TSTP Solution File: SWW209+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:14 EDT 2022
% Result : Timeout 300.03s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 4 08:41:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.96/1.60 *** allocated 10000 integers for termspace/termends
% 0.96/1.60 *** allocated 10000 integers for clauses
% 0.96/1.60 *** allocated 10000 integers for justifications
% 0.96/1.60 *** allocated 15000 integers for termspace/termends
% 0.96/1.60 *** allocated 22500 integers for termspace/termends
% 0.96/1.60 *** allocated 33750 integers for termspace/termends
% 0.96/1.60 Bliksem 1.12
% 0.96/1.60
% 0.96/1.60
% 0.96/1.60 Automatic Strategy Selection
% 0.96/1.60
% 0.96/1.60 *** allocated 50625 integers for termspace/termends
% 0.96/1.60 *** allocated 75937 integers for termspace/termends
% 0.96/1.60 *** allocated 113905 integers for termspace/termends
% 0.96/1.60
% 0.96/1.60 Clauses:
% 0.96/1.60
% 0.96/1.60 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( v_f____, X ), hAPP(
% 0.96/1.60 v_f____, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( v_ga____, X ), hAPP(
% 0.96/1.60 v_ga____, Y ) ) }.
% 0.96/1.60 { c_SEQ_Osubseq( v_f____ ) }.
% 0.96/1.60 { c_SEQ_Osubseq( v_ga____ ) }.
% 0.96/1.60 { hAPP( c_Fun_Ocomp( V0, W, U, T ), hAPP( c_Fun_Ocomp( Z, V0, U, Y ), X ) )
% 0.96/1.60 = hAPP( c_Fun_Ocomp( Z, W, U, hAPP( c_Fun_Ocomp( V0, W, Z, T ), Y ) ), X
% 0.96/1.60 ) }.
% 0.96/1.60 { hAPP( hAPP( c_Fun_Ocomp( W, U, T, Z ), Y ), X ) = hAPP( Z, hAPP( Y, X ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! hAPP( W, hAPP( U, T ) ) = hAPP( Z, hAPP( Y, X ) ), hAPP( hAPP(
% 0.96/1.60 c_Fun_Ocomp( V4, V3, V2, W ), U ), T ) = hAPP( hAPP( c_Fun_Ocomp( V1, V3
% 0.96/1.60 , V0, Z ), Y ), X ) }.
% 0.96/1.60 { ! hAPP( c_Fun_Ocomp( W, U, T, Z ), Y ) = X, hAPP( Z, hAPP( Y, V0 ) ) =
% 0.96/1.60 hAPP( X, V0 ) }.
% 0.96/1.60 { ! hAPP( c_Fun_Ocomp( V1, V0, W, T ), Z ) = hAPP( c_Fun_Ocomp( U, V0, W, Y
% 0.96/1.60 ), X ), hAPP( T, hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.96/1.60 { ! hAPP( c_Fun_Ocomp( V1, V0, W, T ), Z ) = hAPP( c_Fun_Ocomp( U, V0, W, Y
% 0.96/1.60 ), X ), hAPP( T, hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.96/1.60 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.60 { alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.60 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.60 { alpha46( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.96/1.60 ( X, Y ), Z ) ) }.
% 0.96/1.60 { ! alpha46( X, Y, Z ), alpha49( X, Y, Z ), Z = Y }.
% 0.96/1.60 { ! alpha46( X, Y, Z ), alpha49( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! alpha49( X, Y, Z ), alpha46( X, Y, Z ) }.
% 0.96/1.60 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha46( X, Y, Z ) }.
% 0.96/1.60 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.96/1.60 }.
% 0.96/1.60 { ! alpha49( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.96/1.60 X, Y ), Z ) ), alpha49( X, Y, Z ) }.
% 0.96/1.60 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 0.96/1.60 ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol2( X ), skol46( X ) ),
% 0.96/1.60 c_SEQ_Osubseq( X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol2( X ) ), hAPP
% 0.96/1.60 ( X, skol46( X ) ) ), c_SEQ_Osubseq( X ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.60 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! Y = Z }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 Y ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! Z = Y }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 Z ), ! Z = Y }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.60 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.60 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.60 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! Z = Y }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.60 , ! Z = Y }.
% 0.96/1.60 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_OCauchy( X, Y ), !
% 0.96/1.60 c_SEQ_Osubseq( Z ), c_SEQ_OCauchy( X, hAPP( c_Fun_Ocomp( tc_Nat_Onat, X,
% 0.96/1.60 tc_Nat_Onat, Y ), Z ) ) }.
% 0.96/1.60 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ), !
% 0.96/1.60 c_SEQ_Osubseq( Z ), c_SEQ_Oconvergent( X, hAPP( c_Fun_Ocomp( tc_Nat_Onat
% 0.96/1.60 , X, tc_Nat_Onat, Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, Y, Z ) }.
% 0.96/1.60 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X
% 0.96/1.60 , Y ), hAPP( X, c_Nat_OSuc( Y ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol3( X ) ), hAPP
% 0.96/1.60 ( X, c_Nat_OSuc( skol3( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( Y, hAPP( Z, U ), hAPP( Z, T ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 Y, hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 Y, hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.60 { ! c_Record_Oiso__tuple__update__accessor__cong__assist( Z, T, Y, X ), !
% 0.96/1.60 hAPP( W, hAPP( X, U ) ) = hAPP( X, U ), hAPP( hAPP( Y, hAPP( c_Fun_Ocomp
% 0.96/1.60 ( Z, Z, Z, V0 ), W ) ), U ) = hAPP( hAPP( Y, V0 ), U ) }.
% 0.96/1.60 { hAPP( c_Fun_Ocomp( V0, W, U, T ), c_Fun_Oswap( U, V0, Z, Y, X ) ) =
% 0.96/1.60 c_Fun_Oswap( U, W, Z, Y, hAPP( c_Fun_Ocomp( V0, W, U, T ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.60 X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.96/1.60 c_SEQ_OCauchy( X, Y ) }.
% 0.96/1.60 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.96/1.60 c_SEQ_Oconvergent( X, Y ) }.
% 0.96/1.60 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_OCauchy( X, Y ),
% 0.96/1.60 c_SEQ_Oconvergent( X, Y ) }.
% 0.96/1.60 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 0.96/1.60 c_SEQ_OCauchy( X, Y ) }.
% 0.96/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.60 { ! c_Record_Oiso__tuple__update__accessor__cong__assist( T, Z, Y, X ), !
% 0.96/1.60 hAPP( W, hAPP( X, U ) ) = hAPP( X, U ), hAPP( hAPP( Y, W ), U ) = U }.
% 0.96/1.60 { Y = X, Z = X, c_Fun_Oswap( W, U, Y, Z, c_Fun_Oswap( W, U, Z, X,
% 0.96/1.60 c_Fun_Oswap( W, U, Y, Z, T ) ) ) = c_Fun_Oswap( W, U, Y, X, T ) }.
% 0.96/1.60 { c_Fun_Oswap( U, T, Z, Y, c_Fun_Oswap( U, T, Z, Y, X ) ) = X }.
% 0.96/1.60 { c_Fun_Oswap( U, T, Z, Y, X ) = c_Fun_Oswap( U, T, Y, Z, X ) }.
% 0.96/1.60 { c_Fun_Oswap( T, Z, Y, Y, X ) = X }.
% 0.96/1.60 { ! class_Nat_Osemiring__char__0( X ), ! hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), Z = Y }.
% 0.96/1.60 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 0.96/1.60 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.96/1.60 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.96/1.60 { ! c_Nat_OSuc( X ) = X }.
% 0.96/1.60 { ! X = c_Nat_OSuc( X ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! hAPP( Z, U ) = hAPP
% 0.96/1.60 ( Z, T ), U = T }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! U = T, hAPP( Z, U )
% 0.96/1.60 = hAPP( Z, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.96/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.96/1.60 .
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.96/1.60 .
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.96/1.60 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.60 X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.96/1.60 }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, hAPP(
% 0.96/1.60 Y, skol4( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol4( X, Y ) ) ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, hAPP(
% 0.96/1.60 Y, skol5( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol5( X, Y ) ) ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( Y, T ), hAPP( Y, Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, hAPP(
% 0.96/1.60 Y, skol5( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol5( X, Y ) ) ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Nat_Ocompow( Z, Z ), c_Nat_OSuc( Y ) ), X ) = hAPP(
% 0.96/1.60 c_Fun_Ocomp( Z, Z, Z, X ), hAPP( hAPP( c_Nat_Ocompow( Z, Z ), Y ), X ) )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, skol6( X, Y, Z ), skol47( X, Y, Z ) ),
% 0.96/1.60 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ) }.
% 0.96/1.60 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Oorder( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( Y, hAPP( Z, skol6( X, Y, Z ) ), hAPP( Z,
% 0.96/1.60 skol47( X, Y, Z ) ) ), c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z )
% 0.96/1.60 }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.96/1.60 ( X, T, c_Nat_OSuc( Z ), Y ) = c_Nat_Osemiring__1__class_Oof__nat__aux( X
% 0.96/1.60 , T, Z, hAPP( T, Y ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc( Y )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, skol7( Z, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc( Y )
% 0.96/1.60 , X = c_Nat_OSuc( skol7( X, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, skol8( Z, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ), X =
% 0.96/1.60 c_Nat_OSuc( skol8( X, Y ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 0.96/1.60 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 0.96/1.60 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 0.96/1.60 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 0.96/1.60 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 0.96/1.60 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 0.96/1.60 { hAPP( T, hAPP( hAPP( hAPP( c_Nat_Ocompow( Z, Z ), Y ), T ), X ) ) = hAPP
% 0.96/1.60 ( hAPP( hAPP( c_Nat_Ocompow( Z, Z ), Y ), T ), hAPP( T, X ) ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 0.96/1.60 ( X, Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) = Y }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Nat_Ocompow( tc_fun( T, Z ), tc_fun( T, Z ) ), Y ),
% 0.96/1.60 c_Fun_Ocomp( Z, Z, T, X ) ) = c_Fun_Ocomp( Z, Z, T, hAPP( hAPP(
% 0.96/1.60 c_Nat_Ocompow( Z, Z ), Y ), X ) ) }.
% 0.96/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.96/1.60 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Y ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.60 c_Nat_OSuc( X ) ) }.
% 0.96/1.60 { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 0.96/1.60 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X, Y
% 0.96/1.60 ), X ) }.
% 0.96/1.60 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.60 ), alpha1( X, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol10( X ) ) }.
% 0.96/1.60 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { c_Nat_Ofunpow( X ) = c_Nat_Ocompow( X, X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.60 , X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), X ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol11( X ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( Y ) ) ),
% 0.96/1.60 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.60 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc(
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), X =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( skol12( X
% 0.96/1.60 , Y ) ) ) ) }.
% 0.96/1.60 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( Z ) ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Z ) = Y }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ) ) = X }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), X ) = X }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.96/1.60 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.96/1.60 = X }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ) }.
% 0.96/1.60 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Int_Oint ) ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.60 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.96/1.60 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), Z ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y )
% 0.96/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.96/1.60 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 Y ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 Z, Y ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Y ) }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 Y, Z ), T = Y }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 T, Y ), Z = Y }.
% 0.96/1.60 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 Y, T ), Z = Y }.
% 0.96/1.60 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.96/1.60 ) ), T ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.96/1.60 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.60 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.60 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.96/1.60 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 = Y }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ), Z ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.60 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.96/1.60 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.60 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.60 , T ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , T, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , Y, T ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Z, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , T, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , Y, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.60 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.60 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), c_Nat_OSuc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.60 ( X ), Y ) ) }.
% 0.96/1.60 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( X )
% 0.96/1.60 ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.96/1.60 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.60 , X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.60 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.60 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.60 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.60 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.96/1.60 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.96/1.60 { c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( X ) ) ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.60 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.60 ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.60 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha2( X, Y, Z, T ),
% 0.96/1.60 alpha18( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.60 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha18( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.96/1.60 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha2( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 0.96/1.60 alpha19( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.96/1.60 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha19( X, Y, Z, T ) }.
% 0.96/1.60 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.96/1.60 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.96/1.60 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.96/1.60 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.60 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.60 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.96/1.60 .
% 0.96/1.60 { ! c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.60 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.60 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.60 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.96/1.60 ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.60 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.60 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.96/1.60 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.60 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.96/1.60 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.60 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.96/1.60 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Z ) }.
% 0.96/1.60 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.60 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.60 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.60 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.60 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.60 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.96/1.60 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.60 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.96/1.60 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.96/1.60 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.96/1.60 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.96/1.60 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.96/1.60 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.96/1.60 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.96/1.60 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.96/1.60 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.60 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.60 , Y ), X ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.60 tc_Nat_Onat ), X ) = X }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.96/1.60 ( tc_Nat_Onat ) ) = X }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.60 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.60 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.96/1.60 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.60 .
% 0.96/1.60 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.60 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.60 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.96/1.60 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.60 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.60 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.96/1.60 .
% 0.96/1.60 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.60 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.60 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.60 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.96/1.61 , X ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.96/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Nat_Ocompow( T, T ), Z ), hAPP( hAPP( c_Nat_Ocompow( T, T )
% 0.96/1.61 , Y ), X ) ) = hAPP( hAPP( c_Nat_Ocompow( T, T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) }.
% 0.96/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha4( X, Y ), alpha20
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! alpha4( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.96/1.61 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha5( X, Y ), alpha21( X
% 0.96/1.61 , Y ) }.
% 0.96/1.61 { ! alpha5( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha21( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.96/1.61 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol13( X, Y ) ) ) }.
% 0.96/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { c_Groups_Oone__class_Oone( tc_Int_Oint ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.61 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) }.
% 0.96/1.61 { hAPP( hAPP( c_Nat_Ocompow( T, T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ) ), X ) = hAPP( c_Fun_Ocomp( T, T, T, hAPP( hAPP(
% 0.96/1.61 c_Nat_Ocompow( T, T ), Z ), X ) ), hAPP( hAPP( c_Nat_Ocompow( T, T ), Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ), U = Z, T = Y }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.96/1.61 ) ), Z ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ), ! U = T }.
% 0.96/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.96/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.96/1.61 ), ! Z = Y }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.61 = Y }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.96/1.61 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_Nat_Onat ), X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.96/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.96/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.96/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( skol14( X
% 0.96/1.61 ) ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), skol15( Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), X = hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.61 tc_Int_Oint ), skol15( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, T, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), U ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , W ) ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.96/1.61 ), Y ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), v_r ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol16( X, Y, Z ) ) ),
% 0.96/1.61 hAPP( Y, skol16( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z,
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y,
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z =
% 0.96/1.61 Y }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), ! Z = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.96/1.61 , ! Z = Y }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y,
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.96/1.61 Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , Z ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 T ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.96/1.61 Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 U ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.61 , T ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 0.96/1.61 , Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), c_Nat_OSuc( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Nat_OSuc( X ) ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 X ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( X ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( X ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol17( X, Y ) ) }.
% 0.96/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) ) }.
% 0.96/1.61 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), hAPP( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.61 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( Y, hAPP( Z, U ) ), hAPP( Z, T ) ) ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( Y ), ! class_Orderings_Olinorder( X ), !
% 0.96/1.61 c_Orderings_Oorder__class_Ostrict__mono( X, Y, Z ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( Y, hAPP( Z, U ) ), hAPP( Z, T ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha6( X
% 0.96/1.61 , Y, Z ), alpha22( X, Y, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! alpha22( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), alpha22( X, Y, Z ) }.
% 0.96/1.61 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.96/1.61 { ! alpha6( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), alpha6( X, Y, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), alpha7( X, Y, Z ), alpha23( X, Y, Z
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! alpha23( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! alpha23( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), alpha23( X, Y, Z ) }.
% 0.96/1.61 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 0.96/1.61 { ! alpha7( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), alpha7( X, Y, Z ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.96/1.61 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oplus__class_Oplus( X, Y, Y
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , Y, T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.61 ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.61 ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X =
% 0.96/1.61 Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! X = Y, c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.61 ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.96/1.61 ) ), X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, X, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol18( Y ) ) ), hBOOL(
% 0.96/1.61 hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( X, skol18( X ) ) ), hBOOL( hAPP( X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.61 , skol48( X ) ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( X, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X, Y
% 0.96/1.61 ) ), hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.61 tc_Int_Oint ), skol19( X ) ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.61 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol49( Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.61 , Y ) ) ), hBOOL( hAPP( X, skol49( X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), skol20( X, Y ) ) ) }.
% 0.96/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, U, T ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ), U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ) ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.96/1.61 , Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.96/1.61 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.96/1.61 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 0.96/1.61 , X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Z ), X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.96/1.61 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.96/1.61 , Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ) ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( X, U, W ) = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( X ) ) ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.96/1.61 ( tc_Int_Oint ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 Z ), Y ), X ) ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ),
% 0.96/1.61 ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ) ), ! hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ), X ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) ), hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.96/1.61 , X ), Y ) ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.96/1.61 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_RealDef_Oreal, Y ), Z ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 0.96/1.61 ), Y ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.96/1.61 , Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), Y = X, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.61 X ), Z, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X
% 0.96/1.61 ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.96/1.61 X ), Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T
% 0.96/1.61 , X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 0.96/1.61 ), Y = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 0.96/1.61 , X ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 0.96/1.61 .
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.96/1.61 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.96/1.61 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.96/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.96/1.61 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.96/1.61 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Y ), U ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ) ), ! hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 0.96/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), ! hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.61 Z ), Y ), X ) ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ),
% 0.96/1.61 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, U ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol21( X, Y ) ) }.
% 0.96/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol22( X, Y ) ), skol50
% 0.96/1.61 ( X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol50( X, Y ) ) ), hAPP(
% 0.96/1.61 Y, skol22( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.96/1.61 }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.96/1.61 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ), Z = Y }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 0.96/1.61 { ! class_Lattices_Oboolean__algebra( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Z ) ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol23( Z, Y
% 0.96/1.61 ), Y ) }.
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Z ), skol23( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.96/1.61 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.96/1.61 , skol23( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol24( X, Y ) ), skol51
% 0.96/1.61 ( X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.96/1.61 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol24( X, Y ) ) ), hAPP(
% 0.96/1.61 Y, skol51( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.61 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.96/1.61 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.61 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( c_Int_Onat, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.61 , X ) ) = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.96/1.61 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( c_Int_Onat, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 0.96/1.61 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 0.96/1.61 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 0.96/1.61 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 0.96/1.61 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, skol25( X ) ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( X, hAPP
% 0.96/1.61 ( c_Int_Onat, Y ) ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol52( Y ) ) ), hBOOL(
% 0.96/1.61 hAPP( X, Z ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, hAPP( c_Int_Onat, skol52( X ) ) ) ), hBOOL( hAPP( X, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol26( Z ) )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( c_Int_Onat, skol26( X ) )
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X,
% 0.96/1.61 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( X, skol53( X ) ) ) }.
% 0.96/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.96/1.61 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.61 .
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 0.96/1.61 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hAPP( c_Int_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { hAPP( c_Int_Onat, c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.61 ( c_Int_Onat, Y ), hAPP( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Int_Oint, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ),
% 0.96/1.61 hAPP( c_Int_Onat, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP
% 0.96/1.61 ( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP
% 0.96/1.61 ( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X
% 0.96/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ),
% 0.96/1.61 hAPP( c_Int_Onat, X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 0.96/1.61 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( tc_Int_Oint, X ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 0.96/1.61 hAPP( c_Int_Onat, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 0.96/1.61 ) = X }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.61 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X, Y =
% 0.96/1.61 hAPP( c_Int_Onat, X ) }.
% 0.96/1.61 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X, hBOOL
% 0.96/1.61 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 0.96/1.61 { ! Y = hAPP( c_Int_Onat, X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 0.96/1.61 ) = X }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Int_Onat, X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Int_Onat, X ) ) }
% 0.96/1.61 .
% 0.96/1.61 { hAPP( c_Int_Onat, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 0.96/1.61 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.96/1.61 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 0.96/1.61 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.96/1.61 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ) }.
% 0.96/1.61 { alpha47( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.96/1.61 { alpha47( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, Y ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 0.96/1.61 { ! alpha47( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.61 { ! alpha47( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha47
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! hAPP( c_Int_Onat, Y ) = X, alpha8( X, Y ) }.
% 0.96/1.61 { ! hAPP( c_Int_Onat, Y ) = X, alpha24( X, Y ) }.
% 0.96/1.61 { ! alpha8( X, Y ), ! alpha24( X, Y ), hAPP( c_Int_Onat, Y ) = X }.
% 0.96/1.61 { ! alpha24( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha24( X, Y ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha24( X, Y ) }.
% 0.96/1.61 { ! alpha8( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), Y =
% 0.96/1.61 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha8( X, Y ) }.
% 0.96/1.61 { ! Y = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 0.96/1.61 alpha8( X, Y ) }.
% 0.96/1.61 { ! Y = hAPP( c_Int_Onat, X ), alpha9( X, Y ) }.
% 0.96/1.61 { ! Y = hAPP( c_Int_Onat, X ), alpha25( X, Y ) }.
% 0.96/1.61 { ! alpha9( X, Y ), ! alpha25( X, Y ), Y = hAPP( c_Int_Onat, X ) }.
% 0.96/1.61 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha25( X, Y ) }.
% 0.96/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha25( X, Y ) }.
% 0.96/1.61 { ! alpha9( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), X =
% 0.96/1.61 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha9( X, Y ) }.
% 0.96/1.61 { ! X = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ),
% 0.96/1.61 alpha9( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha10( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha26( X, Y ) }.
% 0.96/1.61 { ! alpha10( X, Y ), ! alpha26( X, Y ), hBOOL( hAPP( Y, hAPP( c_Int_Onat, X
% 0.96/1.61 ) ) ) }.
% 0.96/1.61 { ! alpha26( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP( Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha26( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha26
% 0.96/1.61 ( X, Y ) }.
% 0.96/1.61 { ! alpha10( X, Y ), ! X = hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.61 tc_Int_Oint ), Z ), hBOOL( hAPP( Y, Z ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Y, skol27( Z, Y ) ) ), alpha10( X, Y ) }.
% 0.96/1.61 { X = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), skol27( X, Y
% 0.96/1.61 ) ), alpha10( X, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.61 c_Int_Onat, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ),
% 0.96/1.61 hAPP( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 0.96/1.61 c_Int_Onat, X ) ), hAPP( c_Int_Onat, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.96/1.61 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.61 c_Int_Onat, X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), c_Nat_OSuc( hAPP(
% 0.96/1.61 c_Int_Onat, X ) ) = hAPP( c_Int_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), Y ) }
% 0.96/1.61 .
% 0.96/1.61 { c_Int_Onat__aux( Y, X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP
% 0.96/1.61 ( c_Int_Onat, Y ), X ) }.
% 0.96/1.61 { c_Nat__Transfer_Otransfer__morphism( tc_Int_Oint, tc_Nat_Onat, c_Int_Onat
% 0.96/1.61 , c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 0.96/1.61 c_RComplete_Onatceiling( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.61 Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), X ) ) ) }.
% 0.96/1.61 { c_RComplete_Onatfloor( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X }
% 0.96/1.61 .
% 0.96/1.61 { c_RComplete_Onatceiling( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X
% 0.96/1.61 }.
% 0.96/1.61 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.61 tc_RealDef_Oreal ) }.
% 0.96/1.61 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.61 tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ), Y = X }.
% 0.96/1.61 { ! Y = X, hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) ) ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatceiling( X ) ) ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.96/1.61 .
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_RealDef_Oreal ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( X ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_RComplete_Onatfloor( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.96/1.61 Y ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_RealDef_Oreal ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_RealDef_Oreal ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 0.96/1.61 c_RComplete_Onatfloor( X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.96/1.61 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.61 tc_RealDef_Oreal, X ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.96/1.61 X ) ), Y ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_RealDef_Oreal ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_RComplete_Onatfloor( X ), Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.61 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.96/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.96/1.61 c_RComplete_Onatfloor( X ) = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.61 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.96/1.61 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), skol28( X ) ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), c_Nat_OSuc( skol28( X ) ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.96/1.61 ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint
% 0.96/1.61 , Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) = c_Groups_Ouminus__class_Ouminus
% 0.96/1.61 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), hAPP( c_Int_Onat,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), hAPP( c_Int_Onat, Y ) ) }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! c_Int_Oring__1__class_Oof__int( X, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ) }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), c_Int_Oring__1__class_Oof__int( X, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ) }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Int_Oint ), c_Groups_Ozero__class_Ozero( X ) =
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Int_Oring__1__class_Oof__int( X, Z ), c_Int_Oring__1__class_Oof__int
% 0.96/1.61 ( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Int_Oint, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Z ), c_Int_Oring__1__class_Oof__int( X
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, c_Int_Oring__1__class_Oof__int( X, Z ),
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Int_Oring__1__class_Oof__int
% 0.96/1.61 ( X, Z ) ), c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = c_Groups_Oone__class_Oone( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, c_Int_Oring__1__class_Oof__int( X, Y
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! c_Int_Oring__1__class_Oof__int( X, Z )
% 0.96/1.61 = c_Int_Oring__1__class_Oof__int( X, Y ), Z = Y }.
% 0.96/1.61 { ! class_Int_Oring__char__0( X ), ! Z = Y, c_Int_Oring__1__class_Oof__int
% 0.96/1.61 ( X, Z ) = c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X, hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( X ), c_Int_Oring__1__class_Oof__int(
% 0.96/1.61 X, Z ) ), Y ) }.
% 0.96/1.61 { c_Int_Oring__1__class_Oof__int( tc_Int_Oint, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) = Y }.
% 0.96/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.61 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Int_Oring__1__class_Oof__int( X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , c_Int_Oring__1__class_Oof__int( X, Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Int_Oring__1__class_Oof__int( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Int_Oint, Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Int_Oring__1__class_Oof__int( X, Y )
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , c_Groups_Ozero__class_Ozero( X ), c_Int_Oring__1__class_Oof__int( X, Y
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), hAPP( c_Int_Onat, Y ) ) =
% 0.96/1.61 c_Int_Oring__1__class_Oof__int( X, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), Y ) ), X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 0.96/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) = hAPP( c_RealDef_Oreal(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.96/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.96/1.61 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.96/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), Y )
% 0.96/1.61 = hAPP( c_Int_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.61 tc_Int_Oint ), X ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) =
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat
% 0.96/1.61 , X ) ), Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 0.96/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.96/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Y ) }.
% 0.96/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.96/1.61 ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.61 { ! X = hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.96/1.61 , c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.61 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.96/1.61 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.96/1.61 = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 0.96/1.61 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y )
% 0.96/1.61 ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), Y ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.96/1.61 tc_Nat_Onat ) ) = Y }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.96/1.61 .
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.96/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.96/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.96/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.96/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.96/1.61 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , Y ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ) ), ! hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), Z = Y }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.96/1.61 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.96/1.61 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 0.96/1.61 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 0.96/1.61 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), Z ), T = Y }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.96/1.61 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 0.96/1.61 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 0.96/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.96/1.61 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 0.96/1.61 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.96/1.61 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol29( X, Y ) ), X ) =
% 0.96/1.61 Y }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.96/1.61 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.61 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol30( X, Y ) ), X ) =
% 0.96/1.61 Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.96/1.61 skol30( X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), skol31( X, Y ) ) ), X ) ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), c_Nat_OSuc( skol31( X, Y ) ) ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.96/1.61 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), Y ) ), c_Transcendental_Oln( X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 0.96/1.61 ( tc_Nat_Onat ), skol32( X, Y ) ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.96/1.61 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 0.96/1.61 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_RealDef_Oreal, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), c_Transcendental_Oln( Y ) ) }.
% 0.96/1.61 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.96/1.61 ( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.96/1.61 X ) ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.96/1.61 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.96/1.61 ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.96/1.61 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 0.96/1.61 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.96/1.61 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 0.96/1.61 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.96/1.61 X ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 0.96/1.61 X ) ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.96/1.61 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.96/1.61 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 0.96/1.61 }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 0.96/1.61 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ) ), X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol33( Z, T ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol33( X, Y ) ),
% 0.96/1.61 c_Nat_OSuc( Y ) ) = X }.
% 0.96/1.61 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.96/1.61 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.96/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.96/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.61 tc_Nat_Onat, Y, Z ) ) = c_Groups_Ominus__class_Ominus( X, hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), hAPP(
% 0.96/1.61 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.96/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.96/1.61 ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.61 ( tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, X, Z ), Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 0.96/1.61 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.96/1.61 ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.61 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.96/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.96/1.61 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.96/1.61 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.96/1.61 hAPP( Z, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.96/1.61 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.96/1.61 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.96/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.96/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.96/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.96/1.61 ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.96/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 0.96/1.61 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.61 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 0.96/1.61 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 0.96/1.61 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.96/1.61 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.96/1.61 , Y ) ) }.
% 0.96/1.61 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.61 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.96/1.61 X, Z, Y ) }.
% 0.96/1.61 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.61 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 X, Y ) ) }.
% 0.96/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.96/1.61 X, Y ) }.
% 0.96/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.61 Z ) ), U ), T ) = Y }.
% 0.96/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.61 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.61 W ) ), U ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.61 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.61 Z ) ), Y ) ) }.
% 0.96/1.61 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.61 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.96/1.61 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.96/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( X ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.96/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.96/1.61 , Z, Y ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.61 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 0.96/1.61 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.96/1.61 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Int_Oring__1__class_Oof__int( X,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, c_Int_Oring__1__class_Oof__int( X, Z )
% 0.96/1.61 , c_Int_Oring__1__class_Oof__int( X, Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.61 W ) ), U ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.96/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) ), hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.96/1.61 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.96/1.61 Z ) ), U ), T ) ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 0.96/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.96/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) ), Y ) ), hBOOL(
% 0.96/1.61 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 0.96/1.61 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.96/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.96/1.61 ( X, Z, W ) ), U ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.96/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.61 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.96/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.96/1.61 X, W, Z ) ), U ), T ), Y ) }.
% 0.96/1.61 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.96/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.96/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.96/1.61 ( X ), Z ), U ), Y ) ) }.
% 0.96/1.61 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.96/1.61 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.96/1.61 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.96/1.61 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.96/1.61 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.96/1.61 .
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.96/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.96/1.61 ) ) = X }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.61 , alpha11( X, Y, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.61 , alpha27( X, Y, Z ) }.
% 0.96/1.61 { ! alpha11( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.61 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, skol34( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 0.96/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol34( X, Y, Z ) ),
% 0.96/1.61 alpha27( X, Y, Z ) }.
% 0.96/1.61 { ! alpha11( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.61 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha11( X, Y, Z ) }
% 0.96/1.61 .
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha11
% 0.96/1.61 ( X, Y, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.61 , ! alpha12( X, Y, Z ) }.
% 0.96/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.96/1.61 , ! alpha28( X, Y, Z ) }.
% 0.96/1.61 { alpha12( X, Y, Z ), alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.61 { ! alpha28( X, Y, Z ), ! hBOOL( hAPP( Z, skol35( T, U, Z ) ) ) }.
% 0.96/1.61 { ! alpha28( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.96/1.61 skol35( X, Y, Z ) ) }.
% 0.96/1.61 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.96/1.61 ) ), alpha28( X, Y, Z ) }.
% 0.96/1.62 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.62 }.
% 0.96/1.62 { ! alpha12( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Nat_Onat ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12( X, Y, Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) ), hBOOL(
% 0.96/1.62 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) ), Z ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) ), Z ) ),
% 0.96/1.62 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.62 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 X ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) ), hBOOL(
% 0.96/1.62 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) ), hBOOL
% 0.96/1.62 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.96/1.62 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 Y ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! T = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.96/1.62 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.96/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.96/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.96/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.62 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.96/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.96/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.96/1.62 ( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.96/1.62 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.96/1.62 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.96/1.62 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.96/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) }.
% 0.96/1.62 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.96/1.62 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.62 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Nat__Transfer_Otsub( X, Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 0.96/1.62 c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, skol36( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) )
% 0.96/1.62 , X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 0.96/1.62 ( tc_Nat_Onat ), skol36( X ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 0.96/1.62 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.96/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.96/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.62 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Int_Oint, X, Y ) }.
% 0.96/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 0.96/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.96/1.62 ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.62 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Int_Oint, X, Y ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.96/1.62 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.62 ( tc_Int_Oint ) ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.96/1.62 }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.96/1.62 ( tc_Int_Oint ) ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.96/1.62 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ), hAPP( c_RealDef_Oreal(
% 0.96/1.62 tc_Nat_Onat ), Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hAPP(
% 0.96/1.62 c_Int_Onat, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP(
% 0.96/1.62 c_Int_Onat, X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), c_RComplete_Onatfloor(
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 0.96/1.62 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP( c_RealDef_Oreal(
% 0.96/1.62 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 0.96/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), c_RComplete_Onatceiling(
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 0.96/1.62 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.96/1.62 c_RComplete_Onatceiling( X ), Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 0.96/1.62 ) ) ) }.
% 0.96/1.62 { c_Nat__Transfer_Otsub( hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 0.96/1.62 tc_Int_Oint ), Y ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint
% 0.96/1.62 ), X ) ) = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha13( X, Y
% 0.96/1.62 , Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 0.96/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha29( X, Y
% 0.96/1.62 , Z ) }.
% 0.96/1.62 { ! alpha13( X, Y, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z, hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ) }.
% 0.96/1.62 { ! alpha29( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.62 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha29( X, Y, Z ) }
% 0.96/1.62 .
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha29
% 0.96/1.62 ( X, Y, Z ) }.
% 0.96/1.62 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Int_Oint, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y )
% 0.96/1.62 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ) }.
% 0.96/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 0.96/1.62 alpha13( X, Y, Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ), alpha13( X
% 0.96/1.62 , Y, Z ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.96/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.96/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.96/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.96/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.96/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.96/1.62 ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.96/1.62 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.96/1.62 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.96/1.62 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.96/1.62 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.96/1.62 }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.96/1.62 ( tc_Int_Oint, X, Y ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.96/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, Y ), X ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.96/1.62 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.96/1.62 }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.96/1.62 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.96/1.62 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, Z, Y ), X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, X, Y ), X ) }.
% 0.96/1.62 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 0.96/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! alpha14( X, Y ), alpha30( X, Y ), alpha34( X, Y ) }.
% 0.96/1.62 { ! alpha30( X, Y ), alpha14( X, Y ) }.
% 0.96/1.62 { ! alpha34( X, Y ), alpha14( X, Y ) }.
% 0.96/1.62 { ! alpha34( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { ! alpha34( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha34( X, Y ) }.
% 0.96/1.62 { ! alpha30( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.96/1.62 { ! alpha30( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha30( X, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 0.96/1.62 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.96/1.62 ( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, Y, X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, X ), Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, X ), Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, Y, X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), hBOOL(
% 0.96/1.62 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.96/1.62 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 0.96/1.62 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 0.96/1.62 ( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 0.96/1.62 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.96/1.62 alpha15( X, Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.96/1.62 alpha31( X, Y, Z ) }.
% 0.96/1.62 { ! alpha15( X, Z ), ! alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.96/1.62 { ! alpha31( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.96/1.62 { ! alpha31( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.96/1.62 { ! alpha35( X, Y, Z ), ! alpha38( X, Y, Z ), alpha31( X, Y, Z ) }.
% 0.96/1.62 { ! alpha38( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha41( X, Y, Z ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha38( X, Y, Z ) }.
% 0.96/1.62 { ! alpha41( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.96/1.62 { ! alpha41( X, Y, Z ), ! alpha43( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, skol37( T, U, Z ) ) ), alpha41( X, Y, Z ) }.
% 0.96/1.62 { alpha43( X, Y, skol37( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 0.96/1.62 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.96/1.62 skol38( X, T, U ) ) }.
% 0.96/1.62 { ! alpha43( X, Y, Z ), alpha45( X, Y, Z, skol38( X, Y, Z ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha45( X, Y, Z
% 0.96/1.62 , T ), alpha43( X, Y, Z ) }.
% 0.96/1.62 { ! alpha45( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.62 .
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha45( X,
% 0.96/1.62 Y, Z, T ) }.
% 0.96/1.62 { ! alpha35( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y, Z ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Int_Oint ), X ), alpha35( X, Y, Z ) }.
% 0.96/1.62 { ! alpha39( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.96/1.62 { ! alpha39( X, Y, Z ), ! alpha42( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, skol39( T, U, Z ) ) ), alpha39( X, Y, Z ) }.
% 0.96/1.62 { alpha42( X, Y, skol39( X, Y, Z ) ), alpha39( X, Y, Z ) }.
% 0.96/1.62 { ! alpha42( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol40( T, U,
% 0.96/1.62 W ) ) ) }.
% 0.96/1.62 { ! alpha42( X, Y, Z ), alpha44( X, Y, Z, skol40( X, Y, Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha44( X, Y, Z,
% 0.96/1.62 T ), alpha42( X, Y, Z ) }.
% 0.96/1.62 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.96/1.62 ) }.
% 0.96/1.62 { ! alpha44( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.96/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.96/1.62 .
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.96/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha44( X,
% 0.96/1.62 Y, Z, T ) }.
% 0.96/1.62 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.96/1.62 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.96/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 0.96/1.62 ( X, Y ) }.
% 0.96/1.62 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.96/1.62 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, T, Z ) = Y }.
% 0.96/1.62 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha48( X,
% 0.96/1.62 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! hBOOL( hAPP
% 0.96/1.62 ( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, T, Z ) = Y }.
% 0.96/1.62 { ! alpha48( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.96/1.62 { ! alpha48( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha48
% 0.96/1.62 ( X, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.96/1.62 , alpha48( X, Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 0.96/1.62 = c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) }.
% 0.96/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), c_SMT_Oz3div( X, Y )
% 0.96/1.62 = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X,
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol41( Z, Y ) ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP( Y, U
% 0.96/1.62 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Int_Oint, skol41( X, Y ), X ) ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y, T
% 0.96/1.62 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, T, hAPP
% 0.96/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.96/1.62 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 0.96/1.62 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Nat_Onat, Z, Y ), X ) }.
% 0.96/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 0.96/1.62 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.96/1.62 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.96/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Nat_Onat, Y, X ), Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.96/1.62 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.96/1.62 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.96/1.62 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.62 alpha16( X, Z ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.62 alpha32( X, Y, Z ) }.
% 0.96/1.62 { ! alpha16( X, Z ), ! alpha32( X, Y, Z ), hBOOL( hAPP( Z,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.62 { ! alpha32( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 alpha36( X, Y, Z ) }.
% 0.96/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha32( X, Y, Z ) }.
% 0.96/1.62 { ! alpha36( X, Y, Z ), alpha32( X, Y, Z ) }.
% 0.96/1.62 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.96/1.62 ), alpha40( X, Y, Z, T ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol42( X, T, U ), X ),
% 0.96/1.62 alpha36( X, Y, Z ) }.
% 0.96/1.62 { ! alpha40( X, Y, Z, skol42( X, Y, Z ) ), alpha36( X, Y, Z ) }.
% 0.96/1.62 { ! alpha40( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.96/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.96/1.62 hBOOL( hAPP( Z, U ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Z, skol43( U, W, Z, V0 ) ) ), alpha40( X, Y, Z, T ) }.
% 0.96/1.62 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol43( X, Y, Z, T ) )
% 0.96/1.62 , T ), alpha40( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.96/1.62 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.96/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 0.96/1.62 ( X, Y ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.62 c_Int_Onat, Y ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 0.96/1.62 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 0.96/1.62 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Int_Oint, X, Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.62 ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z )
% 0.96/1.62 ) ), Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.96/1.62 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 0.96/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.96/1.62 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.96/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.96/1.62 alpha17( X, Z ), alpha33( X, Y, Z ) }.
% 0.96/1.62 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.62 { ! alpha33( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.96/1.62 tc_Nat_Onat, Y, X ) ) ) }.
% 0.96/1.62 { ! alpha33( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 0.96/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.96/1.62 ), skol44( X, Y, T ) ) ), Y ) ) }.
% 0.96/1.62 { ! alpha33( X, Y, Z ), alpha37( X, Y, Z, skol44( X, Y, Z ) ) }.
% 0.96/1.62 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 0.96/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 0.96/1.62 alpha37( X, Y, Z, T ), alpha33( X, Y, Z ) }.
% 0.96/1.62 { ! alpha37( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.96/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.96/1.62 ( T ) ) ) }.
% 0.96/1.62 { ! alpha37( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.96/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.96/1.62 hBOOL( hAPP( Z, T ) ), alpha37( X, Y, Z, T ) }.
% 0.96/1.62 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.96/1.62 tc_Nat_Onat ) ) ) }.
% 0.96/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.96/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 0.96/1.62 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.96/1.62 ( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.96/1.62 ) ) }.
% 0.96/1.62 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.96/1.62 .
% 0.96/1.62 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.96/1.62 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.96/1.62 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.96/1.62 { class_Power_Opower( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.96/1.62 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.96/1.62 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.96/1.62 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.96/1.62 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.96/1.62 tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.96/1.62 .
% 0.96/1.62 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Nat_Osemiring__char__0( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_SEQ_Ocomplete__space( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.96/1.62 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.96/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol45, skol54 ) }.
% 0.96/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP( c_Fun_Ocomp(
% 0.96/1.62 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____ ), v_ga____ ), skol45 ),
% 0.96/1.62 hAPP( hAPP( c_Fun_Ocomp( tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____ )
% 0.96/1.62 , v_ga____ ), skol54 ) ) }.
% 0.96/1.62
% 0.96/1.62 *** allocated 15000 integers for clauses
% 0.96/1.62 *** allocated 22500 integers for clauses
% 0.96/1.62 *** allocated 33750 integers for clauses
% 0.96/1.62 *** allocated 50625 integers for clauses
% 0.96/1.62 *** allocated 75937 integers for clauses
% 0.96/1.62 percentage equality = 0.260378, percentage horn = 0.914513
% 0.96/1.62 This is a problem with some equality
% 0.96/1.62
% 0.96/1.62
% 0.96/1.62
% 0.96/1.62 Options Used:
% 0.96/1.62
% 0.96/1.62 useres = 1
% 0.96/1.62 useparamod = 1
% 0.96/1.62 useeqrefl = 1
% 0.96/1.62 useeqfact = 1
% 0.96/1.62 usefactor = 1
% 0.96/1.62 usesimpsplitting = 0
% 0.96/1.62 usesimpdemod = 5
% 0.96/1.62 usesimpres = 3
% 0.96/1.62
% 0.96/1.62 resimpinuse = 1000
% 0.96/1.62 resimpclauses = 20000
% 0.96/1.62 substype = eqrewr
% 0.96/1.62 backwardsubs = 1
% 0.96/1.62 selectoldest = 5
% 0.96/1.62
% 0.96/1.62 litorderings [0] = split
% 0.96/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.62
% 0.96/1.62 termordering = kbo
% 0.96/1.62
% 0.96/1.62 litapriori = 0
% 0.96/1.62 termapriori = 1
% 0.96/1.62 litaposteriori = 0
% 0.96/1.62 termaposteriori = 0
% 0.96/1.62 demodaposteriori = 0
% 0.96/1.62 ordereqreflfact = 0
% 0.96/1.62
% 0.96/1.62 litselect = negord
% 0.96/1.62
% 0.96/1.62 maxweight = 15
% 0.96/1.62 maxdepth = 30000
% 0.96/1.62 maxlength = 115
% 0.96/1.62 maxnrvars = 195
% 0.96/1.62 excuselevel = 1
% 0.96/1.62 increasemaxweight = 1
% 0.96/1.62
% 0.96/1.62 maxselected = 10000000
% 0.96/1.62 maxnrclauses = 10000000
% 0.96/1.62
% 0.96/1.62 showgenerated = 0
% 0.96/1.62 showkept = 0
% 0.96/1.62 showselected = 0
% 0.96/1.62 showdeleted = 0
% 0.96/1.62 showresimp = 1
% 0.96/1.62 showstatus = 2000
% 0.96/1.62
% 0.96/1.62 prologoutput = 0
% 0.96/1.62 nrgoals = 5000000
% 0.96/1.62 totalproof = 1
% 0.96/1.62
% 0.96/1.62 Symbols occurring in the translation:
% 0.96/1.62
% 0.96/1.62 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.62 . [1, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.96/1.62 ! [4, 1] (w:0, o:115, a:1, s:1, b:0),
% 0.96/1.62 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.62 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.62 hAPP [38, 2] (w:1, o:235, a:1, s:1, b:0),
% 0.96/1.62 tc_Nat_Onat [41, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.96/1.62 c_Orderings_Oord__class_Oless [42, 3] (w:1, o:290, a:1, s:1, b:0),
% 0.96/1.62 v_f____ [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.96/1.62 v_ga____ [44, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.96/1.62 c_SEQ_Osubseq [45, 1] (w:1, o:123, a:1, s:1, b:0),
% 0.96/1.62 c_Fun_Ocomp [51, 4] (w:1, o:329, a:1, s:1, b:0),
% 0.96/1.62 hBOOL [72, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.96/1.62 class_Orderings_Olinorder [73, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.96/1.62 class_Orderings_Opreorder [74, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.96/1.62 class_Orderings_Oorder [76, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.96/1.62 class_Orderings_Oord [80, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.96/1.62 class_RealVector_Ometric__space [83, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 c_SEQ_OCauchy [84, 2] (w:1, o:236, a:1, s:1, b:0),
% 0.96/1.62 class_SEQ_Ocomplete__space [85, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.96/1.62 c_SEQ_Oconvergent [86, 2] (w:1, o:237, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__idom [87, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_OSuc [88, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.96/1.62 c_Orderings_Oorder__class_Ostrict__mono [89, 3] (w:1, o:291, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Olinordered__semidom [90, 1] (w:1, o:134, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat [91, 1] (w:1, o:161, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 c_Record_Oiso__tuple__update__accessor__cong__assist [94, 4] (w:1, o:
% 0.96/1.62 330, a:1, s:1, b:0),
% 0.96/1.62 c_Fun_Oswap [95, 5] (w:1, o:342, a:1, s:1, b:0),
% 0.96/1.62 class_Nat_Osemiring__char__0 [96, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.96/1.62 tc_Int_Oint [103, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_Ocompow [104, 2] (w:1, o:238, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Osemiring__1 [108, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_Osemiring__1__class_Oof__nat__aux [109, 4] (w:1, o:331, a:1, s:
% 0.96/1.62 1, b:0),
% 0.96/1.62 c_Groups_Ozero__class_Ozero [110, 1] (w:1, o:162, a:1, s:1, b:0),
% 0.96/1.62 tc_fun [112, 2] (w:1, o:262, a:1, s:1, b:0),
% 0.96/1.62 c_Nat_Ofunpow [115, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Otimes__class_Otimes [116, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Ouminus__class_Ouminus [117, 2] (w:1, o:263, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 c_Groups_Oone__class_Oone [118, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ozero [119, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Oplus__class_Oplus [122, 3] (w:1, o:292, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ogroup__add [123, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__ring__strict [124, 1] (w:1, o:132, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Groups_Oab__group__add [129, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Omonoid__mult [130, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ocomm__monoid__mult [131, 1] (w:1, o:171, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Groups_Oone [132, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oab__semigroup__add [133, 1] (w:1, o:173, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Groups_Oab__semigroup__mult [134, 1] (w:1, o:174, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 class_Groups_Ocancel__semigroup__add [135, 1] (w:1, o:175, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Groups_Ocancel__ab__semigroup__add [136, 1] (w:1, o:176, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Osemiring [138, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oidom [139, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__semiring [140, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oring__1__no__zero__divisors [141, 1] (w:1, o:135, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Oring [142, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Olinordered__ab__group__add [143, 1] (w:1, o:169, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Groups_Oordered__ab__group__add [144, 1] (w:1, o:177, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Groups_Omonoid__add [145, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ocomm__monoid__add [146, 1] (w:1, o:179, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Groups_Oordered__ab__semigroup__add__imp__le [147, 1] (w:1, o:
% 0.96/1.62 180, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oordered__cancel__ab__semigroup__add [149, 1] (w:1, o:
% 0.96/1.62 181, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__ring [150, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ono__zero__divisors [151, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Rings_Oring__no__zero__divisors [152, 1] (w:1, o:137, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Omult__zero [153, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ozero__neq__one [154, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oordered__comm__monoid__add [155, 1] (w:1, o:182, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__comm__semiring__strict [156, 1] (w:1, o:145
% 0.96/1.62 , a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Olinordered__semiring__strict [157, 1] (w:1, o:146, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__ring__1 [158, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Ocomm__semiring__1 [159, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.96/1.62 161, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.96/1.62 class_RealVector_Oreal__normed__algebra [162, 1] (w:1, o:154, a:1, s:
% 0.96/1.62 1, b:0),
% 0.96/1.62 class_Rings_Olinordered__semiring__1__strict [176, 1] (w:1, o:147, a:
% 0.96/1.62 1, s:1, b:0),
% 0.96/1.62 c_Orderings_Oord__class_Oless__eq [177, 2] (w:1, o:265, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 tc_RealDef_Oreal [178, 0] (w:1, o:102, a:1, s:1, b:0),
% 0.96/1.62 v_r [179, 0] (w:1, o:103, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Oordered__ab__semigroup__add [180, 1] (w:1, o:184, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Rings_Oordered__cancel__semiring [181, 1] (w:1, o:155, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Oordered__ring [182, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oordered__semiring [183, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 class_Rings_Oordered__comm__semiring [184, 1] (w:1, o:158, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 class_Rings_Olinordered__semiring [187, 1] (w:1, o:148, a:1, s:1, b:0
% 0.96/1.62 ),
% 0.96/1.62 class_Rings_Olinordered__semiring__1 [188, 1] (w:1, o:149, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 c_SEQ_Odecseq [193, 2] (w:1, o:266, a:1, s:1, b:0),
% 0.96/1.62 class_Lattices_Oboolean__algebra [194, 1] (w:1, o:186, a:1, s:1, b:0)
% 0.96/1.62 ,
% 0.96/1.62 class_Lattices_Oab__semigroup__idem__mult [195, 1] (w:1, o:185, a:1
% 0.96/1.62 , s:1, b:0),
% 0.96/1.62 class_Groups_Ouminus [197, 1] (w:1, o:187, a:1, s:1, b:0),
% 0.96/1.62 c_SEQ_Oincseq [199, 2] (w:1, o:267, a:1, s:1, b:0),
% 0.96/1.62 c_RComplete_Onatceiling [200, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.96/1.62 c_RComplete_Onatfloor [201, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.96/1.62 c_Int_Onat [202, 0] (w:1, o:106, a:1, s:1, b:0),
% 0.96/1.62 c_Int_Onat__aux [205, 2] (w:1, o:268, a:1, s:1, b:0),
% 0.96/1.62 c_Nat__Transfer_Otransfer__morphism [206, 4] (w:1, o:332, a:1, s:1
% 0.96/1.62 , b:0),
% 0.96/1.62 c_RealDef_Oreal [207, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.96/1.62 c_Power_Opower__class_Opower [208, 1] (w:1, o:188, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Oring__1 [209, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.62 c_Int_Oring__1__class_Oof__int [210, 2] (w:1, o:269, a:1, s:1, b:0),
% 0.96/1.62
% 0.96/1.62 class_Int_Oring__char__0 [211, 1] (w:1, o:189, a:1, s:1, b:0),
% 0.96/1.62 class_Power_Opower [213, 1] (w:1, o:190, a:1, s:1, b:0),
% 0.96/1.62 class_Rings_Osemiring__0 [214, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.96/1.62 c_Power_Opower_Opower [216, 3] (w:1, o:293, a:1, s:1, b:0),
% 0.96/1.62 c_Transcendental_Oln [220, 1] (w:1, o:191, a:1, s:1, b:0),
% 0.96/1.62 c_Groups_Ominus__class_Ominus [221, 3] (w:1, o:294, a:1, s:1, b:0),
% 0.96/1.62 class_Groups_Ominus [224, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.96/1.62 c_Nat__Transfer_Otsub [228, 2] (w:1, o:264, a:1, s:1, b:0),
% 0.96/1.62 c_Divides_Odiv__class_Odiv [229, 3] (w:1, o:295, a:1, s:1, b:0),
% 0.96/1.62 class_Divides_Osemiring__div [230, 1] (w:1, o:193, a:1, s:1, b:0),
% 0.96/1.62 c_SMT_Oz3div [234, 2] (w:1, o:270, a:1, s:1, b:0),
% 0.96/1.62 tc_HOL_Obool [239, 0] (w:1, o:89, a:1, s:1, b:0),
% 0.96/1.62 alpha1 [240, 2] (w:1, o:271, a:1, s:1, b:1),
% 0.96/1.62 alpha2 [241, 4] (w:1, o:335, a:1, s:1, b:1),
% 0.96/1.62 alpha3 [242, 4] (w:1, o:336, a:1, s:1, b:1),
% 0.96/1.62 alpha4 [243, 2] (w:1, o:274, a:1, s:1, b:1),
% 0.96/1.62 alpha5 [244, 2] (w:1, o:277, a:1, s:1, b:1),
% 0.96/1.62 alpha6 [245, 3] (w:1, o:296, a:1, s:1, b:1),
% 0.96/1.62 alpha7 [246, 3] (w:1, o:297, a:1, s:1, b:1),
% 0.96/1.62 alpha8 [247, 2] (w:1, o:278, a:1, s:1, b:1),
% 0.96/1.62 alpha9 [248, 2] (w:1, o:279, a:1, s:1, b:1),
% 6.01/6.37 alpha10 [249, 2] (w:1, o:280, a:1, s:1, b:1),
% 6.01/6.37 alpha11 [250, 3] (w:1, o:298, a:1, s:1, b:1),
% 6.01/6.37 alpha12 [251, 3] (w:1, o:299, a:1, s:1, b:1),
% 6.01/6.37 alpha13 [252, 3] (w:1, o:300, a:1, s:1, b:1),
% 6.01/6.37 alpha14 [253, 2] (w:1, o:281, a:1, s:1, b:1),
% 6.01/6.37 alpha15 [254, 2] (w:1, o:282, a:1, s:1, b:1),
% 6.01/6.37 alpha16 [255, 2] (w:1, o:283, a:1, s:1, b:1),
% 6.01/6.37 alpha17 [256, 2] (w:1, o:284, a:1, s:1, b:1),
% 6.01/6.37 alpha18 [257, 4] (w:1, o:333, a:1, s:1, b:1),
% 6.01/6.37 alpha19 [258, 4] (w:1, o:334, a:1, s:1, b:1),
% 6.01/6.37 alpha20 [259, 2] (w:1, o:285, a:1, s:1, b:1),
% 6.01/6.37 alpha21 [260, 2] (w:1, o:286, a:1, s:1, b:1),
% 6.01/6.37 alpha22 [261, 3] (w:1, o:301, a:1, s:1, b:1),
% 6.01/6.37 alpha23 [262, 3] (w:1, o:302, a:1, s:1, b:1),
% 6.01/6.37 alpha24 [263, 2] (w:1, o:287, a:1, s:1, b:1),
% 6.01/6.37 alpha25 [264, 2] (w:1, o:288, a:1, s:1, b:1),
% 6.01/6.37 alpha26 [265, 2] (w:1, o:289, a:1, s:1, b:1),
% 6.01/6.37 alpha27 [266, 3] (w:1, o:303, a:1, s:1, b:1),
% 6.01/6.37 alpha28 [267, 3] (w:1, o:304, a:1, s:1, b:1),
% 6.01/6.37 alpha29 [268, 3] (w:1, o:305, a:1, s:1, b:1),
% 6.01/6.37 alpha30 [269, 2] (w:1, o:272, a:1, s:1, b:1),
% 6.01/6.37 alpha31 [270, 3] (w:1, o:306, a:1, s:1, b:1),
% 6.01/6.37 alpha32 [271, 3] (w:1, o:307, a:1, s:1, b:1),
% 6.01/6.37 alpha33 [272, 3] (w:1, o:308, a:1, s:1, b:1),
% 6.01/6.37 alpha34 [273, 2] (w:1, o:273, a:1, s:1, b:1),
% 6.01/6.37 alpha35 [274, 3] (w:1, o:309, a:1, s:1, b:1),
% 6.01/6.37 alpha36 [275, 3] (w:1, o:310, a:1, s:1, b:1),
% 6.01/6.37 alpha37 [276, 4] (w:1, o:337, a:1, s:1, b:1),
% 6.01/6.37 alpha38 [277, 3] (w:1, o:311, a:1, s:1, b:1),
% 6.01/6.37 alpha39 [278, 3] (w:1, o:312, a:1, s:1, b:1),
% 6.01/6.37 alpha40 [279, 4] (w:1, o:338, a:1, s:1, b:1),
% 6.01/6.37 alpha41 [280, 3] (w:1, o:313, a:1, s:1, b:1),
% 6.01/6.37 alpha42 [281, 3] (w:1, o:314, a:1, s:1, b:1),
% 6.01/6.37 alpha43 [282, 3] (w:1, o:315, a:1, s:1, b:1),
% 6.01/6.37 alpha44 [283, 4] (w:1, o:339, a:1, s:1, b:1),
% 6.01/6.37 alpha45 [284, 4] (w:1, o:340, a:1, s:1, b:1),
% 6.01/6.37 alpha46 [285, 3] (w:1, o:316, a:1, s:1, b:1),
% 6.01/6.37 alpha47 [286, 2] (w:1, o:275, a:1, s:1, b:1),
% 6.01/6.37 alpha48 [287, 2] (w:1, o:276, a:1, s:1, b:1),
% 6.01/6.37 alpha49 [288, 3] (w:1, o:317, a:1, s:1, b:1),
% 6.01/6.37 skol1 [289, 2] (w:1, o:239, a:1, s:1, b:1),
% 6.01/6.37 skol2 [290, 1] (w:1, o:200, a:1, s:1, b:1),
% 6.01/6.37 skol3 [291, 1] (w:1, o:204, a:1, s:1, b:1),
% 6.01/6.37 skol4 [292, 2] (w:1, o:244, a:1, s:1, b:1),
% 6.01/6.37 skol5 [293, 2] (w:1, o:246, a:1, s:1, b:1),
% 6.01/6.37 skol6 [294, 3] (w:1, o:318, a:1, s:1, b:1),
% 6.01/6.37 skol7 [295, 2] (w:1, o:247, a:1, s:1, b:1),
% 6.01/6.37 skol8 [296, 2] (w:1, o:248, a:1, s:1, b:1),
% 6.01/6.37 skol9 [297, 2] (w:1, o:249, a:1, s:1, b:1),
% 6.01/6.37 skol10 [298, 1] (w:1, o:194, a:1, s:1, b:1),
% 6.01/6.37 skol11 [299, 1] (w:1, o:195, a:1, s:1, b:1),
% 6.01/6.37 skol12 [300, 2] (w:1, o:250, a:1, s:1, b:1),
% 6.01/6.37 skol13 [301, 2] (w:1, o:251, a:1, s:1, b:1),
% 6.01/6.37 skol14 [302, 1] (w:1, o:196, a:1, s:1, b:1),
% 6.01/6.37 skol15 [303, 1] (w:1, o:197, a:1, s:1, b:1),
% 6.01/6.37 skol16 [304, 3] (w:1, o:319, a:1, s:1, b:1),
% 6.01/6.37 skol17 [305, 2] (w:1, o:252, a:1, s:1, b:1),
% 6.01/6.37 skol18 [306, 1] (w:1, o:198, a:1, s:1, b:1),
% 6.01/6.37 skol19 [307, 1] (w:1, o:199, a:1, s:1, b:1),
% 6.01/6.37 skol20 [308, 2] (w:1, o:253, a:1, s:1, b:1),
% 6.01/6.37 skol21 [309, 2] (w:1, o:254, a:1, s:1, b:1),
% 6.01/6.37 skol22 [310, 2] (w:1, o:255, a:1, s:1, b:1),
% 6.01/6.37 skol23 [311, 2] (w:1, o:256, a:1, s:1, b:1),
% 6.01/6.37 skol24 [312, 2] (w:1, o:257, a:1, s:1, b:1),
% 6.01/6.37 skol25 [313, 1] (w:1, o:201, a:1, s:1, b:1),
% 6.01/6.37 skol26 [314, 1] (w:1, o:202, a:1, s:1, b:1),
% 6.01/6.37 skol27 [315, 2] (w:1, o:258, a:1, s:1, b:1),
% 6.01/6.37 skol28 [316, 1] (w:1, o:203, a:1, s:1, b:1),
% 6.01/6.37 skol29 [317, 2] (w:1, o:259, a:1, s:1, b:1),
% 6.01/6.37 skol30 [318, 2] (w:1, o:240, a:1, s:1, b:1),
% 6.01/6.37 skol31 [319, 2] (w:1, o:241, a:1, s:1, b:1),
% 6.01/6.37 skol32 [320, 2] (w:1, o:242, a:1, s:1, b:1),
% 6.01/6.37 skol33 [321, 2] (w:1, o:243, a:1, s:1, b:1),
% 6.01/6.37 skol34 [322, 3] (w:1, o:320, a:1, s:1, b:1),
% 6.01/6.37 skol35 [323, 3] (w:1, o:321, a:1, s:1, b:1),
% 6.01/6.37 skol36 [324, 1] (w:1, o:205, a:1, s:1, b:1),
% 6.01/6.37 skol37 [325, 3] (w:1, o:322, a:1, s:1, b:1),
% 6.01/6.37 skol38 [326, 3] (w:1, o:323, a:1, s:1, b:1),
% 37.80/38.17 skol39 [327, 3] (w:1, o:324, a:1, s:1, b:1),
% 37.80/38.17 skol40 [328, 3] (w:1, o:325, a:1, s:1, b:1),
% 37.80/38.17 skol41 [329, 2] (w:1, o:245, a:1, s:1, b:1),
% 37.80/38.17 skol42 [330, 3] (w:1, o:326, a:1, s:1, b:1),
% 37.80/38.17 skol43 [331, 4] (w:1, o:341, a:1, s:1, b:1),
% 37.80/38.17 skol44 [332, 3] (w:1, o:327, a:1, s:1, b:1),
% 37.80/38.17 skol45 [333, 0] (w:1, o:15, a:1, s:1, b:1),
% 37.80/38.17 skol46 [334, 1] (w:1, o:206, a:1, s:1, b:1),
% 37.80/38.17 skol47 [335, 3] (w:1, o:328, a:1, s:1, b:1),
% 37.80/38.17 skol48 [336, 1] (w:1, o:207, a:1, s:1, b:1),
% 37.80/38.17 skol49 [337, 1] (w:1, o:208, a:1, s:1, b:1),
% 37.80/38.17 skol50 [338, 2] (w:1, o:260, a:1, s:1, b:1),
% 37.80/38.17 skol51 [339, 2] (w:1, o:261, a:1, s:1, b:1),
% 37.80/38.17 skol52 [340, 1] (w:1, o:209, a:1, s:1, b:1),
% 37.80/38.17 skol53 [341, 1] (w:1, o:210, a:1, s:1, b:1),
% 37.80/38.17 skol54 [342, 0] (w:1, o:16, a:1, s:1, b:1).
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Starting Search:
% 37.80/38.17
% 37.80/38.17 *** allocated 113905 integers for clauses
% 37.80/38.17 *** allocated 170857 integers for clauses
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 3187
% 37.80/38.17 Kept: 2002
% 37.80/38.17 Inuse: 63
% 37.80/38.17 Deleted: 1
% 37.80/38.17 Deletedinuse: 0
% 37.80/38.17
% 37.80/38.17 *** allocated 256285 integers for clauses
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 170857 integers for termspace/termends
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 8052
% 37.80/38.17 Kept: 4009
% 37.80/38.17 Inuse: 221
% 37.80/38.17 Deleted: 2
% 37.80/38.17 Deletedinuse: 0
% 37.80/38.17
% 37.80/38.17 *** allocated 384427 integers for clauses
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 256285 integers for termspace/termends
% 37.80/38.17 *** allocated 576640 integers for clauses
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 15146
% 37.80/38.17 Kept: 6383
% 37.80/38.17 Inuse: 274
% 37.80/38.17 Deleted: 2
% 37.80/38.17 Deletedinuse: 0
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 23060
% 37.80/38.17 Kept: 8560
% 37.80/38.17 Inuse: 329
% 37.80/38.17 Deleted: 2
% 37.80/38.17 Deletedinuse: 0
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 384427 integers for termspace/termends
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 30441
% 37.80/38.17 Kept: 10687
% 37.80/38.17 Inuse: 384
% 37.80/38.17 Deleted: 2
% 37.80/38.17 Deletedinuse: 0
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 864960 integers for clauses
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 39211
% 37.80/38.17 Kept: 13149
% 37.80/38.17 Inuse: 433
% 37.80/38.17 Deleted: 4
% 37.80/38.17 Deletedinuse: 1
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 576640 integers for termspace/termends
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 46396
% 37.80/38.17 Kept: 15164
% 37.80/38.17 Inuse: 472
% 37.80/38.17 Deleted: 7
% 37.80/38.17 Deletedinuse: 2
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 1297440 integers for clauses
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 51862
% 37.80/38.17 Kept: 17200
% 37.80/38.17 Inuse: 511
% 37.80/38.17 Deleted: 7
% 37.80/38.17 Deletedinuse: 2
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 58510
% 37.80/38.17 Kept: 19215
% 37.80/38.17 Inuse: 570
% 37.80/38.17 Deleted: 12
% 37.80/38.17 Deletedinuse: 2
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying clauses:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 65458
% 37.80/38.17 Kept: 21682
% 37.80/38.17 Inuse: 591
% 37.80/38.17 Deleted: 779
% 37.80/38.17 Deletedinuse: 2
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 864960 integers for termspace/termends
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 75357
% 37.80/38.17 Kept: 24292
% 37.80/38.17 Inuse: 651
% 37.80/38.17 Deleted: 779
% 37.80/38.17 Deletedinuse: 2
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 1946160 integers for clauses
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 84427
% 37.80/38.17 Kept: 27114
% 37.80/38.17 Inuse: 698
% 37.80/38.17 Deleted: 786
% 37.80/38.17 Deletedinuse: 6
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 92960
% 37.80/38.17 Kept: 29691
% 37.80/38.17 Inuse: 725
% 37.80/38.17 Deleted: 789
% 37.80/38.17 Deletedinuse: 6
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 100305
% 37.80/38.17 Kept: 31765
% 37.80/38.17 Inuse: 772
% 37.80/38.17 Deleted: 791
% 37.80/38.17 Deletedinuse: 6
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 *** allocated 1297440 integers for termspace/termends
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 109833
% 37.80/38.17 Kept: 34489
% 37.80/38.17 Inuse: 786
% 37.80/38.17 Deleted: 799
% 37.80/38.17 Deletedinuse: 12
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17 Resimplifying inuse:
% 37.80/38.17 Done
% 37.80/38.17
% 37.80/38.17
% 37.80/38.17 Intermediate Status:
% 37.80/38.17 Generated: 118447
% 37.80/38.17 Kept: 36831
% 118.00/118.38 Inuse: 811
% 118.00/118.38 Deleted: 800
% 118.00/118.38 Deletedinuse: 13
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 129838
% 118.00/118.38 Kept: 39072
% 118.00/118.38 Inuse: 831
% 118.00/118.38 Deleted: 800
% 118.00/118.38 Deletedinuse: 13
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 *** allocated 2919240 integers for clauses
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 143801
% 118.00/118.38 Kept: 41719
% 118.00/118.38 Inuse: 841
% 118.00/118.38 Deleted: 800
% 118.00/118.38 Deletedinuse: 13
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying clauses:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 156155
% 118.00/118.38 Kept: 44550
% 118.00/118.38 Inuse: 861
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 164634
% 118.00/118.38 Kept: 47325
% 118.00/118.38 Inuse: 891
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 171299
% 118.00/118.38 Kept: 49644
% 118.00/118.38 Inuse: 911
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 *** allocated 1946160 integers for termspace/termends
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 179519
% 118.00/118.38 Kept: 52482
% 118.00/118.38 Inuse: 946
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 186175
% 118.00/118.38 Kept: 54542
% 118.00/118.38 Inuse: 981
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 193228
% 118.00/118.38 Kept: 56723
% 118.00/118.38 Inuse: 1001
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 199510
% 118.00/118.38 Kept: 58865
% 118.00/118.38 Inuse: 1021
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 212294
% 118.00/118.38 Kept: 61043
% 118.00/118.38 Inuse: 1031
% 118.00/118.38 Deleted: 1241
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 *** allocated 4378860 integers for clauses
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying clauses:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 227093
% 118.00/118.38 Kept: 64153
% 118.00/118.38 Inuse: 1039
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 234414
% 118.00/118.38 Kept: 66156
% 118.00/118.38 Inuse: 1073
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 241562
% 118.00/118.38 Kept: 68202
% 118.00/118.38 Inuse: 1106
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 248704
% 118.00/118.38 Kept: 70226
% 118.00/118.38 Inuse: 1140
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 256722
% 118.00/118.38 Kept: 72489
% 118.00/118.38 Inuse: 1166
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 *** allocated 2919240 integers for termspace/termends
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 264767
% 118.00/118.38 Kept: 74692
% 118.00/118.38 Inuse: 1186
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 271544
% 118.00/118.38 Kept: 76704
% 118.00/118.38 Inuse: 1209
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 278659
% 118.00/118.38 Kept: 78722
% 118.00/118.38 Inuse: 1227
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 284513
% 118.00/118.38 Kept: 80786
% 118.00/118.38 Inuse: 1261
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 288945
% 118.00/118.38 Kept: 82803
% 118.00/118.38 Inuse: 1299
% 118.00/118.38 Deleted: 1381
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying clauses:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 297584
% 118.00/118.38 Kept: 86113
% 118.00/118.38 Inuse: 1336
% 118.00/118.38 Deleted: 2124
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 118.00/118.38 Generated: 307595
% 118.00/118.38 Kept: 89587
% 118.00/118.38 Inuse: 1349
% 118.00/118.38 Deleted: 2126
% 118.00/118.38 Deletedinuse: 14
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38 Resimplifying inuse:
% 118.00/118.38 Done
% 118.00/118.38
% 118.00/118.38
% 118.00/118.38 Intermediate Status:
% 240.08/240.47 Generated: 313271
% 240.08/240.47 Kept: 91771
% 240.08/240.47 Inuse: 1379
% 240.08/240.47 Deleted: 2126
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 342002
% 240.08/240.47 Kept: 95064
% 240.08/240.47 Inuse: 1394
% 240.08/240.47 Deleted: 2126
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 *** allocated 6568290 integers for clauses
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 362879
% 240.08/240.47 Kept: 99352
% 240.08/240.47 Inuse: 1414
% 240.08/240.47 Deleted: 2126
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 374853
% 240.08/240.47 Kept: 102550
% 240.08/240.47 Inuse: 1429
% 240.08/240.47 Deleted: 2126
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying clauses:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 386549
% 240.08/240.47 Kept: 105497
% 240.08/240.47 Inuse: 1439
% 240.08/240.47 Deleted: 2878
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 *** allocated 4378860 integers for termspace/termends
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 398986
% 240.08/240.47 Kept: 109172
% 240.08/240.47 Inuse: 1464
% 240.08/240.47 Deleted: 2878
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 404807
% 240.08/240.47 Kept: 111269
% 240.08/240.47 Inuse: 1469
% 240.08/240.47 Deleted: 2878
% 240.08/240.47 Deletedinuse: 14
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 415502
% 240.08/240.47 Kept: 113271
% 240.08/240.47 Inuse: 1495
% 240.08/240.47 Deleted: 2879
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 426593
% 240.08/240.47 Kept: 116656
% 240.08/240.47 Inuse: 1519
% 240.08/240.47 Deleted: 2879
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 432048
% 240.08/240.47 Kept: 118731
% 240.08/240.47 Inuse: 1524
% 240.08/240.47 Deleted: 2879
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 437483
% 240.08/240.47 Kept: 120812
% 240.08/240.47 Inuse: 1529
% 240.08/240.47 Deleted: 2879
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 458460
% 240.08/240.47 Kept: 124169
% 240.08/240.47 Inuse: 1544
% 240.08/240.47 Deleted: 2879
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying clauses:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 489723
% 240.08/240.47 Kept: 128121
% 240.08/240.47 Inuse: 1559
% 240.08/240.47 Deleted: 3480
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 520033
% 240.08/240.47 Kept: 131457
% 240.08/240.47 Inuse: 1569
% 240.08/240.47 Deleted: 3480
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 529446
% 240.08/240.47 Kept: 133481
% 240.08/240.47 Inuse: 1596
% 240.08/240.47 Deleted: 3480
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 538608
% 240.08/240.47 Kept: 135631
% 240.08/240.47 Inuse: 1619
% 240.08/240.47 Deleted: 3480
% 240.08/240.47 Deletedinuse: 15
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 552057
% 240.08/240.47 Kept: 138237
% 240.08/240.47 Inuse: 1629
% 240.08/240.47 Deleted: 3485
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 559744
% 240.08/240.47 Kept: 140526
% 240.08/240.47 Inuse: 1639
% 240.08/240.47 Deleted: 3485
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 564645
% 240.08/240.47 Kept: 142694
% 240.08/240.47 Inuse: 1644
% 240.08/240.47 Deleted: 3485
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 569564
% 240.08/240.47 Kept: 144870
% 240.08/240.47 Inuse: 1649
% 240.08/240.47 Deleted: 3485
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying clauses:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 574508
% 240.08/240.47 Kept: 147049
% 240.08/240.47 Inuse: 1654
% 240.08/240.47 Deleted: 4307
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 581590
% 240.08/240.47 Kept: 149387
% 240.08/240.47 Inuse: 1684
% 240.08/240.47 Deleted: 4307
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 588725
% 240.08/240.47 Kept: 151399
% 240.08/240.47 Inuse: 1708
% 240.08/240.47 Deleted: 4307
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 602665
% 240.08/240.47 Kept: 153421
% 240.08/240.47 Inuse: 1736
% 240.08/240.47 Deleted: 4307
% 240.08/240.47 Deletedinuse: 20
% 240.08/240.47
% 240.08/240.47 *** allocated 9852435 integers for clauses
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47 Resimplifying inuse:
% 240.08/240.47 Done
% 240.08/240.47
% 240.08/240.47
% 240.08/240.47 Intermediate Status:
% 240.08/240.47 Generated: 615148
% 240.08/240.47 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------