TSTP Solution File: NUM924+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM924+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 : Mon Jul 18 06:27:35 EDT 2022
% Result : Theorem 0.89s 1.38s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM924+2 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.11 % Command : bliksem %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % DateTime : Thu Jul 7 21:18:35 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.89/1.35 *** allocated 10000 integers for termspace/termends
% 0.89/1.35 *** allocated 10000 integers for clauses
% 0.89/1.35 *** allocated 10000 integers for justifications
% 0.89/1.35 *** allocated 15000 integers for termspace/termends
% 0.89/1.35 Bliksem 1.12
% 0.89/1.35
% 0.89/1.35
% 0.89/1.35 Automatic Strategy Selection
% 0.89/1.35
% 0.89/1.35 *** allocated 22500 integers for termspace/termends
% 0.89/1.35 *** allocated 33750 integers for termspace/termends
% 0.89/1.35 *** allocated 50625 integers for termspace/termends
% 0.89/1.35
% 0.89/1.35 Clauses:
% 0.89/1.35
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), is_int( minus_minus_int( X, Y ) ) }.
% 0.89/1.35 { is_int( one_one_int ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), is_int( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), is_int( times_times_int( X, Y ) ) }.
% 0.89/1.35 { is_int( zero_zero_int ) }.
% 0.89/1.35 { is_int( undefined_int( int ) ) }.
% 0.89/1.35 { ! is_int( X ), is_int( bit0( X ) ) }.
% 0.89/1.35 { ! is_int( X ), is_int( bit1( X ) ) }.
% 0.89/1.35 { is_int( min ) }.
% 0.89/1.35 { is_int( pls ) }.
% 0.89/1.35 { ! is_int( X ), is_int( number_number_of_int( X ) ) }.
% 0.89/1.35 { ! is_int( X ), is_int( power_power_int( X, Y ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), is_int( legendre( X, Y ) ) }.
% 0.89/1.35 { is_int( m ) }.
% 0.89/1.35 { is_int( s1 ) }.
% 0.89/1.35 { is_int( s ) }.
% 0.89/1.35 { is_int( t ) }.
% 0.89/1.35 { ord_less_int( t, zero_zero_int ) }.
% 0.89/1.35 { ord_less_int( t, one_one_int ) }.
% 0.89/1.35 { ord_less_int( times_times_int( plus_plus_int( times_times_int(
% 0.89/1.35 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.35 t ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.35 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.35 zero_zero_int ) ) }.
% 0.89/1.35 { plus_plus_int( power_power_int( s, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), one_one_int ) = times_times_int( plus_plus_int( times_times_int
% 0.89/1.35 ( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.35 , t ) }.
% 0.89/1.35 { ! t = zero_zero_int, plus_plus_int( power_power_int( s,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { ! ord_less_eq_int( one_one_int, t ) }.
% 0.89/1.35 { ord_less_int( zero_zero_int, plus_plus_int( times_times_int(
% 0.89/1.35 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.35 }.
% 0.89/1.35 { ! ord_less_real( plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_int( plus_plus_int( power_power_int( X, number_number_of_nat(
% 0.89/1.35 bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) ), zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_real( zero_zero_real, plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ), ! X = zero_zero_real,
% 0.89/1.35 ! Y = zero_zero_real }.
% 0.89/1.35 { X = zero_zero_real, ord_less_real( zero_zero_real, plus_plus_real(
% 0.89/1.35 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }
% 0.89/1.35 .
% 0.89/1.35 { Y = zero_zero_real, ord_less_real( zero_zero_real, plus_plus_real(
% 0.89/1.35 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }
% 0.89/1.35 .
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int,
% 0.89/1.35 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) ) ), ! X = zero_zero_int, ! Y = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), X = zero_zero_int, ord_less_int(
% 0.89/1.35 zero_zero_int, plus_plus_int( power_power_int( X, number_number_of_nat(
% 0.89/1.35 bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), Y = zero_zero_int, ord_less_int(
% 0.89/1.35 zero_zero_int, plus_plus_int( power_power_int( X, number_number_of_nat(
% 0.89/1.35 bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) ) ) }.
% 0.89/1.35 { ! plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.35 { ! plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ) = zero_zero_real, Y = zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, ! Y = zero_zero_real, plus_plus_real(
% 0.89/1.35 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) =
% 0.89/1.35 zero_zero_real }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! plus_plus_int( power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_int, X =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! plus_plus_int( power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_int, Y =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = zero_zero_int, ! Y = zero_zero_int,
% 0.89/1.35 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) ) = zero_zero_int }.
% 0.89/1.35 { ! ord_less_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_real( zero_zero_real, power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! X = zero_zero_real }.
% 0.89/1.35 { X = zero_zero_real, ord_less_real( zero_zero_real, power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { ! is_int( X ), ! ord_less_int( zero_zero_int, power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! X = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), X = zero_zero_int, ord_less_int( zero_zero_int,
% 0.89/1.35 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { power_power_real( one_one_real, number_number_of_nat( bit0( bit1( pls ) )
% 0.89/1.35 ) ) = one_one_real }.
% 0.89/1.35 { power_power_nat( one_one_nat, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) = one_one_nat }.
% 0.89/1.35 { power_power_int( one_one_int, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) = one_one_int }.
% 0.89/1.35 { power_power_real( zero_zero_real, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) = zero_zero_real }.
% 0.89/1.35 { power_power_nat( zero_zero_nat, number_number_of_nat( bit0( bit1( pls ) )
% 0.89/1.35 ) ) = zero_zero_nat }.
% 0.89/1.35 { power_power_int( zero_zero_int, number_number_of_nat( bit0( bit1( pls ) )
% 0.89/1.35 ) ) = zero_zero_int }.
% 0.89/1.35 { ! power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 zero_zero_real, X = zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, power_power_real( X, number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) = zero_zero_real }.
% 0.89/1.35 { ! is_int( X ), ! power_power_int( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ) = zero_zero_int, X = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! X = zero_zero_int, power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_int }.
% 0.89/1.35 { plus_plus_real( one_one_real, number267125858f_real( X ) ) =
% 0.89/1.35 number267125858f_real( plus_plus_int( bit1( pls ), X ) ) }.
% 0.89/1.35 { plus_plus_int( one_one_int, number_number_of_int( X ) ) =
% 0.89/1.35 number_number_of_int( plus_plus_int( bit1( pls ), X ) ) }.
% 0.89/1.35 { plus_plus_real( number267125858f_real( X ), one_one_real ) =
% 0.89/1.35 number267125858f_real( plus_plus_int( X, bit1( pls ) ) ) }.
% 0.89/1.35 { plus_plus_int( number_number_of_int( X ), one_one_int ) =
% 0.89/1.35 number_number_of_int( plus_plus_int( X, bit1( pls ) ) ) }.
% 0.89/1.35 { ord_less_int( t, plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.35 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { is_int( skol1 ) }.
% 0.89/1.35 { plus_plus_int( power_power_int( s, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), one_one_int ) = times_times_int( plus_plus_int( times_times_int
% 0.89/1.35 ( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.35 , skol1 ) }.
% 0.89/1.35 { zprime( plus_plus_int( times_times_int( number_number_of_int( bit0( bit0
% 0.89/1.35 ( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { twoSqu142715416sum2sq( times_times_int( plus_plus_int( times_times_int(
% 0.89/1.35 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.35 t ) ) }.
% 0.89/1.35 { ord_less_eq_int( X, X ) }.
% 0.89/1.35 { ! is_int( X ), number_number_of_int( X ) = X }.
% 0.89/1.35 { times_times_int( X, Y ) = times_times_int( Y, X ) }.
% 0.89/1.35 { ord_less_eq_int( X, Y ), ord_less_eq_int( Y, X ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( times_times_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( number_number_of_int( X ), number_number_of_int( Y ) )
% 0.89/1.35 , ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( number_number_of_int( X ),
% 0.89/1.35 number_number_of_int( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_real( number267125858f_real( X ), number267125858f_real( Y
% 0.89/1.35 ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_real( number267125858f_real( X ),
% 0.89/1.35 number267125858f_real( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( number_number_of_int( X ), number_number_of_int( Y ) )
% 0.89/1.35 , ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( number_number_of_int( X ),
% 0.89/1.35 number_number_of_int( Y ) ) }.
% 0.89/1.35 { times_times_int( times_times_int( X, Y ), Z ) = times_times_int( X,
% 0.89/1.35 times_times_int( Y, Z ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ! ord_less_eq_int( Y, Z ), ord_less_eq_int( X
% 0.89/1.35 , Z ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( X, Y ), !
% 0.89/1.35 ord_less_eq_int( Y, X ), X = Y }.
% 0.89/1.35 { power_power_int( X, plus_plus_nat( Y, Z ) ) = times_times_int(
% 0.89/1.35 power_power_int( X, Y ), power_power_int( X, Z ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit1( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit1( X ), bit1( Y ) ) }.
% 0.89/1.35 { ord_less_eq_int( pls, pls ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit0( X ), bit0( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit0( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit0( X ), bit0( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit0( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( X, Y ), ord_less_eq_int( X
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( X, Y ), ! X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( X, Y ), X = Y,
% 0.89/1.35 ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( plus_plus_int( Z, X ),
% 0.89/1.35 plus_plus_int( Z, Y ) ) }.
% 0.89/1.35 { ! number_number_of_nat( X ) = zero_zero_nat, ord_less_eq_int( X, pls ) }
% 0.89/1.35 .
% 0.89/1.35 { ! ord_less_eq_int( X, pls ), number_number_of_nat( X ) = zero_zero_nat }
% 0.89/1.35 .
% 0.89/1.35 { ! zero_zero_nat = number_number_of_nat( X ), ord_less_eq_int( X, pls ) }
% 0.89/1.35 .
% 0.89/1.35 { ! ord_less_eq_int( X, pls ), zero_zero_nat = number_number_of_nat( X ) }
% 0.89/1.35 .
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ),
% 0.89/1.35 times_times_real( number267125858f_real( X ), number267125858f_real( Y )
% 0.89/1.35 ) = number267125858f_real( times_times_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ), times_times_nat
% 0.89/1.35 ( number_number_of_nat( X ), number_number_of_nat( Y ) ) =
% 0.89/1.35 number_number_of_nat( times_times_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ), times_times_int
% 0.89/1.35 ( number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( times_times_int( X, Y ) ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( X ), times_times_real(
% 0.89/1.35 number267125858f_real( Y ), Z ) ) = times_times_real(
% 0.89/1.35 number267125858f_real( times_times_int( X, Y ) ), Z ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( X ), times_times_int(
% 0.89/1.35 number_number_of_int( Y ), Z ) ) = times_times_int( number_number_of_int
% 0.89/1.35 ( times_times_int( X, Y ) ), Z ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( X ), number267125858f_real( Y )
% 0.89/1.35 ) = number267125858f_real( times_times_int( X, Y ) ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( times_times_int( X, Y ) ) }.
% 0.89/1.35 { number267125858f_real( times_times_int( X, Y ) ) = times_times_real(
% 0.89/1.35 number267125858f_real( X ), number267125858f_real( Y ) ) }.
% 0.89/1.35 { number_number_of_int( times_times_int( X, Y ) ) = times_times_int(
% 0.89/1.35 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_real( plus_plus_real( times_times_real( X, X ),
% 0.89/1.35 times_times_real( Y, Y ) ), zero_zero_real ), X = zero_zero_real }.
% 0.89/1.35 { ! ord_less_eq_real( plus_plus_real( times_times_real( X, X ),
% 0.89/1.35 times_times_real( Y, Y ) ), zero_zero_real ), Y = zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, ! Y = zero_zero_real, ord_less_eq_real(
% 0.89/1.35 plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ),
% 0.89/1.35 zero_zero_real ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( plus_plus_int(
% 0.89/1.35 times_times_int( X, X ), times_times_int( Y, Y ) ), zero_zero_int ), X =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( plus_plus_int(
% 0.89/1.35 times_times_int( X, X ), times_times_int( Y, Y ) ), zero_zero_int ), Y =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = zero_zero_int, ! Y = zero_zero_int,
% 0.89/1.35 ord_less_eq_int( plus_plus_int( times_times_int( X, X ), times_times_int
% 0.89/1.35 ( Y, Y ) ), zero_zero_int ) }.
% 0.89/1.35 { ord_less_eq_real( zero_zero_real, plus_plus_real( times_times_real( X, X
% 0.89/1.35 ), times_times_real( Y, Y ) ) ) }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, plus_plus_int( times_times_int( X, X ),
% 0.89/1.35 times_times_int( Y, Y ) ) ) }.
% 0.89/1.35 { ! ord_less_eq_real( number267125858f_real( X ), zero_zero_real ),
% 0.89/1.35 ord_less_eq_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, pls ), ord_less_eq_real( number267125858f_real( X )
% 0.89/1.35 , zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_eq_int( number_number_of_int( X ), zero_zero_int ),
% 0.89/1.35 ord_less_eq_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, pls ), ord_less_eq_int( number_number_of_int( X ),
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_eq_real( zero_zero_real, number267125858f_real( X ) ),
% 0.89/1.35 ord_less_eq_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ord_less_eq_real( zero_zero_real,
% 0.89/1.35 number267125858f_real( X ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( zero_zero_int, number_number_of_int( X ) ),
% 0.89/1.35 ord_less_eq_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ord_less_eq_int( zero_zero_int,
% 0.89/1.35 number_number_of_int( X ) ) }.
% 0.89/1.35 { ! ord_less_nat( zero_zero_nat, number_number_of_nat( X ) ), ord_less_int
% 0.89/1.35 ( pls, X ) }.
% 0.89/1.35 { ! ord_less_int( pls, X ), ord_less_nat( zero_zero_nat,
% 0.89/1.35 number_number_of_nat( X ) ) }.
% 0.89/1.35 { ! ord_less_eq_real( number267125858f_real( X ), number267125858f_real( Y
% 0.89/1.35 ) ), ! ord_less_real( number267125858f_real( Y ), number267125858f_real
% 0.89/1.35 ( X ) ) }.
% 0.89/1.35 { ord_less_real( number267125858f_real( Y ), number267125858f_real( X ) ),
% 0.89/1.35 ord_less_eq_real( number267125858f_real( X ), number267125858f_real( Y )
% 0.89/1.35 ) }.
% 0.89/1.35 { ! ord_less_eq_nat( number_number_of_nat( X ), number_number_of_nat( Y ) )
% 0.89/1.35 , ! ord_less_nat( number_number_of_nat( Y ), number_number_of_nat( X ) )
% 0.89/1.35 }.
% 0.89/1.35 { ord_less_nat( number_number_of_nat( Y ), number_number_of_nat( X ) ),
% 0.89/1.35 ord_less_eq_nat( number_number_of_nat( X ), number_number_of_nat( Y ) ) }
% 0.89/1.35 .
% 0.89/1.35 { ! ord_less_eq_int( number_number_of_int( X ), number_number_of_int( Y ) )
% 0.89/1.35 , ! ord_less_int( number_number_of_int( Y ), number_number_of_int( X ) )
% 0.89/1.35 }.
% 0.89/1.35 { ord_less_int( number_number_of_int( Y ), number_number_of_int( X ) ),
% 0.89/1.35 ord_less_eq_int( number_number_of_int( X ), number_number_of_int( Y ) ) }
% 0.89/1.35 .
% 0.89/1.35 { ! ord_less_eq_int( pls, bit1( X ) ), ord_less_eq_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ord_less_eq_int( pls, bit1( X ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit0( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit0( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit0( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_eq_int( bit0( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit0( X ), pls ), ord_less_eq_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, pls ), ord_less_eq_int( bit0( X ), pls ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, bit0( X ) ), ord_less_eq_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ord_less_eq_int( pls, bit0( X ) ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ! ord_less_eq_int( Z, T ), ord_less_int(
% 0.89/1.35 plus_plus_int( X, Z ), plus_plus_int( Y, T ) ) }.
% 0.89/1.35 { number_number_of_nat( pls ) = zero_zero_nat }.
% 0.89/1.35 { zero_zero_nat = number_number_of_nat( pls ) }.
% 0.89/1.35 { ! ord_less_eq_real( number267125858f_real( X ), one_one_real ),
% 0.89/1.35 ord_less_eq_int( X, bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, bit1( pls ) ), ord_less_eq_real(
% 0.89/1.35 number267125858f_real( X ), one_one_real ) }.
% 0.89/1.35 { ! ord_less_eq_int( number_number_of_int( X ), one_one_int ),
% 0.89/1.35 ord_less_eq_int( X, bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, bit1( pls ) ), ord_less_eq_int(
% 0.89/1.35 number_number_of_int( X ), one_one_int ) }.
% 0.89/1.35 { ! ord_less_eq_real( one_one_real, number267125858f_real( X ) ),
% 0.89/1.35 ord_less_eq_int( bit1( pls ), X ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( pls ), X ), ord_less_eq_real( one_one_real,
% 0.89/1.35 number267125858f_real( X ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( one_one_int, number_number_of_int( X ) ),
% 0.89/1.35 ord_less_eq_int( bit1( pls ), X ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( pls ), X ), ord_less_eq_int( one_one_int,
% 0.89/1.35 number_number_of_int( X ) ) }.
% 0.89/1.35 { plus_plus_nat( one_one_nat, one_one_nat ) = number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) }.
% 0.89/1.35 { times_times_int( pls, X ) = pls }.
% 0.89/1.35 { times_times_int( bit0( X ), Y ) = bit0( times_times_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_int( number_number_of_int( X ), number_number_of_int( Y ) ),
% 0.89/1.35 ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( number_number_of_int( X ),
% 0.89/1.35 number_number_of_int( Y ) ) }.
% 0.89/1.35 { ! is_int( X ), times_times_int( X, one_one_int ) = X }.
% 0.89/1.35 { ! is_int( X ), times_times_int( one_one_int, X ) = X }.
% 0.89/1.35 { plus_plus_int( number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { times_times_int( plus_plus_int( X, Y ), Z ) = plus_plus_int(
% 0.89/1.35 times_times_int( X, Z ), times_times_int( Y, Z ) ) }.
% 0.89/1.35 { times_times_int( X, plus_plus_int( Y, Z ) ) = plus_plus_int(
% 0.89/1.35 times_times_int( X, Y ), times_times_int( X, Z ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( X ), pls ), ord_less_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_int( X, pls ), ord_less_eq_int( bit1( X ), pls ) }.
% 0.89/1.35 { ! ord_less_int( pls, bit1( X ) ), ord_less_eq_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ord_less_int( pls, bit1( X ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_eq_int( bit1( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( bit1( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_eq_int( bit1( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_int( bit0( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), bit1( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_int( bit0( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_nat( number_number_of_nat( X ), number_number_of_nat( Y ) ),
% 0.89/1.35 alpha1( X, Y ) }.
% 0.89/1.35 { ! ord_less_nat( number_number_of_nat( X ), number_number_of_nat( Y ) ),
% 0.89/1.35 ord_less_int( X, Y ) }.
% 0.89/1.35 { ! alpha1( X, Y ), ! ord_less_int( X, Y ), ord_less_nat(
% 0.89/1.35 number_number_of_nat( X ), number_number_of_nat( Y ) ) }.
% 0.89/1.35 { ! alpha1( X, Y ), ! ord_less_int( X, Y ), ord_less_int( pls, Y ) }.
% 0.89/1.35 { ord_less_int( X, Y ), alpha1( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( pls, Y ), alpha1( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( one_one_int, X ), ord_less_int( zero_zero_int, X ) }.
% 0.89/1.35 { ! ord_less_int( zero_zero_int, X ), ord_less_eq_int( one_one_int, X ) }.
% 0.89/1.35 { number_number_of_nat( bit1( pls ) ) = one_one_nat }.
% 0.89/1.35 { one_one_nat = number_number_of_nat( bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_eq_int( plus_plus_int( X, one_one_int )
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( plus_plus_int( X, one_one_int ), Y ), ord_less_int( X
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_eq_int( plus_plus_int( X, one_one_int )
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! ord_less_int( X, plus_plus_int( Y, one_one_int ) ), ord_less_eq_int( X
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! ord_less_eq_int( X, Y ), ord_less_int( X, plus_plus_int( Y, one_one_int
% 0.89/1.35 ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ), plus_plus_real
% 0.89/1.35 ( number267125858f_real( X ), number267125858f_real( Y ) ) =
% 0.89/1.35 number267125858f_real( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ), plus_plus_nat(
% 0.89/1.35 number_number_of_nat( X ), number_number_of_nat( Y ) ) =
% 0.89/1.35 number_number_of_nat( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( pls, X ), ! ord_less_eq_int( pls, Y ), plus_plus_int(
% 0.89/1.35 number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { ! ord_less_int( Y, pls ), plus_plus_nat( number_number_of_nat( Y ),
% 0.89/1.35 number_number_of_nat( X ) ) = number_number_of_nat( X ) }.
% 0.89/1.35 { ord_less_int( Y, pls ), ! ord_less_int( X, pls ), plus_plus_nat(
% 0.89/1.35 number_number_of_nat( Y ), number_number_of_nat( X ) ) =
% 0.89/1.35 number_number_of_nat( Y ) }.
% 0.89/1.35 { ord_less_int( Y, pls ), ord_less_int( X, pls ), plus_plus_nat(
% 0.89/1.35 number_number_of_nat( Y ), number_number_of_nat( X ) ) =
% 0.89/1.35 number_number_of_nat( plus_plus_int( Y, X ) ) }.
% 0.89/1.35 { ! ord_less_eq_int( zero_zero_int, X ), ord_less_int( zero_zero_int,
% 0.89/1.35 plus_plus_int( one_one_int, X ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! number267125858f_real( X ) =
% 0.89/1.35 number267125858f_real( Y ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = Y, number267125858f_real( X ) =
% 0.89/1.35 number267125858f_real( Y ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! number_number_of_int( X ) =
% 0.89/1.35 number_number_of_int( Y ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = Y, number_number_of_int( X ) =
% 0.89/1.35 number_number_of_int( Y ) }.
% 0.89/1.35 { ! number267125858f_real( X ) = Y, Y = number267125858f_real( X ) }.
% 0.89/1.35 { ! Y = number267125858f_real( X ), number267125858f_real( X ) = Y }.
% 0.89/1.35 { ! is_int( X ), ! number_number_of_int( Y ) = X, X = number_number_of_int
% 0.89/1.35 ( Y ) }.
% 0.89/1.35 { ! is_int( X ), ! X = number_number_of_int( Y ), number_number_of_int( Y )
% 0.89/1.35 = X }.
% 0.89/1.35 { ! number_number_of_nat( X ) = Y, Y = number_number_of_nat( X ) }.
% 0.89/1.35 { ! Y = number_number_of_nat( X ), number_number_of_nat( X ) = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! bit1( X ) = bit1( Y ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = Y, bit1( X ) = bit1( Y ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! bit0( X ) = bit0( Y ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = Y, bit0( X ) = bit0( Y ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ord_less_int( X, Y ), X = Y, ord_less_int(
% 0.89/1.35 Y, X ) }.
% 0.89/1.35 { ! plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.35 zero_zero_real, X = zero_zero_real }.
% 0.89/1.35 { ! plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.35 zero_zero_real, Y = zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, ! Y = zero_zero_real, plus_plus_real(
% 0.89/1.35 times_times_real( X, X ), times_times_real( Y, Y ) ) = zero_zero_real }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! plus_plus_int( times_times_int( X, X ),
% 0.89/1.35 times_times_int( Y, Y ) ) = zero_zero_int, X = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! plus_plus_int( times_times_int( X, X ),
% 0.89/1.35 times_times_int( Y, Y ) ) = zero_zero_int, Y = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = zero_zero_int, ! Y = zero_zero_int,
% 0.89/1.35 plus_plus_int( times_times_int( X, X ), times_times_int( Y, Y ) ) =
% 0.89/1.35 zero_zero_int }.
% 0.89/1.35 { times_times_real( plus_plus_real( X, Y ), number267125858f_real( Z ) ) =
% 0.89/1.35 plus_plus_real( times_times_real( X, number267125858f_real( Z ) ),
% 0.89/1.35 times_times_real( Y, number267125858f_real( Z ) ) ) }.
% 0.89/1.35 { times_times_nat( plus_plus_nat( X, Y ), number_number_of_nat( Z ) ) =
% 0.89/1.35 plus_plus_nat( times_times_nat( X, number_number_of_nat( Z ) ),
% 0.89/1.35 times_times_nat( Y, number_number_of_nat( Z ) ) ) }.
% 0.89/1.35 { times_times_int( plus_plus_int( X, Y ), number_number_of_int( Z ) ) =
% 0.89/1.35 plus_plus_int( times_times_int( X, number_number_of_int( Z ) ),
% 0.89/1.35 times_times_int( Y, number_number_of_int( Z ) ) ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( X ), plus_plus_real( Y, Z ) ) =
% 0.89/1.35 plus_plus_real( times_times_real( number267125858f_real( X ), Y ),
% 0.89/1.35 times_times_real( number267125858f_real( X ), Z ) ) }.
% 0.89/1.35 { times_times_nat( number_number_of_nat( X ), plus_plus_nat( Y, Z ) ) =
% 0.89/1.35 plus_plus_nat( times_times_nat( number_number_of_nat( X ), Y ),
% 0.89/1.35 times_times_nat( number_number_of_nat( X ), Z ) ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( X ), plus_plus_int( Y, Z ) ) =
% 0.89/1.35 plus_plus_int( times_times_int( number_number_of_int( X ), Y ),
% 0.89/1.35 times_times_int( number_number_of_int( X ), Z ) ) }.
% 0.89/1.35 { plus_plus_int( plus_plus_int( X, Y ), Z ) = plus_plus_int( X,
% 0.89/1.35 plus_plus_int( Y, Z ) ) }.
% 0.89/1.35 { plus_plus_int( X, plus_plus_int( Y, Z ) ) = plus_plus_int( Y,
% 0.89/1.35 plus_plus_int( X, Z ) ) }.
% 0.89/1.35 { plus_plus_int( X, Y ) = plus_plus_int( Y, X ) }.
% 0.89/1.35 { zero_zero_int = number_number_of_int( pls ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ! ord_less_int( zero_zero_int, Z ), ord_less_int
% 0.89/1.35 ( times_times_int( Z, X ), times_times_int( Z, Y ) ) }.
% 0.89/1.35 { ! power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ), !
% 0.89/1.35 ord_less_eq_real( zero_zero_real, X ), ! ord_less_eq_real( zero_zero_real
% 0.89/1.35 , Y ), X = Y }.
% 0.89/1.35 { ! power_power_nat( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 power_power_nat( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ), !
% 0.89/1.35 ord_less_eq_nat( zero_zero_nat, X ), ! ord_less_eq_nat( zero_zero_nat, Y
% 0.89/1.35 ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! power_power_int( X, number_number_of_nat
% 0.89/1.35 ( bit0( bit1( pls ) ) ) ) = power_power_int( Y, number_number_of_nat(
% 0.89/1.35 bit0( bit1( pls ) ) ) ), ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.35 ord_less_eq_int( zero_zero_int, Y ), X = Y }.
% 0.89/1.35 { ! ord_less_eq_real( power_power_real( X, number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ) ), ! ord_less_eq_real( zero_zero_real, Y ), ord_less_eq_real( X
% 0.89/1.35 , Y ) }.
% 0.89/1.35 { ! ord_less_eq_nat( power_power_nat( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_nat( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ), ! ord_less_eq_nat( zero_zero_nat, Y ), ord_less_eq_nat( X, Y )
% 0.89/1.35 }.
% 0.89/1.35 { ! ord_less_eq_int( power_power_int( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ), ! ord_less_eq_int( zero_zero_int, Y ), ord_less_eq_int( X, Y )
% 0.89/1.35 }.
% 0.89/1.35 { ord_less_eq_real( zero_zero_real, power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, power_power_int( X, number_number_of_nat
% 0.89/1.35 ( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { ! ord_less_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ), ! ord_less_eq_real( zero_zero_real, Y ), ord_less_real( X, Y )
% 0.89/1.35 }.
% 0.89/1.35 { ! ord_less_nat( power_power_nat( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), power_power_nat( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) ), ! ord_less_eq_nat( zero_zero_nat, Y ), ord_less_nat( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.35 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.35 ) ), ! ord_less_eq_int( zero_zero_int, Y ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_eq_real( plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), zero_zero_real ), X =
% 0.89/1.35 zero_zero_real }.
% 0.89/1.35 { ! ord_less_eq_real( plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), zero_zero_real ), Y =
% 0.89/1.35 zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, ! Y = zero_zero_real, ord_less_eq_real(
% 0.89/1.35 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.35 ) ) ) ), zero_zero_real ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( plus_plus_int(
% 0.89/1.35 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.35 zero_zero_int ), X = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( plus_plus_int(
% 0.89/1.35 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.35 zero_zero_int ), Y = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = zero_zero_int, ! Y = zero_zero_int,
% 0.89/1.35 ord_less_eq_int( plus_plus_int( power_power_int( X, number_number_of_nat
% 0.89/1.35 ( bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0
% 0.89/1.35 ( bit1( pls ) ) ) ) ), zero_zero_int ) }.
% 0.89/1.35 { ord_less_eq_real( zero_zero_real, plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, plus_plus_int( power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.35 { ! ord_less_real( zero_zero_real, plus_plus_real( times_times_real( X, X )
% 0.89/1.35 , times_times_real( Y, Y ) ) ), ! X = zero_zero_real, ! Y =
% 0.89/1.35 zero_zero_real }.
% 0.89/1.35 { X = zero_zero_real, ord_less_real( zero_zero_real, plus_plus_real(
% 0.89/1.35 times_times_real( X, X ), times_times_real( Y, Y ) ) ) }.
% 0.89/1.35 { Y = zero_zero_real, ord_less_real( zero_zero_real, plus_plus_real(
% 0.89/1.35 times_times_real( X, X ), times_times_real( Y, Y ) ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int,
% 0.89/1.35 plus_plus_int( times_times_int( X, X ), times_times_int( Y, Y ) ) ), ! X
% 0.89/1.35 = zero_zero_int, ! Y = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), X = zero_zero_int, ord_less_int(
% 0.89/1.35 zero_zero_int, plus_plus_int( times_times_int( X, X ), times_times_int( Y
% 0.89/1.35 , Y ) ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), Y = zero_zero_int, ord_less_int(
% 0.89/1.35 zero_zero_int, plus_plus_int( times_times_int( X, X ), times_times_int( Y
% 0.89/1.35 , Y ) ) ) }.
% 0.89/1.35 { ! ord_less_real( plus_plus_real( times_times_real( X, X ),
% 0.89/1.35 times_times_real( Y, Y ) ), zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_int( plus_plus_int( times_times_int( X, X ), times_times_int(
% 0.89/1.35 Y, Y ) ), zero_zero_int ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( bit1( pls ) ), X ) = X }.
% 0.89/1.35 { ! is_int( X ), times_times_int( number_number_of_int( bit1( pls ) ), X )
% 0.89/1.35 = X }.
% 0.89/1.35 { times_times_real( X, number267125858f_real( bit1( pls ) ) ) = X }.
% 0.89/1.35 { ! is_int( X ), times_times_int( X, number_number_of_int( bit1( pls ) ) )
% 0.89/1.35 = X }.
% 0.89/1.35 { one_one_int = number_number_of_int( bit1( pls ) ) }.
% 0.89/1.35 { times_times_int( bit1( X ), Y ) = plus_plus_int( bit0( times_times_int( X
% 0.89/1.35 , Y ) ), Y ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int, Y ), !
% 0.89/1.35 times_times_int( Y, X ) = one_one_int, Y = one_one_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int, Y ), !
% 0.89/1.35 times_times_int( Y, X ) = one_one_int, X = one_one_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int, Y ), ! Y =
% 0.89/1.35 one_one_int, ! X = one_one_int, times_times_int( Y, X ) = one_one_int }.
% 0.89/1.35 { ! plus_plus_real( X, X ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.35 { ! X = zero_zero_real, plus_plus_real( X, X ) = zero_zero_real }.
% 0.89/1.35 { ! is_int( X ), ! plus_plus_int( X, X ) = zero_zero_int, X = zero_zero_int
% 0.89/1.35 }.
% 0.89/1.35 { ! is_int( X ), ! X = zero_zero_int, plus_plus_int( X, X ) = zero_zero_int
% 0.89/1.35 }.
% 0.89/1.35 { ! bit1( X ) = pls }.
% 0.89/1.35 { ! pls = bit1( X ) }.
% 0.89/1.35 { ! bit1( X ) = bit0( Y ) }.
% 0.89/1.35 { ! bit0( X ) = bit1( Y ) }.
% 0.89/1.35 { ! is_int( X ), ! bit0( X ) = pls, X = pls }.
% 0.89/1.35 { ! is_int( X ), ! X = pls, bit0( X ) = pls }.
% 0.89/1.35 { ! is_int( X ), ! pls = bit0( X ), pls = X }.
% 0.89/1.35 { ! is_int( X ), ! pls = X, pls = bit0( X ) }.
% 0.89/1.35 { bit0( pls ) = pls }.
% 0.89/1.35 { pls = zero_zero_int }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), bit1( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit1( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), bit1( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit1( X ), bit1( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( pls, pls ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit0( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit0( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! zero_zero_int = one_one_int }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( X, pls ) = X }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( pls, X ) = X }.
% 0.89/1.35 { plus_plus_int( bit0( X ), bit0( Y ) ) = bit0( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { bit0( X ) = plus_plus_int( X, X ) }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( X, zero_zero_int ) = X }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( zero_zero_int, X ) = X }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( plus_plus_int( X, Z ),
% 0.89/1.35 plus_plus_int( Y, Z ) ) }.
% 0.89/1.35 { times_times_real( plus_plus_real( one_one_real, one_one_real ),
% 0.89/1.35 number267125858f_real( X ) ) = number267125858f_real( bit0( X ) ) }.
% 0.89/1.35 { times_times_int( plus_plus_int( one_one_int, one_one_int ),
% 0.89/1.35 number_number_of_int( X ) ) = number_number_of_int( bit0( X ) ) }.
% 0.89/1.35 { power_power_real( X, number_number_of_nat( bit1( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_real( times_times_real( X, X ), X ) }.
% 0.89/1.35 { power_power_nat( X, number_number_of_nat( bit1( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_nat( times_times_nat( X, X ), X ) }.
% 0.89/1.35 { power_power_int( X, number_number_of_nat( bit1( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_int( times_times_int( X, X ), X ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.35 plus_plus_real( X, X ) }.
% 0.89/1.35 { times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.35 plus_plus_nat( X, X ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.35 plus_plus_int( X, X ) }.
% 0.89/1.35 { times_times_real( number267125858f_real( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.35 plus_plus_real( X, X ) }.
% 0.89/1.35 { times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.35 plus_plus_int( X, X ) }.
% 0.89/1.35 { times_times_real( X, number267125858f_real( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 plus_plus_real( X, X ) }.
% 0.89/1.35 { times_times_nat( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 plus_plus_nat( X, X ) }.
% 0.89/1.35 { times_times_int( X, number_number_of_int( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 plus_plus_int( X, X ) }.
% 0.89/1.35 { times_times_real( X, number267125858f_real( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 plus_plus_real( X, X ) }.
% 0.89/1.35 { times_times_int( X, number_number_of_int( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 plus_plus_int( X, X ) }.
% 0.89/1.35 { power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_real( X, X ) }.
% 0.89/1.35 { power_power_nat( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_nat( X, X ) }.
% 0.89/1.35 { power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.35 times_times_int( X, X ) }.
% 0.89/1.35 { ! ord_less_real( plus_plus_real( X, X ), zero_zero_real ), ord_less_real
% 0.89/1.35 ( X, zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_real( X, zero_zero_real ), ord_less_real( plus_plus_real( X, X
% 0.89/1.35 ), zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_int( plus_plus_int( X, X ), zero_zero_int ), ord_less_int( X,
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( X, zero_zero_int ), ord_less_int( plus_plus_int( X, X ),
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { number267125858f_real( pls ) = zero_zero_real }.
% 0.89/1.35 { number_number_of_nat( pls ) = zero_zero_nat }.
% 0.89/1.35 { number_number_of_int( pls ) = zero_zero_int }.
% 0.89/1.35 { number267125858f_real( pls ) = zero_zero_real }.
% 0.89/1.35 { number_number_of_int( pls ) = zero_zero_int }.
% 0.89/1.35 { zero_zero_real = number267125858f_real( pls ) }.
% 0.89/1.35 { zero_zero_int = number_number_of_int( pls ) }.
% 0.89/1.35 { plus_plus_real( number267125858f_real( pls ), X ) = X }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( number_number_of_int( pls ), X ) = X }.
% 0.89/1.35 { plus_plus_real( X, number267125858f_real( pls ) ) = X }.
% 0.89/1.35 { ! is_int( X ), plus_plus_int( X, number_number_of_int( pls ) ) = X }.
% 0.89/1.35 { ! ord_less_real( number267125858f_real( X ), number267125858f_real( Y ) )
% 0.89/1.35 , ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_real( number267125858f_real( X ),
% 0.89/1.35 number267125858f_real( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( number_number_of_int( X ), number_number_of_int( Y ) ),
% 0.89/1.35 ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( number_number_of_int( X ),
% 0.89/1.35 number_number_of_int( Y ) ) }.
% 0.89/1.35 { plus_plus_real( number267125858f_real( X ), plus_plus_real(
% 0.89/1.35 number267125858f_real( Y ), Z ) ) = plus_plus_real( number267125858f_real
% 0.89/1.35 ( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.35 { plus_plus_int( number_number_of_int( X ), plus_plus_int(
% 0.89/1.35 number_number_of_int( Y ), Z ) ) = plus_plus_int( number_number_of_int(
% 0.89/1.35 plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.35 { plus_plus_real( number267125858f_real( X ), number267125858f_real( Y ) )
% 0.89/1.35 = number267125858f_real( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { plus_plus_int( number_number_of_int( X ), number_number_of_int( Y ) ) =
% 0.89/1.35 number_number_of_int( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { number267125858f_real( plus_plus_int( X, Y ) ) = plus_plus_real(
% 0.89/1.35 number267125858f_real( X ), number267125858f_real( Y ) ) }.
% 0.89/1.35 { number_number_of_int( plus_plus_int( X, Y ) ) = plus_plus_int(
% 0.89/1.35 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), pls ), ord_less_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_int( X, pls ), ord_less_int( bit1( X ), pls ) }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit1( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), bit0( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.35 { ! ord_less_int( X, Y ), ord_less_int( bit1( X ), bit0( Y ) ) }.
% 0.89/1.35 { ! ord_less_int( bit1( X ), zero_zero_int ), ord_less_int( X,
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( X, zero_zero_int ), ord_less_int( bit1( X ),
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), pls ), ord_less_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_int( X, pls ), ord_less_int( bit0( X ), pls ) }.
% 0.89/1.35 { ! ord_less_int( pls, bit0( X ) ), ord_less_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_int( pls, X ), ord_less_int( pls, bit0( X ) ) }.
% 0.89/1.35 { ! ord_less_int( pls, zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( bit0( X ), zero_zero_int ), ord_less_int( X,
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( X, zero_zero_int ), ord_less_int( bit0( X ),
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { plus_plus_int( bit1( X ), bit0( Y ) ) = bit1( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { plus_plus_int( bit0( X ), bit1( Y ) ) = bit1( plus_plus_int( X, Y ) ) }.
% 0.89/1.35 { ord_less_int( zero_zero_int, one_one_int ) }.
% 0.89/1.35 { bit1( X ) = plus_plus_int( plus_plus_int( one_one_int, X ), X ) }.
% 0.89/1.35 { ! plus_plus_int( plus_plus_int( one_one_int, X ), X ) = zero_zero_int }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( X, plus_plus_int( Y,
% 0.89/1.35 one_one_int ) ), ord_less_int( X, Y ), X = Y }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( X, Y ), ord_less_int( X,
% 0.89/1.35 plus_plus_int( Y, one_one_int ) ) }.
% 0.89/1.35 { ! is_int( X ), ! is_int( Y ), ! X = Y, ord_less_int( X, plus_plus_int( Y
% 0.89/1.35 , one_one_int ) ) }.
% 0.89/1.35 { power_power_real( number267125858f_real( X ), number_number_of_nat( bit0
% 0.89/1.35 ( bit1( pls ) ) ) ) = times_times_real( number267125858f_real( X ),
% 0.89/1.35 number267125858f_real( X ) ) }.
% 0.89/1.35 { power_power_nat( number_number_of_nat( X ), number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) = times_times_nat( number_number_of_nat( X ),
% 0.89/1.35 number_number_of_nat( X ) ) }.
% 0.89/1.35 { power_power_int( number_number_of_int( X ), number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) = times_times_int( number_number_of_int( X ),
% 0.89/1.35 number_number_of_int( X ) ) }.
% 0.89/1.35 { power_power_real( plus_plus_real( X, Y ), number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) = plus_plus_real( plus_plus_real( power_power_real( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_real(
% 0.89/1.35 times_times_real( number267125858f_real( bit0( bit1( pls ) ) ), X ), Y )
% 0.89/1.35 ) }.
% 0.89/1.35 { power_power_nat( plus_plus_nat( X, Y ), number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ) = plus_plus_nat( plus_plus_nat( power_power_nat( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_nat( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_nat(
% 0.89/1.35 times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ), Y ) )
% 0.89/1.35 }.
% 0.89/1.35 { power_power_int( plus_plus_int( X, Y ), number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ) = plus_plus_int( plus_plus_int( power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_int(
% 0.89/1.35 times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), Y ) )
% 0.89/1.35 }.
% 0.89/1.35 { number267125858f_real( bit0( X ) ) = plus_plus_real( plus_plus_real(
% 0.89/1.35 zero_zero_real, number267125858f_real( X ) ), number267125858f_real( X )
% 0.89/1.35 ) }.
% 0.89/1.35 { number_number_of_int( bit0( X ) ) = plus_plus_int( plus_plus_int(
% 0.89/1.35 zero_zero_int, number_number_of_int( X ) ), number_number_of_int( X ) ) }
% 0.89/1.35 .
% 0.89/1.35 { number267125858f_real( bit1( X ) ) = plus_plus_real( plus_plus_real(
% 0.89/1.35 one_one_real, number267125858f_real( X ) ), number267125858f_real( X ) )
% 0.89/1.35 }.
% 0.89/1.35 { number_number_of_int( bit1( X ) ) = plus_plus_int( plus_plus_int(
% 0.89/1.35 one_one_int, number_number_of_int( X ) ), number_number_of_int( X ) ) }.
% 0.89/1.35 { number267125858f_real( bit1( pls ) ) = one_one_real }.
% 0.89/1.35 { number_number_of_nat( bit1( pls ) ) = one_one_nat }.
% 0.89/1.35 { number_number_of_int( bit1( pls ) ) = one_one_int }.
% 0.89/1.35 { number267125858f_real( bit1( pls ) ) = one_one_real }.
% 0.89/1.35 { number_number_of_int( bit1( pls ) ) = one_one_int }.
% 0.89/1.35 { one_one_real = number267125858f_real( bit1( pls ) ) }.
% 0.89/1.35 { one_one_int = number_number_of_int( bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_int( plus_plus_int( plus_plus_int( one_one_int, X ), X ),
% 0.89/1.35 zero_zero_int ), ord_less_int( X, zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_int( X, zero_zero_int ), ord_less_int( plus_plus_int(
% 0.89/1.35 plus_plus_int( one_one_int, X ), X ), zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_real( number267125858f_real( X ), zero_zero_real ),
% 0.89/1.35 ord_less_int( X, pls ) }.
% 0.89/1.35 { ! ord_less_int( X, pls ), ord_less_real( number267125858f_real( X ),
% 0.89/1.35 zero_zero_real ) }.
% 0.89/1.35 { ! ord_less_int( number_number_of_int( X ), zero_zero_int ), ord_less_int
% 0.89/1.35 ( X, pls ) }.
% 0.89/1.35 { ! ord_less_int( X, pls ), ord_less_int( number_number_of_int( X ),
% 0.89/1.35 zero_zero_int ) }.
% 0.89/1.35 { ! ord_less_real( zero_zero_real, number267125858f_real( X ) ),
% 0.89/1.35 ord_less_int( pls, X ) }.
% 0.89/1.35 { ! ord_less_int( pls, X ), ord_less_real( zero_zero_real,
% 0.89/1.35 number267125858f_real( X ) ) }.
% 0.89/1.35 { ! ord_less_int( zero_zero_int, number_number_of_int( X ) ), ord_less_int
% 0.89/1.35 ( pls, X ) }.
% 0.89/1.35 { ! ord_less_int( pls, X ), ord_less_int( zero_zero_int,
% 0.89/1.35 number_number_of_int( X ) ) }.
% 0.89/1.35 { plus_plus_real( one_one_real, one_one_real ) = number267125858f_real(
% 0.89/1.35 bit0( bit1( pls ) ) ) }.
% 0.89/1.35 { plus_plus_nat( one_one_nat, one_one_nat ) = number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) }.
% 0.89/1.35 { plus_plus_int( one_one_int, one_one_int ) = number_number_of_int( bit0(
% 0.89/1.35 bit1( pls ) ) ) }.
% 0.89/1.35 { plus_plus_real( one_one_real, one_one_real ) = number267125858f_real(
% 0.89/1.35 bit0( bit1( pls ) ) ) }.
% 0.89/1.35 { plus_plus_int( one_one_int, one_one_int ) = number_number_of_int( bit0(
% 0.89/1.35 bit1( pls ) ) ) }.
% 0.89/1.35 { ! ord_less_real( number267125858f_real( X ), one_one_real ), ord_less_int
% 0.89/1.35 ( X, bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_int( X, bit1( pls ) ), ord_less_real( number267125858f_real( X
% 0.89/1.35 ), one_one_real ) }.
% 0.89/1.35 { ! ord_less_int( number_number_of_int( X ), one_one_int ), ord_less_int( X
% 0.89/1.35 , bit1( pls ) ) }.
% 0.89/1.35 { ! ord_less_int( X, bit1( pls ) ), ord_less_int( number_number_of_int( X )
% 0.89/1.35 , one_one_int ) }.
% 0.89/1.35 { ! ord_less_real( one_one_real, number267125858f_real( X ) ), ord_less_int
% 0.89/1.35 ( bit1( pls ), X ) }.
% 0.89/1.35 { ! ord_less_int( bit1( pls ), X ), ord_less_real( one_one_real,
% 0.89/1.35 number267125858f_real( X ) ) }.
% 0.89/1.35 { ! ord_less_int( one_one_int, number_number_of_int( X ) ), ord_less_int(
% 0.89/1.35 bit1( pls ), X ) }.
% 0.89/1.35 { ! ord_less_int( bit1( pls ), X ), ord_less_int( one_one_int,
% 0.89/1.35 number_number_of_int( X ) ) }.
% 0.89/1.35 { dvd_dvd_int( plus_plus_int( times_times_int( number_number_of_int( bit0(
% 0.89/1.35 bit0( bit1( pls ) ) ) ), m ), one_one_int ), plus_plus_int(
% 0.89/1.35 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 one_one_int ) ) }.
% 0.89/1.35 { power_power_int( plus_plus_int( X, Y ), number_number_of_nat( bit1( bit1
% 0.89/1.35 ( pls ) ) ) ) = plus_plus_int( plus_plus_int( plus_plus_int(
% 0.89/1.35 power_power_int( X, number_number_of_nat( bit1( bit1( pls ) ) ) ),
% 0.89/1.35 times_times_int( times_times_int( number_number_of_int( bit1( bit1( pls )
% 0.89/1.35 ) ), power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) )
% 0.89/1.35 , Y ) ), times_times_int( times_times_int( number_number_of_int( bit1(
% 0.89/1.35 bit1( pls ) ) ), X ), power_power_int( Y, number_number_of_nat( bit0(
% 0.89/1.35 bit1( pls ) ) ) ) ) ), power_power_int( Y, number_number_of_nat( bit1(
% 0.89/1.35 bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { power_power_int( plus_plus_int( X, Y ), number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ) = plus_plus_int( plus_plus_int( power_power_int( X,
% 0.89/1.35 number_number_of_nat( bit0( bit1( pls ) ) ) ), times_times_int(
% 0.89/1.35 times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), Y ) )
% 0.89/1.35 , power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.35 { ! is_int( X ), ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_int( X,
% 0.89/1.35 number_number_of_int( bit0( bit1( pls ) ) ) ), X = zero_zero_int, X =
% 0.89/1.35 one_one_int }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, s ) }.
% 0.89/1.35 { ord_less_int( s, plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.35 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { zcong( s1, s, plus_plus_int( times_times_int( number_number_of_int( bit0
% 0.89/1.35 ( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { times_times_int( X, power_power_int( X, number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ) ) = power_power_int( X, number_number_of_nat( bit1( bit1(
% 0.89/1.35 pls ) ) ) ) }.
% 0.89/1.35 { ord_less_eq_int( X, power_power_int( X, number_number_of_nat( bit0( bit1
% 0.89/1.35 ( pls ) ) ) ) ) }.
% 0.89/1.35 { ! ord_less_int( zero_zero_int, X ), ! X = plus_plus_int( Y,
% 0.89/1.35 times_times_int( X, Z ) ), ! ord_less_int( Y, X ), ord_less_eq_int(
% 0.89/1.35 one_one_int, Z ) }.
% 0.89/1.35 { ! ord_less_int( zero_zero_int, X ), ! X = plus_plus_int( Y,
% 0.89/1.35 times_times_int( X, Z ) ), ! ord_less_eq_int( zero_zero_int, Y ),
% 0.89/1.35 ord_less_eq_int( Z, one_one_int ) }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, number_number_of_int( bit0( bit1( pls ) )
% 0.89/1.35 ) ) }.
% 0.89/1.35 { power_power_real( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ), Y ) ) = times_times_real( power_power_real( X, Y ),
% 0.89/1.35 power_power_real( X, Y ) ) }.
% 0.89/1.35 { power_power_nat( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ), Y ) ) = times_times_nat( power_power_nat( X, Y ),
% 0.89/1.35 power_power_nat( X, Y ) ) }.
% 0.89/1.35 { power_power_int( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.35 pls ) ) ), Y ) ) = times_times_int( power_power_int( X, Y ),
% 0.89/1.35 power_power_int( X, Y ) ) }.
% 0.89/1.35 { zcong( power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.35 , power_power_int( s1, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.35 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { is_int( skol2 ) }.
% 0.89/1.35 { ord_less_eq_int( zero_zero_int, skol2 ) }.
% 0.89/1.35 { ord_less_int( skol2, plus_plus_int( times_times_int( number_number_of_int
% 0.89/1.35 ( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { zcong( s1, skol2, plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.35 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.35 { ! is_int( X ), ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_int( X,
% 0.89/1.35 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.35 pls ) ) ) ), m ), one_one_int ) ), ! zcong( s1, X, plus_plus_int(
% 0.89/1.35 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.36 , one_one_int ) ), X = skol2 }.
% 0.89/1.36 { is_int( skol3 ) }.
% 0.89/1.36 { ord_less_eq_int( zero_zero_int, skol3 ) }.
% 0.89/1.36 { ord_less_int( skol3, plus_plus_int( times_times_int( number_number_of_int
% 0.89/1.36 ( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.36 { zcong( s1, skol3, plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.36 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.36 { zcong( power_power_int( s1, number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.36 , number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.36 }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, power_power_nat( X, Y ) ), Y =
% 0.89/1.36 zero_zero_nat, ord_less_nat( zero_zero_nat, X ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, ord_less_nat( zero_zero_nat, power_power_nat( X, Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ord_less_nat( zero_zero_nat,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { ! zprime( X ), ! dvd_dvd_int( X, power_power_int( Y, Z ) ), dvd_dvd_int(
% 0.89/1.36 X, Y ) }.
% 0.89/1.36 { power_power_real( power_power_real( X, Y ), Z ) = power_power_real( X,
% 0.89/1.36 times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { power_power_nat( power_power_nat( X, Y ), Z ) = power_power_nat( X,
% 0.89/1.36 times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { power_power_int( power_power_int( X, Y ), Z ) = power_power_int( X,
% 0.89/1.36 times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { ! zprime( X ), dvd_dvd_int( X, Y ), ! dvd_dvd_int( power_power_int( X, Z
% 0.89/1.36 ), times_times_int( T, Y ) ), dvd_dvd_int( power_power_int( X, Z ), T )
% 0.89/1.36 }.
% 0.89/1.36 { ! zprime( X ), dvd_dvd_int( X, Y ), ! dvd_dvd_int( power_power_int( X, Z
% 0.89/1.36 ), times_times_int( Y, T ) ), dvd_dvd_int( power_power_int( X, Z ), T )
% 0.89/1.36 }.
% 0.89/1.36 { power_power_int( power_power_int( X, Y ), Z ) = power_power_int( X,
% 0.89/1.36 times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { ! ord_less_int( zero_zero_int, X ), ! ord_less_int( X, Y ), ! dvd_dvd_int
% 0.89/1.36 ( Y, X ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( zero_zero_int, Y ), !
% 0.89/1.36 ord_less_eq_int( zero_zero_int, X ), ! dvd_dvd_int( Y, X ), ! dvd_dvd_int
% 0.89/1.36 ( X, Y ), Y = X }.
% 0.89/1.36 { ! is_int( X ), ! dvd_dvd_int( times_times_int( X, Y ), times_times_int( X
% 0.89/1.36 , Z ) ), X = zero_zero_int, dvd_dvd_int( Y, Z ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, plus_plus_int( Y, times_times_int( X, Z ) ) ),
% 0.89/1.36 dvd_dvd_int( X, Y ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), dvd_dvd_int( X, plus_plus_int( Y, times_times_int
% 0.89/1.36 ( X, Z ) ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), ! dvd_dvd_int( X, plus_plus_int( T, U ) ),
% 0.89/1.36 dvd_dvd_int( X, plus_plus_int( plus_plus_int( T, times_times_int( Z, Y )
% 0.89/1.36 ), U ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), ! dvd_dvd_int( X, plus_plus_int( plus_plus_int( T
% 0.89/1.36 , times_times_int( Z, Y ) ), U ) ), dvd_dvd_int( X, plus_plus_int( T, U )
% 0.89/1.36 ) }.
% 0.89/1.36 { zprime( number_number_of_int( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), ! ord_less_int( zero_zero_int, Y ),
% 0.89/1.36 ord_less_eq_int( X, Y ) }.
% 0.89/1.36 { ! twoSqu142715416sum2sq( X ), ! twoSqu142715416sum2sq( Y ),
% 0.89/1.36 twoSqu142715416sum2sq( times_times_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( number_number_of_nat( X ), number_number_of_nat( Y ) )
% 0.89/1.36 , ord_less_eq_int( X, Y ), ord_less_eq_int( X, pls ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, Y ), ord_less_eq_nat( number_number_of_nat( X ),
% 0.89/1.36 number_number_of_nat( Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, pls ), ord_less_eq_nat( number_number_of_nat( X ),
% 0.89/1.36 number_number_of_nat( Y ) ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), times_times_real( Z, T ) ) =
% 0.89/1.36 times_times_real( times_times_real( X, Z ), times_times_real( Y, T ) ) }
% 0.89/1.36 .
% 0.89/1.36 { times_times_nat( times_times_nat( X, Y ), times_times_nat( Z, T ) ) =
% 0.89/1.36 times_times_nat( times_times_nat( X, Z ), times_times_nat( Y, T ) ) }.
% 0.89/1.36 { times_times_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 times_times_int( times_times_int( X, Z ), times_times_int( Y, T ) ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), times_times_real( Z, T ) ) =
% 0.89/1.36 times_times_real( Z, times_times_real( times_times_real( X, Y ), T ) ) }
% 0.89/1.36 .
% 0.89/1.36 { times_times_nat( times_times_nat( X, Y ), times_times_nat( Z, T ) ) =
% 0.89/1.36 times_times_nat( Z, times_times_nat( times_times_nat( X, Y ), T ) ) }.
% 0.89/1.36 { times_times_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 times_times_int( Z, times_times_int( times_times_int( X, Y ), T ) ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), times_times_real( Z, T ) ) =
% 0.89/1.36 times_times_real( X, times_times_real( Y, times_times_real( Z, T ) ) ) }
% 0.89/1.36 .
% 0.89/1.36 { times_times_nat( times_times_nat( X, Y ), times_times_nat( Z, T ) ) =
% 0.89/1.36 times_times_nat( X, times_times_nat( Y, times_times_nat( Z, T ) ) ) }.
% 0.89/1.36 { times_times_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 times_times_int( X, times_times_int( Y, times_times_int( Z, T ) ) ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), Z ) = times_times_real(
% 0.89/1.36 times_times_real( X, Z ), Y ) }.
% 0.89/1.36 { times_times_nat( times_times_nat( X, Y ), Z ) = times_times_nat(
% 0.89/1.36 times_times_nat( X, Z ), Y ) }.
% 0.89/1.36 { times_times_int( times_times_int( X, Y ), Z ) = times_times_int(
% 0.89/1.36 times_times_int( X, Z ), Y ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), Z ) = times_times_real( X,
% 0.89/1.36 times_times_real( Y, Z ) ) }.
% 0.89/1.36 { times_times_nat( times_times_nat( X, Y ), Z ) = times_times_nat( X,
% 0.89/1.36 times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { times_times_int( times_times_int( X, Y ), Z ) = times_times_int( X,
% 0.89/1.36 times_times_int( Y, Z ) ) }.
% 0.89/1.36 { times_times_real( X, times_times_real( Y, Z ) ) = times_times_real(
% 0.89/1.36 times_times_real( X, Y ), Z ) }.
% 0.89/1.36 { times_times_nat( X, times_times_nat( Y, Z ) ) = times_times_nat(
% 0.89/1.36 times_times_nat( X, Y ), Z ) }.
% 0.89/1.36 { times_times_int( X, times_times_int( Y, Z ) ) = times_times_int(
% 0.89/1.36 times_times_int( X, Y ), Z ) }.
% 0.89/1.36 { times_times_real( X, times_times_real( Y, Z ) ) = times_times_real( Y,
% 0.89/1.36 times_times_real( X, Z ) ) }.
% 0.89/1.36 { times_times_nat( X, times_times_nat( Y, Z ) ) = times_times_nat( Y,
% 0.89/1.36 times_times_nat( X, Z ) ) }.
% 0.89/1.36 { times_times_int( X, times_times_int( Y, Z ) ) = times_times_int( Y,
% 0.89/1.36 times_times_int( X, Z ) ) }.
% 0.89/1.36 { times_times_real( X, Y ) = times_times_real( Y, X ) }.
% 0.89/1.36 { times_times_nat( X, Y ) = times_times_nat( Y, X ) }.
% 0.89/1.36 { times_times_int( X, Y ) = times_times_int( Y, X ) }.
% 0.89/1.36 { plus_plus_real( X, Y ) = plus_plus_real( Y, X ) }.
% 0.89/1.36 { plus_plus_nat( X, Y ) = plus_plus_nat( Y, X ) }.
% 0.89/1.36 { plus_plus_int( X, Y ) = plus_plus_int( Y, X ) }.
% 0.89/1.36 { plus_plus_real( X, plus_plus_real( Y, Z ) ) = plus_plus_real( Y,
% 0.89/1.36 plus_plus_real( X, Z ) ) }.
% 0.89/1.36 { plus_plus_nat( X, plus_plus_nat( Y, Z ) ) = plus_plus_nat( Y,
% 0.89/1.36 plus_plus_nat( X, Z ) ) }.
% 0.89/1.36 { plus_plus_int( X, plus_plus_int( Y, Z ) ) = plus_plus_int( Y,
% 0.89/1.36 plus_plus_int( X, Z ) ) }.
% 0.89/1.36 { plus_plus_real( X, plus_plus_real( Y, Z ) ) = plus_plus_real(
% 0.89/1.36 plus_plus_real( X, Y ), Z ) }.
% 0.89/1.36 { plus_plus_nat( X, plus_plus_nat( Y, Z ) ) = plus_plus_nat( plus_plus_nat
% 0.89/1.36 ( X, Y ), Z ) }.
% 0.89/1.36 { plus_plus_int( X, plus_plus_int( Y, Z ) ) = plus_plus_int( plus_plus_int
% 0.89/1.36 ( X, Y ), Z ) }.
% 0.89/1.36 { plus_plus_real( plus_plus_real( X, Y ), Z ) = plus_plus_real( X,
% 0.89/1.36 plus_plus_real( Y, Z ) ) }.
% 0.89/1.36 { plus_plus_nat( plus_plus_nat( X, Y ), Z ) = plus_plus_nat( X,
% 0.89/1.36 plus_plus_nat( Y, Z ) ) }.
% 0.89/1.36 { plus_plus_int( plus_plus_int( X, Y ), Z ) = plus_plus_int( X,
% 0.89/1.36 plus_plus_int( Y, Z ) ) }.
% 0.89/1.36 { plus_plus_real( plus_plus_real( X, Y ), Z ) = plus_plus_real(
% 0.89/1.36 plus_plus_real( X, Z ), Y ) }.
% 0.89/1.36 { plus_plus_nat( plus_plus_nat( X, Y ), Z ) = plus_plus_nat( plus_plus_nat
% 0.89/1.36 ( X, Z ), Y ) }.
% 0.89/1.36 { plus_plus_int( plus_plus_int( X, Y ), Z ) = plus_plus_int( plus_plus_int
% 0.89/1.36 ( X, Z ), Y ) }.
% 0.89/1.36 { plus_plus_real( plus_plus_real( X, Y ), plus_plus_real( Z, T ) ) =
% 0.89/1.36 plus_plus_real( plus_plus_real( X, Z ), plus_plus_real( Y, T ) ) }.
% 0.89/1.36 { plus_plus_nat( plus_plus_nat( X, Y ), plus_plus_nat( Z, T ) ) =
% 0.89/1.36 plus_plus_nat( plus_plus_nat( X, Z ), plus_plus_nat( Y, T ) ) }.
% 0.89/1.36 { plus_plus_int( plus_plus_int( X, Y ), plus_plus_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( plus_plus_int( X, Z ), plus_plus_int( Y, T ) ) }.
% 0.89/1.36 { power_power_real( X, one_one_nat ) = X }.
% 0.89/1.36 { power_power_nat( X, one_one_nat ) = X }.
% 0.89/1.36 { ! is_int( X ), power_power_int( X, one_one_nat ) = X }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, power_power_nat( X, number_number_of_nat(
% 0.89/1.36 Y ) ) ), number_number_of_nat( Y ) = zero_zero_nat, ord_less_nat(
% 0.89/1.36 zero_zero_nat, X ) }.
% 0.89/1.36 { ! number_number_of_nat( Y ) = zero_zero_nat, ord_less_nat( zero_zero_nat
% 0.89/1.36 , power_power_nat( X, number_number_of_nat( Y ) ) ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ord_less_nat( zero_zero_nat,
% 0.89/1.36 power_power_nat( X, number_number_of_nat( Y ) ) ) }.
% 0.89/1.36 { times_times_nat( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.36 plus_plus_nat( X, X ) }.
% 0.89/1.36 { times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ) =
% 0.89/1.36 plus_plus_nat( X, X ) }.
% 0.89/1.36 { ! ord_less_int( Y, pls ), times_times_nat( number_number_of_nat( Y ),
% 0.89/1.36 number_number_of_nat( X ) ) = zero_zero_nat }.
% 0.89/1.36 { ord_less_int( Y, pls ), times_times_nat( number_number_of_nat( Y ),
% 0.89/1.36 number_number_of_nat( X ) ) = number_number_of_nat( times_times_int( Y, X
% 0.89/1.36 ) ) }.
% 0.89/1.36 { ! ord_less_int( Z, pls ), times_times_nat( number_number_of_nat( Z ),
% 0.89/1.36 times_times_nat( number_number_of_nat( X ), Y ) ) = zero_zero_nat }.
% 0.89/1.36 { ord_less_int( Z, pls ), times_times_nat( number_number_of_nat( Z ),
% 0.89/1.36 times_times_nat( number_number_of_nat( X ), Y ) ) = times_times_nat(
% 0.89/1.36 number_number_of_nat( times_times_int( Z, X ) ), Y ) }.
% 0.89/1.36 { power_power_real( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ), Y ) ) = power_power_real( power_power_real( X, Y ),
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { power_power_nat( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ), Y ) ) = power_power_nat( power_power_nat( X, Y ),
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { power_power_int( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ), Y ) ) = power_power_int( power_power_int( X, Y ),
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { ! ord_less_eq_real( power_power_real( X, times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ), zero_zero_real ), X =
% 0.89/1.36 zero_zero_real }.
% 0.89/1.36 { ! is_int( X ), ! ord_less_eq_int( power_power_int( X, times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ), zero_zero_int ), X =
% 0.89/1.36 zero_zero_int }.
% 0.89/1.36 { times_times_real( zero_zero_real, X ) = zero_zero_real }.
% 0.89/1.36 { times_times_nat( zero_zero_nat, X ) = zero_zero_nat }.
% 0.89/1.36 { times_times_int( zero_zero_int, X ) = zero_zero_int }.
% 0.89/1.36 { times_times_real( X, zero_zero_real ) = zero_zero_real }.
% 0.89/1.36 { times_times_nat( X, zero_zero_nat ) = zero_zero_nat }.
% 0.89/1.36 { times_times_int( X, zero_zero_int ) = zero_zero_int }.
% 0.89/1.36 { plus_plus_real( zero_zero_real, X ) = X }.
% 0.89/1.36 { plus_plus_nat( zero_zero_nat, X ) = X }.
% 0.89/1.36 { ! is_int( X ), plus_plus_int( zero_zero_int, X ) = X }.
% 0.89/1.36 { plus_plus_real( X, zero_zero_real ) = X }.
% 0.89/1.36 { plus_plus_nat( X, zero_zero_nat ) = X }.
% 0.89/1.36 { ! is_int( X ), plus_plus_int( X, zero_zero_int ) = X }.
% 0.89/1.36 { ! X = plus_plus_real( X, Y ), Y = zero_zero_real }.
% 0.89/1.36 { ! Y = zero_zero_real, X = plus_plus_real( X, Y ) }.
% 0.89/1.36 { ! X = plus_plus_nat( X, Y ), Y = zero_zero_nat }.
% 0.89/1.36 { ! Y = zero_zero_nat, X = plus_plus_nat( X, Y ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! X = plus_plus_int( X, Y ), Y =
% 0.89/1.36 zero_zero_int }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! Y = zero_zero_int, X = plus_plus_int( X,
% 0.89/1.36 Y ) }.
% 0.89/1.36 { times_times_real( X, plus_plus_real( Y, Z ) ) = plus_plus_real(
% 0.89/1.36 times_times_real( X, Y ), times_times_real( X, Z ) ) }.
% 0.89/1.36 { times_times_nat( X, plus_plus_nat( Y, Z ) ) = plus_plus_nat(
% 0.89/1.36 times_times_nat( X, Y ), times_times_nat( X, Z ) ) }.
% 0.89/1.36 { times_times_int( X, plus_plus_int( Y, Z ) ) = plus_plus_int(
% 0.89/1.36 times_times_int( X, Y ), times_times_int( X, Z ) ) }.
% 0.89/1.36 { Z = T, X = Y, ! plus_plus_real( times_times_real( Z, X ),
% 0.89/1.36 times_times_real( T, Y ) ) = plus_plus_real( times_times_real( Z, Y ),
% 0.89/1.36 times_times_real( T, X ) ) }.
% 0.89/1.36 { plus_plus_real( times_times_real( Z, X ), times_times_real( T, Y ) ) =
% 0.89/1.36 plus_plus_real( times_times_real( Z, Y ), times_times_real( T, X ) ), ! Z
% 0.89/1.36 = T }.
% 0.89/1.36 { plus_plus_real( times_times_real( Z, X ), times_times_real( T, Y ) ) =
% 0.89/1.36 plus_plus_real( times_times_real( Z, Y ), times_times_real( T, X ) ), ! X
% 0.89/1.36 = Y }.
% 0.89/1.36 { Z = T, X = Y, ! plus_plus_nat( times_times_nat( Z, X ), times_times_nat(
% 0.89/1.36 T, Y ) ) = plus_plus_nat( times_times_nat( Z, Y ), times_times_nat( T, X
% 0.89/1.36 ) ) }.
% 0.89/1.36 { plus_plus_nat( times_times_nat( Z, X ), times_times_nat( T, Y ) ) =
% 0.89/1.36 plus_plus_nat( times_times_nat( Z, Y ), times_times_nat( T, X ) ), ! Z =
% 0.89/1.36 T }.
% 0.89/1.36 { plus_plus_nat( times_times_nat( Z, X ), times_times_nat( T, Y ) ) =
% 0.89/1.36 plus_plus_nat( times_times_nat( Z, Y ), times_times_nat( T, X ) ), ! X =
% 0.89/1.36 Y }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), Z = T, X = Y
% 0.89/1.36 , ! plus_plus_int( times_times_int( Z, X ), times_times_int( T, Y ) ) =
% 0.89/1.36 plus_plus_int( times_times_int( Z, Y ), times_times_int( T, X ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), plus_plus_int
% 0.89/1.36 ( times_times_int( Z, X ), times_times_int( T, Y ) ) = plus_plus_int(
% 0.89/1.36 times_times_int( Z, Y ), times_times_int( T, X ) ), ! Z = T }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), plus_plus_int
% 0.89/1.36 ( times_times_int( Z, X ), times_times_int( T, Y ) ) = plus_plus_int(
% 0.89/1.36 times_times_int( Z, Y ), times_times_int( T, X ) ), ! X = Y }.
% 0.89/1.36 { times_times_real( plus_plus_real( X, Y ), Z ) = plus_plus_real(
% 0.89/1.36 times_times_real( X, Z ), times_times_real( Y, Z ) ) }.
% 0.89/1.36 { times_times_nat( plus_plus_nat( X, Y ), Z ) = plus_plus_nat(
% 0.89/1.36 times_times_nat( X, Z ), times_times_nat( Y, Z ) ) }.
% 0.89/1.36 { times_times_int( plus_plus_int( X, Y ), Z ) = plus_plus_int(
% 0.89/1.36 times_times_int( X, Z ), times_times_int( Y, Z ) ) }.
% 0.89/1.36 { plus_plus_real( times_times_real( X, Y ), times_times_real( Z, Y ) ) =
% 0.89/1.36 times_times_real( plus_plus_real( X, Z ), Y ) }.
% 0.89/1.36 { plus_plus_nat( times_times_nat( X, Y ), times_times_nat( Z, Y ) ) =
% 0.89/1.36 times_times_nat( plus_plus_nat( X, Z ), Y ) }.
% 0.89/1.36 { plus_plus_int( times_times_int( X, Y ), times_times_int( Z, Y ) ) =
% 0.89/1.36 times_times_int( plus_plus_int( X, Z ), Y ) }.
% 0.89/1.36 { ! plus_plus_real( times_times_real( X, Y ), times_times_real( Z, T ) ) =
% 0.89/1.36 plus_plus_real( times_times_real( X, T ), times_times_real( Z, Y ) ), X =
% 0.89/1.36 Z, Y = T }.
% 0.89/1.36 { ! X = Z, plus_plus_real( times_times_real( X, Y ), times_times_real( Z, T
% 0.89/1.36 ) ) = plus_plus_real( times_times_real( X, T ), times_times_real( Z, Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { ! Y = T, plus_plus_real( times_times_real( X, Y ), times_times_real( Z, T
% 0.89/1.36 ) ) = plus_plus_real( times_times_real( X, T ), times_times_real( Z, Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { ! plus_plus_nat( times_times_nat( X, Y ), times_times_nat( Z, T ) ) =
% 0.89/1.36 plus_plus_nat( times_times_nat( X, T ), times_times_nat( Z, Y ) ), X = Z
% 0.89/1.36 , Y = T }.
% 0.89/1.36 { ! X = Z, plus_plus_nat( times_times_nat( X, Y ), times_times_nat( Z, T )
% 0.89/1.36 ) = plus_plus_nat( times_times_nat( X, T ), times_times_nat( Z, Y ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! Y = T, plus_plus_nat( times_times_nat( X, Y ), times_times_nat( Z, T )
% 0.89/1.36 ) = plus_plus_nat( times_times_nat( X, T ), times_times_nat( Z, Y ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), !
% 0.89/1.36 plus_plus_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( times_times_int( X, T ), times_times_int( Z, Y ) ), X = Z
% 0.89/1.36 , Y = T }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), ! X = Z,
% 0.89/1.36 plus_plus_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( times_times_int( X, T ), times_times_int( Z, Y ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), ! is_int( T ), ! Y = T,
% 0.89/1.36 plus_plus_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( times_times_int( X, T ), times_times_int( Z, Y ) ) }.
% 0.89/1.36 { times_times_real( one_one_real, X ) = X }.
% 0.89/1.36 { times_times_nat( one_one_nat, X ) = X }.
% 0.89/1.36 { ! is_int( X ), times_times_int( one_one_int, X ) = X }.
% 0.89/1.36 { times_times_real( X, one_one_real ) = X }.
% 0.89/1.36 { times_times_nat( X, one_one_nat ) = X }.
% 0.89/1.36 { ! is_int( X ), times_times_int( X, one_one_int ) = X }.
% 0.89/1.36 { power_power_real( times_times_real( X, Y ), Z ) = times_times_real(
% 0.89/1.36 power_power_real( X, Z ), power_power_real( Y, Z ) ) }.
% 0.89/1.36 { power_power_nat( times_times_nat( X, Y ), Z ) = times_times_nat(
% 0.89/1.36 power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.36 { power_power_int( times_times_int( X, Y ), Z ) = times_times_int(
% 0.89/1.36 power_power_int( X, Z ), power_power_int( Y, Z ) ) }.
% 0.89/1.36 { times_times_real( power_power_real( X, Y ), power_power_real( X, Z ) ) =
% 0.89/1.36 power_power_real( X, plus_plus_nat( Y, Z ) ) }.
% 0.89/1.36 { times_times_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ) =
% 0.89/1.36 power_power_nat( X, plus_plus_nat( Y, Z ) ) }.
% 0.89/1.36 { times_times_int( power_power_int( X, Y ), power_power_int( X, Z ) ) =
% 0.89/1.36 power_power_int( X, plus_plus_nat( Y, Z ) ) }.
% 0.89/1.36 { power_power_real( X, zero_zero_nat ) = one_one_real }.
% 0.89/1.36 { power_power_nat( X, zero_zero_nat ) = one_one_nat }.
% 0.89/1.36 { power_power_int( X, zero_zero_nat ) = one_one_int }.
% 0.89/1.36 { ord_less_eq_int( zero_zero_int, zero_zero_int ) }.
% 0.89/1.36 { ord_less_eq_real( zero_zero_real, power_power_real( X, times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) ) }.
% 0.89/1.36 { ord_less_eq_int( zero_zero_int, power_power_int( X, times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) ) }.
% 0.89/1.36 { X = zero_zero_real, ! T = U, Y = Z, ! plus_plus_real( T, times_times_real
% 0.89/1.36 ( X, Y ) ) = plus_plus_real( U, times_times_real( X, Z ) ) }.
% 0.89/1.36 { X = zero_zero_nat, ! T = U, Y = Z, ! plus_plus_nat( T, times_times_nat( X
% 0.89/1.36 , Y ) ) = plus_plus_nat( U, times_times_nat( X, Z ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! is_int( Z ), Z = zero_zero_int, ! T = U,
% 0.89/1.36 X = Y, ! plus_plus_int( T, times_times_int( Z, X ) ) = plus_plus_int( U,
% 0.89/1.36 times_times_int( Z, Y ) ) }.
% 0.89/1.36 { plus_plus_real( X, X ) = times_times_real( plus_plus_real( one_one_real,
% 0.89/1.36 one_one_real ), X ) }.
% 0.89/1.36 { plus_plus_nat( X, X ) = times_times_nat( plus_plus_nat( one_one_nat,
% 0.89/1.36 one_one_nat ), X ) }.
% 0.89/1.36 { plus_plus_int( X, X ) = times_times_int( plus_plus_int( one_one_int,
% 0.89/1.36 one_one_int ), X ) }.
% 0.89/1.36 { plus_plus_real( X, times_times_real( Y, X ) ) = times_times_real(
% 0.89/1.36 plus_plus_real( Y, one_one_real ), X ) }.
% 0.89/1.36 { plus_plus_nat( X, times_times_nat( Y, X ) ) = times_times_nat(
% 0.89/1.36 plus_plus_nat( Y, one_one_nat ), X ) }.
% 0.89/1.36 { plus_plus_int( X, times_times_int( Y, X ) ) = times_times_int(
% 0.89/1.36 plus_plus_int( Y, one_one_int ), X ) }.
% 0.89/1.36 { plus_plus_real( times_times_real( X, Y ), Y ) = times_times_real(
% 0.89/1.36 plus_plus_real( X, one_one_real ), Y ) }.
% 0.89/1.36 { plus_plus_nat( times_times_nat( X, Y ), Y ) = times_times_nat(
% 0.89/1.36 plus_plus_nat( X, one_one_nat ), Y ) }.
% 0.89/1.36 { plus_plus_int( times_times_int( X, Y ), Y ) = times_times_int(
% 0.89/1.36 plus_plus_int( X, one_one_int ), Y ) }.
% 0.89/1.36 { ! power_power_real( X, number_number_of_nat( Y ) ) = zero_zero_real, X =
% 0.89/1.36 zero_zero_real }.
% 0.89/1.36 { ! power_power_real( X, number_number_of_nat( Y ) ) = zero_zero_real, !
% 0.89/1.36 number_number_of_nat( Y ) = zero_zero_nat }.
% 0.89/1.36 { ! X = zero_zero_real, number_number_of_nat( Y ) = zero_zero_nat,
% 0.89/1.36 power_power_real( X, number_number_of_nat( Y ) ) = zero_zero_real }.
% 0.89/1.36 { ! power_power_nat( X, number_number_of_nat( Y ) ) = zero_zero_nat, X =
% 0.89/1.36 zero_zero_nat }.
% 0.89/1.36 { ! power_power_nat( X, number_number_of_nat( Y ) ) = zero_zero_nat, !
% 0.89/1.36 number_number_of_nat( Y ) = zero_zero_nat }.
% 0.89/1.36 { ! X = zero_zero_nat, number_number_of_nat( Y ) = zero_zero_nat,
% 0.89/1.36 power_power_nat( X, number_number_of_nat( Y ) ) = zero_zero_nat }.
% 0.89/1.36 { ! is_int( X ), ! power_power_int( X, number_number_of_nat( Y ) ) =
% 0.89/1.36 zero_zero_int, X = zero_zero_int }.
% 0.89/1.36 { ! is_int( X ), ! power_power_int( X, number_number_of_nat( Y ) ) =
% 0.89/1.36 zero_zero_int, ! number_number_of_nat( Y ) = zero_zero_nat }.
% 0.89/1.36 { ! is_int( X ), ! X = zero_zero_int, number_number_of_nat( Y ) =
% 0.89/1.36 zero_zero_nat, power_power_int( X, number_number_of_nat( Y ) ) =
% 0.89/1.36 zero_zero_int }.
% 0.89/1.36 { ! ord_less_int( zero_zero_int, X ), ! ord_less_int( zero_zero_int,
% 0.89/1.36 times_times_int( X, Y ) ), ord_less_int( zero_zero_int, Y ) }.
% 0.89/1.36 { ord_less_eq_int( zero_zero_int, one_one_int ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_eq_int( zero_zero_int,
% 0.89/1.36 Y ), ord_less_eq_int( zero_zero_int, times_times_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_eq_int( zero_zero_int,
% 0.89/1.36 Y ), ord_less_eq_int( zero_zero_int, plus_plus_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, X ), ord_less_eq_int( zero_zero_int,
% 0.89/1.36 power_power_int( X, Y ) ) }.
% 0.89/1.36 { ! number_number_of_nat( X ) = zero_zero_nat, power_power_real(
% 0.89/1.36 zero_zero_real, number_number_of_nat( X ) ) = one_one_real }.
% 0.89/1.36 { number_number_of_nat( X ) = zero_zero_nat, power_power_real(
% 0.89/1.36 zero_zero_real, number_number_of_nat( X ) ) = zero_zero_real }.
% 0.89/1.36 { ! number_number_of_nat( X ) = zero_zero_nat, power_power_nat(
% 0.89/1.36 zero_zero_nat, number_number_of_nat( X ) ) = one_one_nat }.
% 0.89/1.36 { number_number_of_nat( X ) = zero_zero_nat, power_power_nat( zero_zero_nat
% 0.89/1.36 , number_number_of_nat( X ) ) = zero_zero_nat }.
% 0.89/1.36 { ! number_number_of_nat( X ) = zero_zero_nat, power_power_int(
% 0.89/1.36 zero_zero_int, number_number_of_nat( X ) ) = one_one_int }.
% 0.89/1.36 { number_number_of_nat( X ) = zero_zero_nat, power_power_int( zero_zero_int
% 0.89/1.36 , number_number_of_nat( X ) ) = zero_zero_int }.
% 0.89/1.36 { ord_less_eq_int( zero_zero_int, number_number_of_int( bit1( bit1( pls ) )
% 0.89/1.36 ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, plus_plus_int( times_times_int( X, Y )
% 0.89/1.36 , Z ) ), ! ord_less_int( Z, X ), ! ord_less_int( zero_zero_int, X ),
% 0.89/1.36 ord_less_eq_int( zero_zero_int, Y ) }.
% 0.89/1.36 { ! ord_less_int( plus_plus_int( times_times_int( X, Y ), Z ),
% 0.89/1.36 zero_zero_int ), ! ord_less_eq_int( zero_zero_int, Z ), ! ord_less_int(
% 0.89/1.36 zero_zero_int, X ), ord_less_eq_int( Y, zero_zero_int ) }.
% 0.89/1.36 { ! ord_less_eq_int( plus_plus_int( times_times_int( X, Y ), Z ),
% 0.89/1.36 plus_plus_int( times_times_int( X, T ), U ) ), ! ord_less_eq_int(
% 0.89/1.36 zero_zero_int, Z ), ! ord_less_int( Z, X ), ! ord_less_int( U, X ),
% 0.89/1.36 ord_less_eq_int( Y, T ) }.
% 0.89/1.36 { ! plus_plus_int( times_times_int( X, Y ), Z ) = plus_plus_int(
% 0.89/1.36 times_times_int( T, U ), W ), ! ord_less_eq_int( zero_zero_int,
% 0.89/1.36 plus_plus_int( times_times_int( T, U ), W ) ), ! ord_less_int( W, T ), !
% 0.89/1.36 ord_less_eq_int( zero_zero_int, Z ), ! ord_less_int( zero_zero_int, T ),
% 0.89/1.36 ! ord_less_eq_int( T, X ), ord_less_eq_int( Y, U ) }.
% 0.89/1.36 { ! ord_less_eq_int( plus_plus_int( times_times_int( X, Y ), Z ),
% 0.89/1.36 plus_plus_int( times_times_int( X, T ), U ) ), ! ord_less_eq_int( U,
% 0.89/1.36 zero_zero_int ), ! ord_less_int( X, U ), ! ord_less_int( X, Z ),
% 0.89/1.36 ord_less_eq_int( T, Y ) }.
% 0.89/1.36 { ! plus_plus_int( times_times_int( X, Y ), Z ) = plus_plus_int(
% 0.89/1.36 times_times_int( T, U ), W ), ! ord_less_int( plus_plus_int(
% 0.89/1.36 times_times_int( T, U ), W ), zero_zero_int ), ! ord_less_int( Z, X ), !
% 0.89/1.36 ord_less_eq_int( zero_zero_int, W ), ! ord_less_int( zero_zero_int, T ),
% 0.89/1.36 ! ord_less_eq_int( T, X ), ord_less_eq_int( U, Y ) }.
% 0.89/1.36 { power_power_int( power_power_int( X, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.36 power_power_int( X, number_number_of_nat( bit0( bit0( bit1( pls ) ) ) ) )
% 0.89/1.36 }.
% 0.89/1.36 { times_times_real( X, X ) = power_power_real( X, number_number_of_nat(
% 0.89/1.36 bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { times_times_nat( X, X ) = power_power_nat( X, number_number_of_nat( bit0
% 0.89/1.36 ( bit1( pls ) ) ) ) }.
% 0.89/1.36 { times_times_int( X, X ) = power_power_int( X, number_number_of_nat( bit0
% 0.89/1.36 ( bit1( pls ) ) ) ) }.
% 0.89/1.36 { zcong( power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.36 , number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.36 }.
% 0.89/1.36 { zcong( X, zero_zero_int, Y ), ! zcong( power_power_int( Z,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ), X, Y ), ! dvd_dvd_int( Y,
% 0.89/1.36 Z ) }.
% 0.89/1.36 { ! is_int( X ), ! zprime( X ), ord_less_int( one_one_int, X ) }.
% 0.89/1.36 { ! is_int( X ), ! zprime( X ), alpha2( X ) }.
% 0.89/1.36 { ! is_int( X ), ! ord_less_int( one_one_int, X ), ! alpha2( X ), zprime( X
% 0.89/1.36 ) }.
% 0.89/1.36 { ! alpha2( X ), ! is_int( Y ), alpha4( X, Y ) }.
% 0.89/1.36 { is_int( skol4( Y ) ), alpha2( X ) }.
% 0.89/1.36 { ! alpha4( X, skol4( X ) ), alpha2( X ) }.
% 0.89/1.36 { ! alpha4( X, Y ), ! alpha6( X, Y ), alpha7( X, Y ) }.
% 0.89/1.36 { alpha6( X, Y ), alpha4( X, Y ) }.
% 0.89/1.36 { ! alpha7( X, Y ), alpha4( X, Y ) }.
% 0.89/1.36 { ! alpha7( X, Y ), Y = one_one_int, Y = X }.
% 0.89/1.36 { ! Y = one_one_int, alpha7( X, Y ) }.
% 0.89/1.36 { ! Y = X, alpha7( X, Y ) }.
% 0.89/1.36 { ! alpha6( X, Y ), ord_less_eq_int( zero_zero_int, Y ) }.
% 0.89/1.36 { ! alpha6( X, Y ), dvd_dvd_int( Y, X ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, Y ), ! dvd_dvd_int( Y, X ), alpha6( X,
% 0.89/1.36 Y ) }.
% 0.89/1.36 { ! is_int( X ), ! zprime( X ), X = number_number_of_int( bit0( bit1( pls )
% 0.89/1.36 ) ), X = number_number_of_int( bit1( bit1( pls ) ) ), ord_less_eq_int(
% 0.89/1.36 number_number_of_int( bit1( bit0( bit1( pls ) ) ) ), X ) }.
% 0.89/1.36 { ord_less_nat( zero_zero_nat, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.36 ) }.
% 0.89/1.36 { is_int( skol5 ) }.
% 0.89/1.36 { zcong( power_power_int( skol5, number_number_of_nat( bit0( bit1( pls ) )
% 0.89/1.36 ) ), number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.36 }.
% 0.89/1.36 { legendre( number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.36 = one_one_int }.
% 0.89/1.36 { bit1( min ) = min }.
% 0.89/1.36 { ! is_int( X ), ! min = bit1( X ), min = X }.
% 0.89/1.36 { ! is_int( X ), ! min = X, min = bit1( X ) }.
% 0.89/1.36 { ! is_int( X ), ! bit1( X ) = min, X = min }.
% 0.89/1.36 { ! is_int( X ), ! X = min, bit1( X ) = min }.
% 0.89/1.36 { ! min = pls }.
% 0.89/1.36 { ! pls = min }.
% 0.89/1.36 { ! min = bit0( X ) }.
% 0.89/1.36 { ! bit0( X ) = min }.
% 0.89/1.36 { ! ord_less_int( min, min ) }.
% 0.89/1.36 { ord_less_eq_int( min, min ) }.
% 0.89/1.36 { ! ord_less_int( bit1( X ), min ), ord_less_int( X, min ) }.
% 0.89/1.36 { ! ord_less_int( X, min ), ord_less_int( bit1( X ), min ) }.
% 0.89/1.36 { ! ord_less_int( min, bit1( X ) ), ord_less_int( min, X ) }.
% 0.89/1.36 { ! ord_less_int( min, X ), ord_less_int( min, bit1( X ) ) }.
% 0.89/1.36 { ! ord_less_int( pls, min ) }.
% 0.89/1.36 { ord_less_int( min, pls ) }.
% 0.89/1.36 { ! ord_less_int( min, bit0( X ) ), ord_less_int( min, X ) }.
% 0.89/1.36 { ! ord_less_int( min, X ), ord_less_int( min, bit0( X ) ) }.
% 0.89/1.36 { ord_less_int( min, zero_zero_int ) }.
% 0.89/1.36 { ! ord_less_eq_int( min, bit1( X ) ), ord_less_eq_int( min, X ) }.
% 0.89/1.36 { ! ord_less_eq_int( min, X ), ord_less_eq_int( min, bit1( X ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( bit1( X ), min ), ord_less_eq_int( X, min ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, min ), ord_less_eq_int( bit1( X ), min ) }.
% 0.89/1.36 { ord_less_eq_int( min, pls ) }.
% 0.89/1.36 { ! ord_less_eq_int( pls, min ) }.
% 0.89/1.36 { ! ord_less_eq_int( bit0( X ), min ), ord_less_eq_int( X, min ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, min ), ord_less_eq_int( bit0( X ), min ) }.
% 0.89/1.36 { ! number_number_of_int( pls ) = number_number_of_int( min ) }.
% 0.89/1.36 { ! ord_less_int( bit0( X ), min ), ord_less_eq_int( X, min ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, min ), ord_less_int( bit0( X ), min ) }.
% 0.89/1.36 { ! ord_less_eq_int( min, bit0( X ) ), ord_less_int( min, X ) }.
% 0.89/1.36 { ! ord_less_int( min, X ), ord_less_eq_int( min, bit0( X ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! times_times_int( X, Y ) = one_one_int,
% 0.89/1.36 alpha3( X, Y ), alpha5( X, Y ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! alpha3( X, Y ), times_times_int( X, Y ) =
% 0.89/1.36 one_one_int }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! alpha5( X, Y ), times_times_int( X, Y ) =
% 0.89/1.36 one_one_int }.
% 0.89/1.36 { ! alpha5( X, Y ), X = number_number_of_int( min ) }.
% 0.89/1.36 { ! alpha5( X, Y ), Y = number_number_of_int( min ) }.
% 0.89/1.36 { ! X = number_number_of_int( min ), ! Y = number_number_of_int( min ),
% 0.89/1.36 alpha5( X, Y ) }.
% 0.89/1.36 { ! alpha3( X, Y ), X = one_one_int }.
% 0.89/1.36 { ! alpha3( X, Y ), Y = one_one_int }.
% 0.89/1.36 { ! X = one_one_int, ! Y = one_one_int, alpha3( X, Y ) }.
% 0.89/1.36 { ! is_int( X ), ! times_times_int( X, Y ) = one_one_int, X = one_one_int,
% 0.89/1.36 X = number_number_of_int( min ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), zcong( Y, X, Z ) }.
% 0.89/1.36 { ! zcong( Y, X, Z ), zcong( X, Y, Z ) }.
% 0.89/1.36 { zcong( X, X, Y ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( Y, T, Z ), zcong( X, T, Z ) }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), X = Y, ord_less_real( X, Y ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), X = Y, ord_less_nat( X, Y ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( X, Y ), X = Y,
% 0.89/1.36 ord_less_int( X, Y ) }.
% 0.89/1.36 { ! ord_less_int( X, Y ), ! ord_less_int( Z, Y ), ord_less_eq_int( X, Z ),
% 0.89/1.36 ord_less_eq_int( Z, X ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! zcong( X, Y, zero_zero_int ), X = Y }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! X = Y, zcong( X, Y, zero_zero_int ) }.
% 0.89/1.36 { zcong( X, Y, one_one_int ) }.
% 0.89/1.36 { zcong( times_times_int( X, Y ), times_times_int( Z, Y ), Y ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), zcong( times_times_int( X, T ), times_times_int( Y, T
% 0.89/1.36 ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), zcong( times_times_int( T, X ), times_times_int( T, Y
% 0.89/1.36 ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, U, Z ), zcong( times_times_int( X, T ),
% 0.89/1.36 times_times_int( Y, U ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, U, Z ), zcong( plus_plus_int( X, T ),
% 0.89/1.36 plus_plus_int( Y, U ), Z ) }.
% 0.89/1.36 { power_power_real( number267125858f_real( min ), times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), X ) ) = one_one_real }.
% 0.89/1.36 { power_power_int( number_number_of_int( min ), times_times_nat(
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ), X ) ) = one_one_int }.
% 0.89/1.36 { ! ord_less_int( zero_zero_int, X ), ! ord_less_int( X, Y ), !
% 0.89/1.36 ord_less_int( zero_zero_int, Z ), ! ord_less_int( Z, X ), ! zcong( X, Z,
% 0.89/1.36 Y ) }.
% 0.89/1.36 { ! is_int( X ), ! zcong( Y, X, Z ), is_int( skol6( T, U, W ) ) }.
% 0.89/1.36 { ! is_int( X ), ! zcong( Y, X, Z ), X = plus_plus_int( Y, times_times_int
% 0.89/1.36 ( Z, skol6( X, Y, Z ) ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( T ), ! X = plus_plus_int( Y, times_times_int( Z
% 0.89/1.36 , T ) ), zcong( Y, X, Z ) }.
% 0.89/1.36 { times_times_real( number267125858f_real( bit0( bit0( bit1( pls ) ) ) ),
% 0.89/1.36 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) =
% 0.89/1.36 power_power_real( times_times_real( number267125858f_real( bit0( bit1(
% 0.89/1.36 pls ) ) ), X ), number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.36 { ! is_int( X ), ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_int( X,
% 0.89/1.36 Y ), ! zcong( X, zero_zero_int, Y ), X = zero_zero_int }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! ord_less_eq_int( zero_zero_int, Y ), !
% 0.89/1.36 ord_less_int( Y, Z ), ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.36 ord_less_int( X, Z ), ! zcong( Y, X, Z ), Y = X }.
% 0.89/1.36 { ! zcong( power_power_int( X, Y ), one_one_int, Z ), zcong(
% 0.89/1.36 power_power_int( X, times_times_nat( Y, T ) ), one_one_int, Z ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, X ), ! zprime( Y ), ! dvd_dvd_int( Y,
% 0.89/1.36 times_times_int( X, Z ) ), dvd_dvd_int( Y, X ), dvd_dvd_int( Y, Z ) }.
% 0.89/1.36 { quadRes( plus_plus_int( times_times_int( number_number_of_int( bit0( bit0
% 0.89/1.36 ( bit1( pls ) ) ) ), m ), one_one_int ), number_number_of_int( min ) ) }
% 0.89/1.36 .
% 0.89/1.36 { dvd_dvd_int( plus_plus_int( times_times_int( number_number_of_int( bit0(
% 0.89/1.36 bit0( bit1( pls ) ) ) ), m ), one_one_int ), minus_minus_int(
% 0.89/1.36 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.36 number_number_of_int( min ) ) ) }.
% 0.89/1.36 { ! ord_less_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), ! zcong
% 0.89/1.36 ( power_power_int( number_number_of_int( min ), Y ), power_power_int(
% 0.89/1.36 number_number_of_int( min ), Z ), X ), power_power_int(
% 0.89/1.36 number_number_of_int( min ), Y ) = power_power_int( number_number_of_int
% 0.89/1.36 ( min ), Z ) }.
% 0.89/1.36 { ! ord_less_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), ! zcong
% 0.89/1.36 ( Y, number_number_of_int( min ), X ), ! zcong( Y, one_one_int, X ) }.
% 0.89/1.36 { minus_minus_int( power_power_int( s, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), number_number_of_int( min ) ) = plus_plus_int(
% 0.89/1.36 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.36 one_one_int ) }.
% 0.89/1.36 { quadRes( plus_plus_int( times_times_int( number_number_of_int( bit0( bit0
% 0.89/1.36 ( bit1( pls ) ) ) ), m ), one_one_int ), number_number_of_int( min ) ), !
% 0.89/1.36 legendre( number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.36 = one_one_int }.
% 0.89/1.36 { ord_less_real( zero_zero_real, times_times_real( X, X ) ), X =
% 0.89/1.36 zero_zero_real }.
% 0.89/1.36 { ! X = zero_zero_real, ! ord_less_real( zero_zero_real, times_times_real(
% 0.89/1.36 X, X ) ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, U, Z ), zcong( minus_minus_int( X, T ),
% 0.89/1.36 minus_minus_int( Y, U ), Z ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, minus_minus_int( Y, Z ) ), ! dvd_dvd_int( X, Z ),
% 0.89/1.36 dvd_dvd_int( X, Y ) }.
% 0.89/1.36 { times_times_int( X, minus_minus_int( Y, Z ) ) = minus_minus_int(
% 0.89/1.36 times_times_int( X, Y ), times_times_int( X, Z ) ) }.
% 0.89/1.36 { times_times_int( minus_minus_int( X, Y ), Z ) = minus_minus_int(
% 0.89/1.36 times_times_int( X, Z ), times_times_int( Y, Z ) ) }.
% 0.89/1.36 { minus_minus_int( bit0( X ), bit0( Y ) ) = bit0( minus_minus_int( X, Y ) )
% 0.89/1.36 }.
% 0.89/1.36 { ! is_int( X ), minus_minus_int( X, pls ) = X }.
% 0.89/1.36 { ! is_int( X ), ! minus_minus_int( X, Y ) = Z, X = plus_plus_int( Z, Y ) }
% 0.89/1.36 .
% 0.89/1.36 { number267125858f_real( minus_minus_int( X, Y ) ) = minus_minus_real(
% 0.89/1.36 number267125858f_real( X ), number267125858f_real( Y ) ) }.
% 0.89/1.36 { number_number_of_int( minus_minus_int( X, Y ) ) = minus_minus_int(
% 0.89/1.36 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.36 { times_times_real( number267125858f_real( X ), minus_minus_real( Y, Z ) )
% 0.89/1.36 = minus_minus_real( times_times_real( number267125858f_real( X ), Y ),
% 0.89/1.36 times_times_real( number267125858f_real( X ), Z ) ) }.
% 0.89/1.36 { times_times_int( number_number_of_int( X ), minus_minus_int( Y, Z ) ) =
% 0.89/1.36 minus_minus_int( times_times_int( number_number_of_int( X ), Y ),
% 0.89/1.36 times_times_int( number_number_of_int( X ), Z ) ) }.
% 0.89/1.36 { times_times_real( minus_minus_real( X, Y ), number267125858f_real( Z ) )
% 0.89/1.36 = minus_minus_real( times_times_real( X, number267125858f_real( Z ) ),
% 0.89/1.36 times_times_real( Y, number267125858f_real( Z ) ) ) }.
% 0.89/1.36 { times_times_int( minus_minus_int( X, Y ), number_number_of_int( Z ) ) =
% 0.89/1.36 minus_minus_int( times_times_int( X, number_number_of_int( Z ) ),
% 0.89/1.36 times_times_int( Y, number_number_of_int( Z ) ) ) }.
% 0.89/1.36 { minus_minus_int( bit1( X ), bit0( Y ) ) = bit1( minus_minus_int( X, Y ) )
% 0.89/1.36 }.
% 0.89/1.36 { minus_minus_int( bit1( X ), bit1( Y ) ) = bit0( minus_minus_int( X, Y ) )
% 0.89/1.36 }.
% 0.89/1.36 { minus_minus_int( pls, bit0( X ) ) = bit0( minus_minus_int( pls, X ) ) }.
% 0.89/1.36 { ! ord_less_int( X, Y ), ord_less_int( minus_minus_int( X, Y ),
% 0.89/1.36 zero_zero_int ) }.
% 0.89/1.36 { ! ord_less_int( minus_minus_int( X, Y ), zero_zero_int ), ord_less_int( X
% 0.89/1.36 , Y ) }.
% 0.89/1.36 { plus_plus_int( times_times_int( minus_minus_int( X, times_times_int( Y, Z
% 0.89/1.36 ) ), T ), times_times_int( minus_minus_int( U, times_times_int( Y, W ) )
% 0.89/1.36 , V0 ) ) = minus_minus_int( plus_plus_int( times_times_int( X, T ),
% 0.89/1.36 times_times_int( U, V0 ) ), times_times_int( Y, plus_plus_int(
% 0.89/1.36 times_times_int( Z, T ), times_times_int( W, V0 ) ) ) ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), dvd_dvd_int( Z, minus_minus_int( X, Y ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( Z, minus_minus_int( X, Y ) ), zcong( X, Y, Z ) }.
% 0.89/1.36 { plus_plus_real( number267125858f_real( X ), minus_minus_real(
% 0.89/1.36 number267125858f_real( Y ), Z ) ) = minus_minus_real(
% 0.89/1.36 number267125858f_real( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.36 { plus_plus_int( number_number_of_int( X ), minus_minus_int(
% 0.89/1.36 number_number_of_int( Y ), Z ) ) = minus_minus_int( number_number_of_int
% 0.89/1.36 ( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.36 { ! is_int( X ), ! ord_less_int( zero_zero_int, X ), ! ord_less_int( X, Y )
% 0.89/1.36 , X = minus_minus_int( Y, one_one_int ), ord_less_int( X, minus_minus_int
% 0.89/1.36 ( Y, one_one_int ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, minus_minus_int( Y, one_one_int ) ), ord_less_int(
% 0.89/1.36 X, Y ) }.
% 0.89/1.36 { ! ord_less_int( X, Y ), ord_less_eq_int( X, minus_minus_int( Y,
% 0.89/1.36 one_one_int ) ) }.
% 0.89/1.36 { minus_minus_int( pls, bit1( X ) ) = bit1( minus_minus_int( min, X ) ) }.
% 0.89/1.36 { minus_minus_int( min, bit1( X ) ) = bit0( minus_minus_int( min, X ) ) }.
% 0.89/1.36 { minus_minus_int( min, bit0( X ) ) = bit1( minus_minus_int( min, X ) ) }.
% 0.89/1.36 { ! zcong( times_times_int( X, minus_minus_int( Y, one_one_int ) ),
% 0.89/1.36 one_one_int, Y ), zcong( X, minus_minus_int( Y, one_one_int ), Y ) }.
% 0.89/1.36 { ! zcong( X, minus_minus_int( Y, one_one_int ), Y ), zcong(
% 0.89/1.36 times_times_int( X, minus_minus_int( Y, one_one_int ) ), one_one_int, Y )
% 0.89/1.36 }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! Y = T, ! zcong( T, U, Z ), zcong( X, U, Z ) }.
% 0.89/1.36 { ! is_int( X ), ! zprime( Y ), ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.36 ord_less_int( X, Y ), ! zcong( times_times_int( X, X ), one_one_int, Y )
% 0.89/1.36 , X = one_one_int, X = minus_minus_int( Y, one_one_int ) }.
% 0.89/1.36 { ! zprime( X ), ! ord_less_int( zero_zero_int, Y ), ! zcong(
% 0.89/1.36 times_times_int( Y, Y ), one_one_int, X ), zcong( Y, one_one_int, X ),
% 0.89/1.36 zcong( Y, minus_minus_int( X, one_one_int ), X ) }.
% 0.89/1.36 { times_times_int( plus_plus_int( X, Y ), minus_minus_int( X, Y ) ) =
% 0.89/1.36 minus_minus_int( power_power_int( X, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.36 ) ) ) ) }.
% 0.89/1.36 { zcong( X, zero_zero_int, X ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, times_times_int( U, X ), Z ), zcong( T,
% 0.89/1.36 times_times_int( U, Y ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, times_times_int( U, Y ), Z ), zcong( T,
% 0.89/1.36 times_times_int( U, X ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, times_times_int( X, U ), Z ), zcong( T,
% 0.89/1.36 times_times_int( Y, U ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), ! zcong( T, times_times_int( Y, U ), Z ), zcong( T,
% 0.89/1.36 times_times_int( X, U ), Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), zcong( plus_plus_int( X, T ), plus_plus_int( Y, T ),
% 0.89/1.36 Z ) }.
% 0.89/1.36 { ! zcong( X, Y, Z ), zcong( power_power_int( X, T ), power_power_int( Y, T
% 0.89/1.36 ), Z ) }.
% 0.89/1.36 { power_power_real( minus_minus_real( X, Y ), number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ) = minus_minus_real( plus_plus_real( power_power_real( X
% 0.89/1.36 , number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_real(
% 0.89/1.36 times_times_real( number267125858f_real( bit0( bit1( pls ) ) ), X ), Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { power_power_int( minus_minus_int( X, Y ), number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ) = minus_minus_int( plus_plus_int( power_power_int( X,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_int(
% 0.89/1.36 times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), Y ) )
% 0.89/1.36 }.
% 0.89/1.36 { power_power_int( minus_minus_int( X, Y ), number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ) = plus_plus_int( minus_minus_int( power_power_int( X,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ), times_times_int(
% 0.89/1.36 times_times_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), Y ) )
% 0.89/1.36 , power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.36 { power_power_int( minus_minus_int( X, Y ), number_number_of_nat( bit1(
% 0.89/1.36 bit1( pls ) ) ) ) = minus_minus_int( plus_plus_int( minus_minus_int(
% 0.89/1.36 power_power_int( X, number_number_of_nat( bit1( bit1( pls ) ) ) ),
% 0.89/1.36 times_times_int( times_times_int( number_number_of_int( bit1( bit1( pls )
% 0.89/1.36 ) ), power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) )
% 0.89/1.36 , Y ) ), times_times_int( times_times_int( number_number_of_int( bit1(
% 0.89/1.36 bit1( pls ) ) ), X ), power_power_int( Y, number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ) ) ), power_power_int( Y, number_number_of_nat( bit1(
% 0.89/1.36 bit1( pls ) ) ) ) ) }.
% 0.89/1.36 { ! is_int( X ), ! is_int( Y ), ! ord_less_int( zero_zero_int, Y ), !
% 0.89/1.36 ord_less_int( zero_zero_int, X ), ! ord_less_int( zero_zero_int, Z ), !
% 0.89/1.36 zcong( Y, X, Z ), ! ord_less_int( Y, Z ), ! ord_less_int( X, Z ), Y = X }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_int( zero_zero_int, X ), ! ord_less_int( X, Y ), ! zcong( X,
% 0.89/1.36 zero_zero_int, Y ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), ord_less_eq_int( Y, zero_zero_int ),
% 0.89/1.36 ord_less_eq_int( X, Y ) }.
% 0.89/1.36 { ! zcong( X, zero_zero_int, Y ), dvd_dvd_int( Y, X ) }.
% 0.89/1.36 { ! dvd_dvd_int( Y, X ), zcong( X, zero_zero_int, Y ) }.
% 0.89/1.36 { ! zcong( X, zero_zero_int, Y ), dvd_dvd_int( Y, X ) }.
% 0.89/1.36 { ! dvd_dvd_int( Y, X ), zcong( X, zero_zero_int, Y ) }.
% 0.89/1.36 { ! zprime( X ), ! dvd_dvd_int( X, times_times_int( Y, Z ) ), dvd_dvd_int(
% 0.89/1.36 X, Y ), dvd_dvd_int( X, Z ) }.
% 0.89/1.36 { ! is_int( X ), ! ord_less_eq_int( zero_zero_int, X ), ! ord_less_int( X,
% 0.89/1.36 Y ), ! zcong( X, zero_zero_int, Y ), X = zero_zero_int }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ! dvd_dvd_int( Y, Z ), dvd_dvd_int( Y
% 0.89/1.36 , power_power_int( Z, X ) ) }.
% 0.89/1.36 { power_power_int( number_number_of_int( min ), X ) = one_one_int,
% 0.89/1.36 power_power_int( number_number_of_int( min ), X ) = number_number_of_int
% 0.89/1.36 ( min ) }.
% 0.89/1.36 { ! zprime( X ), zcong( Y, zero_zero_int, X ), zcong( Z, zero_zero_int, X )
% 0.89/1.36 , ! zcong( times_times_int( Y, Z ), zero_zero_int, X ) }.
% 0.89/1.36 { ! zprime( X ), ! ord_less_int( zero_zero_int, Y ), zcong( Y,
% 0.89/1.36 zero_zero_int, X ), zcong( Z, zero_zero_int, X ), ! zcong(
% 0.89/1.36 times_times_int( Y, Z ), zero_zero_int, X ) }.
% 0.89/1.36 { ! zprime( X ), ! ord_less_int( zero_zero_int, Y ), ! zcong(
% 0.89/1.36 times_times_int( Y, Z ), zero_zero_int, X ), zcong( Y, zero_zero_int, X )
% 0.89/1.36 , zcong( Z, zero_zero_int, X ) }.
% 0.89/1.36 { ! zprime( X ), ! dvd_dvd_int( X, power_power_int( Y, Z ) ), !
% 0.89/1.36 ord_less_nat( zero_zero_nat, Z ), dvd_dvd_int( X, Y ) }.
% 0.89/1.36 { ! zprime( plus_plus_int( times_times_int( number_number_of_int( bit0(
% 0.89/1.36 bit0( bit1( pls ) ) ) ), X ), one_one_int ) ), legendre(
% 0.89/1.36 number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.36 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), X ), one_one_int ) )
% 0.89/1.36 = one_one_int }.
% 0.89/1.36 { ! ord_less_int( number_number_of_int( bit0( bit1( pls ) ) ), X ), ! zcong
% 0.89/1.36 ( one_one_int, number_number_of_int( min ), X ) }.
% 0.89/1.36 { ! zcong( X, zero_zero_int, Y ), legendre( X, Y ) = zero_zero_int }.
% 0.89/1.36 { zcong( X, zero_zero_int, Y ), ! quadRes( Y, X ), legendre( X, Y ) =
% 0.89/1.36 one_one_int }.
% 0.89/1.36 { zcong( X, zero_zero_int, Y ), quadRes( Y, X ), legendre( X, Y ) =
% 0.89/1.36 number_number_of_int( min ) }.
% 0.89/1.36 { ! quadRes( X, Y ), is_int( skol7( Z, T ) ) }.
% 0.89/1.36 { ! quadRes( X, Y ), zcong( power_power_int( skol7( X, Y ),
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ), Y, X ) }.
% 0.89/1.36 { ! is_int( Z ), ! zcong( power_power_int( Z, number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ), Y, X ), quadRes( X, Y ) }.
% 0.89/1.36 { power_power_real( plus_plus_real( X, Y ), number_number_of_nat( bit0(
% 0.89/1.36 bit1( pls ) ) ) ) = plus_plus_real( plus_plus_real( power_power_real( X,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.36 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), times_times_real(
% 0.89/1.36 times_times_real( number267125858f_real( bit0( bit1( pls ) ) ), X ), Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, times_times_nat( Y, X ) = zero_zero_nat }.
% 0.89/1.36 { Y = zero_zero_nat, times_times_nat( Y, X ) = plus_plus_nat( X,
% 0.89/1.36 times_times_nat( minus_minus_nat( Y, one_one_nat ), X ) ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, power_power_nat( X, Y ) = one_one_nat }.
% 0.89/1.36 { Y = zero_zero_nat, power_power_nat( X, Y ) = times_times_nat( X,
% 0.89/1.36 power_power_nat( X, minus_minus_nat( Y, one_one_nat ) ) ) }.
% 0.89/1.36 { minus_minus_nat( power_power_nat( X, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), power_power_nat( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.36 ) ) ) ) = times_times_nat( plus_plus_nat( X, Y ), minus_minus_nat( X, Y
% 0.89/1.36 ) ) }.
% 0.89/1.36 { ! plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.36 ) ) ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.36 { ! plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.36 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.36 ) ) ) ) = zero_zero_real, Y = zero_zero_real }.
% 0.89/1.36 { ! X = zero_zero_real, ! Y = zero_zero_real, plus_plus_real(
% 0.89/1.36 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.36 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) =
% 0.89/1.36 zero_zero_real }.
% 0.89/1.36 { ! zero_zero_real = one_one_real }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ord_less_eq_real( minus_minus_real( X, Y ),
% 0.89/1.36 zero_zero_real ) }.
% 0.89/1.36 { ! ord_less_eq_real( minus_minus_real( X, Y ), zero_zero_real ),
% 0.89/1.36 ord_less_eq_real( X, Y ) }.
% 0.89/1.36 { ! ord_less_real( X, Y ), ord_less_eq_real( X, Y ) }.
% 0.89/1.36 { ! ord_less_real( X, Y ), ! X = Y }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), X = Y, ord_less_real( X, Y ) }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ord_less_real( X, Y ), X = Y }.
% 0.89/1.36 { ! ord_less_real( X, Y ), ord_less_eq_real( X, Y ) }.
% 0.89/1.36 { ! X = Y, ord_less_eq_real( X, Y ) }.
% 0.89/1.36 { times_times_real( times_times_real( X, Y ), Z ) = times_times_real( X,
% 0.89/1.36 times_times_real( Y, Z ) ) }.
% 0.89/1.36 { times_times_real( X, Y ) = times_times_real( Y, X ) }.
% 0.89/1.36 { times_times_real( one_one_real, X ) = X }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ord_less_eq_real( plus_plus_real( Z, X ),
% 0.89/1.36 plus_plus_real( Z, Y ) ) }.
% 0.89/1.36 { minus_minus_real( plus_plus_real( X, Y ), plus_plus_real( Z, T ) ) =
% 0.89/1.36 plus_plus_real( minus_minus_real( X, Z ), minus_minus_real( Y, T ) ) }.
% 0.89/1.36 { minus_minus_int( plus_plus_int( X, Y ), plus_plus_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( minus_minus_int( X, Z ), minus_minus_int( Y, T ) ) }.
% 0.89/1.36 { X = zero_zero_real, ! times_times_real( X, Y ) = times_times_real( X, Z )
% 0.89/1.36 , Y = Z }.
% 0.89/1.36 { X = zero_zero_real, ! Y = Z, times_times_real( X, Y ) = times_times_real
% 0.89/1.36 ( X, Z ) }.
% 0.89/1.36 { X = zero_zero_real, ! times_times_real( Y, X ) = times_times_real( Z, X )
% 0.89/1.36 , Y = Z }.
% 0.89/1.36 { X = zero_zero_real, ! Y = Z, times_times_real( Y, X ) = times_times_real
% 0.89/1.36 ( Z, X ) }.
% 0.89/1.36 { ! times_times_nat( X, Y ) = one_one_nat, X = one_one_nat }.
% 0.89/1.36 { ! times_times_nat( X, Y ) = one_one_nat, Y = one_one_nat }.
% 0.89/1.36 { ! X = one_one_nat, ! Y = one_one_nat, times_times_nat( X, Y ) =
% 0.89/1.36 one_one_nat }.
% 0.89/1.36 { times_times_real( plus_plus_real( X, Y ), Z ) = plus_plus_real(
% 0.89/1.36 times_times_real( X, Z ), times_times_real( Y, Z ) ) }.
% 0.89/1.36 { ! power_power_nat( X, Y ) = zero_zero_nat, ! Y = zero_zero_nat }.
% 0.89/1.36 { ! power_power_nat( X, Y ) = zero_zero_nat, X = zero_zero_nat }.
% 0.89/1.36 { Y = zero_zero_nat, ! X = zero_zero_nat, power_power_nat( X, Y ) =
% 0.89/1.36 zero_zero_nat }.
% 0.89/1.36 { minus_minus_real( times_times_real( X, Y ), times_times_real( Z, T ) ) =
% 0.89/1.36 plus_plus_real( times_times_real( X, minus_minus_real( Y, T ) ),
% 0.89/1.36 times_times_real( minus_minus_real( X, Z ), T ) ) }.
% 0.89/1.36 { minus_minus_int( times_times_int( X, Y ), times_times_int( Z, T ) ) =
% 0.89/1.36 plus_plus_int( times_times_int( X, minus_minus_int( Y, T ) ),
% 0.89/1.36 times_times_int( minus_minus_int( X, Z ), T ) ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_eq_real(
% 0.89/1.36 times_times_real( Y, X ), times_times_real( Z, X ) ), ord_less_eq_real( Y
% 0.89/1.36 , Z ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_eq_real( Y, Z ),
% 0.89/1.36 ord_less_eq_real( times_times_real( Y, X ), times_times_real( Z, X ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_eq_real(
% 0.89/1.36 times_times_real( X, Y ), times_times_real( X, Z ) ), ord_less_eq_real( Y
% 0.89/1.36 , Z ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_eq_real( Y, Z ),
% 0.89/1.36 ord_less_eq_real( times_times_real( X, Y ), times_times_real( X, Z ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_real( Y, Z ),
% 0.89/1.36 ord_less_real( times_times_real( X, Y ), times_times_real( X, Z ) ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_real( zero_zero_real, Y
% 0.89/1.36 ), ord_less_real( zero_zero_real, times_times_real( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_real( times_times_real(
% 0.89/1.36 Y, X ), times_times_real( Z, X ) ), ord_less_real( Y, Z ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_real( Y, Z ),
% 0.89/1.36 ord_less_real( times_times_real( Y, X ), times_times_real( Z, X ) ) }.
% 0.89/1.36 { ! plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.36 zero_zero_real, X = zero_zero_real }.
% 0.89/1.36 { ! plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.36 zero_zero_real, Y = zero_zero_real }.
% 0.89/1.36 { ! X = zero_zero_real, ! Y = zero_zero_real, plus_plus_real(
% 0.89/1.36 times_times_real( X, X ), times_times_real( Y, Y ) ) = zero_zero_real }.
% 0.89/1.36 { ! power_power_nat( X, Y ) = one_one_nat, X = one_one_nat, Y =
% 0.89/1.36 zero_zero_nat }.
% 0.89/1.36 { ! X = one_one_nat, power_power_nat( X, Y ) = one_one_nat }.
% 0.89/1.36 { ! Y = zero_zero_nat, power_power_nat( X, Y ) = one_one_nat }.
% 0.89/1.36 { minus_minus_real( times_times_real( X, X ), one_one_real ) =
% 0.89/1.36 times_times_real( plus_plus_real( X, one_one_real ), minus_minus_real( X
% 0.89/1.36 , one_one_real ) ) }.
% 0.89/1.36 { minus_minus_int( times_times_int( X, X ), one_one_int ) = times_times_int
% 0.89/1.36 ( plus_plus_int( X, one_one_int ), minus_minus_int( X, one_one_int ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), times_times_real( power_power_real( Y
% 0.89/1.36 , minus_minus_nat( X, one_one_nat ) ), Y ) = power_power_real( Y, X ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), times_times_nat( power_power_nat( Y,
% 0.89/1.36 minus_minus_nat( X, one_one_nat ) ), Y ) = power_power_nat( Y, X ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), times_times_int( power_power_int( Y,
% 0.89/1.36 minus_minus_nat( X, one_one_nat ) ), Y ) = power_power_int( Y, X ) }.
% 0.89/1.36 { ord_less_eq_real( one_one_real, power_power_real( number267125858f_real(
% 0.89/1.36 bit0( bit1( pls ) ) ), X ) ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, power_power_real( X, Y ) = one_one_real }.
% 0.89/1.36 { Y = zero_zero_nat, power_power_real( X, Y ) = times_times_real( X,
% 0.89/1.36 power_power_real( X, minus_minus_nat( Y, one_one_nat ) ) ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, power_power_nat( X, Y ) = one_one_nat }.
% 0.89/1.36 { Y = zero_zero_nat, power_power_nat( X, Y ) = times_times_nat( X,
% 0.89/1.36 power_power_nat( X, minus_minus_nat( Y, one_one_nat ) ) ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, power_power_int( X, Y ) = one_one_int }.
% 0.89/1.36 { Y = zero_zero_nat, power_power_int( X, Y ) = times_times_int( X,
% 0.89/1.36 power_power_int( X, minus_minus_nat( Y, one_one_nat ) ) ) }.
% 0.89/1.36 { ! ord_less_real( X, Y ), ! ord_less_eq_real( zero_zero_real, X ), !
% 0.89/1.36 ord_less_nat( zero_zero_nat, Z ), ord_less_real( power_power_real( X, Z )
% 0.89/1.36 , power_power_real( Y, Z ) ) }.
% 0.89/1.36 { ! ord_less_nat( X, Y ), ! ord_less_eq_nat( zero_zero_nat, X ), !
% 0.89/1.36 ord_less_nat( zero_zero_nat, Z ), ord_less_nat( power_power_nat( X, Z ),
% 0.89/1.36 power_power_nat( Y, Z ) ) }.
% 0.89/1.36 { ! ord_less_int( X, Y ), ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.36 ord_less_nat( zero_zero_nat, Z ), ord_less_int( power_power_int( X, Z ),
% 0.89/1.36 power_power_int( Y, Z ) ) }.
% 0.89/1.36 { ord_less_eq_real( X, X ) }.
% 0.89/1.36 { ord_less_eq_real( X, Y ), ord_less_eq_real( Y, X ) }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ! ord_less_eq_real( Y, Z ), ord_less_eq_real
% 0.89/1.36 ( X, Z ) }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ! ord_less_eq_real( Y, X ), X = Y }.
% 0.89/1.36 { X = zero_zero_real, ! power_power_real( X, Y ) = zero_zero_real }.
% 0.89/1.36 { ! is_int( X ), X = zero_zero_int, ! power_power_int( X, Y ) =
% 0.89/1.36 zero_zero_int }.
% 0.89/1.36 { power_power_real( times_times_real( X, Y ), Z ) = times_times_real(
% 0.89/1.36 power_power_real( X, Z ), power_power_real( Y, Z ) ) }.
% 0.89/1.36 { power_power_nat( times_times_nat( X, Y ), Z ) = times_times_nat(
% 0.89/1.36 power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.36 { power_power_int( times_times_int( X, Y ), Z ) = times_times_int(
% 0.89/1.36 power_power_int( X, Z ), power_power_int( Y, Z ) ) }.
% 0.89/1.36 { times_times_real( power_power_real( X, Y ), X ) = times_times_real( X,
% 0.89/1.36 power_power_real( X, Y ) ) }.
% 0.89/1.36 { times_times_nat( power_power_nat( X, Y ), X ) = times_times_nat( X,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { times_times_int( power_power_int( X, Y ), X ) = times_times_int( X,
% 0.89/1.36 power_power_int( X, Y ) ) }.
% 0.89/1.36 { power_power_real( one_one_real, X ) = one_one_real }.
% 0.89/1.36 { power_power_nat( one_one_nat, X ) = one_one_nat }.
% 0.89/1.36 { power_power_int( one_one_int, X ) = one_one_int }.
% 0.89/1.36 { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat( power_power_nat( X, Z ),
% 0.89/1.36 power_power_nat( Y, Z ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), dvd_dvd_int( power_power_int( X, Z ),
% 0.89/1.36 power_power_int( Y, Z ) ) }.
% 0.89/1.36 { ! dvd_dvd_real( X, Y ), dvd_dvd_real( power_power_real( X, Z ),
% 0.89/1.36 power_power_real( Y, Z ) ) }.
% 0.89/1.36 { power_power_real( X, times_times_nat( Y, Z ) ) = power_power_real(
% 0.89/1.36 power_power_real( X, Y ), Z ) }.
% 0.89/1.36 { power_power_nat( X, times_times_nat( Y, Z ) ) = power_power_nat(
% 0.89/1.36 power_power_nat( X, Y ), Z ) }.
% 0.89/1.36 { power_power_int( X, times_times_nat( Y, Z ) ) = power_power_int(
% 0.89/1.36 power_power_int( X, Y ), Z ) }.
% 0.89/1.36 { power_power_real( X, one_one_nat ) = X }.
% 0.89/1.36 { power_power_nat( X, one_one_nat ) = X }.
% 0.89/1.36 { ! is_int( X ), power_power_int( X, one_one_nat ) = X }.
% 0.89/1.36 { ! ord_less_eq_real( X, Y ), ! ord_less_eq_real( zero_zero_real, X ),
% 0.89/1.36 ord_less_eq_real( power_power_real( X, Z ), power_power_real( Y, Z ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_nat( zero_zero_nat, X ),
% 0.89/1.36 ord_less_eq_nat( power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( X, Y ), ! ord_less_eq_int( zero_zero_int, X ),
% 0.89/1.36 ord_less_eq_int( power_power_int( X, Z ), power_power_int( Y, Z ) ) }.
% 0.89/1.36 { ! ord_less_eq_real( zero_zero_real, X ), ord_less_eq_real( zero_zero_real
% 0.89/1.36 , power_power_real( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( zero_zero_nat, X ), ord_less_eq_nat( zero_zero_nat,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( zero_zero_int, X ), ord_less_eq_int( zero_zero_int,
% 0.89/1.36 power_power_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ord_less_real( zero_zero_real,
% 0.89/1.36 power_power_real( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ord_less_nat( zero_zero_nat,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_int( zero_zero_int, X ), ord_less_int( zero_zero_int,
% 0.89/1.36 power_power_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_real( one_one_real, X ), ord_less_eq_real( one_one_real,
% 0.89/1.36 power_power_real( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( one_one_nat, X ), ord_less_eq_nat( one_one_nat,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_int( one_one_int, X ), ord_less_eq_int( one_one_int,
% 0.89/1.36 power_power_int( X, Y ) ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ! power_power_real( X, Y ) =
% 0.89/1.36 power_power_real( X, Z ), Y = Z }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ! Y = Z, power_power_real( X, Y ) =
% 0.89/1.36 power_power_real( X, Z ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ! power_power_nat( X, Y ) =
% 0.89/1.36 power_power_nat( X, Z ), Y = Z }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ! Y = Z, power_power_nat( X, Y ) =
% 0.89/1.36 power_power_nat( X, Z ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ! power_power_int( X, Y ) =
% 0.89/1.36 power_power_int( X, Z ), Y = Z }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ! Y = Z, power_power_int( X, Y ) =
% 0.89/1.36 power_power_int( X, Z ) }.
% 0.89/1.36 { ! power_power_real( X, Y ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.36 { ! power_power_real( X, Y ) = zero_zero_real, ! Y = zero_zero_nat }.
% 0.89/1.36 { ! X = zero_zero_real, Y = zero_zero_nat, power_power_real( X, Y ) =
% 0.89/1.36 zero_zero_real }.
% 0.89/1.36 { ! power_power_nat( X, Y ) = zero_zero_nat, X = zero_zero_nat }.
% 0.89/1.36 { ! power_power_nat( X, Y ) = zero_zero_nat, ! Y = zero_zero_nat }.
% 0.89/1.36 { ! X = zero_zero_nat, Y = zero_zero_nat, power_power_nat( X, Y ) =
% 0.89/1.36 zero_zero_nat }.
% 0.89/1.36 { ! is_int( X ), ! power_power_int( X, Y ) = zero_zero_int, X =
% 0.89/1.36 zero_zero_int }.
% 0.89/1.36 { ! is_int( X ), ! power_power_int( X, Y ) = zero_zero_int, ! Y =
% 0.89/1.36 zero_zero_nat }.
% 0.89/1.36 { ! is_int( X ), ! X = zero_zero_int, Y = zero_zero_nat, power_power_int( X
% 0.89/1.36 , Y ) = zero_zero_int }.
% 0.89/1.36 { power_power_real( X, zero_zero_nat ) = one_one_real }.
% 0.89/1.36 { power_power_nat( X, zero_zero_nat ) = one_one_nat }.
% 0.89/1.36 { power_power_int( X, zero_zero_nat ) = one_one_int }.
% 0.89/1.36 { power_power_real( X, plus_plus_nat( Y, Z ) ) = times_times_real(
% 0.89/1.36 power_power_real( X, Y ), power_power_real( X, Z ) ) }.
% 0.89/1.36 { power_power_nat( X, plus_plus_nat( Y, Z ) ) = times_times_nat(
% 0.89/1.36 power_power_nat( X, Y ), power_power_nat( X, Z ) ) }.
% 0.89/1.36 { power_power_int( X, plus_plus_nat( Y, Z ) ) = times_times_int(
% 0.89/1.36 power_power_int( X, Y ), power_power_int( X, Z ) ) }.
% 0.89/1.36 { ! dvd_dvd_nat( power_power_nat( X, Y ), Z ), ! ord_less_eq_nat( T, Y ),
% 0.89/1.36 dvd_dvd_nat( power_power_nat( X, T ), Z ) }.
% 0.89/1.36 { ! dvd_dvd_int( power_power_int( X, Y ), Z ), ! ord_less_eq_nat( T, Y ),
% 0.89/1.36 dvd_dvd_int( power_power_int( X, T ), Z ) }.
% 0.89/1.36 { ! dvd_dvd_real( power_power_real( X, Y ), Z ), ! ord_less_eq_nat( T, Y )
% 0.89/1.36 , dvd_dvd_real( power_power_real( X, T ), Z ) }.
% 0.89/1.36 { ! dvd_dvd_nat( X, Y ), ! ord_less_eq_nat( Z, T ), dvd_dvd_nat(
% 0.89/1.36 power_power_nat( X, Z ), power_power_nat( Y, T ) ) }.
% 0.89/1.36 { ! dvd_dvd_int( X, Y ), ! ord_less_eq_nat( Z, T ), dvd_dvd_int(
% 0.89/1.36 power_power_int( X, Z ), power_power_int( Y, T ) ) }.
% 0.89/1.36 { ! dvd_dvd_real( X, Y ), ! ord_less_eq_nat( Z, T ), dvd_dvd_real(
% 0.89/1.36 power_power_real( X, Z ), power_power_real( Y, T ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), dvd_dvd_nat( power_power_nat( Z, X ),
% 0.89/1.36 power_power_nat( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), dvd_dvd_int( power_power_int( Z, X ),
% 0.89/1.36 power_power_int( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), dvd_dvd_real( power_power_real( Z, X ),
% 0.89/1.36 power_power_real( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ! ord_less_nat( power_power_nat( X, Y
% 0.89/1.36 ), power_power_nat( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, power_power_nat( X, Y ) ), ord_less_nat(
% 0.89/1.36 zero_zero_nat, X ), Y = zero_zero_nat }.
% 0.89/1.36 { ! ord_less_nat( zero_zero_nat, X ), ord_less_nat( zero_zero_nat,
% 0.89/1.36 power_power_nat( X, Y ) ) }.
% 0.89/1.36 { ! Y = zero_zero_nat, ord_less_nat( zero_zero_nat, power_power_nat( X, Y )
% 0.89/1.36 ) }.
% 0.89/1.36 { ! ord_less_real( power_power_real( X, Z ), power_power_real( Y, Z ) ), !
% 0.89/1.36 ord_less_eq_real( zero_zero_real, Y ), ord_less_real( X, Y ) }.
% 0.89/1.36 { ! ord_less_nat( power_power_nat( X, Z ), power_power_nat( Y, Z ) ), !
% 0.89/1.36 ord_less_eq_nat( zero_zero_nat, Y ), ord_less_nat( X, Y ) }.
% 0.89/1.36 { ! ord_less_int( power_power_int( X, Z ), power_power_int( Y, Z ) ), !
% 0.89/1.36 ord_less_eq_int( zero_zero_int, Y ), ord_less_int( X, Y ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ord_less_real( power_power_real( X, Y
% 0.89/1.36 ), times_times_real( X, power_power_real( X, Y ) ) ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ord_less_nat( power_power_nat( X, Y ),
% 0.89/1.36 times_times_nat( X, power_power_nat( X, Y ) ) ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ord_less_int( power_power_int( X, Y ),
% 0.89/1.36 times_times_int( X, power_power_int( X, Y ) ) ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ord_less_real( one_one_real,
% 0.89/1.36 times_times_real( X, power_power_real( X, Y ) ) ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ord_less_nat( one_one_nat,
% 0.89/1.36 times_times_nat( X, power_power_nat( X, Y ) ) ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ord_less_int( one_one_int,
% 0.89/1.36 times_times_int( X, power_power_int( X, Y ) ) ) }.
% 0.89/1.36 { ! X = zero_zero_nat, power_power_real( zero_zero_real, X ) = one_one_real
% 0.89/1.36 }.
% 0.89/1.36 { X = zero_zero_nat, power_power_real( zero_zero_real, X ) = zero_zero_real
% 0.89/1.36 }.
% 0.89/1.36 { ! X = zero_zero_nat, power_power_nat( zero_zero_nat, X ) = one_one_nat }
% 0.89/1.36 .
% 0.89/1.36 { X = zero_zero_nat, power_power_nat( zero_zero_nat, X ) = zero_zero_nat }
% 0.89/1.36 .
% 0.89/1.36 { ! X = zero_zero_nat, power_power_int( zero_zero_int, X ) = one_one_int }
% 0.89/1.36 .
% 0.89/1.36 { X = zero_zero_nat, power_power_int( zero_zero_int, X ) = zero_zero_int }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_nat( X, Y ), ! ord_less_real( one_one_real, Z ), ord_less_real
% 0.89/1.36 ( power_power_real( Z, X ), power_power_real( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_nat( X, Y ), ! ord_less_nat( one_one_nat, Z ), ord_less_nat(
% 0.89/1.36 power_power_nat( Z, X ), power_power_nat( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_nat( X, Y ), ! ord_less_int( one_one_int, Z ), ord_less_int(
% 0.89/1.36 power_power_int( Z, X ), power_power_int( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ! ord_less_real( power_power_real( X
% 0.89/1.36 , Y ), power_power_real( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ! ord_less_nat( power_power_nat( X, Y )
% 0.89/1.36 , power_power_nat( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ! ord_less_int( power_power_int( X, Y )
% 0.89/1.36 , power_power_int( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ! ord_less_real( power_power_real( X
% 0.89/1.36 , Y ), power_power_real( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_real( one_one_real, X ), ! ord_less_nat( Y, Z ), ord_less_real
% 0.89/1.36 ( power_power_real( X, Y ), power_power_real( X, Z ) ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ! ord_less_nat( power_power_nat( X, Y )
% 0.89/1.36 , power_power_nat( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_nat( one_one_nat, X ), ! ord_less_nat( Y, Z ), ord_less_nat(
% 0.89/1.36 power_power_nat( X, Y ), power_power_nat( X, Z ) ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ! ord_less_int( power_power_int( X, Y )
% 0.89/1.36 , power_power_int( X, Z ) ), ord_less_nat( Y, Z ) }.
% 0.89/1.36 { ! ord_less_int( one_one_int, X ), ! ord_less_nat( Y, Z ), ord_less_int(
% 0.89/1.36 power_power_int( X, Y ), power_power_int( X, Z ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_real( one_one_real, Z ),
% 0.89/1.36 ord_less_eq_real( power_power_real( Z, X ), power_power_real( Z, Y ) ) }
% 0.89/1.36 .
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_nat( one_one_nat, Z ),
% 0.89/1.36 ord_less_eq_nat( power_power_nat( Z, X ), power_power_nat( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_int( one_one_int, Z ),
% 0.89/1.36 ord_less_eq_int( power_power_int( Z, X ), power_power_int( Z, Y ) ) }.
% 0.89/1.36 { ! ord_less_real( zero_zero_real, X ), ! ord_less_real( X, one_one_real )
% 0.89/1.36 , ord_less_real( times_times_real( X, power_power_real( X, Y ) ),
% 0.89/1.36 power_power_real( X, Y ) ) }.
% 0.89/1.38 { ! ord_less_nat( zero_zero_nat, X ), ! ord_less_nat( X, one_one_nat ),
% 0.89/1.38 ord_less_nat( times_times_nat( X, power_power_nat( X, Y ) ),
% 0.89/1.38 power_power_nat( X, Y ) ) }.
% 0.89/1.38 { ! ord_less_int( zero_zero_int, X ), ! ord_less_int( X, one_one_int ),
% 0.89/1.38 ord_less_int( times_times_int( X, power_power_int( X, Y ) ),
% 0.89/1.38 power_power_int( X, Y ) ) }.
% 0.89/1.38 { ! ord_less_nat( X, Y ), ! ord_less_int( zero_zero_int, Z ), !
% 0.89/1.38 ord_less_int( Z, one_one_int ), ord_less_int( power_power_int( Z, Y ),
% 0.89/1.38 power_power_int( Z, X ) ) }.
% 0.89/1.38 { ! ord_less_nat( zero_zero_nat, X ), ! ord_less_real( zero_zero_real, Y )
% 0.89/1.38 , ord_less_real( zero_zero_real, skol8( Z, T ) ) }.
% 0.89/1.38 { ! ord_less_nat( zero_zero_nat, X ), ! ord_less_real( zero_zero_real, Y )
% 0.89/1.38 , power_power_real( skol8( X, Y ), X ) = Y }.
% 0.89/1.38 { ! ord_less_nat( zero_zero_nat, X ), ! ord_less_real( zero_zero_real, Y )
% 0.89/1.38 , ! ord_less_real( zero_zero_real, Z ), ! power_power_real( Z, X ) = Y, Z
% 0.89/1.38 = skol8( X, Y ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), Y = zero_zero_nat, ord_less_eq_nat( X, Y ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat( power_power_nat( X, Z ),
% 0.89/1.38 power_power_nat( Y, Z ) ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat( times_times_nat( Z, X ),
% 0.89/1.38 times_times_nat( Z, Y ) ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat( times_times_nat( X, Z ),
% 0.89/1.38 times_times_nat( Y, Z ) ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), ! dvd_dvd_nat( X, plus_plus_nat( Y, Z ) ),
% 0.89/1.38 dvd_dvd_nat( X, Z ) }.
% 0.89/1.38 { ! dvd_dvd_nat( times_times_nat( X, Y ), times_times_nat( Z, Y ) ), Y =
% 0.89/1.38 zero_zero_nat, dvd_dvd_nat( X, Z ) }.
% 0.89/1.38 { ! Y = zero_zero_nat, dvd_dvd_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, Y ) ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Z ), dvd_dvd_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, Y ) ) }.
% 0.89/1.38 { ! dvd_dvd_nat( power_power_nat( X, Y ), power_power_nat( Z, Y ) ), Y =
% 0.89/1.38 zero_zero_nat, dvd_dvd_nat( X, Z ) }.
% 0.89/1.38 { X = zero_zero_nat, ! dvd_dvd_nat( power_power_nat( Y, X ), Z ),
% 0.89/1.38 dvd_dvd_nat( Y, Z ) }.
% 0.89/1.38 { ! X = plus_plus_nat( times_times_nat( T, Y ), Z ), ! ord_less_nat(
% 0.89/1.38 zero_zero_nat, Z ), ! ord_less_nat( Z, Y ), ! dvd_dvd_nat( Y, X ) }.
% 0.89/1.38 { ! dvd_dvd_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ), !
% 0.89/1.38 ord_less_nat( one_one_nat, X ), ord_less_eq_nat( Y, Z ) }.
% 0.89/1.38 { ! dvd_dvd_nat( X, Y ), Y = zero_zero_nat, Y = X, ord_less_eq_nat(
% 0.89/1.38 times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ), Y ) }
% 0.89/1.38 .
% 0.89/1.38 { ! ord_less_int( plus_plus_int( power_power_int( s, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ), one_one_int ), zero_zero_int ) }.
% 0.89/1.38
% 0.89/1.38 *** allocated 15000 integers for clauses
% 0.89/1.38 *** allocated 22500 integers for clauses
% 0.89/1.38 *** allocated 33750 integers for clauses
% 0.89/1.38 *** allocated 50625 integers for clauses
% 0.89/1.38 percentage equality = 0.365043, percentage horn = 0.903614
% 0.89/1.38 This is a problem with some equality
% 0.89/1.38
% 0.89/1.38
% 0.89/1.38
% 0.89/1.38 Options Used:
% 0.89/1.38
% 0.89/1.38 useres = 1
% 0.89/1.38 useparamod = 1
% 0.89/1.38 useeqrefl = 1
% 0.89/1.38 useeqfact = 1
% 0.89/1.38 usefactor = 1
% 0.89/1.38 usesimpsplitting = 0
% 0.89/1.38 usesimpdemod = 5
% 0.89/1.38 usesimpres = 3
% 0.89/1.38
% 0.89/1.38 resimpinuse = 1000
% 0.89/1.38 resimpclauses = 20000
% 0.89/1.38 substype = eqrewr
% 0.89/1.38 backwardsubs = 1
% 0.89/1.38 selectoldest = 5
% 0.89/1.38
% 0.89/1.38 litorderings [0] = split
% 0.89/1.38 litorderings [1] = extend the termordering, first sorting on arguments
% 0.89/1.38
% 0.89/1.38 termordering = kbo
% 0.89/1.38
% 0.89/1.38 litapriori = 0
% 0.89/1.38 termapriori = 1
% 0.89/1.38 litaposteriori = 0
% 0.89/1.38 termaposteriori = 0
% 0.89/1.38 demodaposteriori = 0
% 0.89/1.38 ordereqreflfact = 0
% 0.89/1.38
% 0.89/1.38 litselect = negord
% 0.89/1.38
% 0.89/1.38 maxweight = 15
% 0.89/1.38 maxdepth = 30000
% 0.89/1.38 maxlength = 115
% 0.89/1.38 maxnrvars = 195
% 0.89/1.38 excuselevel = 1
% 0.89/1.38 increasemaxweight = 1
% 0.89/1.38
% 0.89/1.38 maxselected = 10000000
% 0.89/1.38 maxnrclauses = 10000000
% 0.89/1.38
% 0.89/1.38 showgenerated = 0
% 0.89/1.38 showkept = 0
% 0.89/1.38 showselected = 0
% 0.89/1.38 showdeleted = 0
% 0.89/1.38 showresimp = 1
% 0.89/1.38 showstatus = 2000
% 0.89/1.38
% 0.89/1.38 prologoutput = 0
% 0.89/1.38 nrgoals = 5000000
% 0.89/1.38 totalproof = 1
% 0.89/1.38
% 0.89/1.38 Symbols occurring in the translation:
% 0.89/1.38
% 0.89/1.38 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.38 . [1, 2] (w:1, o:332, a:1, s:1, b:0),
% 0.89/1.38 ! [4, 1] (w:0, o:316, a:1, s:1, b:0),
% 0.89/1.38 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.38 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.38 is_int [37, 1] (w:1, o:321, a:1, s:1, b:0),
% 0.89/1.38 minus_minus_int [38, 2] (w:1, o:357, a:1, s:1, b:0),
% 0.89/1.38 one_one_int [39, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.89/1.38 plus_plus_int [40, 2] (w:1, o:364, a:1, s:1, b:0),
% 0.89/1.38 times_times_int [41, 2] (w:1, o:367, a:1, s:1, b:0),
% 0.89/1.38 zero_zero_int [42, 0] (w:1, o:77, a:1, s:1, b:0),
% 0.89/1.38 int [43, 0] (w:1, o:78, a:1, s:1, b:0),
% 0.89/1.38 undefined_int [44, 1] (w:1, o:324, a:1, s:1, b:0),
% 0.89/1.38 bit0 [45, 1] (w:1, o:326, a:1, s:1, b:0),
% 0.89/1.38 bit1 [46, 1] (w:1, o:327, a:1, s:1, b:0),
% 0.89/1.38 min [47, 0] (w:1, o:79, a:1, s:1, b:0),
% 0.89/1.38 pls [48, 0] (w:1, o:82, a:1, s:1, b:0),
% 0.89/1.38 number_number_of_int [49, 1] (w:1, o:328, a:1, s:1, b:0),
% 0.89/1.38 power_power_int [50, 2] (w:1, o:368, a:1, s:1, b:0),
% 0.89/1.38 legendre [51, 2] (w:1, o:356, a:1, s:1, b:0),
% 0.89/1.38 m [52, 0] (w:1, o:83, a:1, s:1, b:0),
% 0.89/1.38 s1 [53, 0] (w:1, o:84, a:1, s:1, b:0),
% 0.89/1.38 s [54, 0] (w:1, o:85, a:1, s:1, b:0),
% 0.89/1.38 t [55, 0] (w:1, o:90, a:1, s:1, b:0),
% 0.89/1.38 ord_less_int [56, 2] (w:1, o:358, a:1, s:1, b:0),
% 0.89/1.38 number_number_of_nat [57, 1] (w:1, o:329, a:1, s:1, b:0),
% 0.89/1.38 ord_less_eq_int [58, 2] (w:1, o:359, a:1, s:1, b:0),
% 0.89/1.38 power_power_real [61, 2] (w:1, o:369, a:1, s:1, b:0),
% 0.89/1.38 plus_plus_real [62, 2] (w:1, o:370, a:1, s:1, b:0),
% 0.89/1.38 zero_zero_real [63, 0] (w:1, o:155, a:1, s:1, b:0),
% 0.89/1.38 ord_less_real [64, 2] (w:1, o:360, a:1, s:1, b:0),
% 0.89/1.38 one_one_real [69, 0] (w:1, o:80, a:1, s:1, b:0),
% 0.89/1.38 one_one_nat [70, 0] (w:1, o:81, a:1, s:1, b:0),
% 0.89/1.38 power_power_nat [71, 2] (w:1, o:371, a:1, s:1, b:0),
% 0.89/1.38 zero_zero_nat [72, 0] (w:1, o:165, a:1, s:1, b:0),
% 0.89/1.38 number267125858f_real [74, 1] (w:1, o:330, a:1, s:1, b:0),
% 0.89/1.38 zprime [77, 1] (w:1, o:331, a:1, s:1, b:0),
% 0.89/1.38 twoSqu142715416sum2sq [78, 1] (w:1, o:323, a:1, s:1, b:0),
% 0.89/1.38 ord_less_eq_real [85, 2] (w:1, o:361, a:1, s:1, b:0),
% 0.89/1.38 plus_plus_nat [91, 2] (w:1, o:372, a:1, s:1, b:0),
% 0.89/1.38 times_times_real [99, 2] (w:1, o:373, a:1, s:1, b:0),
% 0.89/1.38 times_times_nat [100, 2] (w:1, o:374, a:1, s:1, b:0),
% 0.89/1.38 ord_less_nat [110, 2] (w:1, o:362, a:1, s:1, b:0),
% 0.89/1.38 ord_less_eq_nat [111, 2] (w:1, o:363, a:1, s:1, b:0),
% 0.89/1.38 dvd_dvd_int [161, 2] (w:1, o:375, a:1, s:1, b:0),
% 0.89/1.38 zcong [164, 3] (w:1, o:387, a:1, s:1, b:0),
% 0.89/1.38 quadRes [279, 2] (w:1, o:376, a:1, s:1, b:0),
% 0.89/1.38 minus_minus_real [282, 2] (w:1, o:377, a:1, s:1, b:0),
% 0.89/1.38 minus_minus_nat [294, 2] (w:1, o:378, a:1, s:1, b:0),
% 0.89/1.38 dvd_dvd_nat [322, 2] (w:1, o:379, a:1, s:1, b:0),
% 0.89/1.38 dvd_dvd_real [323, 2] (w:1, o:380, a:1, s:1, b:0),
% 0.89/1.38 alpha1 [374, 2] (w:1, o:381, a:1, s:1, b:1),
% 0.89/1.38 alpha2 [375, 1] (w:1, o:325, a:1, s:1, b:1),
% 0.89/1.38 alpha3 [376, 2] (w:1, o:382, a:1, s:1, b:1),
% 0.89/1.38 alpha4 [377, 2] (w:1, o:383, a:1, s:1, b:1),
% 0.89/1.38 alpha5 [378, 2] (w:1, o:384, a:1, s:1, b:1),
% 0.89/1.38 alpha6 [379, 2] (w:1, o:385, a:1, s:1, b:1),
% 0.89/1.38 alpha7 [380, 2] (w:1, o:386, a:1, s:1, b:1),
% 0.89/1.38 skol1 [381, 0] (w:1, o:86, a:1, s:1, b:1),
% 0.89/1.38 skol2 [382, 0] (w:1, o:87, a:1, s:1, b:1),
% 0.89/1.38 skol3 [383, 0] (w:1, o:88, a:1, s:1, b:1),
% 0.89/1.38 skol4 [384, 1] (w:1, o:322, a:1, s:1, b:1),
% 0.89/1.38 skol5 [385, 0] (w:1, o:89, a:1, s:1, b:1),
% 0.89/1.38 skol6 [386, 3] (w:1, o:388, a:1, s:1, b:1),
% 0.89/1.38 skol7 [387, 2] (w:1, o:365, a:1, s:1, b:1),
% 0.89/1.38 skol8 [388, 2] (w:1, o:366, a:1, s:1, b:1).
% 0.89/1.38
% 0.89/1.38
% 0.89/1.38 Starting Search:
% 0.89/1.38
% 0.89/1.38 *** allocated 75937 integers for clauses
% 0.89/1.38 *** allocated 113905 integers for clauses
% 0.89/1.38 Resimplifying inuse:
% 0.89/1.38 Done
% 0.89/1.38
% 0.89/1.38
% 0.89/1.38 Bliksems!, er is een bewijs:
% 0.89/1.38 % SZS status Theorem
% 0.89/1.38 % SZS output start Refutation
% 0.89/1.38
% 0.89/1.38 (19) {G0,W23,D9,L1,V0,M1} I { ord_less_int( times_times_int( plus_plus_int
% 0.89/1.38 ( times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m
% 0.89/1.38 ), one_one_int ), t ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.38 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.38 zero_zero_int ) ) }.
% 0.89/1.38 (20) {G0,W20,D9,L1,V0,M1} I { times_times_int( plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ), t ) ==> plus_plus_int( power_power_int( s,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.38 (132) {G0,W8,D5,L1,V0,M1} I { number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ==> plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.38 (407) {G0,W5,D3,L1,V1,M1} I { times_times_int( X, zero_zero_int ) ==>
% 0.89/1.38 zero_zero_int }.
% 0.89/1.38 (757) {G1,W9,D5,L1,V0,M1} I;d(132) { ! ord_less_int( plus_plus_int(
% 0.89/1.38 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.38 one_one_int ), zero_zero_int ) }.
% 0.89/1.38 (1305) {G2,W0,D0,L0,V0,M0} S(19);d(20);d(132);d(407);r(757) { }.
% 0.89/1.38
% 0.89/1.38
% 0.89/1.38 % SZS output end Refutation
% 0.89/1.38 found a proof!
% 0.89/1.38
% 0.89/1.38 *** allocated 75937 integers for termspace/termends
% 0.89/1.38
% 0.89/1.38 Unprocessed initial clauses:
% 0.89/1.38
% 0.89/1.38 (1307) {G0,W8,D3,L3,V2,M3} { ! is_int( X ), ! is_int( Y ), is_int(
% 0.89/1.38 minus_minus_int( X, Y ) ) }.
% 0.89/1.38 (1308) {G0,W2,D2,L1,V0,M1} { is_int( one_one_int ) }.
% 0.89/1.38 (1309) {G0,W8,D3,L3,V2,M3} { ! is_int( X ), ! is_int( Y ), is_int(
% 0.89/1.38 plus_plus_int( X, Y ) ) }.
% 0.89/1.38 (1310) {G0,W8,D3,L3,V2,M3} { ! is_int( X ), ! is_int( Y ), is_int(
% 0.89/1.38 times_times_int( X, Y ) ) }.
% 0.89/1.38 (1311) {G0,W2,D2,L1,V0,M1} { is_int( zero_zero_int ) }.
% 0.89/1.38 (1312) {G0,W3,D3,L1,V0,M1} { is_int( undefined_int( int ) ) }.
% 0.89/1.38 (1313) {G0,W5,D3,L2,V1,M2} { ! is_int( X ), is_int( bit0( X ) ) }.
% 0.89/1.38 (1314) {G0,W5,D3,L2,V1,M2} { ! is_int( X ), is_int( bit1( X ) ) }.
% 0.89/1.38 (1315) {G0,W2,D2,L1,V0,M1} { is_int( min ) }.
% 0.89/1.38 (1316) {G0,W2,D2,L1,V0,M1} { is_int( pls ) }.
% 0.89/1.38 (1317) {G0,W5,D3,L2,V1,M2} { ! is_int( X ), is_int( number_number_of_int(
% 0.89/1.38 X ) ) }.
% 0.89/1.38 (1318) {G0,W6,D3,L2,V2,M2} { ! is_int( X ), is_int( power_power_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1319) {G0,W8,D3,L3,V2,M3} { ! is_int( X ), ! is_int( Y ), is_int(
% 0.89/1.38 legendre( X, Y ) ) }.
% 0.89/1.38 (1320) {G0,W2,D2,L1,V0,M1} { is_int( m ) }.
% 0.89/1.38 (1321) {G0,W2,D2,L1,V0,M1} { is_int( s1 ) }.
% 0.89/1.38 (1322) {G0,W2,D2,L1,V0,M1} { is_int( s ) }.
% 0.89/1.38 (1323) {G0,W2,D2,L1,V0,M1} { is_int( t ) }.
% 0.89/1.38 (1324) {G0,W3,D2,L1,V0,M1} { ord_less_int( t, zero_zero_int ) }.
% 0.89/1.38 (1325) {G0,W3,D2,L1,V0,M1} { ord_less_int( t, one_one_int ) }.
% 0.89/1.38 (1326) {G0,W23,D9,L1,V0,M1} { ord_less_int( times_times_int( plus_plus_int
% 0.89/1.38 ( times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m
% 0.89/1.38 ), one_one_int ), t ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.38 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.38 zero_zero_int ) ) }.
% 0.89/1.38 (1327) {G0,W20,D9,L1,V0,M1} { plus_plus_int( power_power_int( s,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) =
% 0.89/1.38 times_times_int( plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.38 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ), t ) }.
% 0.89/1.38 (1328) {G0,W13,D7,L2,V0,M2} { ! t = zero_zero_int, plus_plus_int(
% 0.89/1.38 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 one_one_int ) = zero_zero_int }.
% 0.89/1.38 (1329) {G0,W3,D2,L1,V0,M1} { ! ord_less_eq_int( one_one_int, t ) }.
% 0.89/1.38 (1330) {G0,W11,D8,L1,V0,M1} { ord_less_int( zero_zero_int, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1331) {G0,W15,D7,L1,V2,M1} { ! ord_less_real( plus_plus_real(
% 0.89/1.38 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.38 zero_zero_real ) }.
% 0.89/1.38 (1332) {G0,W15,D7,L1,V2,M1} { ! ord_less_int( plus_plus_int(
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.38 zero_zero_int ) }.
% 0.89/1.38 (1333) {G0,W21,D7,L3,V2,M3} { ! ord_less_real( zero_zero_real,
% 0.89/1.38 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.38 ) ) ) ) ), ! X = zero_zero_real, ! Y = zero_zero_real }.
% 0.89/1.38 (1334) {G0,W18,D7,L2,V2,M2} { X = zero_zero_real, ord_less_real(
% 0.89/1.38 zero_zero_real, plus_plus_real( power_power_real( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ), power_power_real( Y, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.38 (1335) {G0,W18,D7,L2,V2,M2} { Y = zero_zero_real, ord_less_real(
% 0.89/1.38 zero_zero_real, plus_plus_real( power_power_real( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ), power_power_real( Y, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.38 (1336) {G0,W25,D7,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( zero_zero_int, plus_plus_int( power_power_int( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ) ) ) ), ! X = zero_zero_int, ! Y = zero_zero_int }.
% 0.89/1.38 (1337) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), X =
% 0.89/1.38 zero_zero_int, ord_less_int( zero_zero_int, plus_plus_int(
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.38 (1338) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), Y =
% 0.89/1.38 zero_zero_int, ord_less_int( zero_zero_int, plus_plus_int(
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ) }.
% 0.89/1.38 (1339) {G0,W18,D7,L2,V2,M2} { ! plus_plus_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_real, X =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1340) {G0,W18,D7,L2,V2,M2} { ! plus_plus_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_real, Y =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1341) {G0,W21,D7,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.38 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.38 ) ) ) ) = zero_zero_real }.
% 0.89/1.38 (1342) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ) ) = zero_zero_int, X = zero_zero_int }.
% 0.89/1.38 (1343) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ) ) = zero_zero_int, Y = zero_zero_int }.
% 0.89/1.38 (1344) {G0,W25,D7,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! X =
% 0.89/1.38 zero_zero_int, ! Y = zero_zero_int, plus_plus_int( power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_int }.
% 0.89/1.38 (1345) {G0,W8,D6,L1,V1,M1} { ! ord_less_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), zero_zero_real ) }.
% 0.89/1.38 (1346) {G0,W8,D6,L1,V1,M1} { ! ord_less_int( power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), zero_zero_int ) }.
% 0.89/1.38 (1347) {G0,W11,D6,L2,V1,M2} { ! ord_less_real( zero_zero_real,
% 0.89/1.38 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! X
% 0.89/1.38 = zero_zero_real }.
% 0.89/1.38 (1348) {G0,W11,D6,L2,V1,M2} { X = zero_zero_real, ord_less_real(
% 0.89/1.38 zero_zero_real, power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ) ) }.
% 0.89/1.38 (1349) {G0,W13,D6,L3,V1,M3} { ! is_int( X ), ! ord_less_int( zero_zero_int
% 0.89/1.38 , power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ), !
% 0.89/1.38 X = zero_zero_int }.
% 0.89/1.38 (1350) {G0,W13,D6,L3,V1,M3} { ! is_int( X ), X = zero_zero_int,
% 0.89/1.38 ord_less_int( zero_zero_int, power_power_int( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1351) {G0,W8,D6,L1,V0,M1} { power_power_real( one_one_real,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = one_one_real }.
% 0.89/1.38 (1352) {G0,W8,D6,L1,V0,M1} { power_power_nat( one_one_nat,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = one_one_nat }.
% 0.89/1.38 (1353) {G0,W8,D6,L1,V0,M1} { power_power_int( one_one_int,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = one_one_int }.
% 0.89/1.38 (1354) {G0,W8,D6,L1,V0,M1} { power_power_real( zero_zero_real,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_real }.
% 0.89/1.38 (1355) {G0,W8,D6,L1,V0,M1} { power_power_nat( zero_zero_nat,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_nat }.
% 0.89/1.38 (1356) {G0,W8,D6,L1,V0,M1} { power_power_int( zero_zero_int,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_int }.
% 0.89/1.38 (1357) {G0,W11,D6,L2,V1,M2} { ! power_power_real( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.38 (1358) {G0,W11,D6,L2,V1,M2} { ! X = zero_zero_real, power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_real }.
% 0.89/1.38 (1359) {G0,W13,D6,L3,V1,M3} { ! is_int( X ), ! power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = zero_zero_int, X =
% 0.89/1.38 zero_zero_int }.
% 0.89/1.38 (1360) {G0,W13,D6,L3,V1,M3} { ! is_int( X ), ! X = zero_zero_int,
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.38 zero_zero_int }.
% 0.89/1.38 (1361) {G0,W10,D5,L1,V1,M1} { plus_plus_real( one_one_real,
% 0.89/1.38 number267125858f_real( X ) ) = number267125858f_real( plus_plus_int( bit1
% 0.89/1.38 ( pls ), X ) ) }.
% 0.89/1.38 (1362) {G0,W10,D5,L1,V1,M1} { plus_plus_int( one_one_int,
% 0.89/1.38 number_number_of_int( X ) ) = number_number_of_int( plus_plus_int( bit1(
% 0.89/1.38 pls ), X ) ) }.
% 0.89/1.38 (1363) {G0,W10,D5,L1,V1,M1} { plus_plus_real( number267125858f_real( X ),
% 0.89/1.38 one_one_real ) = number267125858f_real( plus_plus_int( X, bit1( pls ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1364) {G0,W10,D5,L1,V1,M1} { plus_plus_int( number_number_of_int( X ),
% 0.89/1.38 one_one_int ) = number_number_of_int( plus_plus_int( X, bit1( pls ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1365) {G0,W11,D8,L1,V0,M1} { ord_less_int( t, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1366) {G0,W2,D2,L1,V0,M1} { is_int( skol1 ) }.
% 0.89/1.38 (1367) {G0,W20,D9,L1,V0,M1} { plus_plus_int( power_power_int( s,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) =
% 0.89/1.38 times_times_int( plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.38 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ), skol1 ) }.
% 0.89/1.38 (1368) {G0,W10,D8,L1,V0,M1} { zprime( plus_plus_int( times_times_int(
% 0.89/1.38 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.38 }.
% 0.89/1.38 (1369) {G0,W12,D9,L1,V0,M1} { twoSqu142715416sum2sq( times_times_int(
% 0.89/1.38 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), m ), one_one_int ), t ) ) }.
% 0.89/1.38 (1370) {G0,W3,D2,L1,V1,M1} { ord_less_eq_int( X, X ) }.
% 0.89/1.38 (1371) {G0,W6,D3,L2,V1,M2} { ! is_int( X ), number_number_of_int( X ) = X
% 0.89/1.38 }.
% 0.89/1.38 (1372) {G0,W7,D3,L1,V2,M1} { times_times_int( X, Y ) = times_times_int( Y
% 0.89/1.38 , X ) }.
% 0.89/1.38 (1373) {G0,W6,D2,L2,V2,M2} { ord_less_eq_int( X, Y ), ord_less_eq_int( Y,
% 0.89/1.38 X ) }.
% 0.89/1.38 (1374) {G0,W10,D4,L1,V2,M1} { times_times_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( times_times_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1375) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( number_number_of_int( X )
% 0.89/1.38 , number_number_of_int( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1376) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.38 (1377) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_real( number267125858f_real( X
% 0.89/1.38 ), number267125858f_real( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1378) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_real(
% 0.89/1.38 number267125858f_real( X ), number267125858f_real( Y ) ) }.
% 0.89/1.38 (1379) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( number_number_of_int( X )
% 0.89/1.38 , number_number_of_int( Y ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1380) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.38 (1381) {G0,W11,D4,L1,V3,M1} { times_times_int( times_times_int( X, Y ), Z
% 0.89/1.38 ) = times_times_int( X, times_times_int( Y, Z ) ) }.
% 0.89/1.38 (1382) {G0,W9,D2,L3,V3,M3} { ! ord_less_eq_int( X, Y ), ! ord_less_eq_int
% 0.89/1.38 ( Y, Z ), ord_less_eq_int( X, Z ) }.
% 0.89/1.38 (1383) {G0,W13,D2,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( X, Y ), ! ord_less_eq_int( Y, X ), X = Y }.
% 0.89/1.38 (1384) {G0,W13,D4,L1,V3,M1} { power_power_int( X, plus_plus_nat( Y, Z ) )
% 0.89/1.38 = times_times_int( power_power_int( X, Y ), power_power_int( X, Z ) ) }.
% 0.89/1.38 (1385) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit1( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1386) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit1( X ), bit1( Y ) ) }.
% 0.89/1.38 (1387) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit1( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1388) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit1( X ), bit1( Y ) ) }.
% 0.89/1.38 (1389) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( pls, pls ) }.
% 0.89/1.38 (1390) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit0( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1391) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit0( X ), bit0( Y ) ) }.
% 0.89/1.38 (1392) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit0( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1393) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit0( X ), bit0( Y ) ) }.
% 0.89/1.38 (1394) {G0,W10,D2,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( X, Y ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1395) {G0,W10,D2,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( X, Y ), ! X = Y }.
% 0.89/1.38 (1396) {G0,W13,D2,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( X, Y ), X = Y, ord_less_int( X, Y ) }.
% 0.89/1.38 (1397) {G0,W10,D3,L2,V3,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 plus_plus_int( Z, X ), plus_plus_int( Z, Y ) ) }.
% 0.89/1.38 (1398) {G0,W7,D3,L2,V1,M2} { ! number_number_of_nat( X ) = zero_zero_nat,
% 0.89/1.38 ord_less_eq_int( X, pls ) }.
% 0.89/1.38 (1399) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, pls ),
% 0.89/1.38 number_number_of_nat( X ) = zero_zero_nat }.
% 0.89/1.38 (1400) {G0,W7,D3,L2,V1,M2} { ! zero_zero_nat = number_number_of_nat( X ),
% 0.89/1.38 ord_less_eq_int( X, pls ) }.
% 0.89/1.38 (1401) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, pls ), zero_zero_nat =
% 0.89/1.38 number_number_of_nat( X ) }.
% 0.89/1.38 (1402) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), times_times_real( number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( Y ) ) = number267125858f_real( times_times_int( X
% 0.89/1.38 , Y ) ) }.
% 0.89/1.38 (1403) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), times_times_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( Y ) ) = number_number_of_nat( times_times_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1404) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), times_times_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( times_times_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1405) {G0,W14,D5,L1,V3,M1} { times_times_real( number267125858f_real( X )
% 0.89/1.38 , times_times_real( number267125858f_real( Y ), Z ) ) = times_times_real
% 0.89/1.38 ( number267125858f_real( times_times_int( X, Y ) ), Z ) }.
% 0.89/1.38 (1406) {G0,W14,D5,L1,V3,M1} { times_times_int( number_number_of_int( X ),
% 0.89/1.38 times_times_int( number_number_of_int( Y ), Z ) ) = times_times_int(
% 0.89/1.38 number_number_of_int( times_times_int( X, Y ) ), Z ) }.
% 0.89/1.38 (1407) {G0,W10,D4,L1,V2,M1} { times_times_real( number267125858f_real( X )
% 0.89/1.38 , number267125858f_real( Y ) ) = number267125858f_real( times_times_int(
% 0.89/1.38 X, Y ) ) }.
% 0.89/1.38 (1408) {G0,W10,D4,L1,V2,M1} { times_times_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( times_times_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1409) {G0,W10,D4,L1,V2,M1} { number267125858f_real( times_times_int( X, Y
% 0.89/1.38 ) ) = times_times_real( number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( Y ) ) }.
% 0.89/1.38 (1410) {G0,W10,D4,L1,V2,M1} { number_number_of_int( times_times_int( X, Y
% 0.89/1.38 ) ) = times_times_int( number_number_of_int( X ), number_number_of_int(
% 0.89/1.38 Y ) ) }.
% 0.89/1.38 (1411) {G0,W12,D4,L2,V2,M2} { ! ord_less_eq_real( plus_plus_real(
% 0.89/1.38 times_times_real( X, X ), times_times_real( Y, Y ) ), zero_zero_real ), X
% 0.89/1.38 = zero_zero_real }.
% 0.89/1.38 (1412) {G0,W12,D4,L2,V2,M2} { ! ord_less_eq_real( plus_plus_real(
% 0.89/1.38 times_times_real( X, X ), times_times_real( Y, Y ) ), zero_zero_real ), Y
% 0.89/1.38 = zero_zero_real }.
% 0.89/1.38 (1413) {G0,W15,D4,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.38 ord_less_eq_real( plus_plus_real( times_times_real( X, X ),
% 0.89/1.38 times_times_real( Y, Y ) ), zero_zero_real ) }.
% 0.89/1.38 (1414) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( plus_plus_int( times_times_int( X, X ), times_times_int
% 0.89/1.38 ( Y, Y ) ), zero_zero_int ), X = zero_zero_int }.
% 0.89/1.38 (1415) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( plus_plus_int( times_times_int( X, X ), times_times_int
% 0.89/1.38 ( Y, Y ) ), zero_zero_int ), Y = zero_zero_int }.
% 0.89/1.38 (1416) {G0,W19,D4,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! X =
% 0.89/1.38 zero_zero_int, ! Y = zero_zero_int, ord_less_eq_int( plus_plus_int(
% 0.89/1.38 times_times_int( X, X ), times_times_int( Y, Y ) ), zero_zero_int ) }.
% 0.89/1.38 (1417) {G0,W9,D4,L1,V2,M1} { ord_less_eq_real( zero_zero_real,
% 0.89/1.38 plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1418) {G0,W9,D4,L1,V2,M1} { ord_less_eq_int( zero_zero_int, plus_plus_int
% 0.89/1.38 ( times_times_int( X, X ), times_times_int( Y, Y ) ) ) }.
% 0.89/1.38 (1419) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_real( number267125858f_real( X
% 0.89/1.38 ), zero_zero_real ), ord_less_eq_int( X, pls ) }.
% 0.89/1.38 (1420) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, pls ), ord_less_eq_real
% 0.89/1.38 ( number267125858f_real( X ), zero_zero_real ) }.
% 0.89/1.38 (1421) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( number_number_of_int( X )
% 0.89/1.38 , zero_zero_int ), ord_less_eq_int( X, pls ) }.
% 0.89/1.38 (1422) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, pls ), ord_less_eq_int
% 0.89/1.38 ( number_number_of_int( X ), zero_zero_int ) }.
% 0.89/1.38 (1423) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_real( zero_zero_real,
% 0.89/1.38 number267125858f_real( X ) ), ord_less_eq_int( pls, X ) }.
% 0.89/1.38 (1424) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, X ), ord_less_eq_real
% 0.89/1.38 ( zero_zero_real, number267125858f_real( X ) ) }.
% 0.89/1.38 (1425) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( zero_zero_int,
% 0.89/1.38 number_number_of_int( X ) ), ord_less_eq_int( pls, X ) }.
% 0.89/1.38 (1426) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, X ), ord_less_eq_int
% 0.89/1.38 ( zero_zero_int, number_number_of_int( X ) ) }.
% 0.89/1.38 (1427) {G0,W7,D3,L2,V1,M2} { ! ord_less_nat( zero_zero_nat,
% 0.89/1.38 number_number_of_nat( X ) ), ord_less_int( pls, X ) }.
% 0.89/1.38 (1428) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, X ), ord_less_nat(
% 0.89/1.38 zero_zero_nat, number_number_of_nat( X ) ) }.
% 0.89/1.38 (1429) {G0,W10,D3,L2,V2,M2} { ! ord_less_eq_real( number267125858f_real( X
% 0.89/1.38 ), number267125858f_real( Y ) ), ! ord_less_real( number267125858f_real
% 0.89/1.38 ( Y ), number267125858f_real( X ) ) }.
% 0.89/1.38 (1430) {G0,W10,D3,L2,V2,M2} { ord_less_real( number267125858f_real( Y ),
% 0.89/1.38 number267125858f_real( X ) ), ord_less_eq_real( number267125858f_real( X
% 0.89/1.38 ), number267125858f_real( Y ) ) }.
% 0.89/1.38 (1431) {G0,W10,D3,L2,V2,M2} { ! ord_less_eq_nat( number_number_of_nat( X )
% 0.89/1.38 , number_number_of_nat( Y ) ), ! ord_less_nat( number_number_of_nat( Y )
% 0.89/1.38 , number_number_of_nat( X ) ) }.
% 0.89/1.38 (1432) {G0,W10,D3,L2,V2,M2} { ord_less_nat( number_number_of_nat( Y ),
% 0.89/1.38 number_number_of_nat( X ) ), ord_less_eq_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( Y ) ) }.
% 0.89/1.38 (1433) {G0,W10,D3,L2,V2,M2} { ! ord_less_eq_int( number_number_of_int( X )
% 0.89/1.38 , number_number_of_int( Y ) ), ! ord_less_int( number_number_of_int( Y )
% 0.89/1.38 , number_number_of_int( X ) ) }.
% 0.89/1.38 (1434) {G0,W10,D3,L2,V2,M2} { ord_less_int( number_number_of_int( Y ),
% 0.89/1.38 number_number_of_int( X ) ), ord_less_eq_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) }.
% 0.89/1.38 (1435) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, bit1( X ) ),
% 0.89/1.38 ord_less_eq_int( pls, X ) }.
% 0.89/1.38 (1436) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, X ), ord_less_eq_int
% 0.89/1.38 ( pls, bit1( X ) ) }.
% 0.89/1.38 (1437) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit0( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1438) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit0( X ), bit1( Y ) ) }.
% 0.89/1.38 (1439) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit0( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1440) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 bit0( X ), bit1( Y ) ) }.
% 0.89/1.38 (1441) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( bit0( X ), pls ),
% 0.89/1.38 ord_less_eq_int( X, pls ) }.
% 0.89/1.38 (1442) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, pls ), ord_less_eq_int
% 0.89/1.38 ( bit0( X ), pls ) }.
% 0.89/1.38 (1443) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, bit0( X ) ),
% 0.89/1.38 ord_less_eq_int( pls, X ) }.
% 0.89/1.38 (1444) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, X ), ord_less_eq_int
% 0.89/1.38 ( pls, bit0( X ) ) }.
% 0.89/1.38 (1445) {G0,W13,D3,L3,V4,M3} { ! ord_less_int( X, Y ), ! ord_less_eq_int( Z
% 0.89/1.38 , T ), ord_less_int( plus_plus_int( X, Z ), plus_plus_int( Y, T ) ) }.
% 0.89/1.38 (1446) {G0,W4,D3,L1,V0,M1} { number_number_of_nat( pls ) = zero_zero_nat
% 0.89/1.38 }.
% 0.89/1.38 (1447) {G0,W4,D3,L1,V0,M1} { zero_zero_nat = number_number_of_nat( pls )
% 0.89/1.38 }.
% 0.89/1.38 (1448) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_real( number267125858f_real( X
% 0.89/1.38 ), one_one_real ), ord_less_eq_int( X, bit1( pls ) ) }.
% 0.89/1.38 (1449) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( X, bit1( pls ) ),
% 0.89/1.38 ord_less_eq_real( number267125858f_real( X ), one_one_real ) }.
% 0.89/1.38 (1450) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( number_number_of_int( X )
% 0.89/1.38 , one_one_int ), ord_less_eq_int( X, bit1( pls ) ) }.
% 0.89/1.38 (1451) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( X, bit1( pls ) ),
% 0.89/1.38 ord_less_eq_int( number_number_of_int( X ), one_one_int ) }.
% 0.89/1.38 (1452) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_real( one_one_real,
% 0.89/1.38 number267125858f_real( X ) ), ord_less_eq_int( bit1( pls ), X ) }.
% 0.89/1.38 (1453) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( bit1( pls ), X ),
% 0.89/1.38 ord_less_eq_real( one_one_real, number267125858f_real( X ) ) }.
% 0.89/1.38 (1454) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( one_one_int,
% 0.89/1.38 number_number_of_int( X ) ), ord_less_eq_int( bit1( pls ), X ) }.
% 0.89/1.38 (1455) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( bit1( pls ), X ),
% 0.89/1.38 ord_less_eq_int( one_one_int, number_number_of_int( X ) ) }.
% 0.89/1.38 (1456) {G0,W8,D5,L1,V0,M1} { plus_plus_nat( one_one_nat, one_one_nat ) =
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1457) {G0,W5,D3,L1,V1,M1} { times_times_int( pls, X ) = pls }.
% 0.89/1.38 (1458) {G0,W9,D4,L1,V2,M1} { times_times_int( bit0( X ), Y ) = bit0(
% 0.89/1.38 times_times_int( X, Y ) ) }.
% 0.89/1.38 (1459) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1460) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int(
% 0.89/1.38 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.38 (1461) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), times_times_int( X,
% 0.89/1.38 one_one_int ) = X }.
% 0.89/1.38 (1462) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), times_times_int( one_one_int,
% 0.89/1.38 X ) = X }.
% 0.89/1.38 (1463) {G0,W10,D4,L1,V2,M1} { plus_plus_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( plus_plus_int( X, Y )
% 0.89/1.38 ) }.
% 0.89/1.38 (1464) {G0,W13,D4,L1,V3,M1} { times_times_int( plus_plus_int( X, Y ), Z )
% 0.89/1.38 = plus_plus_int( times_times_int( X, Z ), times_times_int( Y, Z ) ) }.
% 0.89/1.38 (1465) {G0,W13,D4,L1,V3,M1} { times_times_int( X, plus_plus_int( Y, Z ) )
% 0.89/1.38 = plus_plus_int( times_times_int( X, Y ), times_times_int( X, Z ) ) }.
% 0.89/1.38 (1466) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( bit1( X ), pls ),
% 0.89/1.38 ord_less_int( X, pls ) }.
% 0.89/1.38 (1467) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, pls ), ord_less_eq_int(
% 0.89/1.38 bit1( X ), pls ) }.
% 0.89/1.38 (1468) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, bit1( X ) ),
% 0.89/1.38 ord_less_eq_int( pls, X ) }.
% 0.89/1.38 (1469) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( pls, X ), ord_less_int(
% 0.89/1.38 pls, bit1( X ) ) }.
% 0.89/1.38 (1470) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit1( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1471) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_eq_int( bit1
% 0.89/1.38 ( X ), bit0( Y ) ) }.
% 0.89/1.38 (1472) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( bit1( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1473) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_eq_int( bit1
% 0.89/1.38 ( X ), bit0( Y ) ) }.
% 0.89/1.38 (1474) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit0( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1475) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_int( bit0
% 0.89/1.38 ( X ), bit1( Y ) ) }.
% 0.89/1.38 (1476) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit0( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1477) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_int( bit0
% 0.89/1.38 ( X ), bit1( Y ) ) }.
% 0.89/1.38 (1478) {G0,W8,D3,L2,V2,M2} { ! ord_less_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( Y ) ), alpha1( X, Y ) }.
% 0.89/1.38 (1479) {G0,W8,D3,L2,V2,M2} { ! ord_less_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1480) {G0,W11,D3,L3,V2,M3} { ! alpha1( X, Y ), ! ord_less_int( X, Y ),
% 0.89/1.38 ord_less_nat( number_number_of_nat( X ), number_number_of_nat( Y ) ) }.
% 0.89/1.38 (1481) {G0,W9,D2,L3,V2,M3} { ! alpha1( X, Y ), ! ord_less_int( X, Y ),
% 0.89/1.38 ord_less_int( pls, Y ) }.
% 0.89/1.38 (1482) {G0,W6,D2,L2,V2,M2} { ord_less_int( X, Y ), alpha1( X, Y ) }.
% 0.89/1.38 (1483) {G0,W6,D2,L2,V2,M2} { ! ord_less_int( pls, Y ), alpha1( X, Y ) }.
% 0.89/1.38 (1484) {G0,W6,D2,L2,V1,M2} { ! ord_less_eq_int( one_one_int, X ),
% 0.89/1.38 ord_less_int( zero_zero_int, X ) }.
% 0.89/1.38 (1485) {G0,W6,D2,L2,V1,M2} { ! ord_less_int( zero_zero_int, X ),
% 0.89/1.38 ord_less_eq_int( one_one_int, X ) }.
% 0.89/1.38 (1486) {G0,W5,D4,L1,V0,M1} { number_number_of_nat( bit1( pls ) ) =
% 0.89/1.38 one_one_nat }.
% 0.89/1.38 (1487) {G0,W5,D4,L1,V0,M1} { one_one_nat = number_number_of_nat( bit1( pls
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1488) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 plus_plus_int( X, one_one_int ), Y ) }.
% 0.89/1.38 (1489) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( plus_plus_int( X,
% 0.89/1.38 one_one_int ), Y ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1490) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 plus_plus_int( X, one_one_int ), Y ) }.
% 0.89/1.38 (1491) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, plus_plus_int( Y,
% 0.89/1.38 one_one_int ) ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1492) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_int( X,
% 0.89/1.38 plus_plus_int( Y, one_one_int ) ) }.
% 0.89/1.38 (1493) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), plus_plus_real( number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( Y ) ) = number267125858f_real( plus_plus_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1494) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), plus_plus_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( Y ) ) = number_number_of_nat( plus_plus_int( X, Y )
% 0.89/1.38 ) }.
% 0.89/1.38 (1495) {G0,W16,D4,L3,V2,M3} { ! ord_less_eq_int( pls, X ), !
% 0.89/1.38 ord_less_eq_int( pls, Y ), plus_plus_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( plus_plus_int( X, Y )
% 0.89/1.38 ) }.
% 0.89/1.38 (1496) {G0,W11,D4,L2,V2,M2} { ! ord_less_int( Y, pls ), plus_plus_nat(
% 0.89/1.38 number_number_of_nat( Y ), number_number_of_nat( X ) ) =
% 0.89/1.38 number_number_of_nat( X ) }.
% 0.89/1.38 (1497) {G0,W14,D4,L3,V2,M3} { ord_less_int( Y, pls ), ! ord_less_int( X,
% 0.89/1.38 pls ), plus_plus_nat( number_number_of_nat( Y ), number_number_of_nat( X
% 0.89/1.38 ) ) = number_number_of_nat( Y ) }.
% 0.89/1.38 (1498) {G0,W16,D4,L3,V2,M3} { ord_less_int( Y, pls ), ord_less_int( X, pls
% 0.89/1.38 ), plus_plus_nat( number_number_of_nat( Y ), number_number_of_nat( X ) )
% 0.89/1.38 = number_number_of_nat( plus_plus_int( Y, X ) ) }.
% 0.89/1.38 (1499) {G0,W8,D3,L2,V1,M2} { ! ord_less_eq_int( zero_zero_int, X ),
% 0.89/1.38 ord_less_int( zero_zero_int, plus_plus_int( one_one_int, X ) ) }.
% 0.89/1.38 (1500) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 number267125858f_real( X ) = number267125858f_real( Y ), X = Y }.
% 0.89/1.38 (1501) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y,
% 0.89/1.38 number267125858f_real( X ) = number267125858f_real( Y ) }.
% 0.89/1.38 (1502) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 number_number_of_int( X ) = number_number_of_int( Y ), X = Y }.
% 0.89/1.38 (1503) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y,
% 0.89/1.38 number_number_of_int( X ) = number_number_of_int( Y ) }.
% 0.89/1.38 (1504) {G0,W8,D3,L2,V2,M2} { ! number267125858f_real( X ) = Y, Y =
% 0.89/1.38 number267125858f_real( X ) }.
% 0.89/1.38 (1505) {G0,W8,D3,L2,V2,M2} { ! Y = number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( X ) = Y }.
% 0.89/1.38 (1506) {G0,W10,D3,L3,V2,M3} { ! is_int( X ), ! number_number_of_int( Y ) =
% 0.89/1.38 X, X = number_number_of_int( Y ) }.
% 0.89/1.38 (1507) {G0,W10,D3,L3,V2,M3} { ! is_int( X ), ! X = number_number_of_int( Y
% 0.89/1.38 ), number_number_of_int( Y ) = X }.
% 0.89/1.38 (1508) {G0,W8,D3,L2,V2,M2} { ! number_number_of_nat( X ) = Y, Y =
% 0.89/1.38 number_number_of_nat( X ) }.
% 0.89/1.38 (1509) {G0,W8,D3,L2,V2,M2} { ! Y = number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( X ) = Y }.
% 0.89/1.38 (1510) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! bit1( X ) =
% 0.89/1.38 bit1( Y ), X = Y }.
% 0.89/1.38 (1511) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y, bit1
% 0.89/1.38 ( X ) = bit1( Y ) }.
% 0.89/1.38 (1512) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! bit0( X ) =
% 0.89/1.38 bit0( Y ), X = Y }.
% 0.89/1.38 (1513) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y, bit0
% 0.89/1.38 ( X ) = bit0( Y ) }.
% 0.89/1.38 (1514) {G0,W13,D2,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ord_less_int(
% 0.89/1.38 X, Y ), X = Y, ord_less_int( Y, X ) }.
% 0.89/1.38 (1515) {G0,W12,D4,L2,V2,M2} { ! plus_plus_real( times_times_real( X, X ),
% 0.89/1.38 times_times_real( Y, Y ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.38 (1516) {G0,W12,D4,L2,V2,M2} { ! plus_plus_real( times_times_real( X, X ),
% 0.89/1.38 times_times_real( Y, Y ) ) = zero_zero_real, Y = zero_zero_real }.
% 0.89/1.38 (1517) {G0,W15,D4,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.38 plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1518) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 plus_plus_int( times_times_int( X, X ), times_times_int( Y, Y ) ) =
% 0.89/1.38 zero_zero_int, X = zero_zero_int }.
% 0.89/1.38 (1519) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 plus_plus_int( times_times_int( X, X ), times_times_int( Y, Y ) ) =
% 0.89/1.38 zero_zero_int, Y = zero_zero_int }.
% 0.89/1.38 (1520) {G0,W19,D4,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! X =
% 0.89/1.38 zero_zero_int, ! Y = zero_zero_int, plus_plus_int( times_times_int( X, X
% 0.89/1.38 ), times_times_int( Y, Y ) ) = zero_zero_int }.
% 0.89/1.38 (1521) {G0,W16,D5,L1,V3,M1} { times_times_real( plus_plus_real( X, Y ),
% 0.89/1.38 number267125858f_real( Z ) ) = plus_plus_real( times_times_real( X,
% 0.89/1.38 number267125858f_real( Z ) ), times_times_real( Y, number267125858f_real
% 0.89/1.38 ( Z ) ) ) }.
% 0.89/1.38 (1522) {G0,W16,D5,L1,V3,M1} { times_times_nat( plus_plus_nat( X, Y ),
% 0.89/1.38 number_number_of_nat( Z ) ) = plus_plus_nat( times_times_nat( X,
% 0.89/1.38 number_number_of_nat( Z ) ), times_times_nat( Y, number_number_of_nat( Z
% 0.89/1.38 ) ) ) }.
% 0.89/1.38 (1523) {G0,W16,D5,L1,V3,M1} { times_times_int( plus_plus_int( X, Y ),
% 0.89/1.38 number_number_of_int( Z ) ) = plus_plus_int( times_times_int( X,
% 0.89/1.38 number_number_of_int( Z ) ), times_times_int( Y, number_number_of_int( Z
% 0.89/1.38 ) ) ) }.
% 0.89/1.38 (1524) {G0,W16,D5,L1,V3,M1} { times_times_real( number267125858f_real( X )
% 0.89/1.38 , plus_plus_real( Y, Z ) ) = plus_plus_real( times_times_real(
% 0.89/1.38 number267125858f_real( X ), Y ), times_times_real( number267125858f_real
% 0.89/1.38 ( X ), Z ) ) }.
% 0.89/1.38 (1525) {G0,W16,D5,L1,V3,M1} { times_times_nat( number_number_of_nat( X ),
% 0.89/1.38 plus_plus_nat( Y, Z ) ) = plus_plus_nat( times_times_nat(
% 0.89/1.38 number_number_of_nat( X ), Y ), times_times_nat( number_number_of_nat( X
% 0.89/1.38 ), Z ) ) }.
% 0.89/1.38 (1526) {G0,W16,D5,L1,V3,M1} { times_times_int( number_number_of_int( X ),
% 0.89/1.38 plus_plus_int( Y, Z ) ) = plus_plus_int( times_times_int(
% 0.89/1.38 number_number_of_int( X ), Y ), times_times_int( number_number_of_int( X
% 0.89/1.38 ), Z ) ) }.
% 0.89/1.38 (1527) {G0,W11,D4,L1,V3,M1} { plus_plus_int( plus_plus_int( X, Y ), Z ) =
% 0.89/1.38 plus_plus_int( X, plus_plus_int( Y, Z ) ) }.
% 0.89/1.38 (1528) {G0,W11,D4,L1,V3,M1} { plus_plus_int( X, plus_plus_int( Y, Z ) ) =
% 0.89/1.38 plus_plus_int( Y, plus_plus_int( X, Z ) ) }.
% 0.89/1.38 (1529) {G0,W7,D3,L1,V2,M1} { plus_plus_int( X, Y ) = plus_plus_int( Y, X )
% 0.89/1.38 }.
% 0.89/1.38 (1530) {G0,W4,D3,L1,V0,M1} { zero_zero_int = number_number_of_int( pls )
% 0.89/1.38 }.
% 0.89/1.38 (1531) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( X, Y ), ! ord_less_int(
% 0.89/1.38 zero_zero_int, Z ), ord_less_int( times_times_int( Z, X ),
% 0.89/1.38 times_times_int( Z, Y ) ) }.
% 0.89/1.38 (1532) {G0,W22,D6,L4,V2,M4} { ! power_power_real( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ) = power_power_real( Y, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ), ! ord_less_eq_real( zero_zero_real, X ), !
% 0.89/1.38 ord_less_eq_real( zero_zero_real, Y ), X = Y }.
% 0.89/1.38 (1533) {G0,W22,D6,L4,V2,M4} { ! power_power_nat( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = power_power_nat( Y, number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ) ), ! ord_less_eq_nat( zero_zero_nat, X ), !
% 0.89/1.38 ord_less_eq_nat( zero_zero_nat, Y ), X = Y }.
% 0.89/1.38 (1534) {G0,W26,D6,L6,V2,M6} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) =
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ), !
% 0.89/1.38 ord_less_eq_int( zero_zero_int, X ), ! ord_less_eq_int( zero_zero_int, Y
% 0.89/1.38 ), X = Y }.
% 0.89/1.38 (1535) {G0,W19,D6,L3,V2,M3} { ! ord_less_eq_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_real(
% 0.89/1.38 zero_zero_real, Y ), ord_less_eq_real( X, Y ) }.
% 0.89/1.38 (1536) {G0,W19,D6,L3,V2,M3} { ! ord_less_eq_nat( power_power_nat( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_nat( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_nat(
% 0.89/1.38 zero_zero_nat, Y ), ord_less_eq_nat( X, Y ) }.
% 0.89/1.38 (1537) {G0,W19,D6,L3,V2,M3} { ! ord_less_eq_int( power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_int(
% 0.89/1.38 zero_zero_int, Y ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1538) {G0,W8,D6,L1,V1,M1} { ord_less_eq_real( zero_zero_real,
% 0.89/1.38 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1539) {G0,W8,D6,L1,V1,M1} { ord_less_eq_int( zero_zero_int,
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1540) {G0,W19,D6,L3,V2,M3} { ! ord_less_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_real(
% 0.89/1.38 zero_zero_real, Y ), ord_less_real( X, Y ) }.
% 0.89/1.38 (1541) {G0,W19,D6,L3,V2,M3} { ! ord_less_nat( power_power_nat( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_nat( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_nat(
% 0.89/1.38 zero_zero_nat, Y ), ord_less_nat( X, Y ) }.
% 0.89/1.38 (1542) {G0,W19,D6,L3,V2,M3} { ! ord_less_int( power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), ! ord_less_eq_int(
% 0.89/1.38 zero_zero_int, Y ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1543) {G0,W18,D7,L2,V2,M2} { ! ord_less_eq_real( plus_plus_real(
% 0.89/1.38 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.38 zero_zero_real ), X = zero_zero_real }.
% 0.89/1.38 (1544) {G0,W18,D7,L2,V2,M2} { ! ord_less_eq_real( plus_plus_real(
% 0.89/1.38 power_power_real( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_real( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.38 zero_zero_real ), Y = zero_zero_real }.
% 0.89/1.38 (1545) {G0,W21,D7,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.38 ord_less_eq_real( plus_plus_real( power_power_real( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), zero_zero_real ) }.
% 0.89/1.38 (1546) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( plus_plus_int( power_power_int( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ) ) ), zero_zero_int ), X = zero_zero_int }.
% 0.89/1.38 (1547) {G0,W22,D7,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( plus_plus_int( power_power_int( X, number_number_of_nat
% 0.89/1.38 ( bit0( bit1( pls ) ) ) ), power_power_int( Y, number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ) ) ), zero_zero_int ), Y = zero_zero_int }.
% 0.89/1.38 (1548) {G0,W25,D7,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! X =
% 0.89/1.38 zero_zero_int, ! Y = zero_zero_int, ord_less_eq_int( plus_plus_int(
% 0.89/1.38 power_power_int( X, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ),
% 0.89/1.38 zero_zero_int ) }.
% 0.89/1.38 (1549) {G0,W15,D7,L1,V2,M1} { ord_less_eq_real( zero_zero_real,
% 0.89/1.38 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.38 ) ) ) ) ) }.
% 0.89/1.38 (1550) {G0,W15,D7,L1,V2,M1} { ord_less_eq_int( zero_zero_int,
% 0.89/1.38 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ) ) ) }.
% 0.89/1.38 (1551) {G0,W15,D4,L3,V2,M3} { ! ord_less_real( zero_zero_real,
% 0.89/1.38 plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) ), !
% 0.89/1.38 X = zero_zero_real, ! Y = zero_zero_real }.
% 0.89/1.38 (1552) {G0,W12,D4,L2,V2,M2} { X = zero_zero_real, ord_less_real(
% 0.89/1.38 zero_zero_real, plus_plus_real( times_times_real( X, X ),
% 0.89/1.38 times_times_real( Y, Y ) ) ) }.
% 0.89/1.38 (1553) {G0,W12,D4,L2,V2,M2} { Y = zero_zero_real, ord_less_real(
% 0.89/1.38 zero_zero_real, plus_plus_real( times_times_real( X, X ),
% 0.89/1.38 times_times_real( Y, Y ) ) ) }.
% 0.89/1.38 (1554) {G0,W19,D4,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( zero_zero_int, plus_plus_int( times_times_int( X, X ), times_times_int
% 0.89/1.38 ( Y, Y ) ) ), ! X = zero_zero_int, ! Y = zero_zero_int }.
% 0.89/1.38 (1555) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), X =
% 0.89/1.38 zero_zero_int, ord_less_int( zero_zero_int, plus_plus_int(
% 0.89/1.38 times_times_int( X, X ), times_times_int( Y, Y ) ) ) }.
% 0.89/1.38 (1556) {G0,W16,D4,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), Y =
% 0.89/1.38 zero_zero_int, ord_less_int( zero_zero_int, plus_plus_int(
% 0.89/1.38 times_times_int( X, X ), times_times_int( Y, Y ) ) ) }.
% 0.89/1.38 (1557) {G0,W9,D4,L1,V2,M1} { ! ord_less_real( plus_plus_real(
% 0.89/1.38 times_times_real( X, X ), times_times_real( Y, Y ) ), zero_zero_real )
% 0.89/1.38 }.
% 0.89/1.38 (1558) {G0,W9,D4,L1,V2,M1} { ! ord_less_int( plus_plus_int(
% 0.89/1.38 times_times_int( X, X ), times_times_int( Y, Y ) ), zero_zero_int ) }.
% 0.89/1.38 (1559) {G0,W7,D5,L1,V1,M1} { times_times_real( number267125858f_real( bit1
% 0.89/1.38 ( pls ) ), X ) = X }.
% 0.89/1.38 (1560) {G0,W9,D5,L2,V1,M2} { ! is_int( X ), times_times_int(
% 0.89/1.38 number_number_of_int( bit1( pls ) ), X ) = X }.
% 0.89/1.38 (1561) {G0,W7,D5,L1,V1,M1} { times_times_real( X, number267125858f_real(
% 0.89/1.38 bit1( pls ) ) ) = X }.
% 0.89/1.38 (1562) {G0,W9,D5,L2,V1,M2} { ! is_int( X ), times_times_int( X,
% 0.89/1.38 number_number_of_int( bit1( pls ) ) ) = X }.
% 0.89/1.38 (1563) {G0,W5,D4,L1,V0,M1} { one_one_int = number_number_of_int( bit1( pls
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1564) {G0,W11,D5,L1,V2,M1} { times_times_int( bit1( X ), Y ) =
% 0.89/1.38 plus_plus_int( bit0( times_times_int( X, Y ) ), Y ) }.
% 0.89/1.38 (1565) {G0,W15,D3,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( zero_zero_int, Y ), ! times_times_int( Y, X ) = one_one_int, Y =
% 0.89/1.38 one_one_int }.
% 0.89/1.38 (1566) {G0,W15,D3,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( zero_zero_int, Y ), ! times_times_int( Y, X ) = one_one_int, X =
% 0.89/1.38 one_one_int }.
% 0.89/1.38 (1567) {G0,W18,D3,L6,V2,M6} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( zero_zero_int, Y ), ! Y = one_one_int, ! X = one_one_int,
% 0.89/1.38 times_times_int( Y, X ) = one_one_int }.
% 0.89/1.38 (1568) {G0,W8,D3,L2,V1,M2} { ! plus_plus_real( X, X ) = zero_zero_real, X
% 0.89/1.38 = zero_zero_real }.
% 0.89/1.38 (1569) {G0,W8,D3,L2,V1,M2} { ! X = zero_zero_real, plus_plus_real( X, X )
% 0.89/1.38 = zero_zero_real }.
% 0.89/1.38 (1570) {G0,W10,D3,L3,V1,M3} { ! is_int( X ), ! plus_plus_int( X, X ) =
% 0.89/1.38 zero_zero_int, X = zero_zero_int }.
% 0.89/1.38 (1571) {G0,W10,D3,L3,V1,M3} { ! is_int( X ), ! X = zero_zero_int,
% 0.89/1.38 plus_plus_int( X, X ) = zero_zero_int }.
% 0.89/1.38 (1572) {G0,W4,D3,L1,V1,M1} { ! bit1( X ) = pls }.
% 0.89/1.38 (1573) {G0,W4,D3,L1,V1,M1} { ! pls = bit1( X ) }.
% 0.89/1.38 (1574) {G0,W5,D3,L1,V2,M1} { ! bit1( X ) = bit0( Y ) }.
% 0.89/1.38 (1575) {G0,W5,D3,L1,V2,M1} { ! bit0( X ) = bit1( Y ) }.
% 0.89/1.38 (1576) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! bit0( X ) = pls, X = pls }.
% 0.89/1.38 (1577) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! X = pls, bit0( X ) = pls }.
% 0.89/1.38 (1578) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! pls = bit0( X ), pls = X }.
% 0.89/1.38 (1579) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! pls = X, pls = bit0( X ) }.
% 0.89/1.38 (1580) {G0,W4,D3,L1,V0,M1} { bit0( pls ) = pls }.
% 0.89/1.38 (1581) {G0,W3,D2,L1,V0,M1} { pls = zero_zero_int }.
% 0.89/1.38 (1582) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit1( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1583) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit1( X
% 0.89/1.38 ), bit1( Y ) ) }.
% 0.89/1.38 (1584) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit1( X ), bit1( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1585) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit1( X
% 0.89/1.38 ), bit1( Y ) ) }.
% 0.89/1.38 (1586) {G0,W3,D2,L1,V0,M1} { ! ord_less_int( pls, pls ) }.
% 0.89/1.38 (1587) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit0( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1588) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit0( X
% 0.89/1.38 ), bit0( Y ) ) }.
% 0.89/1.38 (1589) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit0( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1590) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit0( X
% 0.89/1.38 ), bit0( Y ) ) }.
% 0.89/1.38 (1591) {G0,W3,D2,L1,V0,M1} { ! zero_zero_int = one_one_int }.
% 0.89/1.38 (1592) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( X, pls ) = X
% 0.89/1.38 }.
% 0.89/1.38 (1593) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( pls, X ) = X
% 0.89/1.38 }.
% 0.89/1.38 (1594) {G0,W10,D4,L1,V2,M1} { plus_plus_int( bit0( X ), bit0( Y ) ) = bit0
% 0.89/1.38 ( plus_plus_int( X, Y ) ) }.
% 0.89/1.38 (1595) {G0,W6,D3,L1,V1,M1} { bit0( X ) = plus_plus_int( X, X ) }.
% 0.89/1.38 (1596) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( X,
% 0.89/1.38 zero_zero_int ) = X }.
% 0.89/1.38 (1597) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( zero_zero_int,
% 0.89/1.38 X ) = X }.
% 0.89/1.38 (1598) {G0,W10,D3,L2,V3,M2} { ! ord_less_int( X, Y ), ord_less_int(
% 0.89/1.38 plus_plus_int( X, Z ), plus_plus_int( Y, Z ) ) }.
% 0.89/1.38 (1599) {G0,W10,D4,L1,V1,M1} { times_times_real( plus_plus_real(
% 0.89/1.38 one_one_real, one_one_real ), number267125858f_real( X ) ) =
% 0.89/1.38 number267125858f_real( bit0( X ) ) }.
% 0.89/1.38 (1600) {G0,W10,D4,L1,V1,M1} { times_times_int( plus_plus_int( one_one_int
% 0.89/1.38 , one_one_int ), number_number_of_int( X ) ) = number_number_of_int( bit0
% 0.89/1.38 ( X ) ) }.
% 0.89/1.38 (1601) {G0,W12,D6,L1,V1,M1} { power_power_real( X, number_number_of_nat(
% 0.89/1.38 bit1( bit1( pls ) ) ) ) = times_times_real( times_times_real( X, X ), X )
% 0.89/1.38 }.
% 0.89/1.38 (1602) {G0,W12,D6,L1,V1,M1} { power_power_nat( X, number_number_of_nat(
% 0.89/1.38 bit1( bit1( pls ) ) ) ) = times_times_nat( times_times_nat( X, X ), X )
% 0.89/1.38 }.
% 0.89/1.38 (1603) {G0,W12,D6,L1,V1,M1} { power_power_int( X, number_number_of_nat(
% 0.89/1.38 bit1( bit1( pls ) ) ) ) = times_times_int( times_times_int( X, X ), X )
% 0.89/1.38 }.
% 0.89/1.38 (1604) {G0,W10,D6,L1,V1,M1} { times_times_real( number267125858f_real(
% 0.89/1.38 bit0( bit1( pls ) ) ), X ) = plus_plus_real( X, X ) }.
% 0.89/1.38 (1605) {G0,W10,D6,L1,V1,M1} { times_times_nat( number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ), X ) = plus_plus_nat( X, X ) }.
% 0.89/1.38 (1606) {G0,W10,D6,L1,V1,M1} { times_times_int( number_number_of_int( bit0
% 0.89/1.38 ( bit1( pls ) ) ), X ) = plus_plus_int( X, X ) }.
% 0.89/1.38 (1607) {G0,W10,D6,L1,V1,M1} { times_times_real( number267125858f_real(
% 0.89/1.38 bit0( bit1( pls ) ) ), X ) = plus_plus_real( X, X ) }.
% 0.89/1.38 (1608) {G0,W10,D6,L1,V1,M1} { times_times_int( number_number_of_int( bit0
% 0.89/1.38 ( bit1( pls ) ) ), X ) = plus_plus_int( X, X ) }.
% 0.89/1.38 (1609) {G0,W10,D6,L1,V1,M1} { times_times_real( X, number267125858f_real(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_real( X, X ) }.
% 0.89/1.38 (1610) {G0,W10,D6,L1,V1,M1} { times_times_nat( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_nat( X, X ) }.
% 0.89/1.38 (1611) {G0,W10,D6,L1,V1,M1} { times_times_int( X, number_number_of_int(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_int( X, X ) }.
% 0.89/1.38 (1612) {G0,W10,D6,L1,V1,M1} { times_times_real( X, number267125858f_real(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_real( X, X ) }.
% 0.89/1.38 (1613) {G0,W10,D6,L1,V1,M1} { times_times_int( X, number_number_of_int(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_int( X, X ) }.
% 0.89/1.38 (1614) {G0,W10,D6,L1,V1,M1} { power_power_real( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = times_times_real( X, X ) }.
% 0.89/1.38 (1615) {G0,W10,D6,L1,V1,M1} { power_power_nat( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = times_times_nat( X, X ) }.
% 0.89/1.38 (1616) {G0,W10,D6,L1,V1,M1} { power_power_int( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = times_times_int( X, X ) }.
% 0.89/1.38 (1617) {G0,W8,D3,L2,V1,M2} { ! ord_less_real( plus_plus_real( X, X ),
% 0.89/1.38 zero_zero_real ), ord_less_real( X, zero_zero_real ) }.
% 0.89/1.38 (1618) {G0,W8,D3,L2,V1,M2} { ! ord_less_real( X, zero_zero_real ),
% 0.89/1.38 ord_less_real( plus_plus_real( X, X ), zero_zero_real ) }.
% 0.89/1.38 (1619) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( plus_plus_int( X, X ),
% 0.89/1.38 zero_zero_int ), ord_less_int( X, zero_zero_int ) }.
% 0.89/1.38 (1620) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( X, zero_zero_int ),
% 0.89/1.38 ord_less_int( plus_plus_int( X, X ), zero_zero_int ) }.
% 0.89/1.38 (1621) {G0,W4,D3,L1,V0,M1} { number267125858f_real( pls ) = zero_zero_real
% 0.89/1.38 }.
% 0.89/1.38 (1622) {G0,W4,D3,L1,V0,M1} { number_number_of_nat( pls ) = zero_zero_nat
% 0.89/1.38 }.
% 0.89/1.38 (1623) {G0,W4,D3,L1,V0,M1} { number_number_of_int( pls ) = zero_zero_int
% 0.89/1.38 }.
% 0.89/1.38 (1624) {G0,W4,D3,L1,V0,M1} { number267125858f_real( pls ) = zero_zero_real
% 0.89/1.38 }.
% 0.89/1.38 (1625) {G0,W4,D3,L1,V0,M1} { number_number_of_int( pls ) = zero_zero_int
% 0.89/1.38 }.
% 0.89/1.38 (1626) {G0,W4,D3,L1,V0,M1} { zero_zero_real = number267125858f_real( pls )
% 0.89/1.38 }.
% 0.89/1.38 (1627) {G0,W4,D3,L1,V0,M1} { zero_zero_int = number_number_of_int( pls )
% 0.89/1.38 }.
% 0.89/1.38 (1628) {G0,W6,D4,L1,V1,M1} { plus_plus_real( number267125858f_real( pls )
% 0.89/1.38 , X ) = X }.
% 0.89/1.38 (1629) {G0,W8,D4,L2,V1,M2} { ! is_int( X ), plus_plus_int(
% 0.89/1.38 number_number_of_int( pls ), X ) = X }.
% 0.89/1.38 (1630) {G0,W6,D4,L1,V1,M1} { plus_plus_real( X, number267125858f_real( pls
% 0.89/1.38 ) ) = X }.
% 0.89/1.38 (1631) {G0,W8,D4,L2,V1,M2} { ! is_int( X ), plus_plus_int( X,
% 0.89/1.38 number_number_of_int( pls ) ) = X }.
% 0.89/1.38 (1632) {G0,W8,D3,L2,V2,M2} { ! ord_less_real( number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1633) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_real(
% 0.89/1.38 number267125858f_real( X ), number267125858f_real( Y ) ) }.
% 0.89/1.38 (1634) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ), ord_less_int( X, Y ) }.
% 0.89/1.38 (1635) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int(
% 0.89/1.38 number_number_of_int( X ), number_number_of_int( Y ) ) }.
% 0.89/1.38 (1636) {G0,W14,D5,L1,V3,M1} { plus_plus_real( number267125858f_real( X ),
% 0.89/1.38 plus_plus_real( number267125858f_real( Y ), Z ) ) = plus_plus_real(
% 0.89/1.38 number267125858f_real( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.38 (1637) {G0,W14,D5,L1,V3,M1} { plus_plus_int( number_number_of_int( X ),
% 0.89/1.38 plus_plus_int( number_number_of_int( Y ), Z ) ) = plus_plus_int(
% 0.89/1.38 number_number_of_int( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.38 (1638) {G0,W10,D4,L1,V2,M1} { plus_plus_real( number267125858f_real( X ),
% 0.89/1.38 number267125858f_real( Y ) ) = number267125858f_real( plus_plus_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1639) {G0,W10,D4,L1,V2,M1} { plus_plus_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_int( Y ) ) = number_number_of_int( plus_plus_int( X, Y )
% 0.89/1.38 ) }.
% 0.89/1.38 (1640) {G0,W10,D4,L1,V2,M1} { number267125858f_real( plus_plus_int( X, Y )
% 0.89/1.38 ) = plus_plus_real( number267125858f_real( X ), number267125858f_real( Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1641) {G0,W10,D4,L1,V2,M1} { number_number_of_int( plus_plus_int( X, Y )
% 0.89/1.38 ) = plus_plus_int( number_number_of_int( X ), number_number_of_int( Y )
% 0.89/1.38 ) }.
% 0.89/1.38 (1642) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit1( X ), pls ),
% 0.89/1.38 ord_less_int( X, pls ) }.
% 0.89/1.38 (1643) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, pls ), ord_less_int( bit1
% 0.89/1.38 ( X ), pls ) }.
% 0.89/1.38 (1644) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit1( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1645) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit1( X
% 0.89/1.38 ), bit0( Y ) ) }.
% 0.89/1.38 (1646) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( bit1( X ), bit0( Y ) ),
% 0.89/1.38 ord_less_int( X, Y ) }.
% 0.89/1.38 (1647) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int( bit1( X
% 0.89/1.38 ), bit0( Y ) ) }.
% 0.89/1.38 (1648) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit1( X ), zero_zero_int ),
% 0.89/1.38 ord_less_int( X, zero_zero_int ) }.
% 0.89/1.38 (1649) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, zero_zero_int ),
% 0.89/1.38 ord_less_int( bit1( X ), zero_zero_int ) }.
% 0.89/1.38 (1650) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit0( X ), pls ),
% 0.89/1.38 ord_less_int( X, pls ) }.
% 0.89/1.38 (1651) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, pls ), ord_less_int( bit0
% 0.89/1.38 ( X ), pls ) }.
% 0.89/1.38 (1652) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, bit0( X ) ),
% 0.89/1.38 ord_less_int( pls, X ) }.
% 0.89/1.38 (1653) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, X ), ord_less_int( pls,
% 0.89/1.38 bit0( X ) ) }.
% 0.89/1.38 (1654) {G0,W3,D2,L1,V0,M1} { ! ord_less_int( pls, zero_zero_int ) }.
% 0.89/1.38 (1655) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit0( X ), zero_zero_int ),
% 0.89/1.38 ord_less_int( X, zero_zero_int ) }.
% 0.89/1.38 (1656) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, zero_zero_int ),
% 0.89/1.38 ord_less_int( bit0( X ), zero_zero_int ) }.
% 0.89/1.38 (1657) {G0,W10,D4,L1,V2,M1} { plus_plus_int( bit1( X ), bit0( Y ) ) = bit1
% 0.89/1.38 ( plus_plus_int( X, Y ) ) }.
% 0.89/1.38 (1658) {G0,W10,D4,L1,V2,M1} { plus_plus_int( bit0( X ), bit1( Y ) ) = bit1
% 0.89/1.38 ( plus_plus_int( X, Y ) ) }.
% 0.89/1.38 (1659) {G0,W3,D2,L1,V0,M1} { ord_less_int( zero_zero_int, one_one_int )
% 0.89/1.38 }.
% 0.89/1.38 (1660) {G0,W8,D4,L1,V1,M1} { bit1( X ) = plus_plus_int( plus_plus_int(
% 0.89/1.38 one_one_int, X ), X ) }.
% 0.89/1.38 (1661) {G0,W7,D4,L1,V1,M1} { ! plus_plus_int( plus_plus_int( one_one_int,
% 0.89/1.38 X ), X ) = zero_zero_int }.
% 0.89/1.38 (1662) {G0,W15,D3,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( X, plus_plus_int( Y, one_one_int ) ), ord_less_int( X, Y ), X = Y }.
% 0.89/1.38 (1663) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.38 ( X, Y ), ord_less_int( X, plus_plus_int( Y, one_one_int ) ) }.
% 0.89/1.38 (1664) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y,
% 0.89/1.38 ord_less_int( X, plus_plus_int( Y, one_one_int ) ) }.
% 0.89/1.38 (1665) {G0,W13,D6,L1,V1,M1} { power_power_real( number267125858f_real( X )
% 0.89/1.38 , number_number_of_nat( bit0( bit1( pls ) ) ) ) = times_times_real(
% 0.89/1.38 number267125858f_real( X ), number267125858f_real( X ) ) }.
% 0.89/1.38 (1666) {G0,W13,D6,L1,V1,M1} { power_power_nat( number_number_of_nat( X ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = times_times_nat(
% 0.89/1.38 number_number_of_nat( X ), number_number_of_nat( X ) ) }.
% 0.89/1.38 (1667) {G0,W13,D6,L1,V1,M1} { power_power_int( number_number_of_int( X ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = times_times_int(
% 0.89/1.38 number_number_of_int( X ), number_number_of_int( X ) ) }.
% 0.89/1.38 (1668) {G0,W31,D8,L1,V2,M1} { power_power_real( plus_plus_real( X, Y ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_real(
% 0.89/1.38 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.38 ) ) ) ), times_times_real( times_times_real( number267125858f_real( bit0
% 0.89/1.38 ( bit1( pls ) ) ), X ), Y ) ) }.
% 0.89/1.38 (1669) {G0,W31,D8,L1,V2,M1} { power_power_nat( plus_plus_nat( X, Y ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_nat(
% 0.89/1.38 plus_plus_nat( power_power_nat( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), power_power_nat( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ) ), times_times_nat( times_times_nat( number_number_of_nat( bit0( bit1
% 0.89/1.38 ( pls ) ) ), X ), Y ) ) }.
% 0.89/1.38 (1670) {G0,W31,D8,L1,V2,M1} { power_power_int( plus_plus_int( X, Y ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_int(
% 0.89/1.38 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.38 ) ), times_times_int( times_times_int( number_number_of_int( bit0( bit1
% 0.89/1.38 ( pls ) ) ), X ), Y ) ) }.
% 0.89/1.38 (1671) {G0,W11,D5,L1,V1,M1} { number267125858f_real( bit0( X ) ) =
% 0.89/1.38 plus_plus_real( plus_plus_real( zero_zero_real, number267125858f_real( X
% 0.89/1.38 ) ), number267125858f_real( X ) ) }.
% 0.89/1.38 (1672) {G0,W11,D5,L1,V1,M1} { number_number_of_int( bit0( X ) ) =
% 0.89/1.38 plus_plus_int( plus_plus_int( zero_zero_int, number_number_of_int( X ) )
% 0.89/1.38 , number_number_of_int( X ) ) }.
% 0.89/1.38 (1673) {G0,W11,D5,L1,V1,M1} { number267125858f_real( bit1( X ) ) =
% 0.89/1.38 plus_plus_real( plus_plus_real( one_one_real, number267125858f_real( X )
% 0.89/1.38 ), number267125858f_real( X ) ) }.
% 0.89/1.38 (1674) {G0,W11,D5,L1,V1,M1} { number_number_of_int( bit1( X ) ) =
% 0.89/1.38 plus_plus_int( plus_plus_int( one_one_int, number_number_of_int( X ) ),
% 0.89/1.38 number_number_of_int( X ) ) }.
% 0.89/1.38 (1675) {G0,W5,D4,L1,V0,M1} { number267125858f_real( bit1( pls ) ) =
% 0.89/1.38 one_one_real }.
% 0.89/1.38 (1676) {G0,W5,D4,L1,V0,M1} { number_number_of_nat( bit1( pls ) ) =
% 0.89/1.38 one_one_nat }.
% 0.89/1.38 (1677) {G0,W5,D4,L1,V0,M1} { number_number_of_int( bit1( pls ) ) =
% 0.89/1.38 one_one_int }.
% 0.89/1.38 (1678) {G0,W5,D4,L1,V0,M1} { number267125858f_real( bit1( pls ) ) =
% 0.89/1.38 one_one_real }.
% 0.89/1.38 (1679) {G0,W5,D4,L1,V0,M1} { number_number_of_int( bit1( pls ) ) =
% 0.89/1.38 one_one_int }.
% 0.89/1.38 (1680) {G0,W5,D4,L1,V0,M1} { one_one_real = number267125858f_real( bit1(
% 0.89/1.38 pls ) ) }.
% 0.89/1.38 (1681) {G0,W5,D4,L1,V0,M1} { one_one_int = number_number_of_int( bit1( pls
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1682) {G0,W10,D4,L2,V1,M2} { ! ord_less_int( plus_plus_int( plus_plus_int
% 0.89/1.38 ( one_one_int, X ), X ), zero_zero_int ), ord_less_int( X, zero_zero_int
% 0.89/1.38 ) }.
% 0.89/1.38 (1683) {G0,W10,D4,L2,V1,M2} { ! ord_less_int( X, zero_zero_int ),
% 0.89/1.38 ord_less_int( plus_plus_int( plus_plus_int( one_one_int, X ), X ),
% 0.89/1.38 zero_zero_int ) }.
% 0.89/1.38 (1684) {G0,W7,D3,L2,V1,M2} { ! ord_less_real( number267125858f_real( X ),
% 0.89/1.38 zero_zero_real ), ord_less_int( X, pls ) }.
% 0.89/1.38 (1685) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, pls ), ord_less_real(
% 0.89/1.38 number267125858f_real( X ), zero_zero_real ) }.
% 0.89/1.38 (1686) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( number_number_of_int( X ),
% 0.89/1.38 zero_zero_int ), ord_less_int( X, pls ) }.
% 0.89/1.38 (1687) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, pls ), ord_less_int(
% 0.89/1.38 number_number_of_int( X ), zero_zero_int ) }.
% 0.89/1.38 (1688) {G0,W7,D3,L2,V1,M2} { ! ord_less_real( zero_zero_real,
% 0.89/1.38 number267125858f_real( X ) ), ord_less_int( pls, X ) }.
% 0.89/1.38 (1689) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, X ), ord_less_real(
% 0.89/1.38 zero_zero_real, number267125858f_real( X ) ) }.
% 0.89/1.38 (1690) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( zero_zero_int,
% 0.89/1.38 number_number_of_int( X ) ), ord_less_int( pls, X ) }.
% 0.89/1.38 (1691) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( pls, X ), ord_less_int(
% 0.89/1.38 zero_zero_int, number_number_of_int( X ) ) }.
% 0.89/1.38 (1692) {G0,W8,D5,L1,V0,M1} { plus_plus_real( one_one_real, one_one_real )
% 0.89/1.38 = number267125858f_real( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1693) {G0,W8,D5,L1,V0,M1} { plus_plus_nat( one_one_nat, one_one_nat ) =
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1694) {G0,W8,D5,L1,V0,M1} { plus_plus_int( one_one_int, one_one_int ) =
% 0.89/1.38 number_number_of_int( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1695) {G0,W8,D5,L1,V0,M1} { plus_plus_real( one_one_real, one_one_real )
% 0.89/1.38 = number267125858f_real( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1696) {G0,W8,D5,L1,V0,M1} { plus_plus_int( one_one_int, one_one_int ) =
% 0.89/1.38 number_number_of_int( bit0( bit1( pls ) ) ) }.
% 0.89/1.38 (1697) {G0,W8,D3,L2,V1,M2} { ! ord_less_real( number267125858f_real( X ),
% 0.89/1.38 one_one_real ), ord_less_int( X, bit1( pls ) ) }.
% 0.89/1.38 (1698) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( X, bit1( pls ) ),
% 0.89/1.38 ord_less_real( number267125858f_real( X ), one_one_real ) }.
% 0.89/1.38 (1699) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( number_number_of_int( X ),
% 0.89/1.38 one_one_int ), ord_less_int( X, bit1( pls ) ) }.
% 0.89/1.38 (1700) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( X, bit1( pls ) ),
% 0.89/1.38 ord_less_int( number_number_of_int( X ), one_one_int ) }.
% 0.89/1.38 (1701) {G0,W8,D3,L2,V1,M2} { ! ord_less_real( one_one_real,
% 0.89/1.38 number267125858f_real( X ) ), ord_less_int( bit1( pls ), X ) }.
% 0.89/1.38 (1702) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( bit1( pls ), X ),
% 0.89/1.38 ord_less_real( one_one_real, number267125858f_real( X ) ) }.
% 0.89/1.38 (1703) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( one_one_int,
% 0.89/1.38 number_number_of_int( X ) ), ord_less_int( bit1( pls ), X ) }.
% 0.89/1.38 (1704) {G0,W8,D3,L2,V1,M2} { ! ord_less_int( bit1( pls ), X ),
% 0.89/1.38 ord_less_int( one_one_int, number_number_of_int( X ) ) }.
% 0.89/1.38 (1705) {G0,W18,D8,L1,V0,M1} { dvd_dvd_int( plus_plus_int( times_times_int
% 0.89/1.38 ( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.38 , plus_plus_int( power_power_int( s, number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), one_one_int ) ) }.
% 0.89/1.38 (1706) {G0,W50,D11,L1,V2,M1} { power_power_int( plus_plus_int( X, Y ),
% 0.89/1.38 number_number_of_nat( bit1( bit1( pls ) ) ) ) = plus_plus_int(
% 0.89/1.38 plus_plus_int( plus_plus_int( power_power_int( X, number_number_of_nat(
% 0.89/1.38 bit1( bit1( pls ) ) ) ), times_times_int( times_times_int(
% 0.89/1.38 number_number_of_int( bit1( bit1( pls ) ) ), power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), Y ) ), times_times_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit1( bit1( pls ) ) ), X ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ),
% 0.89/1.38 power_power_int( Y, number_number_of_nat( bit1( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1707) {G0,W31,D9,L1,V2,M1} { power_power_int( plus_plus_int( X, Y ),
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_int(
% 0.89/1.38 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.38 ) ) ) ), times_times_int( times_times_int( number_number_of_int( bit0(
% 0.89/1.38 bit1( pls ) ) ), X ), Y ) ), power_power_int( Y, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1708) {G0,W17,D5,L5,V1,M5} { ! is_int( X ), ! ord_less_eq_int(
% 0.89/1.38 zero_zero_int, X ), ! ord_less_int( X, number_number_of_int( bit0( bit1(
% 0.89/1.38 pls ) ) ) ), X = zero_zero_int, X = one_one_int }.
% 0.89/1.38 (1709) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( zero_zero_int, s ) }.
% 0.89/1.38 (1710) {G0,W11,D8,L1,V0,M1} { ord_less_int( s, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1711) {G0,W12,D8,L1,V0,M1} { zcong( s1, s, plus_plus_int( times_times_int
% 0.89/1.38 ( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.38 ) }.
% 0.89/1.38 (1712) {G0,W15,D7,L1,V1,M1} { times_times_int( X, power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit1( bit1( pls ) ) ) ) }.
% 0.89/1.38 (1713) {G0,W8,D6,L1,V1,M1} { ord_less_eq_int( X, power_power_int( X,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.38 (1714) {G0,W16,D4,L4,V3,M4} { ! ord_less_int( zero_zero_int, X ), ! X =
% 0.89/1.38 plus_plus_int( Y, times_times_int( X, Z ) ), ! ord_less_int( Y, X ),
% 0.89/1.38 ord_less_eq_int( one_one_int, Z ) }.
% 0.89/1.38 (1715) {G0,W16,D4,L4,V3,M4} { ! ord_less_int( zero_zero_int, X ), ! X =
% 0.89/1.38 plus_plus_int( Y, times_times_int( X, Z ) ), ! ord_less_eq_int(
% 0.89/1.38 zero_zero_int, Y ), ord_less_eq_int( Z, one_one_int ) }.
% 0.89/1.38 (1716) {G0,W6,D5,L1,V0,M1} { ord_less_eq_int( zero_zero_int,
% 0.89/1.38 number_number_of_int( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.38 (1717) {G0,W16,D7,L1,V2,M1} { power_power_real( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = times_times_real(
% 0.89/1.38 power_power_real( X, Y ), power_power_real( X, Y ) ) }.
% 0.89/1.38 (1718) {G0,W16,D7,L1,V2,M1} { power_power_nat( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = times_times_nat(
% 0.89/1.38 power_power_nat( X, Y ), power_power_nat( X, Y ) ) }.
% 0.89/1.38 (1719) {G0,W16,D7,L1,V2,M1} { power_power_int( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = times_times_int(
% 0.89/1.38 power_power_int( X, Y ), power_power_int( X, Y ) ) }.
% 0.89/1.38 (1720) {G0,W22,D8,L1,V0,M1} { zcong( power_power_int( s,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( s1,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1721) {G0,W2,D2,L1,V0,M1} { is_int( skol2 ) }.
% 0.89/1.38 (1722) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( zero_zero_int, skol2 ) }.
% 0.89/1.38 (1723) {G0,W11,D8,L1,V0,M1} { ord_less_int( skol2, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1724) {G0,W12,D8,L1,V0,M1} { zcong( s1, skol2, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1725) {G0,W31,D8,L5,V1,M5} { ! is_int( X ), ! ord_less_eq_int(
% 0.89/1.38 zero_zero_int, X ), ! ord_less_int( X, plus_plus_int( times_times_int(
% 0.89/1.38 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) )
% 0.89/1.38 , ! zcong( s1, X, plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.38 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ) ), X = skol2 }.
% 0.89/1.38 (1726) {G0,W2,D2,L1,V0,M1} { is_int( skol3 ) }.
% 0.89/1.38 (1727) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( zero_zero_int, skol3 ) }.
% 0.89/1.38 (1728) {G0,W11,D8,L1,V0,M1} { ord_less_int( skol3, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1729) {G0,W12,D8,L1,V0,M1} { zcong( s1, skol3, plus_plus_int(
% 0.89/1.38 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.38 , one_one_int ) ) }.
% 0.89/1.38 (1730) {G0,W18,D8,L1,V0,M1} { zcong( power_power_int( s1,
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ) ), number_number_of_int( min
% 0.89/1.38 ), plus_plus_int( times_times_int( number_number_of_int( bit0( bit0(
% 0.89/1.38 bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.38 (1731) {G0,W11,D3,L3,V2,M3} { ! ord_less_nat( zero_zero_nat,
% 0.89/1.38 power_power_nat( X, Y ) ), Y = zero_zero_nat, ord_less_nat( zero_zero_nat
% 0.89/1.38 , X ) }.
% 0.89/1.38 (1732) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, ord_less_nat(
% 0.89/1.38 zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.38 (1733) {G0,W8,D3,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.38 ord_less_nat( zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.38 (1734) {G0,W10,D3,L3,V3,M3} { ! zprime( X ), ! dvd_dvd_int( X,
% 0.89/1.38 power_power_int( Y, Z ) ), dvd_dvd_int( X, Y ) }.
% 0.89/1.38 (1735) {G0,W11,D4,L1,V3,M1} { power_power_real( power_power_real( X, Y ),
% 0.89/1.38 Z ) = power_power_real( X, times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1736) {G0,W11,D4,L1,V3,M1} { power_power_nat( power_power_nat( X, Y ), Z
% 0.89/1.38 ) = power_power_nat( X, times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1737) {G0,W11,D4,L1,V3,M1} { power_power_int( power_power_int( X, Y ), Z
% 0.89/1.38 ) = power_power_int( X, times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1738) {G0,W17,D3,L4,V4,M4} { ! zprime( X ), dvd_dvd_int( X, Y ), !
% 0.89/1.38 dvd_dvd_int( power_power_int( X, Z ), times_times_int( T, Y ) ),
% 0.89/1.38 dvd_dvd_int( power_power_int( X, Z ), T ) }.
% 0.89/1.38 (1739) {G0,W17,D3,L4,V4,M4} { ! zprime( X ), dvd_dvd_int( X, Y ), !
% 0.89/1.38 dvd_dvd_int( power_power_int( X, Z ), times_times_int( Y, T ) ),
% 0.89/1.38 dvd_dvd_int( power_power_int( X, Z ), T ) }.
% 0.89/1.38 (1740) {G0,W11,D4,L1,V3,M1} { power_power_int( power_power_int( X, Y ), Z
% 0.89/1.38 ) = power_power_int( X, times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1741) {G0,W9,D2,L3,V2,M3} { ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.38 ord_less_int( X, Y ), ! dvd_dvd_int( Y, X ) }.
% 0.89/1.38 (1742) {G0,W19,D2,L7,V2,M7} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.38 ord_less_eq_int( zero_zero_int, Y ), ! ord_less_eq_int( zero_zero_int, X
% 0.89/1.38 ), ! dvd_dvd_int( Y, X ), ! dvd_dvd_int( X, Y ), Y = X }.
% 0.89/1.38 (1743) {G0,W15,D3,L4,V3,M4} { ! is_int( X ), ! dvd_dvd_int(
% 0.89/1.38 times_times_int( X, Y ), times_times_int( X, Z ) ), X = zero_zero_int,
% 0.89/1.38 dvd_dvd_int( Y, Z ) }.
% 0.89/1.38 (1744) {G0,W10,D4,L2,V3,M2} { ! dvd_dvd_int( X, plus_plus_int( Y,
% 0.89/1.38 times_times_int( X, Z ) ) ), dvd_dvd_int( X, Y ) }.
% 0.89/1.38 (1745) {G0,W10,D4,L2,V3,M2} { ! dvd_dvd_int( X, Y ), dvd_dvd_int( X,
% 0.89/1.38 plus_plus_int( Y, times_times_int( X, Z ) ) ) }.
% 0.89/1.38 (1746) {G0,W17,D5,L3,V5,M3} { ! dvd_dvd_int( X, Y ), ! dvd_dvd_int( X,
% 0.89/1.38 plus_plus_int( T, U ) ), dvd_dvd_int( X, plus_plus_int( plus_plus_int( T
% 0.89/1.38 , times_times_int( Z, Y ) ), U ) ) }.
% 0.89/1.38 (1747) {G0,W17,D5,L3,V5,M3} { ! dvd_dvd_int( X, Y ), ! dvd_dvd_int( X,
% 0.89/1.38 plus_plus_int( plus_plus_int( T, times_times_int( Z, Y ) ), U ) ),
% 0.89/1.38 dvd_dvd_int( X, plus_plus_int( T, U ) ) }.
% 0.89/1.38 (1748) {G0,W5,D5,L1,V0,M1} { zprime( number_number_of_int( bit0( bit1( pls
% 0.89/1.38 ) ) ) ) }.
% 0.89/1.38 (1749) {G0,W9,D2,L3,V2,M3} { ! dvd_dvd_int( X, Y ), ! ord_less_int(
% 0.89/1.38 zero_zero_int, Y ), ord_less_eq_int( X, Y ) }.
% 0.89/1.38 (1750) {G0,W8,D3,L3,V2,M3} { ! twoSqu142715416sum2sq( X ), !
% 0.89/1.38 twoSqu142715416sum2sq( Y ), twoSqu142715416sum2sq( times_times_int( X, Y
% 0.89/1.38 ) ) }.
% 0.89/1.38 (1751) {G0,W11,D3,L3,V2,M3} { ! ord_less_eq_nat( number_number_of_nat( X )
% 0.89/1.38 , number_number_of_nat( Y ) ), ord_less_eq_int( X, Y ), ord_less_eq_int(
% 0.89/1.38 X, pls ) }.
% 0.89/1.38 (1752) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, Y ), ord_less_eq_nat(
% 0.89/1.38 number_number_of_nat( X ), number_number_of_nat( Y ) ) }.
% 0.89/1.38 (1753) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, pls ), ord_less_eq_nat
% 0.89/1.38 ( number_number_of_nat( X ), number_number_of_nat( Y ) ) }.
% 0.89/1.38 (1754) {G0,W15,D4,L1,V4,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.38 times_times_real( Z, T ) ) = times_times_real( times_times_real( X, Z ),
% 0.89/1.38 times_times_real( Y, T ) ) }.
% 0.89/1.38 (1755) {G0,W15,D4,L1,V4,M1} { times_times_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, T ) ) = times_times_nat( times_times_nat( X, Z ),
% 0.89/1.38 times_times_nat( Y, T ) ) }.
% 0.89/1.38 (1756) {G0,W15,D4,L1,V4,M1} { times_times_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, T ) ) = times_times_int( times_times_int( X, Z ),
% 0.89/1.38 times_times_int( Y, T ) ) }.
% 0.89/1.38 (1757) {G0,W15,D5,L1,V4,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.38 times_times_real( Z, T ) ) = times_times_real( Z, times_times_real(
% 0.89/1.38 times_times_real( X, Y ), T ) ) }.
% 0.89/1.38 (1758) {G0,W15,D5,L1,V4,M1} { times_times_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, T ) ) = times_times_nat( Z, times_times_nat(
% 0.89/1.38 times_times_nat( X, Y ), T ) ) }.
% 0.89/1.38 (1759) {G0,W15,D5,L1,V4,M1} { times_times_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, T ) ) = times_times_int( Z, times_times_int(
% 0.89/1.38 times_times_int( X, Y ), T ) ) }.
% 0.89/1.38 (1760) {G0,W15,D5,L1,V4,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.38 times_times_real( Z, T ) ) = times_times_real( X, times_times_real( Y,
% 0.89/1.38 times_times_real( Z, T ) ) ) }.
% 0.89/1.38 (1761) {G0,W15,D5,L1,V4,M1} { times_times_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, T ) ) = times_times_nat( X, times_times_nat( Y,
% 0.89/1.38 times_times_nat( Z, T ) ) ) }.
% 0.89/1.38 (1762) {G0,W15,D5,L1,V4,M1} { times_times_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, T ) ) = times_times_int( X, times_times_int( Y,
% 0.89/1.38 times_times_int( Z, T ) ) ) }.
% 0.89/1.38 (1763) {G0,W11,D4,L1,V3,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.38 Z ) = times_times_real( times_times_real( X, Z ), Y ) }.
% 0.89/1.38 (1764) {G0,W11,D4,L1,V3,M1} { times_times_nat( times_times_nat( X, Y ), Z
% 0.89/1.38 ) = times_times_nat( times_times_nat( X, Z ), Y ) }.
% 0.89/1.38 (1765) {G0,W11,D4,L1,V3,M1} { times_times_int( times_times_int( X, Y ), Z
% 0.89/1.38 ) = times_times_int( times_times_int( X, Z ), Y ) }.
% 0.89/1.38 (1766) {G0,W11,D4,L1,V3,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.38 Z ) = times_times_real( X, times_times_real( Y, Z ) ) }.
% 0.89/1.38 (1767) {G0,W11,D4,L1,V3,M1} { times_times_nat( times_times_nat( X, Y ), Z
% 0.89/1.38 ) = times_times_nat( X, times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1768) {G0,W11,D4,L1,V3,M1} { times_times_int( times_times_int( X, Y ), Z
% 0.89/1.38 ) = times_times_int( X, times_times_int( Y, Z ) ) }.
% 0.89/1.38 (1769) {G0,W11,D4,L1,V3,M1} { times_times_real( X, times_times_real( Y, Z
% 0.89/1.38 ) ) = times_times_real( times_times_real( X, Y ), Z ) }.
% 0.89/1.38 (1770) {G0,W11,D4,L1,V3,M1} { times_times_nat( X, times_times_nat( Y, Z )
% 0.89/1.38 ) = times_times_nat( times_times_nat( X, Y ), Z ) }.
% 0.89/1.38 (1771) {G0,W11,D4,L1,V3,M1} { times_times_int( X, times_times_int( Y, Z )
% 0.89/1.38 ) = times_times_int( times_times_int( X, Y ), Z ) }.
% 0.89/1.38 (1772) {G0,W11,D4,L1,V3,M1} { times_times_real( X, times_times_real( Y, Z
% 0.89/1.38 ) ) = times_times_real( Y, times_times_real( X, Z ) ) }.
% 0.89/1.38 (1773) {G0,W11,D4,L1,V3,M1} { times_times_nat( X, times_times_nat( Y, Z )
% 0.89/1.38 ) = times_times_nat( Y, times_times_nat( X, Z ) ) }.
% 0.89/1.38 (1774) {G0,W11,D4,L1,V3,M1} { times_times_int( X, times_times_int( Y, Z )
% 0.89/1.38 ) = times_times_int( Y, times_times_int( X, Z ) ) }.
% 0.89/1.38 (1775) {G0,W7,D3,L1,V2,M1} { times_times_real( X, Y ) = times_times_real(
% 0.89/1.38 Y, X ) }.
% 0.89/1.38 (1776) {G0,W7,D3,L1,V2,M1} { times_times_nat( X, Y ) = times_times_nat( Y
% 0.89/1.38 , X ) }.
% 0.89/1.38 (1777) {G0,W7,D3,L1,V2,M1} { times_times_int( X, Y ) = times_times_int( Y
% 0.89/1.38 , X ) }.
% 0.89/1.38 (1778) {G0,W7,D3,L1,V2,M1} { plus_plus_real( X, Y ) = plus_plus_real( Y, X
% 0.89/1.38 ) }.
% 0.89/1.38 (1779) {G0,W7,D3,L1,V2,M1} { plus_plus_nat( X, Y ) = plus_plus_nat( Y, X )
% 0.89/1.38 }.
% 0.89/1.38 (1780) {G0,W7,D3,L1,V2,M1} { plus_plus_int( X, Y ) = plus_plus_int( Y, X )
% 0.89/1.38 }.
% 0.89/1.38 (1781) {G0,W11,D4,L1,V3,M1} { plus_plus_real( X, plus_plus_real( Y, Z ) )
% 0.89/1.38 = plus_plus_real( Y, plus_plus_real( X, Z ) ) }.
% 0.89/1.38 (1782) {G0,W11,D4,L1,V3,M1} { plus_plus_nat( X, plus_plus_nat( Y, Z ) ) =
% 0.89/1.38 plus_plus_nat( Y, plus_plus_nat( X, Z ) ) }.
% 0.89/1.38 (1783) {G0,W11,D4,L1,V3,M1} { plus_plus_int( X, plus_plus_int( Y, Z ) ) =
% 0.89/1.38 plus_plus_int( Y, plus_plus_int( X, Z ) ) }.
% 0.89/1.38 (1784) {G0,W11,D4,L1,V3,M1} { plus_plus_real( X, plus_plus_real( Y, Z ) )
% 0.89/1.38 = plus_plus_real( plus_plus_real( X, Y ), Z ) }.
% 0.89/1.38 (1785) {G0,W11,D4,L1,V3,M1} { plus_plus_nat( X, plus_plus_nat( Y, Z ) ) =
% 0.89/1.38 plus_plus_nat( plus_plus_nat( X, Y ), Z ) }.
% 0.89/1.38 (1786) {G0,W11,D4,L1,V3,M1} { plus_plus_int( X, plus_plus_int( Y, Z ) ) =
% 0.89/1.38 plus_plus_int( plus_plus_int( X, Y ), Z ) }.
% 0.89/1.38 (1787) {G0,W11,D4,L1,V3,M1} { plus_plus_real( plus_plus_real( X, Y ), Z )
% 0.89/1.38 = plus_plus_real( X, plus_plus_real( Y, Z ) ) }.
% 0.89/1.38 (1788) {G0,W11,D4,L1,V3,M1} { plus_plus_nat( plus_plus_nat( X, Y ), Z ) =
% 0.89/1.38 plus_plus_nat( X, plus_plus_nat( Y, Z ) ) }.
% 0.89/1.38 (1789) {G0,W11,D4,L1,V3,M1} { plus_plus_int( plus_plus_int( X, Y ), Z ) =
% 0.89/1.38 plus_plus_int( X, plus_plus_int( Y, Z ) ) }.
% 0.89/1.38 (1790) {G0,W11,D4,L1,V3,M1} { plus_plus_real( plus_plus_real( X, Y ), Z )
% 0.89/1.38 = plus_plus_real( plus_plus_real( X, Z ), Y ) }.
% 0.89/1.38 (1791) {G0,W11,D4,L1,V3,M1} { plus_plus_nat( plus_plus_nat( X, Y ), Z ) =
% 0.89/1.38 plus_plus_nat( plus_plus_nat( X, Z ), Y ) }.
% 0.89/1.38 (1792) {G0,W11,D4,L1,V3,M1} { plus_plus_int( plus_plus_int( X, Y ), Z ) =
% 0.89/1.38 plus_plus_int( plus_plus_int( X, Z ), Y ) }.
% 0.89/1.38 (1793) {G0,W15,D4,L1,V4,M1} { plus_plus_real( plus_plus_real( X, Y ),
% 0.89/1.38 plus_plus_real( Z, T ) ) = plus_plus_real( plus_plus_real( X, Z ),
% 0.89/1.38 plus_plus_real( Y, T ) ) }.
% 0.89/1.38 (1794) {G0,W15,D4,L1,V4,M1} { plus_plus_nat( plus_plus_nat( X, Y ),
% 0.89/1.38 plus_plus_nat( Z, T ) ) = plus_plus_nat( plus_plus_nat( X, Z ),
% 0.89/1.38 plus_plus_nat( Y, T ) ) }.
% 0.89/1.38 (1795) {G0,W15,D4,L1,V4,M1} { plus_plus_int( plus_plus_int( X, Y ),
% 0.89/1.38 plus_plus_int( Z, T ) ) = plus_plus_int( plus_plus_int( X, Z ),
% 0.89/1.38 plus_plus_int( Y, T ) ) }.
% 0.89/1.38 (1796) {G0,W5,D3,L1,V1,M1} { power_power_real( X, one_one_nat ) = X }.
% 0.89/1.38 (1797) {G0,W5,D3,L1,V1,M1} { power_power_nat( X, one_one_nat ) = X }.
% 0.89/1.38 (1798) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), power_power_int( X,
% 0.89/1.38 one_one_nat ) = X }.
% 0.89/1.38 (1799) {G0,W13,D4,L3,V2,M3} { ! ord_less_nat( zero_zero_nat,
% 0.89/1.38 power_power_nat( X, number_number_of_nat( Y ) ) ), number_number_of_nat(
% 0.89/1.38 Y ) = zero_zero_nat, ord_less_nat( zero_zero_nat, X ) }.
% 0.89/1.38 (1800) {G0,W10,D4,L2,V2,M2} { ! number_number_of_nat( Y ) = zero_zero_nat
% 0.89/1.38 , ord_less_nat( zero_zero_nat, power_power_nat( X, number_number_of_nat(
% 0.89/1.38 Y ) ) ) }.
% 0.89/1.38 (1801) {G0,W9,D4,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.38 ord_less_nat( zero_zero_nat, power_power_nat( X, number_number_of_nat( Y
% 0.89/1.38 ) ) ) }.
% 0.89/1.38 (1802) {G0,W10,D6,L1,V1,M1} { times_times_nat( X, number_number_of_nat(
% 0.89/1.38 bit0( bit1( pls ) ) ) ) = plus_plus_nat( X, X ) }.
% 0.89/1.38 (1803) {G0,W10,D6,L1,V1,M1} { times_times_nat( number_number_of_nat( bit0
% 0.89/1.38 ( bit1( pls ) ) ), X ) = plus_plus_nat( X, X ) }.
% 0.89/1.38 (1804) {G0,W10,D4,L2,V2,M2} { ! ord_less_int( Y, pls ), times_times_nat(
% 0.89/1.38 number_number_of_nat( Y ), number_number_of_nat( X ) ) = zero_zero_nat
% 0.89/1.38 }.
% 0.89/1.38 (1805) {G0,W13,D4,L2,V2,M2} { ord_less_int( Y, pls ), times_times_nat(
% 0.89/1.38 number_number_of_nat( Y ), number_number_of_nat( X ) ) =
% 0.89/1.38 number_number_of_nat( times_times_int( Y, X ) ) }.
% 0.89/1.38 (1806) {G0,W12,D5,L2,V3,M2} { ! ord_less_int( Z, pls ), times_times_nat(
% 0.89/1.38 number_number_of_nat( Z ), times_times_nat( number_number_of_nat( X ), Y
% 0.89/1.38 ) ) = zero_zero_nat }.
% 0.89/1.38 (1807) {G0,W17,D5,L2,V3,M2} { ord_less_int( Z, pls ), times_times_nat(
% 0.89/1.38 number_number_of_nat( Z ), times_times_nat( number_number_of_nat( X ), Y
% 0.89/1.38 ) ) = times_times_nat( number_number_of_nat( times_times_int( Z, X ) ),
% 0.89/1.38 Y ) }.
% 0.89/1.38 (1808) {G0,W17,D7,L1,V2,M1} { power_power_real( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = power_power_real(
% 0.89/1.38 power_power_real( X, Y ), number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1809) {G0,W17,D7,L1,V2,M1} { power_power_nat( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = power_power_nat(
% 0.89/1.38 power_power_nat( X, Y ), number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1810) {G0,W17,D7,L1,V2,M1} { power_power_int( X, times_times_nat(
% 0.89/1.38 number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ) = power_power_int(
% 0.89/1.38 power_power_int( X, Y ), number_number_of_nat( bit0( bit1( pls ) ) ) )
% 0.89/1.38 }.
% 0.89/1.38 (1811) {G0,W13,D7,L2,V2,M2} { ! ord_less_eq_real( power_power_real( X,
% 0.89/1.38 times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), Y ) ),
% 0.89/1.38 zero_zero_real ), X = zero_zero_real }.
% 0.89/1.38 (1812) {G0,W15,D7,L3,V2,M3} { ! is_int( X ), ! ord_less_eq_int(
% 0.89/1.38 power_power_int( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.38 pls ) ) ), Y ) ), zero_zero_int ), X = zero_zero_int }.
% 0.89/1.38 (1813) {G0,W5,D3,L1,V1,M1} { times_times_real( zero_zero_real, X ) =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1814) {G0,W5,D3,L1,V1,M1} { times_times_nat( zero_zero_nat, X ) =
% 0.89/1.38 zero_zero_nat }.
% 0.89/1.38 (1815) {G0,W5,D3,L1,V1,M1} { times_times_int( zero_zero_int, X ) =
% 0.89/1.38 zero_zero_int }.
% 0.89/1.38 (1816) {G0,W5,D3,L1,V1,M1} { times_times_real( X, zero_zero_real ) =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1817) {G0,W5,D3,L1,V1,M1} { times_times_nat( X, zero_zero_nat ) =
% 0.89/1.38 zero_zero_nat }.
% 0.89/1.38 (1818) {G0,W5,D3,L1,V1,M1} { times_times_int( X, zero_zero_int ) =
% 0.89/1.38 zero_zero_int }.
% 0.89/1.38 (1819) {G0,W5,D3,L1,V1,M1} { plus_plus_real( zero_zero_real, X ) = X }.
% 0.89/1.38 (1820) {G0,W5,D3,L1,V1,M1} { plus_plus_nat( zero_zero_nat, X ) = X }.
% 0.89/1.38 (1821) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( zero_zero_int,
% 0.89/1.38 X ) = X }.
% 0.89/1.38 (1822) {G0,W5,D3,L1,V1,M1} { plus_plus_real( X, zero_zero_real ) = X }.
% 0.89/1.38 (1823) {G0,W5,D3,L1,V1,M1} { plus_plus_nat( X, zero_zero_nat ) = X }.
% 0.89/1.38 (1824) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), plus_plus_int( X,
% 0.89/1.38 zero_zero_int ) = X }.
% 0.89/1.38 (1825) {G0,W8,D3,L2,V2,M2} { ! X = plus_plus_real( X, Y ), Y =
% 0.89/1.38 zero_zero_real }.
% 0.89/1.38 (1826) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_real, X = plus_plus_real( X,
% 0.89/1.38 Y ) }.
% 0.89/1.38 (1827) {G0,W8,D3,L2,V2,M2} { ! X = plus_plus_nat( X, Y ), Y =
% 0.89/1.38 zero_zero_nat }.
% 0.89/1.38 (1828) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, X = plus_plus_nat( X, Y
% 0.89/1.38 ) }.
% 0.89/1.38 (1829) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X =
% 0.89/1.38 plus_plus_int( X, Y ), Y = zero_zero_int }.
% 0.89/1.38 (1830) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! Y =
% 0.89/1.38 zero_zero_int, X = plus_plus_int( X, Y ) }.
% 0.89/1.38 (1831) {G0,W13,D4,L1,V3,M1} { times_times_real( X, plus_plus_real( Y, Z )
% 0.89/1.38 ) = plus_plus_real( times_times_real( X, Y ), times_times_real( X, Z ) )
% 0.89/1.38 }.
% 0.89/1.38 (1832) {G0,W13,D4,L1,V3,M1} { times_times_nat( X, plus_plus_nat( Y, Z ) )
% 0.89/1.38 = plus_plus_nat( times_times_nat( X, Y ), times_times_nat( X, Z ) ) }.
% 0.89/1.38 (1833) {G0,W13,D4,L1,V3,M1} { times_times_int( X, plus_plus_int( Y, Z ) )
% 0.89/1.38 = plus_plus_int( times_times_int( X, Y ), times_times_int( X, Z ) ) }.
% 0.89/1.38 (1834) {G0,W21,D4,L3,V4,M3} { Z = T, X = Y, ! plus_plus_real(
% 0.89/1.38 times_times_real( Z, X ), times_times_real( T, Y ) ) = plus_plus_real(
% 0.89/1.38 times_times_real( Z, Y ), times_times_real( T, X ) ) }.
% 0.89/1.38 (1835) {G0,W18,D4,L2,V4,M2} { plus_plus_real( times_times_real( Z, X ),
% 0.89/1.38 times_times_real( T, Y ) ) = plus_plus_real( times_times_real( Z, Y ),
% 0.89/1.38 times_times_real( T, X ) ), ! Z = T }.
% 0.89/1.38 (1836) {G0,W18,D4,L2,V4,M2} { plus_plus_real( times_times_real( Z, X ),
% 0.89/1.38 times_times_real( T, Y ) ) = plus_plus_real( times_times_real( Z, Y ),
% 0.89/1.38 times_times_real( T, X ) ), ! X = Y }.
% 0.89/1.38 (1837) {G0,W21,D4,L3,V4,M3} { Z = T, X = Y, ! plus_plus_nat(
% 0.89/1.38 times_times_nat( Z, X ), times_times_nat( T, Y ) ) = plus_plus_nat(
% 0.89/1.38 times_times_nat( Z, Y ), times_times_nat( T, X ) ) }.
% 0.89/1.38 (1838) {G0,W18,D4,L2,V4,M2} { plus_plus_nat( times_times_nat( Z, X ),
% 0.89/1.38 times_times_nat( T, Y ) ) = plus_plus_nat( times_times_nat( Z, Y ),
% 0.89/1.38 times_times_nat( T, X ) ), ! Z = T }.
% 0.89/1.38 (1839) {G0,W18,D4,L2,V4,M2} { plus_plus_nat( times_times_nat( Z, X ),
% 0.89/1.38 times_times_nat( T, Y ) ) = plus_plus_nat( times_times_nat( Z, Y ),
% 0.89/1.38 times_times_nat( T, X ) ), ! X = Y }.
% 0.89/1.38 (1840) {G0,W29,D4,L7,V4,M7} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), Z = T, X = Y, ! plus_plus_int( times_times_int( Z, X ),
% 0.89/1.38 times_times_int( T, Y ) ) = plus_plus_int( times_times_int( Z, Y ),
% 0.89/1.38 times_times_int( T, X ) ) }.
% 0.89/1.38 (1841) {G0,W26,D4,L6,V4,M6} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), plus_plus_int( times_times_int( Z, X ), times_times_int
% 0.89/1.38 ( T, Y ) ) = plus_plus_int( times_times_int( Z, Y ), times_times_int( T,
% 0.89/1.38 X ) ), ! Z = T }.
% 0.89/1.38 (1842) {G0,W26,D4,L6,V4,M6} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), plus_plus_int( times_times_int( Z, X ), times_times_int
% 0.89/1.38 ( T, Y ) ) = plus_plus_int( times_times_int( Z, Y ), times_times_int( T,
% 0.89/1.38 X ) ), ! X = Y }.
% 0.89/1.38 (1843) {G0,W13,D4,L1,V3,M1} { times_times_real( plus_plus_real( X, Y ), Z
% 0.89/1.38 ) = plus_plus_real( times_times_real( X, Z ), times_times_real( Y, Z ) )
% 0.89/1.38 }.
% 0.89/1.38 (1844) {G0,W13,D4,L1,V3,M1} { times_times_nat( plus_plus_nat( X, Y ), Z )
% 0.89/1.38 = plus_plus_nat( times_times_nat( X, Z ), times_times_nat( Y, Z ) ) }.
% 0.89/1.38 (1845) {G0,W13,D4,L1,V3,M1} { times_times_int( plus_plus_int( X, Y ), Z )
% 0.89/1.38 = plus_plus_int( times_times_int( X, Z ), times_times_int( Y, Z ) ) }.
% 0.89/1.38 (1846) {G0,W13,D4,L1,V3,M1} { plus_plus_real( times_times_real( X, Y ),
% 0.89/1.38 times_times_real( Z, Y ) ) = times_times_real( plus_plus_real( X, Z ), Y
% 0.89/1.38 ) }.
% 0.89/1.38 (1847) {G0,W13,D4,L1,V3,M1} { plus_plus_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, Y ) ) = times_times_nat( plus_plus_nat( X, Z ), Y )
% 0.89/1.38 }.
% 0.89/1.38 (1848) {G0,W13,D4,L1,V3,M1} { plus_plus_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, Y ) ) = times_times_int( plus_plus_int( X, Z ), Y )
% 0.89/1.38 }.
% 0.89/1.38 (1849) {G0,W21,D4,L3,V4,M3} { ! plus_plus_real( times_times_real( X, Y ),
% 0.89/1.38 times_times_real( Z, T ) ) = plus_plus_real( times_times_real( X, T ),
% 0.89/1.38 times_times_real( Z, Y ) ), X = Z, Y = T }.
% 0.89/1.38 (1850) {G0,W18,D4,L2,V4,M2} { ! X = Z, plus_plus_real( times_times_real( X
% 0.89/1.38 , Y ), times_times_real( Z, T ) ) = plus_plus_real( times_times_real( X,
% 0.89/1.38 T ), times_times_real( Z, Y ) ) }.
% 0.89/1.38 (1851) {G0,W18,D4,L2,V4,M2} { ! Y = T, plus_plus_real( times_times_real( X
% 0.89/1.38 , Y ), times_times_real( Z, T ) ) = plus_plus_real( times_times_real( X,
% 0.89/1.38 T ), times_times_real( Z, Y ) ) }.
% 0.89/1.38 (1852) {G0,W21,D4,L3,V4,M3} { ! plus_plus_nat( times_times_nat( X, Y ),
% 0.89/1.38 times_times_nat( Z, T ) ) = plus_plus_nat( times_times_nat( X, T ),
% 0.89/1.38 times_times_nat( Z, Y ) ), X = Z, Y = T }.
% 0.89/1.38 (1853) {G0,W18,D4,L2,V4,M2} { ! X = Z, plus_plus_nat( times_times_nat( X,
% 0.89/1.38 Y ), times_times_nat( Z, T ) ) = plus_plus_nat( times_times_nat( X, T ),
% 0.89/1.38 times_times_nat( Z, Y ) ) }.
% 0.89/1.38 (1854) {G0,W18,D4,L2,V4,M2} { ! Y = T, plus_plus_nat( times_times_nat( X,
% 0.89/1.38 Y ), times_times_nat( Z, T ) ) = plus_plus_nat( times_times_nat( X, T ),
% 0.89/1.38 times_times_nat( Z, Y ) ) }.
% 0.89/1.38 (1855) {G0,W29,D4,L7,V4,M7} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), ! plus_plus_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, T ) ) = plus_plus_int( times_times_int( X, T ),
% 0.89/1.38 times_times_int( Z, Y ) ), X = Z, Y = T }.
% 0.89/1.38 (1856) {G0,W26,D4,L6,V4,M6} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), ! X = Z, plus_plus_int( times_times_int( X, Y ),
% 0.89/1.38 times_times_int( Z, T ) ) = plus_plus_int( times_times_int( X, T ),
% 0.89/1.38 times_times_int( Z, Y ) ) }.
% 0.89/1.38 (1857) {G0,W26,D4,L6,V4,M6} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.38 , ! is_int( T ), ! Y = T, plus_plus_int( times_times_int( X, Y ),
% 0.89/1.39 times_times_int( Z, T ) ) = plus_plus_int( times_times_int( X, T ),
% 0.89/1.39 times_times_int( Z, Y ) ) }.
% 0.89/1.39 (1858) {G0,W5,D3,L1,V1,M1} { times_times_real( one_one_real, X ) = X }.
% 0.89/1.39 (1859) {G0,W5,D3,L1,V1,M1} { times_times_nat( one_one_nat, X ) = X }.
% 0.89/1.39 (1860) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), times_times_int( one_one_int,
% 0.89/1.39 X ) = X }.
% 0.89/1.39 (1861) {G0,W5,D3,L1,V1,M1} { times_times_real( X, one_one_real ) = X }.
% 0.89/1.39 (1862) {G0,W5,D3,L1,V1,M1} { times_times_nat( X, one_one_nat ) = X }.
% 0.89/1.39 (1863) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), times_times_int( X,
% 0.89/1.39 one_one_int ) = X }.
% 0.89/1.39 (1864) {G0,W13,D4,L1,V3,M1} { power_power_real( times_times_real( X, Y ),
% 0.89/1.39 Z ) = times_times_real( power_power_real( X, Z ), power_power_real( Y, Z
% 0.89/1.39 ) ) }.
% 0.89/1.39 (1865) {G0,W13,D4,L1,V3,M1} { power_power_nat( times_times_nat( X, Y ), Z
% 0.89/1.39 ) = times_times_nat( power_power_nat( X, Z ), power_power_nat( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (1866) {G0,W13,D4,L1,V3,M1} { power_power_int( times_times_int( X, Y ), Z
% 0.89/1.39 ) = times_times_int( power_power_int( X, Z ), power_power_int( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (1867) {G0,W13,D4,L1,V3,M1} { times_times_real( power_power_real( X, Y ),
% 0.89/1.39 power_power_real( X, Z ) ) = power_power_real( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (1868) {G0,W13,D4,L1,V3,M1} { times_times_nat( power_power_nat( X, Y ),
% 0.89/1.39 power_power_nat( X, Z ) ) = power_power_nat( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (1869) {G0,W13,D4,L1,V3,M1} { times_times_int( power_power_int( X, Y ),
% 0.89/1.39 power_power_int( X, Z ) ) = power_power_int( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (1870) {G0,W5,D3,L1,V1,M1} { power_power_real( X, zero_zero_nat ) =
% 0.89/1.39 one_one_real }.
% 0.89/1.39 (1871) {G0,W5,D3,L1,V1,M1} { power_power_nat( X, zero_zero_nat ) =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (1872) {G0,W5,D3,L1,V1,M1} { power_power_int( X, zero_zero_nat ) =
% 0.89/1.39 one_one_int }.
% 0.89/1.39 (1873) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( zero_zero_int, zero_zero_int
% 0.89/1.39 ) }.
% 0.89/1.39 (1874) {G0,W10,D7,L1,V2,M1} { ord_less_eq_real( zero_zero_real,
% 0.89/1.39 power_power_real( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ), Y ) ) ) }.
% 0.89/1.39 (1875) {G0,W10,D7,L1,V2,M1} { ord_less_eq_int( zero_zero_int,
% 0.89/1.39 power_power_int( X, times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ), Y ) ) ) }.
% 0.89/1.39 (1876) {G0,W20,D4,L4,V5,M4} { X = zero_zero_real, ! T = U, Y = Z, !
% 0.89/1.39 plus_plus_real( T, times_times_real( X, Y ) ) = plus_plus_real( U,
% 0.89/1.39 times_times_real( X, Z ) ) }.
% 0.89/1.39 (1877) {G0,W20,D4,L4,V5,M4} { X = zero_zero_nat, ! T = U, Y = Z, !
% 0.89/1.39 plus_plus_nat( T, times_times_nat( X, Y ) ) = plus_plus_nat( U,
% 0.89/1.39 times_times_nat( X, Z ) ) }.
% 0.89/1.39 (1878) {G0,W26,D4,L7,V5,M7} { ! is_int( X ), ! is_int( Y ), ! is_int( Z )
% 0.89/1.39 , Z = zero_zero_int, ! T = U, X = Y, ! plus_plus_int( T, times_times_int
% 0.89/1.39 ( Z, X ) ) = plus_plus_int( U, times_times_int( Z, Y ) ) }.
% 0.89/1.39 (1879) {G0,W9,D4,L1,V1,M1} { plus_plus_real( X, X ) = times_times_real(
% 0.89/1.39 plus_plus_real( one_one_real, one_one_real ), X ) }.
% 0.89/1.39 (1880) {G0,W9,D4,L1,V1,M1} { plus_plus_nat( X, X ) = times_times_nat(
% 0.89/1.39 plus_plus_nat( one_one_nat, one_one_nat ), X ) }.
% 0.89/1.39 (1881) {G0,W9,D4,L1,V1,M1} { plus_plus_int( X, X ) = times_times_int(
% 0.89/1.39 plus_plus_int( one_one_int, one_one_int ), X ) }.
% 0.89/1.39 (1882) {G0,W11,D4,L1,V2,M1} { plus_plus_real( X, times_times_real( Y, X )
% 0.89/1.39 ) = times_times_real( plus_plus_real( Y, one_one_real ), X ) }.
% 0.89/1.39 (1883) {G0,W11,D4,L1,V2,M1} { plus_plus_nat( X, times_times_nat( Y, X ) )
% 0.89/1.39 = times_times_nat( plus_plus_nat( Y, one_one_nat ), X ) }.
% 0.89/1.39 (1884) {G0,W11,D4,L1,V2,M1} { plus_plus_int( X, times_times_int( Y, X ) )
% 0.89/1.39 = times_times_int( plus_plus_int( Y, one_one_int ), X ) }.
% 0.89/1.39 (1885) {G0,W11,D4,L1,V2,M1} { plus_plus_real( times_times_real( X, Y ), Y
% 0.89/1.39 ) = times_times_real( plus_plus_real( X, one_one_real ), Y ) }.
% 0.89/1.39 (1886) {G0,W11,D4,L1,V2,M1} { plus_plus_nat( times_times_nat( X, Y ), Y )
% 0.89/1.39 = times_times_nat( plus_plus_nat( X, one_one_nat ), Y ) }.
% 0.89/1.39 (1887) {G0,W11,D4,L1,V2,M1} { plus_plus_int( times_times_int( X, Y ), Y )
% 0.89/1.39 = times_times_int( plus_plus_int( X, one_one_int ), Y ) }.
% 0.89/1.39 (1888) {G0,W9,D4,L2,V2,M2} { ! power_power_real( X, number_number_of_nat(
% 0.89/1.39 Y ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.39 (1889) {G0,W10,D4,L2,V2,M2} { ! power_power_real( X, number_number_of_nat
% 0.89/1.39 ( Y ) ) = zero_zero_real, ! number_number_of_nat( Y ) = zero_zero_nat }.
% 0.89/1.39 (1890) {G0,W13,D4,L3,V2,M3} { ! X = zero_zero_real, number_number_of_nat(
% 0.89/1.39 Y ) = zero_zero_nat, power_power_real( X, number_number_of_nat( Y ) ) =
% 0.89/1.39 zero_zero_real }.
% 0.89/1.39 (1891) {G0,W9,D4,L2,V2,M2} { ! power_power_nat( X, number_number_of_nat( Y
% 0.89/1.39 ) ) = zero_zero_nat, X = zero_zero_nat }.
% 0.89/1.39 (1892) {G0,W10,D4,L2,V2,M2} { ! power_power_nat( X, number_number_of_nat(
% 0.89/1.39 Y ) ) = zero_zero_nat, ! number_number_of_nat( Y ) = zero_zero_nat }.
% 0.89/1.39 (1893) {G0,W13,D4,L3,V2,M3} { ! X = zero_zero_nat, number_number_of_nat( Y
% 0.89/1.39 ) = zero_zero_nat, power_power_nat( X, number_number_of_nat( Y ) ) =
% 0.89/1.39 zero_zero_nat }.
% 0.89/1.39 (1894) {G0,W11,D4,L3,V2,M3} { ! is_int( X ), ! power_power_int( X,
% 0.89/1.39 number_number_of_nat( Y ) ) = zero_zero_int, X = zero_zero_int }.
% 0.89/1.39 (1895) {G0,W12,D4,L3,V2,M3} { ! is_int( X ), ! power_power_int( X,
% 0.89/1.39 number_number_of_nat( Y ) ) = zero_zero_int, ! number_number_of_nat( Y )
% 0.89/1.39 = zero_zero_nat }.
% 0.89/1.39 (1896) {G0,W15,D4,L4,V2,M4} { ! is_int( X ), ! X = zero_zero_int,
% 0.89/1.39 number_number_of_nat( Y ) = zero_zero_nat, power_power_int( X,
% 0.89/1.39 number_number_of_nat( Y ) ) = zero_zero_int }.
% 0.89/1.39 (1897) {G0,W11,D3,L3,V2,M3} { ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_int( zero_zero_int, times_times_int( X, Y ) ), ord_less_int(
% 0.89/1.39 zero_zero_int, Y ) }.
% 0.89/1.39 (1898) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( zero_zero_int, one_one_int )
% 0.89/1.39 }.
% 0.89/1.39 (1899) {G0,W11,D3,L3,V2,M3} { ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_eq_int( zero_zero_int, Y ), ord_less_eq_int( zero_zero_int,
% 0.89/1.39 times_times_int( X, Y ) ) }.
% 0.89/1.39 (1900) {G0,W11,D3,L3,V2,M3} { ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_eq_int( zero_zero_int, Y ), ord_less_eq_int( zero_zero_int,
% 0.89/1.39 plus_plus_int( X, Y ) ) }.
% 0.89/1.39 (1901) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( zero_zero_int, X ),
% 0.89/1.39 ord_less_eq_int( zero_zero_int, power_power_int( X, Y ) ) }.
% 0.89/1.39 (1902) {G0,W10,D4,L2,V1,M2} { ! number_number_of_nat( X ) = zero_zero_nat
% 0.89/1.39 , power_power_real( zero_zero_real, number_number_of_nat( X ) ) =
% 0.89/1.39 one_one_real }.
% 0.89/1.39 (1903) {G0,W10,D4,L2,V1,M2} { number_number_of_nat( X ) = zero_zero_nat,
% 0.89/1.39 power_power_real( zero_zero_real, number_number_of_nat( X ) ) =
% 0.89/1.39 zero_zero_real }.
% 0.89/1.39 (1904) {G0,W10,D4,L2,V1,M2} { ! number_number_of_nat( X ) = zero_zero_nat
% 0.89/1.39 , power_power_nat( zero_zero_nat, number_number_of_nat( X ) ) =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (1905) {G0,W10,D4,L2,V1,M2} { number_number_of_nat( X ) = zero_zero_nat,
% 0.89/1.39 power_power_nat( zero_zero_nat, number_number_of_nat( X ) ) =
% 0.89/1.39 zero_zero_nat }.
% 0.89/1.39 (1906) {G0,W10,D4,L2,V1,M2} { ! number_number_of_nat( X ) = zero_zero_nat
% 0.89/1.39 , power_power_int( zero_zero_int, number_number_of_nat( X ) ) =
% 0.89/1.39 one_one_int }.
% 0.89/1.39 (1907) {G0,W10,D4,L2,V1,M2} { number_number_of_nat( X ) = zero_zero_nat,
% 0.89/1.39 power_power_int( zero_zero_int, number_number_of_nat( X ) ) =
% 0.89/1.39 zero_zero_int }.
% 0.89/1.39 (1908) {G0,W6,D5,L1,V0,M1} { ord_less_eq_int( zero_zero_int,
% 0.89/1.39 number_number_of_int( bit1( bit1( pls ) ) ) ) }.
% 0.89/1.39 (1909) {G0,W16,D4,L4,V3,M4} { ! ord_less_eq_int( zero_zero_int,
% 0.89/1.39 plus_plus_int( times_times_int( X, Y ), Z ) ), ! ord_less_int( Z, X ), !
% 0.89/1.39 ord_less_int( zero_zero_int, X ), ord_less_eq_int( zero_zero_int, Y ) }.
% 0.89/1.39 (1910) {G0,W16,D4,L4,V3,M4} { ! ord_less_int( plus_plus_int(
% 0.89/1.39 times_times_int( X, Y ), Z ), zero_zero_int ), ! ord_less_eq_int(
% 0.89/1.39 zero_zero_int, Z ), ! ord_less_int( zero_zero_int, X ), ord_less_eq_int(
% 0.89/1.39 Y, zero_zero_int ) }.
% 0.89/1.39 (1911) {G0,W23,D4,L5,V5,M5} { ! ord_less_eq_int( plus_plus_int(
% 0.89/1.39 times_times_int( X, Y ), Z ), plus_plus_int( times_times_int( X, T ), U )
% 0.89/1.39 ), ! ord_less_eq_int( zero_zero_int, Z ), ! ord_less_int( Z, X ), !
% 0.89/1.39 ord_less_int( U, X ), ord_less_eq_int( Y, T ) }.
% 0.89/1.39 (1912) {G0,W33,D4,L7,V6,M7} { ! plus_plus_int( times_times_int( X, Y ), Z
% 0.89/1.39 ) = plus_plus_int( times_times_int( T, U ), W ), ! ord_less_eq_int(
% 0.89/1.39 zero_zero_int, plus_plus_int( times_times_int( T, U ), W ) ), !
% 0.89/1.39 ord_less_int( W, T ), ! ord_less_eq_int( zero_zero_int, Z ), !
% 0.89/1.39 ord_less_int( zero_zero_int, T ), ! ord_less_eq_int( T, X ),
% 0.89/1.39 ord_less_eq_int( Y, U ) }.
% 0.89/1.39 (1913) {G0,W23,D4,L5,V5,M5} { ! ord_less_eq_int( plus_plus_int(
% 0.89/1.39 times_times_int( X, Y ), Z ), plus_plus_int( times_times_int( X, T ), U )
% 0.89/1.39 ), ! ord_less_eq_int( U, zero_zero_int ), ! ord_less_int( X, U ), !
% 0.89/1.39 ord_less_int( X, Z ), ord_less_eq_int( T, Y ) }.
% 0.89/1.39 (1914) {G0,W33,D4,L7,V6,M7} { ! plus_plus_int( times_times_int( X, Y ), Z
% 0.89/1.39 ) = plus_plus_int( times_times_int( T, U ), W ), ! ord_less_int(
% 0.89/1.39 plus_plus_int( times_times_int( T, U ), W ), zero_zero_int ), !
% 0.89/1.39 ord_less_int( Z, X ), ! ord_less_eq_int( zero_zero_int, W ), !
% 0.89/1.39 ord_less_int( zero_zero_int, T ), ! ord_less_eq_int( T, X ),
% 0.89/1.39 ord_less_eq_int( U, Y ) }.
% 0.89/1.39 (1915) {G0,W19,D7,L1,V1,M1} { power_power_int( power_power_int( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), number_number_of_nat( bit0
% 0.89/1.39 ( bit1( pls ) ) ) ) = power_power_int( X, number_number_of_nat( bit0(
% 0.89/1.39 bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.39 (1916) {G0,W10,D6,L1,V1,M1} { times_times_real( X, X ) = power_power_real
% 0.89/1.39 ( X, number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.39 (1917) {G0,W10,D6,L1,V1,M1} { times_times_nat( X, X ) = power_power_nat( X
% 0.89/1.39 , number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.39 (1918) {G0,W10,D6,L1,V1,M1} { times_times_int( X, X ) = power_power_int( X
% 0.89/1.39 , number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.39 (1919) {G0,W18,D8,L1,V0,M1} { zcong( power_power_int( s,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), number_number_of_int( min
% 0.89/1.39 ), plus_plus_int( times_times_int( number_number_of_int( bit0( bit0(
% 0.89/1.39 bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.39 (1920) {G0,W16,D6,L3,V3,M3} { zcong( X, zero_zero_int, Y ), ! zcong(
% 0.89/1.39 power_power_int( Z, number_number_of_nat( bit0( bit1( pls ) ) ) ), X, Y )
% 0.89/1.39 , ! dvd_dvd_int( Y, Z ) }.
% 0.89/1.39 (1921) {G0,W7,D2,L3,V1,M3} { ! is_int( X ), ! zprime( X ), ord_less_int(
% 0.89/1.39 one_one_int, X ) }.
% 0.89/1.39 (1922) {G0,W6,D2,L3,V1,M3} { ! is_int( X ), ! zprime( X ), alpha2( X ) }.
% 0.89/1.39 (1923) {G0,W9,D2,L4,V1,M4} { ! is_int( X ), ! ord_less_int( one_one_int, X
% 0.89/1.39 ), ! alpha2( X ), zprime( X ) }.
% 0.89/1.39 (1924) {G0,W7,D2,L3,V2,M3} { ! alpha2( X ), ! is_int( Y ), alpha4( X, Y )
% 0.89/1.39 }.
% 0.89/1.39 (1925) {G0,W5,D3,L2,V2,M2} { is_int( skol4( Y ) ), alpha2( X ) }.
% 0.89/1.39 (1926) {G0,W6,D3,L2,V1,M2} { ! alpha4( X, skol4( X ) ), alpha2( X ) }.
% 0.89/1.39 (1927) {G0,W9,D2,L3,V2,M3} { ! alpha4( X, Y ), ! alpha6( X, Y ), alpha7( X
% 0.89/1.39 , Y ) }.
% 0.89/1.39 (1928) {G0,W6,D2,L2,V2,M2} { alpha6( X, Y ), alpha4( X, Y ) }.
% 0.89/1.39 (1929) {G0,W6,D2,L2,V2,M2} { ! alpha7( X, Y ), alpha4( X, Y ) }.
% 0.89/1.39 (1930) {G0,W9,D2,L3,V2,M3} { ! alpha7( X, Y ), Y = one_one_int, Y = X }.
% 0.89/1.39 (1931) {G0,W6,D2,L2,V2,M2} { ! Y = one_one_int, alpha7( X, Y ) }.
% 0.89/1.39 (1932) {G0,W6,D2,L2,V2,M2} { ! Y = X, alpha7( X, Y ) }.
% 0.89/1.39 (1933) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), ord_less_eq_int(
% 0.89/1.39 zero_zero_int, Y ) }.
% 0.89/1.39 (1934) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), dvd_dvd_int( Y, X ) }.
% 0.89/1.39 (1935) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_int( zero_zero_int, Y ), !
% 0.89/1.39 dvd_dvd_int( Y, X ), alpha6( X, Y ) }.
% 0.89/1.39 (1936) {G0,W23,D6,L5,V1,M5} { ! is_int( X ), ! zprime( X ), X =
% 0.89/1.39 number_number_of_int( bit0( bit1( pls ) ) ), X = number_number_of_int(
% 0.89/1.39 bit1( bit1( pls ) ) ), ord_less_eq_int( number_number_of_int( bit1( bit0
% 0.89/1.39 ( bit1( pls ) ) ) ), X ) }.
% 0.89/1.39 (1937) {G0,W6,D5,L1,V0,M1} { ord_less_nat( zero_zero_nat,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) }.
% 0.89/1.39 (1938) {G0,W2,D2,L1,V0,M1} { is_int( skol5 ) }.
% 0.89/1.39 (1939) {G0,W18,D8,L1,V0,M1} { zcong( power_power_int( skol5,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), number_number_of_int( min
% 0.89/1.39 ), plus_plus_int( times_times_int( number_number_of_int( bit0( bit0(
% 0.89/1.39 bit1( pls ) ) ) ), m ), one_one_int ) ) }.
% 0.89/1.39 (1940) {G0,W14,D9,L1,V0,M1} { legendre( number_number_of_int( min ),
% 0.89/1.39 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), m ), one_one_int ) ) = one_one_int }.
% 0.89/1.39 (1941) {G0,W4,D3,L1,V0,M1} { bit1( min ) = min }.
% 0.89/1.39 (1942) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! min = bit1( X ), min = X }.
% 0.89/1.39 (1943) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! min = X, min = bit1( X ) }.
% 0.89/1.39 (1944) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! bit1( X ) = min, X = min }.
% 0.89/1.39 (1945) {G0,W9,D3,L3,V1,M3} { ! is_int( X ), ! X = min, bit1( X ) = min }.
% 0.89/1.39 (1946) {G0,W3,D2,L1,V0,M1} { ! min = pls }.
% 0.89/1.39 (1947) {G0,W3,D2,L1,V0,M1} { ! pls = min }.
% 0.89/1.39 (1948) {G0,W4,D3,L1,V1,M1} { ! min = bit0( X ) }.
% 0.89/1.39 (1949) {G0,W4,D3,L1,V1,M1} { ! bit0( X ) = min }.
% 0.89/1.39 (1950) {G0,W3,D2,L1,V0,M1} { ! ord_less_int( min, min ) }.
% 0.89/1.39 (1951) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( min, min ) }.
% 0.89/1.39 (1952) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit1( X ), min ),
% 0.89/1.39 ord_less_int( X, min ) }.
% 0.89/1.39 (1953) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( X, min ), ord_less_int( bit1
% 0.89/1.39 ( X ), min ) }.
% 0.89/1.39 (1954) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( min, bit1( X ) ),
% 0.89/1.39 ord_less_int( min, X ) }.
% 0.89/1.39 (1955) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( min, X ), ord_less_int( min,
% 0.89/1.39 bit1( X ) ) }.
% 0.89/1.39 (1956) {G0,W3,D2,L1,V0,M1} { ! ord_less_int( pls, min ) }.
% 0.89/1.39 (1957) {G0,W3,D2,L1,V0,M1} { ord_less_int( min, pls ) }.
% 0.89/1.39 (1958) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( min, bit0( X ) ),
% 0.89/1.39 ord_less_int( min, X ) }.
% 0.89/1.39 (1959) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( min, X ), ord_less_int( min,
% 0.89/1.39 bit0( X ) ) }.
% 0.89/1.39 (1960) {G0,W3,D2,L1,V0,M1} { ord_less_int( min, zero_zero_int ) }.
% 0.89/1.39 (1961) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( min, bit1( X ) ),
% 0.89/1.39 ord_less_eq_int( min, X ) }.
% 0.89/1.39 (1962) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( min, X ), ord_less_eq_int
% 0.89/1.39 ( min, bit1( X ) ) }.
% 0.89/1.39 (1963) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( bit1( X ), min ),
% 0.89/1.39 ord_less_eq_int( X, min ) }.
% 0.89/1.39 (1964) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, min ), ord_less_eq_int
% 0.89/1.39 ( bit1( X ), min ) }.
% 0.89/1.39 (1965) {G0,W3,D2,L1,V0,M1} { ord_less_eq_int( min, pls ) }.
% 0.89/1.39 (1966) {G0,W3,D2,L1,V0,M1} { ! ord_less_eq_int( pls, min ) }.
% 0.89/1.39 (1967) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( bit0( X ), min ),
% 0.89/1.39 ord_less_eq_int( X, min ) }.
% 0.89/1.39 (1968) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, min ), ord_less_eq_int
% 0.89/1.39 ( bit0( X ), min ) }.
% 0.89/1.39 (1969) {G0,W5,D3,L1,V0,M1} { ! number_number_of_int( pls ) =
% 0.89/1.39 number_number_of_int( min ) }.
% 0.89/1.39 (1970) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( bit0( X ), min ),
% 0.89/1.39 ord_less_eq_int( X, min ) }.
% 0.89/1.39 (1971) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( X, min ), ord_less_int(
% 0.89/1.39 bit0( X ), min ) }.
% 0.89/1.39 (1972) {G0,W7,D3,L2,V1,M2} { ! ord_less_eq_int( min, bit0( X ) ),
% 0.89/1.39 ord_less_int( min, X ) }.
% 0.89/1.39 (1973) {G0,W7,D3,L2,V1,M2} { ! ord_less_int( min, X ), ord_less_eq_int(
% 0.89/1.39 min, bit0( X ) ) }.
% 0.89/1.39 (1974) {G0,W15,D3,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.39 times_times_int( X, Y ) = one_one_int, alpha3( X, Y ), alpha5( X, Y ) }.
% 0.89/1.39 (1975) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! alpha3( X, Y
% 0.89/1.39 ), times_times_int( X, Y ) = one_one_int }.
% 0.89/1.39 (1976) {G0,W12,D3,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! alpha5( X, Y
% 0.89/1.39 ), times_times_int( X, Y ) = one_one_int }.
% 0.89/1.39 (1977) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), X = number_number_of_int(
% 0.89/1.39 min ) }.
% 0.89/1.39 (1978) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), Y = number_number_of_int(
% 0.89/1.39 min ) }.
% 0.89/1.39 (1979) {G0,W11,D3,L3,V2,M3} { ! X = number_number_of_int( min ), ! Y =
% 0.89/1.39 number_number_of_int( min ), alpha5( X, Y ) }.
% 0.89/1.39 (1980) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), X = one_one_int }.
% 0.89/1.39 (1981) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), Y = one_one_int }.
% 0.89/1.39 (1982) {G0,W9,D2,L3,V2,M3} { ! X = one_one_int, ! Y = one_one_int, alpha3
% 0.89/1.39 ( X, Y ) }.
% 0.89/1.39 (1983) {G0,W14,D3,L4,V2,M4} { ! is_int( X ), ! times_times_int( X, Y ) =
% 0.89/1.39 one_one_int, X = one_one_int, X = number_number_of_int( min ) }.
% 0.89/1.39 (1984) {G0,W8,D2,L2,V3,M2} { ! zcong( X, Y, Z ), zcong( Y, X, Z ) }.
% 0.89/1.39 (1985) {G0,W8,D2,L2,V3,M2} { ! zcong( Y, X, Z ), zcong( X, Y, Z ) }.
% 0.89/1.39 (1986) {G0,W4,D2,L1,V2,M1} { zcong( X, X, Y ) }.
% 0.89/1.39 (1987) {G0,W12,D2,L3,V4,M3} { ! zcong( X, Y, Z ), ! zcong( Y, T, Z ),
% 0.89/1.39 zcong( X, T, Z ) }.
% 0.89/1.39 (1988) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_real( X, Y ), X = Y,
% 0.89/1.39 ord_less_real( X, Y ) }.
% 0.89/1.39 (1989) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_nat( X, Y ), X = Y,
% 0.89/1.39 ord_less_nat( X, Y ) }.
% 0.89/1.39 (1990) {G0,W13,D2,L5,V2,M5} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.39 ord_less_eq_int( X, Y ), X = Y, ord_less_int( X, Y ) }.
% 0.89/1.39 (1991) {G0,W12,D2,L4,V3,M4} { ! ord_less_int( X, Y ), ! ord_less_int( Z, Y
% 0.89/1.39 ), ord_less_eq_int( X, Z ), ord_less_eq_int( Z, X ) }.
% 0.89/1.39 (1992) {G0,W11,D2,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! zcong( X, Y
% 0.89/1.39 , zero_zero_int ), X = Y }.
% 0.89/1.39 (1993) {G0,W11,D2,L4,V2,M4} { ! is_int( X ), ! is_int( Y ), ! X = Y, zcong
% 0.89/1.39 ( X, Y, zero_zero_int ) }.
% 0.89/1.39 (1994) {G0,W4,D2,L1,V2,M1} { zcong( X, Y, one_one_int ) }.
% 0.89/1.39 (1995) {G0,W8,D3,L1,V3,M1} { zcong( times_times_int( X, Y ),
% 0.89/1.39 times_times_int( Z, Y ), Y ) }.
% 0.89/1.39 (1996) {G0,W12,D3,L2,V4,M2} { ! zcong( X, Y, Z ), zcong( times_times_int(
% 0.89/1.39 X, T ), times_times_int( Y, T ), Z ) }.
% 0.89/1.39 (1997) {G0,W12,D3,L2,V4,M2} { ! zcong( X, Y, Z ), zcong( times_times_int(
% 0.89/1.39 T, X ), times_times_int( T, Y ), Z ) }.
% 0.89/1.39 (1998) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T, U, Z ),
% 0.89/1.39 zcong( times_times_int( X, T ), times_times_int( Y, U ), Z ) }.
% 0.89/1.39 (1999) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T, U, Z ),
% 0.89/1.39 zcong( plus_plus_int( X, T ), plus_plus_int( Y, U ), Z ) }.
% 0.89/1.39 (2000) {G0,W11,D7,L1,V1,M1} { power_power_real( number267125858f_real( min
% 0.89/1.39 ), times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ) ) =
% 0.89/1.39 one_one_real }.
% 0.89/1.39 (2001) {G0,W11,D7,L1,V1,M1} { power_power_int( number_number_of_int( min )
% 0.89/1.39 , times_times_nat( number_number_of_nat( bit0( bit1( pls ) ) ), X ) ) =
% 0.89/1.39 one_one_int }.
% 0.89/1.39 (2002) {G0,W16,D2,L5,V3,M5} { ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_int( X, Y ), ! ord_less_int( zero_zero_int, Z ), ! ord_less_int
% 0.89/1.39 ( Z, X ), ! zcong( X, Z, Y ) }.
% 0.89/1.39 (2003) {G0,W11,D3,L3,V6,M3} { ! is_int( X ), ! zcong( Y, X, Z ), is_int(
% 0.89/1.39 skol6( T, U, W ) ) }.
% 0.89/1.39 (2004) {G0,W16,D5,L3,V3,M3} { ! is_int( X ), ! zcong( Y, X, Z ), X =
% 0.89/1.39 plus_plus_int( Y, times_times_int( Z, skol6( X, Y, Z ) ) ) }.
% 0.89/1.39 (2005) {G0,W15,D4,L4,V4,M4} { ! is_int( X ), ! is_int( T ), ! X =
% 0.89/1.39 plus_plus_int( Y, times_times_int( Z, T ) ), zcong( Y, X, Z ) }.
% 0.89/1.39 (2006) {G0,W24,D7,L1,V1,M1} { times_times_real( number267125858f_real(
% 0.89/1.39 bit0( bit0( bit1( pls ) ) ) ), power_power_real( X, number_number_of_nat
% 0.89/1.39 ( bit0( bit1( pls ) ) ) ) ) = power_power_real( times_times_real(
% 0.89/1.39 number267125858f_real( bit0( bit1( pls ) ) ), X ), number_number_of_nat(
% 0.89/1.39 bit0( bit1( pls ) ) ) ) }.
% 0.89/1.39 (2007) {G0,W15,D2,L5,V2,M5} { ! is_int( X ), ! ord_less_eq_int(
% 0.89/1.39 zero_zero_int, X ), ! ord_less_int( X, Y ), ! zcong( X, zero_zero_int, Y
% 0.89/1.39 ), X = zero_zero_int }.
% 0.89/1.39 (2008) {G0,W23,D2,L8,V3,M8} { ! is_int( X ), ! is_int( Y ), !
% 0.89/1.39 ord_less_eq_int( zero_zero_int, Y ), ! ord_less_int( Y, Z ), !
% 0.89/1.39 ord_less_eq_int( zero_zero_int, X ), ! ord_less_int( X, Z ), ! zcong( Y,
% 0.89/1.39 X, Z ), Y = X }.
% 0.89/1.39 (2009) {G0,W14,D4,L2,V4,M2} { ! zcong( power_power_int( X, Y ),
% 0.89/1.39 one_one_int, Z ), zcong( power_power_int( X, times_times_nat( Y, T ) ),
% 0.89/1.39 one_one_int, Z ) }.
% 0.89/1.39 (2010) {G0,W16,D3,L5,V3,M5} { ! ord_less_eq_int( zero_zero_int, X ), !
% 0.89/1.39 zprime( Y ), ! dvd_dvd_int( Y, times_times_int( X, Z ) ), dvd_dvd_int( Y
% 0.89/1.39 , X ), dvd_dvd_int( Y, Z ) }.
% 0.89/1.39 (2011) {G0,W12,D8,L1,V0,M1} { quadRes( plus_plus_int( times_times_int(
% 0.89/1.39 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.39 number_number_of_int( min ) ) }.
% 0.89/1.39 (2012) {G0,W19,D8,L1,V0,M1} { dvd_dvd_int( plus_plus_int( times_times_int
% 0.89/1.39 ( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.39 , minus_minus_int( power_power_int( s, number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), number_number_of_int( min ) ) ) }.
% 0.89/1.39 (2013) {G0,W25,D5,L3,V3,M3} { ! ord_less_int( number_number_of_int( bit0(
% 0.89/1.39 bit1( pls ) ) ), X ), ! zcong( power_power_int( number_number_of_int( min
% 0.89/1.39 ), Y ), power_power_int( number_number_of_int( min ), Z ), X ),
% 0.89/1.39 power_power_int( number_number_of_int( min ), Y ) = power_power_int(
% 0.89/1.39 number_number_of_int( min ), Z ) }.
% 0.89/1.39 (2014) {G0,W15,D5,L3,V2,M3} { ! ord_less_int( number_number_of_int( bit0(
% 0.89/1.39 bit1( pls ) ) ), X ), ! zcong( Y, number_number_of_int( min ), X ), !
% 0.89/1.39 zcong( Y, one_one_int, X ) }.
% 0.89/1.39 (2015) {G0,W18,D7,L1,V0,M1} { minus_minus_int( power_power_int( s,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), number_number_of_int( min
% 0.89/1.39 ) ) = plus_plus_int( power_power_int( s, number_number_of_nat( bit0(
% 0.89/1.39 bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.39 (2016) {G0,W26,D9,L2,V0,M2} { quadRes( plus_plus_int( times_times_int(
% 0.89/1.39 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.39 number_number_of_int( min ) ), ! legendre( number_number_of_int( min ),
% 0.89/1.39 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), m ), one_one_int ) ) = one_one_int }.
% 0.89/1.39 (2017) {G0,W8,D3,L2,V1,M2} { ord_less_real( zero_zero_real,
% 0.89/1.39 times_times_real( X, X ) ), X = zero_zero_real }.
% 0.89/1.39 (2018) {G0,W8,D3,L2,V1,M2} { ! X = zero_zero_real, ! ord_less_real(
% 0.89/1.39 zero_zero_real, times_times_real( X, X ) ) }.
% 0.89/1.39 (2019) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T, U, Z ),
% 0.89/1.39 zcong( minus_minus_int( X, T ), minus_minus_int( Y, U ), Z ) }.
% 0.89/1.39 (2020) {G0,W11,D3,L3,V3,M3} { ! dvd_dvd_int( X, minus_minus_int( Y, Z ) )
% 0.89/1.39 , ! dvd_dvd_int( X, Z ), dvd_dvd_int( X, Y ) }.
% 0.89/1.39 (2021) {G0,W13,D4,L1,V3,M1} { times_times_int( X, minus_minus_int( Y, Z )
% 0.89/1.39 ) = minus_minus_int( times_times_int( X, Y ), times_times_int( X, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2022) {G0,W13,D4,L1,V3,M1} { times_times_int( minus_minus_int( X, Y ), Z
% 0.89/1.39 ) = minus_minus_int( times_times_int( X, Z ), times_times_int( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2023) {G0,W10,D4,L1,V2,M1} { minus_minus_int( bit0( X ), bit0( Y ) ) =
% 0.89/1.39 bit0( minus_minus_int( X, Y ) ) }.
% 0.89/1.39 (2024) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), minus_minus_int( X, pls ) = X
% 0.89/1.39 }.
% 0.89/1.39 (2025) {G0,W12,D3,L3,V3,M3} { ! is_int( X ), ! minus_minus_int( X, Y ) = Z
% 0.89/1.39 , X = plus_plus_int( Z, Y ) }.
% 0.89/1.39 (2026) {G0,W10,D4,L1,V2,M1} { number267125858f_real( minus_minus_int( X, Y
% 0.89/1.39 ) ) = minus_minus_real( number267125858f_real( X ),
% 0.89/1.39 number267125858f_real( Y ) ) }.
% 0.89/1.39 (2027) {G0,W10,D4,L1,V2,M1} { number_number_of_int( minus_minus_int( X, Y
% 0.89/1.39 ) ) = minus_minus_int( number_number_of_int( X ), number_number_of_int(
% 0.89/1.39 Y ) ) }.
% 0.89/1.39 (2028) {G0,W16,D5,L1,V3,M1} { times_times_real( number267125858f_real( X )
% 0.89/1.39 , minus_minus_real( Y, Z ) ) = minus_minus_real( times_times_real(
% 0.89/1.39 number267125858f_real( X ), Y ), times_times_real( number267125858f_real
% 0.89/1.39 ( X ), Z ) ) }.
% 0.89/1.39 (2029) {G0,W16,D5,L1,V3,M1} { times_times_int( number_number_of_int( X ),
% 0.89/1.39 minus_minus_int( Y, Z ) ) = minus_minus_int( times_times_int(
% 0.89/1.39 number_number_of_int( X ), Y ), times_times_int( number_number_of_int( X
% 0.89/1.39 ), Z ) ) }.
% 0.89/1.39 (2030) {G0,W16,D5,L1,V3,M1} { times_times_real( minus_minus_real( X, Y ),
% 0.89/1.39 number267125858f_real( Z ) ) = minus_minus_real( times_times_real( X,
% 0.89/1.39 number267125858f_real( Z ) ), times_times_real( Y, number267125858f_real
% 0.89/1.39 ( Z ) ) ) }.
% 0.89/1.39 (2031) {G0,W16,D5,L1,V3,M1} { times_times_int( minus_minus_int( X, Y ),
% 0.89/1.39 number_number_of_int( Z ) ) = minus_minus_int( times_times_int( X,
% 0.89/1.39 number_number_of_int( Z ) ), times_times_int( Y, number_number_of_int( Z
% 0.89/1.39 ) ) ) }.
% 0.89/1.39 (2032) {G0,W10,D4,L1,V2,M1} { minus_minus_int( bit1( X ), bit0( Y ) ) =
% 0.89/1.39 bit1( minus_minus_int( X, Y ) ) }.
% 0.89/1.39 (2033) {G0,W10,D4,L1,V2,M1} { minus_minus_int( bit1( X ), bit1( Y ) ) =
% 0.89/1.39 bit0( minus_minus_int( X, Y ) ) }.
% 0.89/1.39 (2034) {G0,W9,D4,L1,V1,M1} { minus_minus_int( pls, bit0( X ) ) = bit0(
% 0.89/1.39 minus_minus_int( pls, X ) ) }.
% 0.89/1.39 (2035) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_int(
% 0.89/1.39 minus_minus_int( X, Y ), zero_zero_int ) }.
% 0.89/1.39 (2036) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( minus_minus_int( X, Y ),
% 0.89/1.39 zero_zero_int ), ord_less_int( X, Y ) }.
% 0.89/1.39 (2037) {G0,W33,D6,L1,V7,M1} { plus_plus_int( times_times_int(
% 0.89/1.39 minus_minus_int( X, times_times_int( Y, Z ) ), T ), times_times_int(
% 0.89/1.39 minus_minus_int( U, times_times_int( Y, W ) ), V0 ) ) = minus_minus_int(
% 0.89/1.39 plus_plus_int( times_times_int( X, T ), times_times_int( U, V0 ) ),
% 0.89/1.39 times_times_int( Y, plus_plus_int( times_times_int( Z, T ),
% 0.89/1.39 times_times_int( W, V0 ) ) ) ) }.
% 0.89/1.39 (2038) {G0,W9,D3,L2,V3,M2} { ! zcong( X, Y, Z ), dvd_dvd_int( Z,
% 0.89/1.39 minus_minus_int( X, Y ) ) }.
% 0.89/1.39 (2039) {G0,W9,D3,L2,V3,M2} { ! dvd_dvd_int( Z, minus_minus_int( X, Y ) ),
% 0.89/1.39 zcong( X, Y, Z ) }.
% 0.89/1.39 (2040) {G0,W14,D5,L1,V3,M1} { plus_plus_real( number267125858f_real( X ),
% 0.89/1.39 minus_minus_real( number267125858f_real( Y ), Z ) ) = minus_minus_real(
% 0.89/1.39 number267125858f_real( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.39 (2041) {G0,W14,D5,L1,V3,M1} { plus_plus_int( number_number_of_int( X ),
% 0.89/1.39 minus_minus_int( number_number_of_int( Y ), Z ) ) = minus_minus_int(
% 0.89/1.39 number_number_of_int( plus_plus_int( X, Y ) ), Z ) }.
% 0.89/1.39 (2042) {G0,W18,D3,L5,V2,M5} { ! is_int( X ), ! ord_less_int( zero_zero_int
% 0.89/1.39 , X ), ! ord_less_int( X, Y ), X = minus_minus_int( Y, one_one_int ),
% 0.89/1.39 ord_less_int( X, minus_minus_int( Y, one_one_int ) ) }.
% 0.89/1.39 (2043) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( X, minus_minus_int( Y,
% 0.89/1.39 one_one_int ) ), ord_less_int( X, Y ) }.
% 0.89/1.39 (2044) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( X, Y ), ord_less_eq_int( X,
% 0.89/1.39 minus_minus_int( Y, one_one_int ) ) }.
% 0.89/1.39 (2045) {G0,W9,D4,L1,V1,M1} { minus_minus_int( pls, bit1( X ) ) = bit1(
% 0.89/1.39 minus_minus_int( min, X ) ) }.
% 0.89/1.39 (2046) {G0,W9,D4,L1,V1,M1} { minus_minus_int( min, bit1( X ) ) = bit0(
% 0.89/1.39 minus_minus_int( min, X ) ) }.
% 0.89/1.39 (2047) {G0,W9,D4,L1,V1,M1} { minus_minus_int( min, bit0( X ) ) = bit1(
% 0.89/1.39 minus_minus_int( min, X ) ) }.
% 0.89/1.39 (2048) {G0,W14,D4,L2,V2,M2} { ! zcong( times_times_int( X, minus_minus_int
% 0.89/1.39 ( Y, one_one_int ) ), one_one_int, Y ), zcong( X, minus_minus_int( Y,
% 0.89/1.39 one_one_int ), Y ) }.
% 0.89/1.39 (2049) {G0,W14,D4,L2,V2,M2} { ! zcong( X, minus_minus_int( Y, one_one_int
% 0.89/1.39 ), Y ), zcong( times_times_int( X, minus_minus_int( Y, one_one_int ) ),
% 0.89/1.39 one_one_int, Y ) }.
% 0.89/1.39 (2050) {G0,W15,D2,L4,V5,M4} { ! zcong( X, Y, Z ), ! Y = T, ! zcong( T, U,
% 0.89/1.39 Z ), zcong( X, U, Z ) }.
% 0.89/1.39 (2051) {G0,W24,D3,L7,V2,M7} { ! is_int( X ), ! zprime( Y ), ! ord_less_int
% 0.89/1.39 ( zero_zero_int, X ), ! ord_less_int( X, Y ), ! zcong( times_times_int( X
% 0.89/1.39 , X ), one_one_int, Y ), X = one_one_int, X = minus_minus_int( Y,
% 0.89/1.39 one_one_int ) }.
% 0.89/1.39 (2052) {G0,W21,D3,L5,V2,M5} { ! zprime( X ), ! ord_less_int( zero_zero_int
% 0.89/1.39 , Y ), ! zcong( times_times_int( Y, Y ), one_one_int, X ), zcong( Y,
% 0.89/1.39 one_one_int, X ), zcong( Y, minus_minus_int( X, one_one_int ), X ) }.
% 0.89/1.39 (2053) {G0,W21,D7,L1,V2,M1} { times_times_int( plus_plus_int( X, Y ),
% 0.89/1.39 minus_minus_int( X, Y ) ) = minus_minus_int( power_power_int( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_int( Y,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.39 (2054) {G0,W4,D2,L1,V1,M1} { zcong( X, zero_zero_int, X ) }.
% 0.89/1.39 (2055) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T,
% 0.89/1.39 times_times_int( U, X ), Z ), zcong( T, times_times_int( U, Y ), Z ) }.
% 0.89/1.39 (2056) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T,
% 0.89/1.39 times_times_int( U, Y ), Z ), zcong( T, times_times_int( U, X ), Z ) }.
% 0.89/1.39 (2057) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T,
% 0.89/1.39 times_times_int( X, U ), Z ), zcong( T, times_times_int( Y, U ), Z ) }.
% 0.89/1.39 (2058) {G0,W16,D3,L3,V5,M3} { ! zcong( X, Y, Z ), ! zcong( T,
% 0.89/1.39 times_times_int( Y, U ), Z ), zcong( T, times_times_int( X, U ), Z ) }.
% 0.89/1.39 (2059) {G0,W12,D3,L2,V4,M2} { ! zcong( X, Y, Z ), zcong( plus_plus_int( X
% 0.89/1.39 , T ), plus_plus_int( Y, T ), Z ) }.
% 0.89/1.39 (2060) {G0,W12,D3,L2,V4,M2} { ! zcong( X, Y, Z ), zcong( power_power_int(
% 0.89/1.39 X, T ), power_power_int( Y, T ), Z ) }.
% 0.89/1.39 (2061) {G0,W31,D8,L1,V2,M1} { power_power_real( minus_minus_real( X, Y ),
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) = minus_minus_real(
% 0.89/1.39 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.39 ) ) ) ), times_times_real( times_times_real( number267125858f_real( bit0
% 0.89/1.39 ( bit1( pls ) ) ), X ), Y ) ) }.
% 0.89/1.39 (2062) {G0,W31,D8,L1,V2,M1} { power_power_int( minus_minus_int( X, Y ),
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) = minus_minus_int(
% 0.89/1.39 plus_plus_int( power_power_int( X, number_number_of_nat( bit0( bit1( pls
% 0.89/1.39 ) ) ) ), power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) )
% 0.89/1.39 ) ), times_times_int( times_times_int( number_number_of_int( bit0( bit1
% 0.89/1.39 ( pls ) ) ), X ), Y ) ) }.
% 0.89/1.39 (2063) {G0,W31,D9,L1,V2,M1} { power_power_int( minus_minus_int( X, Y ),
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_int(
% 0.89/1.39 minus_minus_int( power_power_int( X, number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), times_times_int( times_times_int( number_number_of_int( bit0
% 0.89/1.39 ( bit1( pls ) ) ), X ), Y ) ), power_power_int( Y, number_number_of_nat(
% 0.89/1.39 bit0( bit1( pls ) ) ) ) ) }.
% 0.89/1.39 (2064) {G0,W50,D11,L1,V2,M1} { power_power_int( minus_minus_int( X, Y ),
% 0.89/1.39 number_number_of_nat( bit1( bit1( pls ) ) ) ) = minus_minus_int(
% 0.89/1.39 plus_plus_int( minus_minus_int( power_power_int( X, number_number_of_nat
% 0.89/1.39 ( bit1( bit1( pls ) ) ) ), times_times_int( times_times_int(
% 0.89/1.39 number_number_of_int( bit1( bit1( pls ) ) ), power_power_int( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) ), Y ) ), times_times_int(
% 0.89/1.39 times_times_int( number_number_of_int( bit1( bit1( pls ) ) ), X ),
% 0.89/1.39 power_power_int( Y, number_number_of_nat( bit0( bit1( pls ) ) ) ) ) ),
% 0.89/1.39 power_power_int( Y, number_number_of_nat( bit1( bit1( pls ) ) ) ) ) }.
% 0.89/1.39 (2065) {G0,W26,D2,L9,V3,M9} { ! is_int( X ), ! is_int( Y ), ! ord_less_int
% 0.89/1.39 ( zero_zero_int, Y ), ! ord_less_int( zero_zero_int, X ), ! ord_less_int
% 0.89/1.39 ( zero_zero_int, Z ), ! zcong( Y, X, Z ), ! ord_less_int( Y, Z ), !
% 0.89/1.39 ord_less_int( X, Z ), Y = X }.
% 0.89/1.39 (2066) {G0,W10,D2,L3,V2,M3} { ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_int( X, Y ), ! zcong( X, zero_zero_int, Y ) }.
% 0.89/1.39 (2067) {G0,W9,D2,L3,V2,M3} { ! dvd_dvd_int( X, Y ), ord_less_eq_int( Y,
% 0.89/1.39 zero_zero_int ), ord_less_eq_int( X, Y ) }.
% 0.89/1.39 (2068) {G0,W7,D2,L2,V2,M2} { ! zcong( X, zero_zero_int, Y ), dvd_dvd_int(
% 0.89/1.39 Y, X ) }.
% 0.89/1.39 (2069) {G0,W7,D2,L2,V2,M2} { ! dvd_dvd_int( Y, X ), zcong( X,
% 0.89/1.39 zero_zero_int, Y ) }.
% 0.89/1.39 (2070) {G0,W7,D2,L2,V2,M2} { ! zcong( X, zero_zero_int, Y ), dvd_dvd_int(
% 0.89/1.39 Y, X ) }.
% 0.89/1.39 (2071) {G0,W7,D2,L2,V2,M2} { ! dvd_dvd_int( Y, X ), zcong( X,
% 0.89/1.39 zero_zero_int, Y ) }.
% 0.89/1.39 (2072) {G0,W13,D3,L4,V3,M4} { ! zprime( X ), ! dvd_dvd_int( X,
% 0.89/1.39 times_times_int( Y, Z ) ), dvd_dvd_int( X, Y ), dvd_dvd_int( X, Z ) }.
% 0.89/1.39 (2073) {G0,W15,D2,L5,V2,M5} { ! is_int( X ), ! ord_less_eq_int(
% 0.89/1.39 zero_zero_int, X ), ! ord_less_int( X, Y ), ! zcong( X, zero_zero_int, Y
% 0.89/1.39 ), X = zero_zero_int }.
% 0.89/1.39 (2074) {G0,W11,D3,L3,V3,M3} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 dvd_dvd_int( Y, Z ), dvd_dvd_int( Y, power_power_int( Z, X ) ) }.
% 0.89/1.39 (2075) {G0,W13,D4,L2,V1,M2} { power_power_int( number_number_of_int( min )
% 0.89/1.39 , X ) = one_one_int, power_power_int( number_number_of_int( min ), X ) =
% 0.89/1.39 number_number_of_int( min ) }.
% 0.89/1.39 (2076) {G0,W16,D3,L4,V3,M4} { ! zprime( X ), zcong( Y, zero_zero_int, X )
% 0.89/1.39 , zcong( Z, zero_zero_int, X ), ! zcong( times_times_int( Y, Z ),
% 0.89/1.39 zero_zero_int, X ) }.
% 0.89/1.39 (2077) {G0,W19,D3,L5,V3,M5} { ! zprime( X ), ! ord_less_int( zero_zero_int
% 0.89/1.39 , Y ), zcong( Y, zero_zero_int, X ), zcong( Z, zero_zero_int, X ), !
% 0.89/1.39 zcong( times_times_int( Y, Z ), zero_zero_int, X ) }.
% 0.89/1.39 (2078) {G0,W19,D3,L5,V3,M5} { ! zprime( X ), ! ord_less_int( zero_zero_int
% 0.89/1.39 , Y ), ! zcong( times_times_int( Y, Z ), zero_zero_int, X ), zcong( Y,
% 0.89/1.39 zero_zero_int, X ), zcong( Z, zero_zero_int, X ) }.
% 0.89/1.39 (2079) {G0,W13,D3,L4,V3,M4} { ! zprime( X ), ! dvd_dvd_int( X,
% 0.89/1.39 power_power_int( Y, Z ) ), ! ord_less_nat( zero_zero_nat, Z ),
% 0.89/1.39 dvd_dvd_int( X, Y ) }.
% 0.89/1.39 (2080) {G0,W24,D9,L2,V1,M2} { ! zprime( plus_plus_int( times_times_int(
% 0.89/1.39 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), X ), one_one_int ) )
% 0.89/1.39 , legendre( number_number_of_int( min ), plus_plus_int( times_times_int(
% 0.89/1.39 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), X ), one_one_int ) )
% 0.89/1.39 = one_one_int }.
% 0.89/1.39 (2081) {G0,W11,D5,L2,V1,M2} { ! ord_less_int( number_number_of_int( bit0(
% 0.89/1.39 bit1( pls ) ) ), X ), ! zcong( one_one_int, number_number_of_int( min ),
% 0.89/1.39 X ) }.
% 0.89/1.39 (2082) {G0,W9,D3,L2,V2,M2} { ! zcong( X, zero_zero_int, Y ), legendre( X,
% 0.89/1.39 Y ) = zero_zero_int }.
% 0.89/1.39 (2083) {G0,W12,D3,L3,V2,M3} { zcong( X, zero_zero_int, Y ), ! quadRes( Y,
% 0.89/1.39 X ), legendre( X, Y ) = one_one_int }.
% 0.89/1.39 (2084) {G0,W13,D3,L3,V2,M3} { zcong( X, zero_zero_int, Y ), quadRes( Y, X
% 0.89/1.39 ), legendre( X, Y ) = number_number_of_int( min ) }.
% 0.89/1.39 (2085) {G0,W7,D3,L2,V4,M2} { ! quadRes( X, Y ), is_int( skol7( Z, T ) )
% 0.89/1.39 }.
% 0.89/1.39 (2086) {G0,W14,D6,L2,V2,M2} { ! quadRes( X, Y ), zcong( power_power_int(
% 0.89/1.39 skol7( X, Y ), number_number_of_nat( bit0( bit1( pls ) ) ) ), Y, X ) }.
% 0.89/1.39 (2087) {G0,W14,D6,L3,V3,M3} { ! is_int( Z ), ! zcong( power_power_int( Z,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), Y, X ), quadRes( X, Y )
% 0.89/1.39 }.
% 0.89/1.39 (2088) {G0,W31,D8,L1,V2,M1} { power_power_real( plus_plus_real( X, Y ),
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) = plus_plus_real(
% 0.89/1.39 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.39 ) ) ) ), times_times_real( times_times_real( number267125858f_real( bit0
% 0.89/1.39 ( bit1( pls ) ) ), X ), Y ) ) }.
% 0.89/1.39 (2089) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, times_times_nat( Y, X )
% 0.89/1.39 = zero_zero_nat }.
% 0.89/1.39 (2090) {G0,W14,D5,L2,V2,M2} { Y = zero_zero_nat, times_times_nat( Y, X ) =
% 0.89/1.39 plus_plus_nat( X, times_times_nat( minus_minus_nat( Y, one_one_nat ), X
% 0.89/1.39 ) ) }.
% 0.89/1.39 (2091) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, power_power_nat( X, Y )
% 0.89/1.39 = one_one_nat }.
% 0.89/1.39 (2092) {G0,W14,D5,L2,V2,M2} { Y = zero_zero_nat, power_power_nat( X, Y ) =
% 0.89/1.39 times_times_nat( X, power_power_nat( X, minus_minus_nat( Y, one_one_nat
% 0.89/1.39 ) ) ) }.
% 0.89/1.39 (2093) {G0,W21,D7,L1,V2,M1} { minus_minus_nat( power_power_nat( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_nat( Y,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = times_times_nat(
% 0.89/1.39 plus_plus_nat( X, Y ), minus_minus_nat( X, Y ) ) }.
% 0.89/1.39 (2094) {G0,W18,D7,L2,V2,M2} { ! plus_plus_real( power_power_real( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_real, X =
% 0.89/1.39 zero_zero_real }.
% 0.89/1.39 (2095) {G0,W18,D7,L2,V2,M2} { ! plus_plus_real( power_power_real( X,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), power_power_real( Y,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ) ) = zero_zero_real, Y =
% 0.89/1.39 zero_zero_real }.
% 0.89/1.39 (2096) {G0,W21,D7,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.39 plus_plus_real( power_power_real( X, number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), power_power_real( Y, number_number_of_nat( bit0( bit1( pls )
% 0.89/1.39 ) ) ) ) = zero_zero_real }.
% 0.89/1.39 (2097) {G0,W3,D2,L1,V0,M1} { ! zero_zero_real = one_one_real }.
% 0.89/1.39 (2098) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_real( X, Y ), ord_less_eq_real
% 0.89/1.39 ( minus_minus_real( X, Y ), zero_zero_real ) }.
% 0.89/1.39 (2099) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_real( minus_minus_real( X, Y )
% 0.89/1.39 , zero_zero_real ), ord_less_eq_real( X, Y ) }.
% 0.89/1.39 (2100) {G0,W6,D2,L2,V2,M2} { ! ord_less_real( X, Y ), ord_less_eq_real( X
% 0.89/1.39 , Y ) }.
% 0.89/1.39 (2101) {G0,W6,D2,L2,V2,M2} { ! ord_less_real( X, Y ), ! X = Y }.
% 0.89/1.39 (2102) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_real( X, Y ), X = Y,
% 0.89/1.39 ord_less_real( X, Y ) }.
% 0.89/1.39 (2103) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_real( X, Y ), ord_less_real( X
% 0.89/1.39 , Y ), X = Y }.
% 0.89/1.39 (2104) {G0,W6,D2,L2,V2,M2} { ! ord_less_real( X, Y ), ord_less_eq_real( X
% 0.89/1.39 , Y ) }.
% 0.89/1.39 (2105) {G0,W6,D2,L2,V2,M2} { ! X = Y, ord_less_eq_real( X, Y ) }.
% 0.89/1.39 (2106) {G0,W11,D4,L1,V3,M1} { times_times_real( times_times_real( X, Y ),
% 0.89/1.39 Z ) = times_times_real( X, times_times_real( Y, Z ) ) }.
% 0.89/1.39 (2107) {G0,W7,D3,L1,V2,M1} { times_times_real( X, Y ) = times_times_real(
% 0.89/1.39 Y, X ) }.
% 0.89/1.39 (2108) {G0,W5,D3,L1,V1,M1} { times_times_real( one_one_real, X ) = X }.
% 0.89/1.39 (2109) {G0,W10,D3,L2,V3,M2} { ! ord_less_eq_real( X, Y ), ord_less_eq_real
% 0.89/1.39 ( plus_plus_real( Z, X ), plus_plus_real( Z, Y ) ) }.
% 0.89/1.39 (2110) {G0,W15,D4,L1,V4,M1} { minus_minus_real( plus_plus_real( X, Y ),
% 0.89/1.39 plus_plus_real( Z, T ) ) = plus_plus_real( minus_minus_real( X, Z ),
% 0.89/1.39 minus_minus_real( Y, T ) ) }.
% 0.89/1.39 (2111) {G0,W15,D4,L1,V4,M1} { minus_minus_int( plus_plus_int( X, Y ),
% 0.89/1.39 plus_plus_int( Z, T ) ) = plus_plus_int( minus_minus_int( X, Z ),
% 0.89/1.39 minus_minus_int( Y, T ) ) }.
% 0.89/1.39 (2112) {G0,W13,D3,L3,V3,M3} { X = zero_zero_real, ! times_times_real( X, Y
% 0.89/1.39 ) = times_times_real( X, Z ), Y = Z }.
% 0.89/1.39 (2113) {G0,W13,D3,L3,V3,M3} { X = zero_zero_real, ! Y = Z,
% 0.89/1.39 times_times_real( X, Y ) = times_times_real( X, Z ) }.
% 0.89/1.39 (2114) {G0,W13,D3,L3,V3,M3} { X = zero_zero_real, ! times_times_real( Y, X
% 0.89/1.39 ) = times_times_real( Z, X ), Y = Z }.
% 0.89/1.39 (2115) {G0,W13,D3,L3,V3,M3} { X = zero_zero_real, ! Y = Z,
% 0.89/1.39 times_times_real( Y, X ) = times_times_real( Z, X ) }.
% 0.89/1.39 (2116) {G0,W8,D3,L2,V2,M2} { ! times_times_nat( X, Y ) = one_one_nat, X =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (2117) {G0,W8,D3,L2,V2,M2} { ! times_times_nat( X, Y ) = one_one_nat, Y =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (2118) {G0,W11,D3,L3,V2,M3} { ! X = one_one_nat, ! Y = one_one_nat,
% 0.89/1.39 times_times_nat( X, Y ) = one_one_nat }.
% 0.89/1.39 (2119) {G0,W13,D4,L1,V3,M1} { times_times_real( plus_plus_real( X, Y ), Z
% 0.89/1.39 ) = plus_plus_real( times_times_real( X, Z ), times_times_real( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2120) {G0,W8,D3,L2,V2,M2} { ! power_power_nat( X, Y ) = zero_zero_nat, !
% 0.89/1.39 Y = zero_zero_nat }.
% 0.89/1.39 (2121) {G0,W8,D3,L2,V2,M2} { ! power_power_nat( X, Y ) = zero_zero_nat, X
% 0.89/1.39 = zero_zero_nat }.
% 0.89/1.39 (2122) {G0,W11,D3,L3,V2,M3} { Y = zero_zero_nat, ! X = zero_zero_nat,
% 0.89/1.39 power_power_nat( X, Y ) = zero_zero_nat }.
% 0.89/1.39 (2123) {G0,W19,D5,L1,V4,M1} { minus_minus_real( times_times_real( X, Y ),
% 0.89/1.39 times_times_real( Z, T ) ) = plus_plus_real( times_times_real( X,
% 0.89/1.39 minus_minus_real( Y, T ) ), times_times_real( minus_minus_real( X, Z ), T
% 0.89/1.39 ) ) }.
% 0.89/1.39 (2124) {G0,W19,D5,L1,V4,M1} { minus_minus_int( times_times_int( X, Y ),
% 0.89/1.39 times_times_int( Z, T ) ) = plus_plus_int( times_times_int( X,
% 0.89/1.39 minus_minus_int( Y, T ) ), times_times_int( minus_minus_int( X, Z ), T )
% 0.89/1.39 ) }.
% 0.89/1.39 (2125) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_eq_real( times_times_real( Y, X ), times_times_real( Z, X ) ),
% 0.89/1.39 ord_less_eq_real( Y, Z ) }.
% 0.89/1.39 (2126) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_eq_real( Y, Z ), ord_less_eq_real( times_times_real( Y, X ),
% 0.89/1.39 times_times_real( Z, X ) ) }.
% 0.89/1.39 (2127) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_eq_real( times_times_real( X, Y ), times_times_real( X, Z ) ),
% 0.89/1.39 ord_less_eq_real( Y, Z ) }.
% 0.89/1.39 (2128) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_eq_real( Y, Z ), ord_less_eq_real( times_times_real( X, Y ),
% 0.89/1.39 times_times_real( X, Z ) ) }.
% 0.89/1.39 (2129) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_real( Y, Z ), ord_less_real( times_times_real( X, Y ),
% 0.89/1.39 times_times_real( X, Z ) ) }.
% 0.89/1.39 (2130) {G0,W11,D3,L3,V2,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_real( zero_zero_real, Y ), ord_less_real( zero_zero_real,
% 0.89/1.39 times_times_real( X, Y ) ) }.
% 0.89/1.39 (2131) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_real( times_times_real( Y, X ), times_times_real( Z, X ) ),
% 0.89/1.39 ord_less_real( Y, Z ) }.
% 0.89/1.39 (2132) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_real( Y, Z ), ord_less_real( times_times_real( Y, X ),
% 0.89/1.39 times_times_real( Z, X ) ) }.
% 0.89/1.39 (2133) {G0,W12,D4,L2,V2,M2} { ! plus_plus_real( times_times_real( X, X ),
% 0.89/1.39 times_times_real( Y, Y ) ) = zero_zero_real, X = zero_zero_real }.
% 0.89/1.39 (2134) {G0,W12,D4,L2,V2,M2} { ! plus_plus_real( times_times_real( X, X ),
% 0.89/1.39 times_times_real( Y, Y ) ) = zero_zero_real, Y = zero_zero_real }.
% 0.89/1.39 (2135) {G0,W15,D4,L3,V2,M3} { ! X = zero_zero_real, ! Y = zero_zero_real,
% 0.89/1.39 plus_plus_real( times_times_real( X, X ), times_times_real( Y, Y ) ) =
% 0.89/1.39 zero_zero_real }.
% 0.89/1.39 (2136) {G0,W11,D3,L3,V2,M3} { ! power_power_nat( X, Y ) = one_one_nat, X =
% 0.89/1.39 one_one_nat, Y = zero_zero_nat }.
% 0.89/1.39 (2137) {G0,W8,D3,L2,V2,M2} { ! X = one_one_nat, power_power_nat( X, Y ) =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (2138) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, power_power_nat( X, Y )
% 0.89/1.39 = one_one_nat }.
% 0.89/1.39 (2139) {G0,W13,D4,L1,V1,M1} { minus_minus_real( times_times_real( X, X ),
% 0.89/1.39 one_one_real ) = times_times_real( plus_plus_real( X, one_one_real ),
% 0.89/1.39 minus_minus_real( X, one_one_real ) ) }.
% 0.89/1.39 (2140) {G0,W13,D4,L1,V1,M1} { minus_minus_int( times_times_int( X, X ),
% 0.89/1.39 one_one_int ) = times_times_int( plus_plus_int( X, one_one_int ),
% 0.89/1.39 minus_minus_int( X, one_one_int ) ) }.
% 0.89/1.39 (2141) {G0,W14,D5,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.39 times_times_real( power_power_real( Y, minus_minus_nat( X, one_one_nat )
% 0.89/1.39 ), Y ) = power_power_real( Y, X ) }.
% 0.89/1.39 (2142) {G0,W14,D5,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.39 times_times_nat( power_power_nat( Y, minus_minus_nat( X, one_one_nat ) )
% 0.89/1.39 , Y ) = power_power_nat( Y, X ) }.
% 0.89/1.39 (2143) {G0,W14,D5,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.39 times_times_int( power_power_int( Y, minus_minus_nat( X, one_one_nat ) )
% 0.89/1.39 , Y ) = power_power_int( Y, X ) }.
% 0.89/1.39 (2144) {G0,W8,D6,L1,V1,M1} { ord_less_eq_real( one_one_real,
% 0.89/1.39 power_power_real( number267125858f_real( bit0( bit1( pls ) ) ), X ) ) }.
% 0.89/1.39 (2145) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, power_power_real( X, Y )
% 0.89/1.39 = one_one_real }.
% 0.89/1.39 (2146) {G0,W14,D5,L2,V2,M2} { Y = zero_zero_nat, power_power_real( X, Y )
% 0.89/1.39 = times_times_real( X, power_power_real( X, minus_minus_nat( Y,
% 0.89/1.39 one_one_nat ) ) ) }.
% 0.89/1.39 (2147) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, power_power_nat( X, Y )
% 0.89/1.39 = one_one_nat }.
% 0.89/1.39 (2148) {G0,W14,D5,L2,V2,M2} { Y = zero_zero_nat, power_power_nat( X, Y ) =
% 0.89/1.39 times_times_nat( X, power_power_nat( X, minus_minus_nat( Y, one_one_nat
% 0.89/1.39 ) ) ) }.
% 0.89/1.39 (2149) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, power_power_int( X, Y )
% 0.89/1.39 = one_one_int }.
% 0.89/1.39 (2150) {G0,W14,D5,L2,V2,M2} { Y = zero_zero_nat, power_power_int( X, Y ) =
% 0.89/1.39 times_times_int( X, power_power_int( X, minus_minus_nat( Y, one_one_nat
% 0.89/1.39 ) ) ) }.
% 0.89/1.39 (2151) {G0,W16,D3,L4,V3,M4} { ! ord_less_real( X, Y ), ! ord_less_eq_real
% 0.89/1.39 ( zero_zero_real, X ), ! ord_less_nat( zero_zero_nat, Z ), ord_less_real
% 0.89/1.39 ( power_power_real( X, Z ), power_power_real( Y, Z ) ) }.
% 0.89/1.39 (2152) {G0,W16,D3,L4,V3,M4} { ! ord_less_nat( X, Y ), ! ord_less_eq_nat(
% 0.89/1.39 zero_zero_nat, X ), ! ord_less_nat( zero_zero_nat, Z ), ord_less_nat(
% 0.89/1.39 power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.39 (2153) {G0,W16,D3,L4,V3,M4} { ! ord_less_int( X, Y ), ! ord_less_eq_int(
% 0.89/1.39 zero_zero_int, X ), ! ord_less_nat( zero_zero_nat, Z ), ord_less_int(
% 0.89/1.39 power_power_int( X, Z ), power_power_int( Y, Z ) ) }.
% 0.89/1.39 (2154) {G0,W3,D2,L1,V1,M1} { ord_less_eq_real( X, X ) }.
% 0.89/1.39 (2155) {G0,W6,D2,L2,V2,M2} { ord_less_eq_real( X, Y ), ord_less_eq_real( Y
% 0.89/1.39 , X ) }.
% 0.89/1.39 (2156) {G0,W9,D2,L3,V3,M3} { ! ord_less_eq_real( X, Y ), !
% 0.89/1.39 ord_less_eq_real( Y, Z ), ord_less_eq_real( X, Z ) }.
% 0.89/1.39 (2157) {G0,W9,D2,L3,V2,M3} { ! ord_less_eq_real( X, Y ), !
% 0.89/1.39 ord_less_eq_real( Y, X ), X = Y }.
% 0.89/1.39 (2158) {G0,W8,D3,L2,V2,M2} { X = zero_zero_real, ! power_power_real( X, Y
% 0.89/1.39 ) = zero_zero_real }.
% 0.89/1.39 (2159) {G0,W10,D3,L3,V2,M3} { ! is_int( X ), X = zero_zero_int, !
% 0.89/1.39 power_power_int( X, Y ) = zero_zero_int }.
% 0.89/1.39 (2160) {G0,W13,D4,L1,V3,M1} { power_power_real( times_times_real( X, Y ),
% 0.89/1.39 Z ) = times_times_real( power_power_real( X, Z ), power_power_real( Y, Z
% 0.89/1.39 ) ) }.
% 0.89/1.39 (2161) {G0,W13,D4,L1,V3,M1} { power_power_nat( times_times_nat( X, Y ), Z
% 0.89/1.39 ) = times_times_nat( power_power_nat( X, Z ), power_power_nat( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2162) {G0,W13,D4,L1,V3,M1} { power_power_int( times_times_int( X, Y ), Z
% 0.89/1.39 ) = times_times_int( power_power_int( X, Z ), power_power_int( Y, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2163) {G0,W11,D4,L1,V2,M1} { times_times_real( power_power_real( X, Y ),
% 0.89/1.39 X ) = times_times_real( X, power_power_real( X, Y ) ) }.
% 0.89/1.39 (2164) {G0,W11,D4,L1,V2,M1} { times_times_nat( power_power_nat( X, Y ), X
% 0.89/1.39 ) = times_times_nat( X, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2165) {G0,W11,D4,L1,V2,M1} { times_times_int( power_power_int( X, Y ), X
% 0.89/1.39 ) = times_times_int( X, power_power_int( X, Y ) ) }.
% 0.89/1.39 (2166) {G0,W5,D3,L1,V1,M1} { power_power_real( one_one_real, X ) =
% 0.89/1.39 one_one_real }.
% 0.89/1.39 (2167) {G0,W5,D3,L1,V1,M1} { power_power_nat( one_one_nat, X ) =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (2168) {G0,W5,D3,L1,V1,M1} { power_power_int( one_one_int, X ) =
% 0.89/1.39 one_one_int }.
% 0.89/1.39 (2169) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat(
% 0.89/1.39 power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.39 (2170) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_int( X, Y ), dvd_dvd_int(
% 0.89/1.39 power_power_int( X, Z ), power_power_int( Y, Z ) ) }.
% 0.89/1.39 (2171) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_real( X, Y ), dvd_dvd_real(
% 0.89/1.39 power_power_real( X, Z ), power_power_real( Y, Z ) ) }.
% 0.89/1.39 (2172) {G0,W11,D4,L1,V3,M1} { power_power_real( X, times_times_nat( Y, Z )
% 0.89/1.39 ) = power_power_real( power_power_real( X, Y ), Z ) }.
% 0.89/1.39 (2173) {G0,W11,D4,L1,V3,M1} { power_power_nat( X, times_times_nat( Y, Z )
% 0.89/1.39 ) = power_power_nat( power_power_nat( X, Y ), Z ) }.
% 0.89/1.39 (2174) {G0,W11,D4,L1,V3,M1} { power_power_int( X, times_times_nat( Y, Z )
% 0.89/1.39 ) = power_power_int( power_power_int( X, Y ), Z ) }.
% 0.89/1.39 (2175) {G0,W5,D3,L1,V1,M1} { power_power_real( X, one_one_nat ) = X }.
% 0.89/1.39 (2176) {G0,W5,D3,L1,V1,M1} { power_power_nat( X, one_one_nat ) = X }.
% 0.89/1.39 (2177) {G0,W7,D3,L2,V1,M2} { ! is_int( X ), power_power_int( X,
% 0.89/1.39 one_one_nat ) = X }.
% 0.89/1.39 (2178) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_real( X, Y ), !
% 0.89/1.39 ord_less_eq_real( zero_zero_real, X ), ord_less_eq_real( power_power_real
% 0.89/1.39 ( X, Z ), power_power_real( Y, Z ) ) }.
% 0.89/1.39 (2179) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_nat
% 0.89/1.39 ( zero_zero_nat, X ), ord_less_eq_nat( power_power_nat( X, Z ),
% 0.89/1.39 power_power_nat( Y, Z ) ) }.
% 0.89/1.39 (2180) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_int( X, Y ), ! ord_less_eq_int
% 0.89/1.39 ( zero_zero_int, X ), ord_less_eq_int( power_power_int( X, Z ),
% 0.89/1.39 power_power_int( Y, Z ) ) }.
% 0.89/1.39 (2181) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_real( zero_zero_real, X ),
% 0.89/1.39 ord_less_eq_real( zero_zero_real, power_power_real( X, Y ) ) }.
% 0.89/1.39 (2182) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_nat( zero_zero_nat, X ),
% 0.89/1.39 ord_less_eq_nat( zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2183) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( zero_zero_int, X ),
% 0.89/1.39 ord_less_eq_int( zero_zero_int, power_power_int( X, Y ) ) }.
% 0.89/1.39 (2184) {G0,W8,D3,L2,V2,M2} { ! ord_less_real( zero_zero_real, X ),
% 0.89/1.39 ord_less_real( zero_zero_real, power_power_real( X, Y ) ) }.
% 0.89/1.39 (2185) {G0,W8,D3,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.39 ord_less_nat( zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2186) {G0,W8,D3,L2,V2,M2} { ! ord_less_int( zero_zero_int, X ),
% 0.89/1.39 ord_less_int( zero_zero_int, power_power_int( X, Y ) ) }.
% 0.89/1.39 (2187) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_real( one_one_real, X ),
% 0.89/1.39 ord_less_eq_real( one_one_real, power_power_real( X, Y ) ) }.
% 0.89/1.39 (2188) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_nat( one_one_nat, X ),
% 0.89/1.39 ord_less_eq_nat( one_one_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2189) {G0,W8,D3,L2,V2,M2} { ! ord_less_eq_int( one_one_int, X ),
% 0.89/1.39 ord_less_eq_int( one_one_int, power_power_int( X, Y ) ) }.
% 0.89/1.39 (2190) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( one_one_real, X ), !
% 0.89/1.39 power_power_real( X, Y ) = power_power_real( X, Z ), Y = Z }.
% 0.89/1.39 (2191) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( one_one_real, X ), ! Y = Z
% 0.89/1.39 , power_power_real( X, Y ) = power_power_real( X, Z ) }.
% 0.89/1.39 (2192) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( one_one_nat, X ), !
% 0.89/1.39 power_power_nat( X, Y ) = power_power_nat( X, Z ), Y = Z }.
% 0.89/1.39 (2193) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( one_one_nat, X ), ! Y = Z,
% 0.89/1.39 power_power_nat( X, Y ) = power_power_nat( X, Z ) }.
% 0.89/1.39 (2194) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( one_one_int, X ), !
% 0.89/1.39 power_power_int( X, Y ) = power_power_int( X, Z ), Y = Z }.
% 0.89/1.39 (2195) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( one_one_int, X ), ! Y = Z,
% 0.89/1.39 power_power_int( X, Y ) = power_power_int( X, Z ) }.
% 0.89/1.39 (2196) {G0,W8,D3,L2,V2,M2} { ! power_power_real( X, Y ) = zero_zero_real,
% 0.89/1.39 X = zero_zero_real }.
% 0.89/1.39 (2197) {G0,W8,D3,L2,V2,M2} { ! power_power_real( X, Y ) = zero_zero_real,
% 0.89/1.39 ! Y = zero_zero_nat }.
% 0.89/1.39 (2198) {G0,W11,D3,L3,V2,M3} { ! X = zero_zero_real, Y = zero_zero_nat,
% 0.89/1.39 power_power_real( X, Y ) = zero_zero_real }.
% 0.89/1.39 (2199) {G0,W8,D3,L2,V2,M2} { ! power_power_nat( X, Y ) = zero_zero_nat, X
% 0.89/1.39 = zero_zero_nat }.
% 0.89/1.39 (2200) {G0,W8,D3,L2,V2,M2} { ! power_power_nat( X, Y ) = zero_zero_nat, !
% 0.89/1.39 Y = zero_zero_nat }.
% 0.89/1.39 (2201) {G0,W11,D3,L3,V2,M3} { ! X = zero_zero_nat, Y = zero_zero_nat,
% 0.89/1.39 power_power_nat( X, Y ) = zero_zero_nat }.
% 0.89/1.39 (2202) {G0,W10,D3,L3,V2,M3} { ! is_int( X ), ! power_power_int( X, Y ) =
% 0.89/1.39 zero_zero_int, X = zero_zero_int }.
% 0.89/1.39 (2203) {G0,W10,D3,L3,V2,M3} { ! is_int( X ), ! power_power_int( X, Y ) =
% 0.89/1.39 zero_zero_int, ! Y = zero_zero_nat }.
% 0.89/1.39 (2204) {G0,W13,D3,L4,V2,M4} { ! is_int( X ), ! X = zero_zero_int, Y =
% 0.89/1.39 zero_zero_nat, power_power_int( X, Y ) = zero_zero_int }.
% 0.89/1.39 (2205) {G0,W5,D3,L1,V1,M1} { power_power_real( X, zero_zero_nat ) =
% 0.89/1.39 one_one_real }.
% 0.89/1.39 (2206) {G0,W5,D3,L1,V1,M1} { power_power_nat( X, zero_zero_nat ) =
% 0.89/1.39 one_one_nat }.
% 0.89/1.39 (2207) {G0,W5,D3,L1,V1,M1} { power_power_int( X, zero_zero_nat ) =
% 0.89/1.39 one_one_int }.
% 0.89/1.39 (2208) {G0,W13,D4,L1,V3,M1} { power_power_real( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 = times_times_real( power_power_real( X, Y ), power_power_real( X, Z ) )
% 0.89/1.39 }.
% 0.89/1.39 (2209) {G0,W13,D4,L1,V3,M1} { power_power_nat( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 = times_times_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ) }.
% 0.89/1.39 (2210) {G0,W13,D4,L1,V3,M1} { power_power_int( X, plus_plus_nat( Y, Z ) )
% 0.89/1.39 = times_times_int( power_power_int( X, Y ), power_power_int( X, Z ) ) }.
% 0.89/1.39 (2211) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_nat( power_power_nat( X, Y ), Z )
% 0.89/1.39 , ! ord_less_eq_nat( T, Y ), dvd_dvd_nat( power_power_nat( X, T ), Z )
% 0.89/1.39 }.
% 0.89/1.39 (2212) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_int( power_power_int( X, Y ), Z )
% 0.89/1.39 , ! ord_less_eq_nat( T, Y ), dvd_dvd_int( power_power_int( X, T ), Z )
% 0.89/1.39 }.
% 0.89/1.39 (2213) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_real( power_power_real( X, Y ), Z
% 0.89/1.39 ), ! ord_less_eq_nat( T, Y ), dvd_dvd_real( power_power_real( X, T ), Z
% 0.89/1.39 ) }.
% 0.89/1.39 (2214) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_nat( X, Y ), ! ord_less_eq_nat( Z
% 0.89/1.39 , T ), dvd_dvd_nat( power_power_nat( X, Z ), power_power_nat( Y, T ) )
% 0.89/1.39 }.
% 0.89/1.39 (2215) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_int( X, Y ), ! ord_less_eq_nat( Z
% 0.89/1.39 , T ), dvd_dvd_int( power_power_int( X, Z ), power_power_int( Y, T ) )
% 0.89/1.39 }.
% 0.89/1.39 (2216) {G0,W13,D3,L3,V4,M3} { ! dvd_dvd_real( X, Y ), ! ord_less_eq_nat( Z
% 0.89/1.39 , T ), dvd_dvd_real( power_power_real( X, Z ), power_power_real( Y, T ) )
% 0.89/1.39 }.
% 0.89/1.39 (2217) {G0,W10,D3,L2,V3,M2} { ! ord_less_eq_nat( X, Y ), dvd_dvd_nat(
% 0.89/1.39 power_power_nat( Z, X ), power_power_nat( Z, Y ) ) }.
% 0.89/1.39 (2218) {G0,W10,D3,L2,V3,M2} { ! ord_less_eq_nat( X, Y ), dvd_dvd_int(
% 0.89/1.39 power_power_int( Z, X ), power_power_int( Z, Y ) ) }.
% 0.89/1.39 (2219) {G0,W10,D3,L2,V3,M2} { ! ord_less_eq_nat( X, Y ), dvd_dvd_real(
% 0.89/1.39 power_power_real( Z, X ), power_power_real( Z, Y ) ) }.
% 0.89/1.39 (2220) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 ord_less_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2221) {G0,W11,D3,L3,V2,M3} { ! ord_less_nat( zero_zero_nat,
% 0.89/1.39 power_power_nat( X, Y ) ), ord_less_nat( zero_zero_nat, X ), Y =
% 0.89/1.39 zero_zero_nat }.
% 0.89/1.39 (2222) {G0,W8,D3,L2,V2,M2} { ! ord_less_nat( zero_zero_nat, X ),
% 0.89/1.39 ord_less_nat( zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2223) {G0,W8,D3,L2,V2,M2} { ! Y = zero_zero_nat, ord_less_nat(
% 0.89/1.39 zero_zero_nat, power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2224) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( power_power_real( X, Z ),
% 0.89/1.39 power_power_real( Y, Z ) ), ! ord_less_eq_real( zero_zero_real, Y ),
% 0.89/1.39 ord_less_real( X, Y ) }.
% 0.89/1.39 (2225) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( power_power_nat( X, Z ),
% 0.89/1.39 power_power_nat( Y, Z ) ), ! ord_less_eq_nat( zero_zero_nat, Y ),
% 0.89/1.39 ord_less_nat( X, Y ) }.
% 0.89/1.39 (2226) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( power_power_int( X, Z ),
% 0.89/1.39 power_power_int( Y, Z ) ), ! ord_less_eq_int( zero_zero_int, Y ),
% 0.89/1.39 ord_less_int( X, Y ) }.
% 0.89/1.39 (2227) {G0,W12,D4,L2,V2,M2} { ! ord_less_real( one_one_real, X ),
% 0.89/1.39 ord_less_real( power_power_real( X, Y ), times_times_real( X,
% 0.89/1.39 power_power_real( X, Y ) ) ) }.
% 0.89/1.39 (2228) {G0,W12,D4,L2,V2,M2} { ! ord_less_nat( one_one_nat, X ),
% 0.89/1.39 ord_less_nat( power_power_nat( X, Y ), times_times_nat( X,
% 0.89/1.39 power_power_nat( X, Y ) ) ) }.
% 0.89/1.39 (2229) {G0,W12,D4,L2,V2,M2} { ! ord_less_int( one_one_int, X ),
% 0.89/1.39 ord_less_int( power_power_int( X, Y ), times_times_int( X,
% 0.89/1.39 power_power_int( X, Y ) ) ) }.
% 0.89/1.39 (2230) {G0,W10,D4,L2,V2,M2} { ! ord_less_real( one_one_real, X ),
% 0.89/1.39 ord_less_real( one_one_real, times_times_real( X, power_power_real( X, Y
% 0.89/1.39 ) ) ) }.
% 0.89/1.39 (2231) {G0,W10,D4,L2,V2,M2} { ! ord_less_nat( one_one_nat, X ),
% 0.89/1.39 ord_less_nat( one_one_nat, times_times_nat( X, power_power_nat( X, Y ) )
% 0.89/1.39 ) }.
% 0.89/1.39 (2232) {G0,W10,D4,L2,V2,M2} { ! ord_less_int( one_one_int, X ),
% 0.89/1.39 ord_less_int( one_one_int, times_times_int( X, power_power_int( X, Y ) )
% 0.89/1.39 ) }.
% 0.89/1.39 (2233) {G0,W8,D3,L2,V1,M2} { ! X = zero_zero_nat, power_power_real(
% 0.89/1.39 zero_zero_real, X ) = one_one_real }.
% 0.89/1.39 (2234) {G0,W8,D3,L2,V1,M2} { X = zero_zero_nat, power_power_real(
% 0.89/1.39 zero_zero_real, X ) = zero_zero_real }.
% 0.89/1.39 (2235) {G0,W8,D3,L2,V1,M2} { ! X = zero_zero_nat, power_power_nat(
% 0.89/1.39 zero_zero_nat, X ) = one_one_nat }.
% 0.89/1.39 (2236) {G0,W8,D3,L2,V1,M2} { X = zero_zero_nat, power_power_nat(
% 0.89/1.39 zero_zero_nat, X ) = zero_zero_nat }.
% 0.89/1.39 (2237) {G0,W8,D3,L2,V1,M2} { ! X = zero_zero_nat, power_power_int(
% 0.89/1.39 zero_zero_int, X ) = one_one_int }.
% 0.89/1.39 (2238) {G0,W8,D3,L2,V1,M2} { X = zero_zero_nat, power_power_int(
% 0.89/1.39 zero_zero_int, X ) = zero_zero_int }.
% 0.89/1.39 (2239) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( X, Y ), ! ord_less_real(
% 0.89/1.39 one_one_real, Z ), ord_less_real( power_power_real( Z, X ),
% 0.89/1.39 power_power_real( Z, Y ) ) }.
% 0.89/1.39 (2240) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( X, Y ), ! ord_less_nat(
% 0.89/1.39 one_one_nat, Z ), ord_less_nat( power_power_nat( Z, X ), power_power_nat
% 0.89/1.39 ( Z, Y ) ) }.
% 0.89/1.39 (2241) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( X, Y ), ! ord_less_int(
% 0.89/1.39 one_one_int, Z ), ord_less_int( power_power_int( Z, X ), power_power_int
% 0.89/1.39 ( Z, Y ) ) }.
% 0.89/1.39 (2242) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( one_one_real, X ), !
% 0.89/1.39 ord_less_real( power_power_real( X, Y ), power_power_real( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2243) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( one_one_nat, X ), !
% 0.89/1.39 ord_less_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2244) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( one_one_int, X ), !
% 0.89/1.39 ord_less_int( power_power_int( X, Y ), power_power_int( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2245) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( one_one_real, X ), !
% 0.89/1.39 ord_less_real( power_power_real( X, Y ), power_power_real( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2246) {G0,W13,D3,L3,V3,M3} { ! ord_less_real( one_one_real, X ), !
% 0.89/1.39 ord_less_nat( Y, Z ), ord_less_real( power_power_real( X, Y ),
% 0.89/1.39 power_power_real( X, Z ) ) }.
% 0.89/1.39 (2247) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( one_one_nat, X ), !
% 0.89/1.39 ord_less_nat( power_power_nat( X, Y ), power_power_nat( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2248) {G0,W13,D3,L3,V3,M3} { ! ord_less_nat( one_one_nat, X ), !
% 0.89/1.39 ord_less_nat( Y, Z ), ord_less_nat( power_power_nat( X, Y ),
% 0.89/1.39 power_power_nat( X, Z ) ) }.
% 0.89/1.39 (2249) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( one_one_int, X ), !
% 0.89/1.39 ord_less_int( power_power_int( X, Y ), power_power_int( X, Z ) ),
% 0.89/1.39 ord_less_nat( Y, Z ) }.
% 0.89/1.39 (2250) {G0,W13,D3,L3,V3,M3} { ! ord_less_int( one_one_int, X ), !
% 0.89/1.39 ord_less_nat( Y, Z ), ord_less_int( power_power_int( X, Y ),
% 0.89/1.39 power_power_int( X, Z ) ) }.
% 0.89/1.39 (2251) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_nat( X, Y ), !
% 0.89/1.39 ord_less_eq_real( one_one_real, Z ), ord_less_eq_real( power_power_real(
% 0.89/1.39 Z, X ), power_power_real( Z, Y ) ) }.
% 0.89/1.39 (2252) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_nat
% 0.89/1.39 ( one_one_nat, Z ), ord_less_eq_nat( power_power_nat( Z, X ),
% 0.89/1.39 power_power_nat( Z, Y ) ) }.
% 0.89/1.39 (2253) {G0,W13,D3,L3,V3,M3} { ! ord_less_eq_nat( X, Y ), ! ord_less_eq_int
% 0.89/1.39 ( one_one_int, Z ), ord_less_eq_int( power_power_int( Z, X ),
% 0.89/1.39 power_power_int( Z, Y ) ) }.
% 0.89/1.39 (2254) {G0,W15,D4,L3,V2,M3} { ! ord_less_real( zero_zero_real, X ), !
% 0.89/1.39 ord_less_real( X, one_one_real ), ord_less_real( times_times_real( X,
% 0.89/1.39 power_power_real( X, Y ) ), power_power_real( X, Y ) ) }.
% 0.89/1.39 (2255) {G0,W15,D4,L3,V2,M3} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 ord_less_nat( X, one_one_nat ), ord_less_nat( times_times_nat( X,
% 0.89/1.39 power_power_nat( X, Y ) ), power_power_nat( X, Y ) ) }.
% 0.89/1.39 (2256) {G0,W15,D4,L3,V2,M3} { ! ord_less_int( zero_zero_int, X ), !
% 0.89/1.39 ord_less_int( X, one_one_int ), ord_less_int( times_times_int( X,
% 0.89/1.39 power_power_int( X, Y ) ), power_power_int( X, Y ) ) }.
% 0.89/1.39 (2257) {G0,W16,D3,L4,V3,M4} { ! ord_less_nat( X, Y ), ! ord_less_int(
% 0.89/1.39 zero_zero_int, Z ), ! ord_less_int( Z, one_one_int ), ord_less_int(
% 0.89/1.39 power_power_int( Z, Y ), power_power_int( Z, X ) ) }.
% 0.89/1.39 (2258) {G0,W11,D3,L3,V4,M3} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 ord_less_real( zero_zero_real, Y ), ord_less_real( zero_zero_real, skol8
% 0.89/1.39 ( Z, T ) ) }.
% 0.89/1.39 (2259) {G0,W13,D4,L3,V2,M3} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 ord_less_real( zero_zero_real, Y ), power_power_real( skol8( X, Y ), X )
% 0.89/1.39 = Y }.
% 0.89/1.39 (2260) {G0,W19,D3,L5,V3,M5} { ! ord_less_nat( zero_zero_nat, X ), !
% 0.89/1.39 ord_less_real( zero_zero_real, Y ), ! ord_less_real( zero_zero_real, Z )
% 0.89/1.39 , ! power_power_real( Z, X ) = Y, Z = skol8( X, Y ) }.
% 0.89/1.39 (2261) {G0,W9,D2,L3,V2,M3} { ! dvd_dvd_nat( X, Y ), Y = zero_zero_nat,
% 0.89/1.39 ord_less_eq_nat( X, Y ) }.
% 0.89/1.39 (2262) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat(
% 0.89/1.39 power_power_nat( X, Z ), power_power_nat( Y, Z ) ) }.
% 0.89/1.39 (2263) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat(
% 0.89/1.39 times_times_nat( Z, X ), times_times_nat( Z, Y ) ) }.
% 0.89/1.39 (2264) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_nat( X, Y ), dvd_dvd_nat(
% 0.89/1.39 times_times_nat( X, Z ), times_times_nat( Y, Z ) ) }.
% 0.89/1.39 (2265) {G0,W11,D3,L3,V3,M3} { ! dvd_dvd_nat( X, Y ), ! dvd_dvd_nat( X,
% 0.89/1.39 plus_plus_nat( Y, Z ) ), dvd_dvd_nat( X, Z ) }.
% 0.89/1.39 (2266) {G0,W13,D3,L3,V3,M3} { ! dvd_dvd_nat( times_times_nat( X, Y ),
% 0.89/1.39 times_times_nat( Z, Y ) ), Y = zero_zero_nat, dvd_dvd_nat( X, Z ) }.
% 0.89/1.39 (2267) {G0,W10,D3,L2,V3,M2} { ! Y = zero_zero_nat, dvd_dvd_nat(
% 0.89/1.39 times_times_nat( X, Y ), times_times_nat( Z, Y ) ) }.
% 0.89/1.39 (2268) {G0,W10,D3,L2,V3,M2} { ! dvd_dvd_nat( X, Z ), dvd_dvd_nat(
% 0.89/1.39 times_times_nat( X, Y ), times_times_nat( Z, Y ) ) }.
% 0.89/1.39 (2269) {G0,W13,D3,L3,V3,M3} { ! dvd_dvd_nat( power_power_nat( X, Y ),
% 0.89/1.39 power_power_nat( Z, Y ) ), Y = zero_zero_nat, dvd_dvd_nat( X, Z ) }.
% 0.89/1.39 (2270) {G0,W11,D3,L3,V3,M3} { X = zero_zero_nat, ! dvd_dvd_nat(
% 0.89/1.39 power_power_nat( Y, X ), Z ), dvd_dvd_nat( Y, Z ) }.
% 0.89/1.39 (2271) {G0,W16,D4,L4,V4,M4} { ! X = plus_plus_nat( times_times_nat( T, Y )
% 0.89/1.39 , Z ), ! ord_less_nat( zero_zero_nat, Z ), ! ord_less_nat( Z, Y ), !
% 0.89/1.39 dvd_dvd_nat( Y, X ) }.
% 0.89/1.39 (2272) {G0,W13,D3,L3,V3,M3} { ! dvd_dvd_nat( power_power_nat( X, Y ),
% 0.89/1.39 power_power_nat( X, Z ) ), ! ord_less_nat( one_one_nat, X ),
% 0.89/1.39 ord_less_eq_nat( Y, Z ) }.
% 0.89/1.39 (2273) {G0,W17,D6,L4,V2,M4} { ! dvd_dvd_nat( X, Y ), Y = zero_zero_nat, Y
% 0.89/1.39 = X, ord_less_eq_nat( times_times_nat( number_number_of_nat( bit0( bit1(
% 0.89/1.39 pls ) ) ), X ), Y ) }.
% 0.89/1.39 (2274) {G0,W10,D7,L1,V0,M1} { ! ord_less_int( plus_plus_int(
% 0.89/1.39 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.39 one_one_int ), zero_zero_int ) }.
% 0.89/1.39
% 0.89/1.39
% 0.89/1.39 Total Proof:
% 0.89/1.39
% 0.89/1.39 subsumption: (19) {G0,W23,D9,L1,V0,M1} I { ord_less_int( times_times_int(
% 0.89/1.39 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), m ), one_one_int ), t ), times_times_int( plus_plus_int(
% 0.89/1.39 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.39 , one_one_int ), zero_zero_int ) ) }.
% 0.89/1.39 parent0: (1326) {G0,W23,D9,L1,V0,M1} { ord_less_int( times_times_int(
% 0.89/1.39 plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1(
% 0.89/1.39 pls ) ) ) ), m ), one_one_int ), t ), times_times_int( plus_plus_int(
% 0.89/1.39 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.39 , one_one_int ), zero_zero_int ) ) }.
% 0.89/1.39 substitution0:
% 0.89/1.39 end
% 0.89/1.39 permutation0:
% 0.89/1.39 0 ==> 0
% 0.89/1.39 end
% 0.89/1.39
% 0.89/1.39 eqswap: (2283) {G0,W20,D9,L1,V0,M1} { times_times_int( plus_plus_int(
% 0.89/1.39 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.39 , one_one_int ), t ) = plus_plus_int( power_power_int( s,
% 0.89/1.39 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.39 parent0[0]: (1327) {G0,W20,D9,L1,V0,M1} { plus_plus_int( power_power_int(
% 0.89/1.39 s, number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) =
% 0.89/1.39 times_times_int( plus_plus_int( times_times_int( number_number_of_int(
% 0.89/1.39 bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ), t ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 subsumption: (20) {G0,W20,D9,L1,V0,M1} I { times_times_int( plus_plus_int(
% 0.89/1.42 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.42 , one_one_int ), t ) ==> plus_plus_int( power_power_int( s,
% 0.89/1.42 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.42 parent0: (2283) {G0,W20,D9,L1,V0,M1} { times_times_int( plus_plus_int(
% 0.89/1.42 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.42 , one_one_int ), t ) = plus_plus_int( power_power_int( s,
% 0.89/1.42 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 permutation0:
% 0.89/1.42 0 ==> 0
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 eqswap: (2444) {G0,W8,D5,L1,V0,M1} { number_number_of_nat( bit0( bit1( pls
% 0.89/1.42 ) ) ) = plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.42 parent0[0]: (1456) {G0,W8,D5,L1,V0,M1} { plus_plus_nat( one_one_nat,
% 0.89/1.42 one_one_nat ) = number_number_of_nat( bit0( bit1( pls ) ) ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 subsumption: (132) {G0,W8,D5,L1,V0,M1} I { number_number_of_nat( bit0( bit1
% 0.89/1.42 ( pls ) ) ) ==> plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.42 parent0: (2444) {G0,W8,D5,L1,V0,M1} { number_number_of_nat( bit0( bit1(
% 0.89/1.42 pls ) ) ) = plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 permutation0:
% 0.89/1.42 0 ==> 0
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 *** allocated 170857 integers for clauses
% 0.89/1.42 subsumption: (407) {G0,W5,D3,L1,V1,M1} I { times_times_int( X,
% 0.89/1.42 zero_zero_int ) ==> zero_zero_int }.
% 0.89/1.42 parent0: (1818) {G0,W5,D3,L1,V1,M1} { times_times_int( X, zero_zero_int )
% 0.89/1.42 = zero_zero_int }.
% 0.89/1.42 substitution0:
% 0.89/1.42 X := X
% 0.89/1.42 end
% 0.89/1.42 permutation0:
% 0.89/1.42 0 ==> 0
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 *** allocated 113905 integers for termspace/termends
% 0.89/1.42 *** allocated 256285 integers for clauses
% 0.89/1.42 paramod: (8936) {G1,W9,D5,L1,V0,M1} { ! ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), zero_zero_int ) }.
% 0.89/1.42 parent0[0]: (132) {G0,W8,D5,L1,V0,M1} I { number_number_of_nat( bit0( bit1
% 0.89/1.42 ( pls ) ) ) ==> plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.42 parent1[0; 5]: (2274) {G0,W10,D7,L1,V0,M1} { ! ord_less_int( plus_plus_int
% 0.89/1.42 ( power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.42 one_one_int ), zero_zero_int ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 substitution1:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 subsumption: (757) {G1,W9,D5,L1,V0,M1} I;d(132) { ! ord_less_int(
% 0.89/1.42 plus_plus_int( power_power_int( s, plus_plus_nat( one_one_nat,
% 0.89/1.42 one_one_nat ) ), one_one_int ), zero_zero_int ) }.
% 0.89/1.42 parent0: (8936) {G1,W9,D5,L1,V0,M1} { ! ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), zero_zero_int ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 permutation0:
% 0.89/1.42 0 ==> 0
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 paramod: (8940) {G1,W20,D9,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.42 one_one_int ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.42 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.42 zero_zero_int ) ) }.
% 0.89/1.42 parent0[0]: (20) {G0,W20,D9,L1,V0,M1} I { times_times_int( plus_plus_int(
% 0.89/1.42 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.42 , one_one_int ), t ) ==> plus_plus_int( power_power_int( s,
% 0.89/1.42 number_number_of_nat( bit0( bit1( pls ) ) ) ), one_one_int ) }.
% 0.89/1.42 parent1[0; 1]: (19) {G0,W23,D9,L1,V0,M1} I { ord_less_int( times_times_int
% 0.89/1.42 ( plus_plus_int( times_times_int( number_number_of_int( bit0( bit0( bit1
% 0.89/1.42 ( pls ) ) ) ), m ), one_one_int ), t ), times_times_int( plus_plus_int(
% 0.89/1.42 times_times_int( number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m )
% 0.89/1.42 , one_one_int ), zero_zero_int ) ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 substitution1:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 paramod: (8941) {G1,W19,D9,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.42 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.42 zero_zero_int ) ) }.
% 0.89/1.42 parent0[0]: (132) {G0,W8,D5,L1,V0,M1} I { number_number_of_nat( bit0( bit1
% 0.89/1.42 ( pls ) ) ) ==> plus_plus_nat( one_one_nat, one_one_nat ) }.
% 0.89/1.42 parent1[0; 4]: (8940) {G1,W20,D9,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, number_number_of_nat( bit0( bit1( pls ) ) ) ),
% 0.89/1.42 one_one_int ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.42 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.42 zero_zero_int ) ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 substitution1:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 paramod: (8942) {G1,W9,D5,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), zero_zero_int ) }.
% 0.89/1.42 parent0[0]: (407) {G0,W5,D3,L1,V1,M1} I { times_times_int( X, zero_zero_int
% 0.89/1.42 ) ==> zero_zero_int }.
% 0.89/1.42 parent1[0; 8]: (8941) {G1,W19,D9,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), times_times_int( plus_plus_int( times_times_int(
% 0.89/1.42 number_number_of_int( bit0( bit0( bit1( pls ) ) ) ), m ), one_one_int ),
% 0.89/1.42 zero_zero_int ) ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 X := plus_plus_int( times_times_int( number_number_of_int( bit0( bit0(
% 0.89/1.42 bit1( pls ) ) ) ), m ), one_one_int )
% 0.89/1.42 end
% 0.89/1.42 substitution1:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 resolution: (8943) {G2,W0,D0,L0,V0,M0} { }.
% 0.89/1.42 parent0[0]: (757) {G1,W9,D5,L1,V0,M1} I;d(132) { ! ord_less_int(
% 0.89/1.42 plus_plus_int( power_power_int( s, plus_plus_nat( one_one_nat,
% 0.89/1.42 one_one_nat ) ), one_one_int ), zero_zero_int ) }.
% 0.89/1.42 parent1[0]: (8942) {G1,W9,D5,L1,V0,M1} { ord_less_int( plus_plus_int(
% 0.89/1.42 power_power_int( s, plus_plus_nat( one_one_nat, one_one_nat ) ),
% 0.89/1.42 one_one_int ), zero_zero_int ) }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 substitution1:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 subsumption: (1305) {G2,W0,D0,L0,V0,M0} S(19);d(20);d(132);d(407);r(757) {
% 0.89/1.42 }.
% 0.89/1.42 parent0: (8943) {G2,W0,D0,L0,V0,M0} { }.
% 0.89/1.42 substitution0:
% 0.89/1.42 end
% 0.89/1.42 permutation0:
% 0.89/1.42 end
% 0.89/1.42
% 0.89/1.42 Proof check complete!
% 0.89/1.42
% 0.89/1.42 Memory use:
% 0.89/1.42
% 0.89/1.42 space for terms: 41597
% 0.89/1.42 space for clauses: 89004
% 0.89/1.42
% 0.89/1.42
% 0.89/1.42 clauses generated: 2083
% 0.89/1.42 clauses kept: 1306
% 0.89/1.42 clauses selected: 52
% 0.89/1.42 clauses deleted: 4
% 0.89/1.42 clauses inuse deleted: 0
% 0.89/1.42
% 0.89/1.42 subsentry: 56406
% 0.89/1.42 literals s-matched: 15949
% 0.89/1.42 literals matched: 14116
% 0.89/1.42 full subsumption: 5200
% 0.89/1.42
% 0.89/1.42 checksum: 890597235
% 0.89/1.42
% 0.89/1.42
% 0.89/1.42 Bliksem ended
%------------------------------------------------------------------------------