73.52/73.90 Kept: 99577
% 73.52/73.90 Inuse: 1316
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 295194
% 73.52/73.90 Kept: 101613
% 73.52/73.90 Inuse: 1345
% 73.52/73.90 Deleted: 2806
% 73.52/73.90 Deletedinuse: 3
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying clauses:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 317145
% 73.52/73.90 Kept: 106696
% 73.52/73.90 Inuse: 1376
% 73.52/73.90 Deleted: 2961
% 73.52/73.90 Deletedinuse: 5
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 322524
% 73.52/73.90 Kept: 110392
% 73.52/73.90 Inuse: 1381
% 73.52/73.90 Deleted: 2962
% 73.52/73.90 Deletedinuse: 6
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 73.52/73.90
% 73.52/73.90
% 73.52/73.90 Intermediate Status:
% 73.52/73.90 Generated: 329835
% 73.52/73.90 Kept: 112408
% 73.52/73.90 Inuse: 1407
% 73.52/73.90 Deleted: 2962
% 73.52/73.90 Deletedinuse: 6
% 73.52/73.90
% 73.52/73.90 Resimplifying inuse:
% 73.52/73.90 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 336064
% 123.02/123.44 Kept: 116331
% 123.02/123.44 Inuse: 1416
% 123.02/123.44 Deleted: 2962
% 123.02/123.44 Deletedinuse: 6
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 341650
% 123.02/123.44 Kept: 120150
% 123.02/123.44 Inuse: 1421
% 123.02/123.44 Deleted: 2962
% 123.02/123.44 Deletedinuse: 6
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 *** allocated 4378860 integers for termspace/termends
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 349785
% 123.02/123.44 Kept: 122540
% 123.02/123.44 Inuse: 1436
% 123.02/123.44 Deleted: 2962
% 123.02/123.44 Deletedinuse: 6
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying clauses:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 358247
% 123.02/123.44 Kept: 124716
% 123.02/123.44 Inuse: 1456
% 123.02/123.44 Deleted: 3019
% 123.02/123.44 Deletedinuse: 7
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 365778
% 123.02/123.44 Kept: 127149
% 123.02/123.44 Inuse: 1466
% 123.02/123.44 Deleted: 3020
% 123.02/123.44 Deletedinuse: 8
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 372617
% 123.02/123.44 Kept: 129833
% 123.02/123.44 Inuse: 1476
% 123.02/123.44 Deleted: 3020
% 123.02/123.44 Deletedinuse: 8
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 380068
% 123.02/123.44 Kept: 131999
% 123.02/123.44 Inuse: 1501
% 123.02/123.44 Deleted: 3020
% 123.02/123.44 Deletedinuse: 8
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 387529
% 123.02/123.44 Kept: 134535
% 123.02/123.44 Inuse: 1511
% 123.02/123.44 Deleted: 3020
% 123.02/123.44 Deletedinuse: 8
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 397279
% 123.02/123.44 Kept: 136689
% 123.02/123.44 Inuse: 1516
% 123.02/123.44 Deleted: 3020
% 123.02/123.44 Deletedinuse: 8
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 404771
% 123.02/123.44 Kept: 138780
% 123.02/123.44 Inuse: 1546
% 123.02/123.44 Deleted: 3025
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 422644
% 123.02/123.44 Kept: 143729
% 123.02/123.44 Inuse: 1561
% 123.02/123.44 Deleted: 3025
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying clauses:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 430314
% 123.02/123.44 Kept: 145746
% 123.02/123.44 Inuse: 1589
% 123.02/123.44 Deleted: 3598
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 *** allocated 9852435 integers for clauses
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 441608
% 123.02/123.44 Kept: 151135
% 123.02/123.44 Inuse: 1611
% 123.02/123.44 Deleted: 3598
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 449593
% 123.02/123.44 Kept: 153514
% 123.02/123.44 Inuse: 1636
% 123.02/123.44 Deleted: 3598
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 462530
% 123.02/123.44 Kept: 159255
% 123.02/123.44 Inuse: 1666
% 123.02/123.44 Deleted: 3598
% 123.02/123.44 Deletedinuse: 13
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 471457
% 123.02/123.44 Kept: 162197
% 123.02/123.44 Inuse: 1686
% 123.02/123.44 Deleted: 3599
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying clauses:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 481728
% 123.02/123.44 Kept: 164213
% 123.02/123.44 Inuse: 1721
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 505387
% 123.02/123.44 Kept: 170480
% 123.02/123.44 Inuse: 1749
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 523530
% 123.02/123.44 Kept: 173633
% 123.02/123.44 Inuse: 1769
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 *** allocated 6568290 integers for termspace/termends
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 531645
% 123.02/123.44 Kept: 175637
% 123.02/123.44 Inuse: 1797
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 551816
% 123.02/123.44 Kept: 179421
% 123.02/123.44 Inuse: 1819
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 558944
% 123.02/123.44 Kept: 181633
% 123.02/123.44 Inuse: 1839
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44
% 123.02/123.44 Intermediate Status:
% 123.02/123.44 Generated: 564523
% 123.02/123.44 Kept: 183719
% 123.02/123.44 Inuse: 1859
% 123.02/123.44 Deleted: 3936
% 123.02/123.44 Deletedinuse: 14
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying clauses:
% 123.02/123.44 Done
% 123.02/123.44
% 123.02/123.44 Resimplifying inuse:
% 123.02/123.44 DoCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------