TSTP Solution File: ARI719_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI719_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 : 300s
% DateTime : Wed Aug 30 17:48:55 EDT 2023
% Result : Theorem 36.83s 5.98s
% Output : Proof 63.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : ARI719_1 : TPTP v8.1.2. Released v6.3.0.
% 0.12/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 19:03:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.18/0.57 ________ _____
% 0.18/0.57 ___ __ \_________(_)________________________________
% 0.18/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.57
% 0.18/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.57 (2023-06-19)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2023
% 0.18/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.57 Amanda Stjerna.
% 0.18/0.57 Free software under BSD-3-Clause.
% 0.18/0.57
% 0.18/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.58 Running up to 7 provers in parallel.
% 0.18/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.42/0.93 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.42/0.93 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.94/1.05 Prover 1: Preprocessing ...
% 1.94/1.05 Prover 4: Preprocessing ...
% 2.56/1.16 Prover 6: Preprocessing ...
% 2.56/1.17 Prover 0: Preprocessing ...
% 2.56/1.18 Prover 5: Preprocessing ...
% 2.56/1.19 Prover 3: Preprocessing ...
% 3.19/1.20 Prover 2: Preprocessing ...
% 7.83/1.99 Prover 6: Proving ...
% 8.40/2.02 Prover 1: Constructing countermodel ...
% 8.40/2.10 Prover 4: Constructing countermodel ...
% 9.00/2.15 Prover 0: Proving ...
% 12.43/2.68 Prover 1: gave up
% 12.43/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.92/2.74 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 13.37/2.82 Prover 7: Preprocessing ...
% 13.37/2.86 Prover 3: Constructing countermodel ...
% 14.10/2.88 Prover 2: Proving ...
% 15.02/3.06 Prover 5: Proving ...
% 18.39/3.48 Prover 7: Warning: ignoring some quantifiers
% 18.39/3.52 Prover 7: Constructing countermodel ...
% 36.83/5.97 Prover 3: proved (5380ms)
% 36.83/5.98
% 36.83/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.83/5.98
% 36.83/5.98 Prover 5: stopped
% 36.83/5.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 36.83/5.98 Prover 0: stopped
% 36.83/5.98 Prover 2: stopped
% 36.83/5.98 Prover 6: stopped
% 36.83/5.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 36.83/5.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 36.83/5.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 36.83/5.98 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 36.83/5.98 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 36.83/5.98 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 36.83/5.98 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 36.83/5.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 36.83/5.99 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 36.83/6.00 Prover 8: Preprocessing ...
% 36.83/6.00 Prover 13: Preprocessing ...
% 37.60/6.03 Prover 11: Preprocessing ...
% 37.60/6.05 Prover 10: Preprocessing ...
% 37.60/6.06 Prover 16: Preprocessing ...
% 38.06/6.11 Prover 8: Warning: ignoring some quantifiers
% 38.06/6.12 Prover 8: Constructing countermodel ...
% 39.10/6.24 Prover 13: Warning: ignoring some quantifiers
% 39.10/6.25 Prover 13: Constructing countermodel ...
% 39.89/6.37 Prover 8: gave up
% 39.89/6.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 39.89/6.38 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation
% 40.37/6.43 Prover 19: Preprocessing ...
% 40.37/6.52 Prover 13: gave up
% 40.37/6.62 Prover 10: Warning: ignoring some quantifiers
% 40.37/6.65 Prover 10: Constructing countermodel ...
% 43.06/6.81 Prover 11: Constructing countermodel ...
% 43.70/6.85 Prover 16: Warning: ignoring some quantifiers
% 43.70/6.87 Prover 16: Constructing countermodel ...
% 51.00/7.84 Prover 19: Warning: ignoring some quantifiers
% 51.51/7.86 Prover 19: Constructing countermodel ...
% 62.27/9.26 Prover 16: Found proof (size 29)
% 62.27/9.26 Prover 16: proved (3282ms)
% 62.27/9.26 Prover 11: stopped
% 62.27/9.26 Prover 19: stopped
% 62.27/9.27 Prover 7: stopped
% 62.27/9.27 Prover 4: stopped
% 62.45/9.28 Prover 10: stopped
% 62.45/9.28
% 62.45/9.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.45/9.28
% 62.45/9.29 % SZS output start Proof for theBenchmark
% 62.45/9.30 Assumptions after simplification:
% 62.45/9.30 ---------------------------------
% 62.45/9.30
% 62.45/9.30 (prove)
% 62.69/9.33 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$sum(v0, real_-3/10) = v1) | ?
% 62.69/9.33 [v2: $real] : ? [v3: $real] : ? [v4: $real] : ( ~ (v4 = v3) &
% 62.69/9.33 real_$sum(v0, real_1/2) = v2 & real_$floor(v2) = v3 & real_$floor(v1) =
% 62.69/9.33 v4))
% 62.69/9.33
% 62.69/9.33 (input)
% 63.28/9.51 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_9/100) &
% 63.28/9.51 ~ (real_very_large = real_-5/3) & ~ (real_very_large = real_-10/3) & ~
% 63.28/9.51 (real_very_large = real_-4/5) & ~ (real_very_large = real_3/10) & ~
% 63.28/9.51 (real_very_large = real_-3/5) & ~ (real_very_large = real_-3/20) & ~
% 63.28/9.51 (real_very_large = real_4/5) & ~ (real_very_large = real_1/5) & ~
% 63.28/9.51 (real_very_large = real_2) & ~ (real_very_large = real_1/4) & ~
% 63.28/9.51 (real_very_large = real_1) & ~ (real_very_large = real_-1/2) & ~
% 63.28/9.51 (real_very_large = real_-3/10) & ~ (real_very_large = real_1/2) & ~
% 63.28/9.51 (real_very_large = real_0) & ~ (real_very_small = real_9/100) & ~
% 63.28/9.51 (real_very_small = real_-5/3) & ~ (real_very_small = real_-10/3) & ~
% 63.28/9.51 (real_very_small = real_-4/5) & ~ (real_very_small = real_3/10) & ~
% 63.28/9.51 (real_very_small = real_-3/5) & ~ (real_very_small = real_-3/20) & ~
% 63.28/9.51 (real_very_small = real_4/5) & ~ (real_very_small = real_1/5) & ~
% 63.28/9.51 (real_very_small = real_2) & ~ (real_very_small = real_1/4) & ~
% 63.28/9.51 (real_very_small = real_1) & ~ (real_very_small = real_-1/2) & ~
% 63.28/9.51 (real_very_small = real_-3/10) & ~ (real_very_small = real_1/2) & ~
% 63.28/9.51 (real_very_small = real_0) & ~ (real_9/100 = real_-5/3) & ~ (real_9/100 =
% 63.28/9.51 real_-10/3) & ~ (real_9/100 = real_-4/5) & ~ (real_9/100 = real_3/10) & ~
% 63.28/9.51 (real_9/100 = real_-3/5) & ~ (real_9/100 = real_-3/20) & ~ (real_9/100 =
% 63.28/9.51 real_4/5) & ~ (real_9/100 = real_1/5) & ~ (real_9/100 = real_2) & ~
% 63.28/9.51 (real_9/100 = real_1/4) & ~ (real_9/100 = real_1) & ~ (real_9/100 =
% 63.28/9.51 real_-1/2) & ~ (real_9/100 = real_-3/10) & ~ (real_9/100 = real_1/2) & ~
% 63.28/9.51 (real_9/100 = real_0) & ~ (real_-5/3 = real_-10/3) & ~ (real_-5/3 =
% 63.28/9.51 real_-4/5) & ~ (real_-5/3 = real_3/10) & ~ (real_-5/3 = real_-3/5) & ~
% 63.28/9.51 (real_-5/3 = real_-3/20) & ~ (real_-5/3 = real_4/5) & ~ (real_-5/3 =
% 63.28/9.51 real_1/5) & ~ (real_-5/3 = real_2) & ~ (real_-5/3 = real_1/4) & ~
% 63.28/9.51 (real_-5/3 = real_1) & ~ (real_-5/3 = real_-1/2) & ~ (real_-5/3 =
% 63.28/9.51 real_-3/10) & ~ (real_-5/3 = real_1/2) & ~ (real_-5/3 = real_0) & ~
% 63.28/9.51 (real_-10/3 = real_-4/5) & ~ (real_-10/3 = real_3/10) & ~ (real_-10/3 =
% 63.28/9.51 real_-3/5) & ~ (real_-10/3 = real_-3/20) & ~ (real_-10/3 = real_4/5) & ~
% 63.28/9.51 (real_-10/3 = real_1/5) & ~ (real_-10/3 = real_2) & ~ (real_-10/3 =
% 63.28/9.51 real_1/4) & ~ (real_-10/3 = real_1) & ~ (real_-10/3 = real_-1/2) & ~
% 63.28/9.51 (real_-10/3 = real_-3/10) & ~ (real_-10/3 = real_1/2) & ~ (real_-10/3 =
% 63.28/9.51 real_0) & ~ (real_-4/5 = real_3/10) & ~ (real_-4/5 = real_-3/5) & ~
% 63.28/9.51 (real_-4/5 = real_-3/20) & ~ (real_-4/5 = real_4/5) & ~ (real_-4/5 =
% 63.28/9.51 real_1/5) & ~ (real_-4/5 = real_2) & ~ (real_-4/5 = real_1/4) & ~
% 63.28/9.51 (real_-4/5 = real_1) & ~ (real_-4/5 = real_-1/2) & ~ (real_-4/5 =
% 63.28/9.51 real_-3/10) & ~ (real_-4/5 = real_1/2) & ~ (real_-4/5 = real_0) & ~
% 63.28/9.51 (real_3/10 = real_-3/5) & ~ (real_3/10 = real_-3/20) & ~ (real_3/10 =
% 63.28/9.51 real_4/5) & ~ (real_3/10 = real_1/5) & ~ (real_3/10 = real_2) & ~
% 63.28/9.51 (real_3/10 = real_1/4) & ~ (real_3/10 = real_1) & ~ (real_3/10 = real_-1/2)
% 63.28/9.51 & ~ (real_3/10 = real_-3/10) & ~ (real_3/10 = real_1/2) & ~ (real_3/10 =
% 63.28/9.51 real_0) & ~ (real_-3/5 = real_-3/20) & ~ (real_-3/5 = real_4/5) & ~
% 63.28/9.51 (real_-3/5 = real_1/5) & ~ (real_-3/5 = real_2) & ~ (real_-3/5 = real_1/4) &
% 63.28/9.51 ~ (real_-3/5 = real_1) & ~ (real_-3/5 = real_-1/2) & ~ (real_-3/5 =
% 63.28/9.51 real_-3/10) & ~ (real_-3/5 = real_1/2) & ~ (real_-3/5 = real_0) & ~
% 63.28/9.51 (real_-3/20 = real_4/5) & ~ (real_-3/20 = real_1/5) & ~ (real_-3/20 =
% 63.28/9.52 real_2) & ~ (real_-3/20 = real_1/4) & ~ (real_-3/20 = real_1) & ~
% 63.28/9.52 (real_-3/20 = real_-1/2) & ~ (real_-3/20 = real_-3/10) & ~ (real_-3/20 =
% 63.28/9.52 real_1/2) & ~ (real_-3/20 = real_0) & ~ (real_4/5 = real_1/5) & ~
% 63.28/9.52 (real_4/5 = real_2) & ~ (real_4/5 = real_1/4) & ~ (real_4/5 = real_1) & ~
% 63.28/9.52 (real_4/5 = real_-1/2) & ~ (real_4/5 = real_-3/10) & ~ (real_4/5 = real_1/2)
% 63.28/9.52 & ~ (real_4/5 = real_0) & ~ (real_1/5 = real_2) & ~ (real_1/5 = real_1/4) &
% 63.28/9.52 ~ (real_1/5 = real_1) & ~ (real_1/5 = real_-1/2) & ~ (real_1/5 =
% 63.28/9.52 real_-3/10) & ~ (real_1/5 = real_1/2) & ~ (real_1/5 = real_0) & ~ (real_2
% 63.28/9.52 = real_1/4) & ~ (real_2 = real_1) & ~ (real_2 = real_-1/2) & ~ (real_2 =
% 63.28/9.52 real_-3/10) & ~ (real_2 = real_1/2) & ~ (real_2 = real_0) & ~ (real_1/4 =
% 63.28/9.52 real_1) & ~ (real_1/4 = real_-1/2) & ~ (real_1/4 = real_-3/10) & ~
% 63.28/9.52 (real_1/4 = real_1/2) & ~ (real_1/4 = real_0) & ~ (real_1 = real_-1/2) & ~
% 63.28/9.52 (real_1 = real_-3/10) & ~ (real_1 = real_1/2) & ~ (real_1 = real_0) & ~
% 63.28/9.52 (real_-1/2 = real_-3/10) & ~ (real_-1/2 = real_1/2) & ~ (real_-1/2 = real_0)
% 63.28/9.52 & ~ (real_-3/10 = real_1/2) & ~ (real_-3/10 = real_0) & ~ (real_1/2 =
% 63.28/9.52 real_0) & int_$to_real(2) = real_2 & int_$to_real(1) = real_1 &
% 63.28/9.52 int_$to_real(0) = real_0 & real_$to_real(real_9/100) = real_9/100 &
% 63.28/9.52 real_$to_real(real_-5/3) = real_-5/3 & real_$to_real(real_-10/3) = real_-10/3
% 63.28/9.52 & real_$to_real(real_-4/5) = real_-4/5 & real_$to_real(real_3/10) = real_3/10
% 63.28/9.52 & real_$to_real(real_-3/5) = real_-3/5 & real_$to_real(real_-3/20) =
% 63.28/9.52 real_-3/20 & real_$to_real(real_4/5) = real_4/5 & real_$to_real(real_1/5) =
% 63.28/9.52 real_1/5 & real_$to_real(real_2) = real_2 & real_$to_real(real_1/4) = real_1/4
% 63.28/9.52 & real_$to_real(real_1) = real_1 & real_$to_real(real_-1/2) = real_-1/2 &
% 63.28/9.52 real_$to_real(real_-3/10) = real_-3/10 & real_$to_real(real_1/2) = real_1/2 &
% 63.28/9.52 real_$to_real(real_0) = real_0 & real_$to_rat(real_9/100) = rat_9/100 &
% 63.28/9.52 real_$to_rat(real_-5/3) = rat_-5/3 & real_$to_rat(real_-10/3) = rat_-10/3 &
% 63.28/9.52 real_$to_rat(real_-4/5) = rat_-4/5 & real_$to_rat(real_3/10) = rat_3/10 &
% 63.28/9.52 real_$to_rat(real_-3/5) = rat_-3/5 & real_$to_rat(real_-3/20) = rat_-3/20 &
% 63.28/9.52 real_$to_rat(real_4/5) = rat_4/5 & real_$to_rat(real_1/5) = rat_1/5 &
% 63.28/9.52 real_$to_rat(real_2) = rat_2 & real_$to_rat(real_1/4) = rat_1/4 &
% 63.28/9.52 real_$to_rat(real_1) = rat_1 & real_$to_rat(real_-1/2) = rat_-1/2 &
% 63.28/9.52 real_$to_rat(real_-3/10) = rat_-3/10 & real_$to_rat(real_1/2) = rat_1/2 &
% 63.28/9.52 real_$to_rat(real_0) = rat_0 & real_$to_int(real_9/100) = 0 &
% 63.28/9.52 real_$to_int(real_-5/3) = -2 & real_$to_int(real_-10/3) = -4 &
% 63.28/9.52 real_$to_int(real_-4/5) = -1 & real_$to_int(real_3/10) = 0 &
% 63.28/9.52 real_$to_int(real_-3/5) = -1 & real_$to_int(real_-3/20) = -1 &
% 63.28/9.52 real_$to_int(real_4/5) = 0 & real_$to_int(real_1/5) = 0 & real_$to_int(real_2)
% 63.28/9.52 = 2 & real_$to_int(real_1/4) = 0 & real_$to_int(real_1) = 1 &
% 63.28/9.52 real_$to_int(real_-1/2) = -1 & real_$to_int(real_-3/10) = -1 &
% 63.28/9.52 real_$to_int(real_1/2) = 0 & real_$to_int(real_0) = 0 &
% 63.28/9.52 real_$round(real_9/100) = real_0 & real_$round(real_3/10) = real_0 &
% 63.28/9.52 real_$round(real_-3/20) = real_0 & real_$round(real_4/5) = real_1 &
% 63.28/9.52 real_$round(real_1/5) = real_0 & real_$round(real_2) = real_2 &
% 63.28/9.52 real_$round(real_1/4) = real_0 & real_$round(real_1) = real_1 &
% 63.28/9.52 real_$round(real_-1/2) = real_0 & real_$round(real_-3/10) = real_0 &
% 63.28/9.52 real_$round(real_1/2) = real_1 & real_$round(real_0) = real_0 &
% 63.28/9.52 real_$truncate(real_9/100) = real_0 & real_$truncate(real_-4/5) = real_0 &
% 63.28/9.52 real_$truncate(real_3/10) = real_0 & real_$truncate(real_-3/5) = real_0 &
% 63.28/9.52 real_$truncate(real_-3/20) = real_0 & real_$truncate(real_4/5) = real_0 &
% 63.28/9.52 real_$truncate(real_1/5) = real_0 & real_$truncate(real_2) = real_2 &
% 63.28/9.52 real_$truncate(real_1/4) = real_0 & real_$truncate(real_1) = real_1 &
% 63.28/9.52 real_$truncate(real_-1/2) = real_0 & real_$truncate(real_-3/10) = real_0 &
% 63.28/9.52 real_$truncate(real_1/2) = real_0 & real_$truncate(real_0) = real_0 &
% 63.28/9.52 real_$ceiling(real_9/100) = real_1 & real_$ceiling(real_-4/5) = real_0 &
% 63.28/9.52 real_$ceiling(real_3/10) = real_1 & real_$ceiling(real_-3/5) = real_0 &
% 63.28/9.52 real_$ceiling(real_-3/20) = real_0 & real_$ceiling(real_4/5) = real_1 &
% 63.28/9.52 real_$ceiling(real_1/5) = real_1 & real_$ceiling(real_2) = real_2 &
% 63.28/9.52 real_$ceiling(real_1/4) = real_1 & real_$ceiling(real_1) = real_1 &
% 63.28/9.52 real_$ceiling(real_-1/2) = real_0 & real_$ceiling(real_-3/10) = real_0 &
% 63.28/9.52 real_$ceiling(real_1/2) = real_1 & real_$ceiling(real_0) = real_0 &
% 63.28/9.52 real_$quotient(real_9/100, real_9/100) = real_1 & real_$quotient(real_9/100,
% 63.28/9.52 real_3/10) = real_3/10 & real_$quotient(real_9/100, real_-3/5) = real_-3/20
% 63.28/9.52 & real_$quotient(real_9/100, real_-3/20) = real_-3/5 &
% 63.28/9.52 real_$quotient(real_9/100, real_1) = real_9/100 & real_$quotient(real_9/100,
% 63.28/9.52 real_-3/10) = real_-3/10 & real_$quotient(real_-5/3, real_-5/3) = real_1 &
% 63.28/9.52 real_$quotient(real_-5/3, real_-10/3) = real_1/2 & real_$quotient(real_-5/3,
% 63.28/9.52 real_1) = real_-5/3 & real_$quotient(real_-5/3, real_1/2) = real_-10/3 &
% 63.28/9.52 real_$quotient(real_-10/3, real_-5/3) = real_2 & real_$quotient(real_-10/3,
% 63.28/9.52 real_-10/3) = real_1 & real_$quotient(real_-10/3, real_2) = real_-5/3 &
% 63.28/9.52 real_$quotient(real_-10/3, real_1) = real_-10/3 & real_$quotient(real_-4/5,
% 63.28/9.52 real_-4/5) = real_1 & real_$quotient(real_-4/5, real_1) = real_-4/5 &
% 63.28/9.52 real_$quotient(real_3/10, real_3/10) = real_1 & real_$quotient(real_3/10,
% 63.28/9.52 real_-3/5) = real_-1/2 & real_$quotient(real_3/10, real_1) = real_3/10 &
% 63.28/9.52 real_$quotient(real_3/10, real_-1/2) = real_-3/5 & real_$quotient(real_-3/5,
% 63.28/9.52 real_-3/5) = real_1 & real_$quotient(real_-3/5, real_2) = real_-3/10 &
% 63.28/9.52 real_$quotient(real_-3/5, real_1) = real_-3/5 & real_$quotient(real_-3/5,
% 63.28/9.52 real_-3/10) = real_2 & real_$quotient(real_-3/20, real_9/100) = real_-5/3 &
% 63.28/9.52 real_$quotient(real_-3/20, real_-5/3) = real_9/100 &
% 63.28/9.52 real_$quotient(real_-3/20, real_3/10) = real_-1/2 & real_$quotient(real_-3/20,
% 63.28/9.52 real_-3/5) = real_1/4 & real_$quotient(real_-3/20, real_-3/20) = real_1 &
% 63.28/9.52 real_$quotient(real_-3/20, real_1/4) = real_-3/5 & real_$quotient(real_-3/20,
% 63.28/9.52 real_1) = real_-3/20 & real_$quotient(real_-3/20, real_-1/2) = real_3/10 &
% 63.28/9.52 real_$quotient(real_-3/20, real_-3/10) = real_1/2 & real_$quotient(real_-3/20,
% 63.28/9.52 real_1/2) = real_-3/10 & real_$quotient(real_4/5, real_4/5) = real_1 &
% 63.28/9.52 real_$quotient(real_4/5, real_1) = real_4/5 & real_$quotient(real_1/5,
% 63.28/9.52 real_4/5) = real_1/4 & real_$quotient(real_1/5, real_1/5) = real_1 &
% 63.28/9.52 real_$quotient(real_1/5, real_1/4) = real_4/5 & real_$quotient(real_1/5,
% 63.28/9.52 real_1) = real_1/5 & real_$quotient(real_2, real_-10/3) = real_-3/5 &
% 63.28/9.53 real_$quotient(real_2, real_-3/5) = real_-10/3 & real_$quotient(real_2,
% 63.28/9.53 real_2) = real_1 & real_$quotient(real_2, real_1) = real_2 &
% 63.28/9.53 real_$quotient(real_1/4, real_-5/3) = real_-3/20 & real_$quotient(real_1/4,
% 63.28/9.53 real_-3/20) = real_-5/3 & real_$quotient(real_1/4, real_1/4) = real_1 &
% 63.28/9.53 real_$quotient(real_1/4, real_1) = real_1/4 & real_$quotient(real_1/4,
% 63.28/9.53 real_-1/2) = real_-1/2 & real_$quotient(real_1/4, real_1/2) = real_1/2 &
% 63.28/9.53 real_$quotient(real_1, real_-5/3) = real_-3/5 & real_$quotient(real_1,
% 63.28/9.53 real_-10/3) = real_-3/10 & real_$quotient(real_1, real_-3/5) = real_-5/3 &
% 63.28/9.53 real_$quotient(real_1, real_2) = real_1/2 & real_$quotient(real_1, real_1) =
% 63.28/9.53 real_1 & real_$quotient(real_1, real_-3/10) = real_-10/3 &
% 63.28/9.53 real_$quotient(real_1, real_1/2) = real_2 & real_$quotient(real_-1/2,
% 63.28/9.53 real_-5/3) = real_3/10 & real_$quotient(real_-1/2, real_3/10) = real_-5/3 &
% 63.28/9.53 real_$quotient(real_-1/2, real_1) = real_-1/2 & real_$quotient(real_-1/2,
% 63.28/9.53 real_-1/2) = real_1 & real_$quotient(real_-3/10, real_9/100) = real_-10/3 &
% 63.28/9.53 real_$quotient(real_-3/10, real_-10/3) = real_9/100 &
% 63.28/9.53 real_$quotient(real_-3/10, real_-3/5) = real_1/2 & real_$quotient(real_-3/10,
% 63.28/9.53 real_-3/20) = real_2 & real_$quotient(real_-3/10, real_2) = real_-3/20 &
% 63.28/9.53 real_$quotient(real_-3/10, real_1) = real_-3/10 & real_$quotient(real_-3/10,
% 63.28/9.53 real_-3/10) = real_1 & real_$quotient(real_-3/10, real_1/2) = real_-3/5 &
% 63.28/9.53 real_$quotient(real_1/2, real_-5/3) = real_-3/10 & real_$quotient(real_1/2,
% 63.28/9.53 real_-10/3) = real_-3/20 & real_$quotient(real_1/2, real_-3/20) = real_-10/3
% 63.28/9.53 & real_$quotient(real_1/2, real_2) = real_1/4 & real_$quotient(real_1/2,
% 63.28/9.53 real_1/4) = real_2 & real_$quotient(real_1/2, real_1) = real_1/2 &
% 63.28/9.53 real_$quotient(real_1/2, real_-3/10) = real_-5/3 & real_$quotient(real_1/2,
% 63.28/9.53 real_1/2) = real_1 & real_$quotient(real_0, real_9/100) = real_0 &
% 63.28/9.53 real_$quotient(real_0, real_-5/3) = real_0 & real_$quotient(real_0,
% 63.28/9.53 real_-10/3) = real_0 & real_$quotient(real_0, real_-4/5) = real_0 &
% 63.28/9.53 real_$quotient(real_0, real_3/10) = real_0 & real_$quotient(real_0, real_-3/5)
% 63.28/9.53 = real_0 & real_$quotient(real_0, real_-3/20) = real_0 &
% 63.28/9.53 real_$quotient(real_0, real_4/5) = real_0 & real_$quotient(real_0, real_1/5) =
% 63.28/9.53 real_0 & real_$quotient(real_0, real_2) = real_0 & real_$quotient(real_0,
% 63.28/9.53 real_1/4) = real_0 & real_$quotient(real_0, real_1) = real_0 &
% 63.28/9.53 real_$quotient(real_0, real_-1/2) = real_0 & real_$quotient(real_0,
% 63.28/9.53 real_-3/10) = real_0 & real_$quotient(real_0, real_1/2) = real_0 &
% 63.28/9.53 real_$product(real_9/100, real_-5/3) = real_-3/20 & real_$product(real_9/100,
% 63.28/9.53 real_-10/3) = real_-3/10 & real_$product(real_9/100, real_1) = real_9/100 &
% 63.28/9.53 real_$product(real_9/100, real_0) = real_0 & real_$product(real_-5/3,
% 63.28/9.53 real_9/100) = real_-3/20 & real_$product(real_-5/3, real_3/10) = real_-1/2 &
% 63.28/9.53 real_$product(real_-5/3, real_-3/5) = real_1 & real_$product(real_-5/3,
% 63.28/9.53 real_-3/20) = real_1/4 & real_$product(real_-5/3, real_2) = real_-10/3 &
% 63.28/9.53 real_$product(real_-5/3, real_1) = real_-5/3 & real_$product(real_-5/3,
% 63.28/9.53 real_-3/10) = real_1/2 & real_$product(real_-5/3, real_0) = real_0 &
% 63.28/9.53 real_$product(real_-10/3, real_9/100) = real_-3/10 & real_$product(real_-10/3,
% 63.28/9.53 real_-3/5) = real_2 & real_$product(real_-10/3, real_-3/20) = real_1/2 &
% 63.28/9.53 real_$product(real_-10/3, real_1) = real_-10/3 & real_$product(real_-10/3,
% 63.28/9.53 real_-3/10) = real_1 & real_$product(real_-10/3, real_1/2) = real_-5/3 &
% 63.28/9.53 real_$product(real_-10/3, real_0) = real_0 & real_$product(real_-4/5, real_1)
% 63.28/9.53 = real_-4/5 & real_$product(real_-4/5, real_0) = real_0 &
% 63.28/9.53 real_$product(real_3/10, real_-5/3) = real_-1/2 & real_$product(real_3/10,
% 63.28/9.53 real_3/10) = real_9/100 & real_$product(real_3/10, real_1) = real_3/10 &
% 63.28/9.53 real_$product(real_3/10, real_-1/2) = real_-3/20 & real_$product(real_3/10,
% 63.28/9.53 real_0) = real_0 & real_$product(real_-3/5, real_-5/3) = real_1 &
% 63.28/9.53 real_$product(real_-3/5, real_-10/3) = real_2 & real_$product(real_-3/5,
% 63.28/9.53 real_-3/20) = real_9/100 & real_$product(real_-3/5, real_1/4) = real_-3/20 &
% 63.28/9.53 real_$product(real_-3/5, real_1) = real_-3/5 & real_$product(real_-3/5,
% 63.28/9.53 real_-1/2) = real_3/10 & real_$product(real_-3/5, real_1/2) = real_-3/10 &
% 63.28/9.53 real_$product(real_-3/5, real_0) = real_0 & real_$product(real_-3/20,
% 63.28/9.53 real_-5/3) = real_1/4 & real_$product(real_-3/20, real_-10/3) = real_1/2 &
% 63.28/9.53 real_$product(real_-3/20, real_-3/5) = real_9/100 & real_$product(real_-3/20,
% 63.28/9.53 real_2) = real_-3/10 & real_$product(real_-3/20, real_1) = real_-3/20 &
% 63.28/9.53 real_$product(real_-3/20, real_0) = real_0 & real_$product(real_4/5, real_1/4)
% 63.28/9.53 = real_1/5 & real_$product(real_4/5, real_1) = real_4/5 &
% 63.28/9.53 real_$product(real_4/5, real_0) = real_0 & real_$product(real_1/5, real_1) =
% 63.28/9.53 real_1/5 & real_$product(real_1/5, real_0) = real_0 & real_$product(real_2,
% 63.28/9.53 real_-5/3) = real_-10/3 & real_$product(real_2, real_-3/20) = real_-3/10 &
% 63.28/9.53 real_$product(real_2, real_1/4) = real_1/2 & real_$product(real_2, real_1) =
% 63.28/9.53 real_2 & real_$product(real_2, real_-3/10) = real_-3/5 & real_$product(real_2,
% 63.28/9.53 real_1/2) = real_1 & real_$product(real_2, real_0) = real_0 &
% 63.28/9.53 real_$product(real_1/4, real_-3/5) = real_-3/20 & real_$product(real_1/4,
% 63.28/9.53 real_4/5) = real_1/5 & real_$product(real_1/4, real_2) = real_1/2 &
% 63.28/9.53 real_$product(real_1/4, real_1) = real_1/4 & real_$product(real_1/4, real_0) =
% 63.28/9.53 real_0 & real_$product(real_1, real_9/100) = real_9/100 &
% 63.28/9.53 real_$product(real_1, real_-5/3) = real_-5/3 & real_$product(real_1,
% 63.28/9.53 real_-10/3) = real_-10/3 & real_$product(real_1, real_-4/5) = real_-4/5 &
% 63.28/9.53 real_$product(real_1, real_3/10) = real_3/10 & real_$product(real_1,
% 63.28/9.53 real_-3/5) = real_-3/5 & real_$product(real_1, real_-3/20) = real_-3/20 &
% 63.28/9.53 real_$product(real_1, real_4/5) = real_4/5 & real_$product(real_1, real_1/5) =
% 63.28/9.53 real_1/5 & real_$product(real_1, real_2) = real_2 & real_$product(real_1,
% 63.28/9.53 real_1/4) = real_1/4 & real_$product(real_1, real_1) = real_1 &
% 63.28/9.53 real_$product(real_1, real_-1/2) = real_-1/2 & real_$product(real_1,
% 63.28/9.53 real_-3/10) = real_-3/10 & real_$product(real_1, real_1/2) = real_1/2 &
% 63.28/9.53 real_$product(real_1, real_0) = real_0 & real_$product(real_-1/2, real_3/10) =
% 63.28/9.53 real_-3/20 & real_$product(real_-1/2, real_-3/5) = real_3/10 &
% 63.28/9.53 real_$product(real_-1/2, real_1) = real_-1/2 & real_$product(real_-1/2,
% 63.28/9.53 real_-1/2) = real_1/4 & real_$product(real_-1/2, real_0) = real_0 &
% 63.28/9.53 real_$product(real_-3/10, real_-5/3) = real_1/2 & real_$product(real_-3/10,
% 63.28/9.53 real_-10/3) = real_1 & real_$product(real_-3/10, real_2) = real_-3/5 &
% 63.28/9.53 real_$product(real_-3/10, real_1) = real_-3/10 & real_$product(real_-3/10,
% 63.28/9.53 real_-3/10) = real_9/100 & real_$product(real_-3/10, real_1/2) = real_-3/20
% 63.28/9.53 & real_$product(real_-3/10, real_0) = real_0 & real_$product(real_1/2,
% 63.28/9.53 real_-10/3) = real_-5/3 & real_$product(real_1/2, real_-3/5) = real_-3/10 &
% 63.28/9.53 real_$product(real_1/2, real_2) = real_1 & real_$product(real_1/2, real_1) =
% 63.28/9.53 real_1/2 & real_$product(real_1/2, real_-3/10) = real_-3/20 &
% 63.28/9.53 real_$product(real_1/2, real_1/2) = real_1/4 & real_$product(real_1/2, real_0)
% 63.28/9.53 = real_0 & real_$product(real_0, real_9/100) = real_0 & real_$product(real_0,
% 63.28/9.53 real_-5/3) = real_0 & real_$product(real_0, real_-10/3) = real_0 &
% 63.28/9.54 real_$product(real_0, real_-4/5) = real_0 & real_$product(real_0, real_3/10) =
% 63.28/9.54 real_0 & real_$product(real_0, real_-3/5) = real_0 & real_$product(real_0,
% 63.28/9.54 real_-3/20) = real_0 & real_$product(real_0, real_4/5) = real_0 &
% 63.28/9.54 real_$product(real_0, real_1/5) = real_0 & real_$product(real_0, real_2) =
% 63.28/9.54 real_0 & real_$product(real_0, real_1/4) = real_0 & real_$product(real_0,
% 63.28/9.54 real_1) = real_0 & real_$product(real_0, real_-1/2) = real_0 &
% 63.28/9.54 real_$product(real_0, real_-3/10) = real_0 & real_$product(real_0, real_1/2) =
% 63.28/9.54 real_0 & real_$product(real_0, real_0) = real_0 & real_$difference(real_9/100,
% 63.28/9.54 real_9/100) = real_0 & real_$difference(real_9/100, real_0) = real_9/100 &
% 63.28/9.54 real_$difference(real_-5/3, real_-5/3) = real_0 & real_$difference(real_-5/3,
% 63.28/9.54 real_0) = real_-5/3 & real_$difference(real_-10/3, real_-5/3) = real_-5/3 &
% 63.28/9.54 real_$difference(real_-10/3, real_-10/3) = real_0 &
% 63.28/9.54 real_$difference(real_-10/3, real_0) = real_-10/3 &
% 63.28/9.54 real_$difference(real_-4/5, real_-4/5) = real_0 & real_$difference(real_-4/5,
% 63.28/9.54 real_-1/2) = real_-3/10 & real_$difference(real_-4/5, real_-3/10) =
% 63.28/9.54 real_-1/2 & real_$difference(real_-4/5, real_0) = real_-4/5 &
% 63.28/9.54 real_$difference(real_3/10, real_3/10) = real_0 & real_$difference(real_3/10,
% 63.28/9.54 real_4/5) = real_-1/2 & real_$difference(real_3/10, real_-1/2) = real_4/5 &
% 63.28/9.54 real_$difference(real_3/10, real_0) = real_3/10 & real_$difference(real_-3/5,
% 63.28/9.54 real_-4/5) = real_1/5 & real_$difference(real_-3/5, real_-3/5) = real_0 &
% 63.28/9.54 real_$difference(real_-3/5, real_1/5) = real_-4/5 &
% 63.28/9.54 real_$difference(real_-3/5, real_-3/10) = real_-3/10 &
% 63.28/9.54 real_$difference(real_-3/5, real_0) = real_-3/5 & real_$difference(real_-3/20,
% 63.28/9.54 real_-3/20) = real_0 & real_$difference(real_-3/20, real_0) = real_-3/20 &
% 63.28/9.54 real_$difference(real_4/5, real_3/10) = real_1/2 & real_$difference(real_4/5,
% 63.28/9.54 real_4/5) = real_0 & real_$difference(real_4/5, real_1/2) = real_3/10 &
% 63.28/9.54 real_$difference(real_4/5, real_0) = real_4/5 & real_$difference(real_1/5,
% 63.28/9.54 real_-4/5) = real_1 & real_$difference(real_1/5, real_-3/5) = real_4/5 &
% 63.28/9.54 real_$difference(real_1/5, real_4/5) = real_-3/5 & real_$difference(real_1/5,
% 63.28/9.54 real_1/5) = real_0 & real_$difference(real_1/5, real_1) = real_-4/5 &
% 63.28/9.54 real_$difference(real_1/5, real_-3/10) = real_1/2 & real_$difference(real_1/5,
% 63.28/9.54 real_1/2) = real_-3/10 & real_$difference(real_1/5, real_0) = real_1/5 &
% 63.28/9.54 real_$difference(real_2, real_2) = real_0 & real_$difference(real_2, real_1) =
% 63.28/9.54 real_1 & real_$difference(real_2, real_0) = real_2 &
% 63.28/9.54 real_$difference(real_1/4, real_1/4) = real_0 & real_$difference(real_1/4,
% 63.28/9.54 real_0) = real_1/4 & real_$difference(real_1, real_4/5) = real_1/5 &
% 63.28/9.54 real_$difference(real_1, real_1/5) = real_4/5 & real_$difference(real_1,
% 63.28/9.54 real_1) = real_0 & real_$difference(real_1, real_1/2) = real_1/2 &
% 63.28/9.54 real_$difference(real_1, real_0) = real_1 & real_$difference(real_-1/2,
% 63.28/9.54 real_-4/5) = real_3/10 & real_$difference(real_-1/2, real_3/10) = real_-4/5
% 63.28/9.54 & real_$difference(real_-1/2, real_-1/2) = real_0 &
% 63.28/9.54 real_$difference(real_-1/2, real_0) = real_-1/2 & real_$difference(real_-3/10,
% 63.28/9.54 real_-4/5) = real_1/2 & real_$difference(real_-3/10, real_3/10) = real_-3/5
% 63.28/9.54 & real_$difference(real_-3/10, real_-3/5) = real_3/10 &
% 63.28/9.54 real_$difference(real_-3/10, real_-3/20) = real_-3/20 &
% 63.28/9.54 real_$difference(real_-3/10, real_1/5) = real_-1/2 &
% 63.28/9.54 real_$difference(real_-3/10, real_-1/2) = real_1/5 &
% 63.28/9.54 real_$difference(real_-3/10, real_-3/10) = real_0 &
% 63.28/9.54 real_$difference(real_-3/10, real_1/2) = real_-4/5 &
% 63.28/9.54 real_$difference(real_-3/10, real_0) = real_-3/10 & real_$difference(real_1/2,
% 63.28/9.54 real_3/10) = real_1/5 & real_$difference(real_1/2, real_4/5) = real_-3/10 &
% 63.28/9.54 real_$difference(real_1/2, real_1/5) = real_3/10 & real_$difference(real_1/2,
% 63.28/9.54 real_1/4) = real_1/4 & real_$difference(real_1/2, real_1) = real_-1/2 &
% 63.28/9.54 real_$difference(real_1/2, real_-1/2) = real_1 & real_$difference(real_1/2,
% 63.28/9.54 real_-3/10) = real_4/5 & real_$difference(real_1/2, real_1/2) = real_0 &
% 63.28/9.54 real_$difference(real_1/2, real_0) = real_1/2 & real_$difference(real_0,
% 63.28/9.54 real_-4/5) = real_4/5 & real_$difference(real_0, real_3/10) = real_-3/10 &
% 63.28/9.54 real_$difference(real_0, real_4/5) = real_-4/5 & real_$difference(real_0,
% 63.28/9.54 real_-1/2) = real_1/2 & real_$difference(real_0, real_-3/10) = real_3/10 &
% 63.28/9.54 real_$difference(real_0, real_1/2) = real_-1/2 & real_$difference(real_0,
% 63.28/9.54 real_0) = real_0 & real_$uminus(real_-4/5) = real_4/5 &
% 63.28/9.54 real_$uminus(real_3/10) = real_-3/10 & real_$uminus(real_4/5) = real_-4/5 &
% 63.28/9.54 real_$uminus(real_-1/2) = real_1/2 & real_$uminus(real_-3/10) = real_3/10 &
% 63.28/9.54 real_$uminus(real_1/2) = real_-1/2 & real_$uminus(real_0) = real_0 &
% 63.28/9.54 real_$sum(real_9/100, real_0) = real_9/100 & real_$sum(real_-5/3, real_-5/3) =
% 63.28/9.54 real_-10/3 & real_$sum(real_-5/3, real_0) = real_-5/3 & real_$sum(real_-10/3,
% 63.28/9.54 real_0) = real_-10/3 & real_$sum(real_-4/5, real_3/10) = real_-1/2 &
% 63.28/9.54 real_$sum(real_-4/5, real_4/5) = real_0 & real_$sum(real_-4/5, real_1/5) =
% 63.28/9.54 real_-3/5 & real_$sum(real_-4/5, real_1) = real_1/5 & real_$sum(real_-4/5,
% 63.28/9.54 real_1/2) = real_-3/10 & real_$sum(real_-4/5, real_0) = real_-4/5 &
% 63.28/9.54 real_$sum(real_3/10, real_-4/5) = real_-1/2 & real_$sum(real_3/10, real_-3/5)
% 63.28/9.54 = real_-3/10 & real_$sum(real_3/10, real_1/5) = real_1/2 &
% 63.28/9.54 real_$sum(real_3/10, real_-3/10) = real_0 & real_$sum(real_3/10, real_1/2) =
% 63.28/9.54 real_4/5 & real_$sum(real_3/10, real_0) = real_3/10 & real_$sum(real_-3/5,
% 63.28/9.54 real_3/10) = real_-3/10 & real_$sum(real_-3/5, real_4/5) = real_1/5 &
% 63.28/9.54 real_$sum(real_-3/5, real_0) = real_-3/5 & real_$sum(real_-3/20, real_-3/20) =
% 63.28/9.54 real_-3/10 & real_$sum(real_-3/20, real_0) = real_-3/20 & real_$sum(real_4/5,
% 63.28/9.54 real_-4/5) = real_0 & real_$sum(real_4/5, real_-3/5) = real_1/5 &
% 63.28/9.54 real_$sum(real_4/5, real_1/5) = real_1 & real_$sum(real_4/5, real_-1/2) =
% 63.28/9.54 real_3/10 & real_$sum(real_4/5, real_-3/10) = real_1/2 & real_$sum(real_4/5,
% 63.28/9.54 real_0) = real_4/5 & real_$sum(real_1/5, real_-4/5) = real_-3/5 &
% 63.28/9.54 real_$sum(real_1/5, real_3/10) = real_1/2 & real_$sum(real_1/5, real_4/5) =
% 63.28/9.54 real_1 & real_$sum(real_1/5, real_-1/2) = real_-3/10 & real_$sum(real_1/5,
% 63.28/9.54 real_0) = real_1/5 & real_$sum(real_2, real_0) = real_2 &
% 63.28/9.54 real_$sum(real_1/4, real_1/4) = real_1/2 & real_$sum(real_1/4, real_0) =
% 63.28/9.54 real_1/4 & real_$sum(real_1, real_-4/5) = real_1/5 & real_$sum(real_1, real_1)
% 63.28/9.54 = real_2 & real_$sum(real_1, real_-1/2) = real_1/2 & real_$sum(real_1, real_0)
% 63.28/9.54 = real_1 & real_$sum(real_-1/2, real_4/5) = real_3/10 & real_$sum(real_-1/2,
% 63.28/9.54 real_1/5) = real_-3/10 & real_$sum(real_-1/2, real_1) = real_1/2 &
% 63.28/9.54 real_$sum(real_-1/2, real_-3/10) = real_-4/5 & real_$sum(real_-1/2, real_1/2)
% 63.28/9.54 = real_0 & real_$sum(real_-1/2, real_0) = real_-1/2 & real_$sum(real_-3/10,
% 63.28/9.54 real_3/10) = real_0 & real_$sum(real_-3/10, real_4/5) = real_1/2 &
% 63.28/9.54 real_$sum(real_-3/10, real_-1/2) = real_-4/5 & real_$sum(real_-3/10,
% 63.28/9.54 real_-3/10) = real_-3/5 & real_$sum(real_-3/10, real_1/2) = real_1/5 &
% 63.28/9.54 real_$sum(real_-3/10, real_0) = real_-3/10 & real_$sum(real_1/2, real_-4/5) =
% 63.28/9.54 real_-3/10 & real_$sum(real_1/2, real_3/10) = real_4/5 & real_$sum(real_1/2,
% 63.28/9.54 real_-1/2) = real_0 & real_$sum(real_1/2, real_-3/10) = real_1/5 &
% 63.28/9.54 real_$sum(real_1/2, real_1/2) = real_1 & real_$sum(real_1/2, real_0) =
% 63.28/9.54 real_1/2 & real_$sum(real_0, real_9/100) = real_9/100 & real_$sum(real_0,
% 63.67/9.54 real_-5/3) = real_-5/3 & real_$sum(real_0, real_-10/3) = real_-10/3 &
% 63.67/9.54 real_$sum(real_0, real_-4/5) = real_-4/5 & real_$sum(real_0, real_3/10) =
% 63.67/9.54 real_3/10 & real_$sum(real_0, real_-3/5) = real_-3/5 & real_$sum(real_0,
% 63.67/9.54 real_-3/20) = real_-3/20 & real_$sum(real_0, real_4/5) = real_4/5 &
% 63.67/9.54 real_$sum(real_0, real_1/5) = real_1/5 & real_$sum(real_0, real_2) = real_2 &
% 63.67/9.54 real_$sum(real_0, real_1/4) = real_1/4 & real_$sum(real_0, real_1) = real_1 &
% 63.67/9.54 real_$sum(real_0, real_-1/2) = real_-1/2 & real_$sum(real_0, real_-3/10) =
% 63.67/9.54 real_-3/10 & real_$sum(real_0, real_1/2) = real_1/2 & real_$sum(real_0,
% 63.67/9.54 real_0) = real_0 & real_$floor(real_9/100) = real_0 & real_$floor(real_3/10)
% 63.67/9.54 = real_0 & real_$floor(real_4/5) = real_0 & real_$floor(real_1/5) = real_0 &
% 63.67/9.54 real_$floor(real_2) = real_2 & real_$floor(real_1/4) = real_0 &
% 63.67/9.54 real_$floor(real_1) = real_1 & real_$floor(real_1/2) = real_0 &
% 63.67/9.54 real_$floor(real_0) = real_0 & real_$is_rat(real_9/100) &
% 63.67/9.54 real_$is_rat(real_-5/3) & real_$is_rat(real_-10/3) & real_$is_rat(real_-4/5) &
% 63.67/9.54 real_$is_rat(real_3/10) & real_$is_rat(real_-3/5) & real_$is_rat(real_-3/20) &
% 63.67/9.54 real_$is_rat(real_4/5) & real_$is_rat(real_1/5) & real_$is_rat(real_2) &
% 63.67/9.54 real_$is_rat(real_1/4) & real_$is_rat(real_1) & real_$is_rat(real_-1/2) &
% 63.67/9.54 real_$is_rat(real_-3/10) & real_$is_rat(real_1/2) & real_$is_rat(real_0) &
% 63.67/9.54 real_$is_int(real_2) & real_$is_int(real_1) & real_$is_int(real_0) &
% 63.67/9.54 real_$greatereq(real_9/100, real_9/100) & real_$greatereq(real_9/100,
% 63.67/9.54 real_-5/3) & real_$greatereq(real_9/100, real_-10/3) &
% 63.67/9.54 real_$greatereq(real_9/100, real_-4/5) & real_$greatereq(real_9/100,
% 63.67/9.54 real_-3/5) & real_$greatereq(real_9/100, real_-3/20) &
% 63.67/9.54 real_$greatereq(real_9/100, real_-1/2) & real_$greatereq(real_9/100,
% 63.67/9.54 real_-3/10) & real_$greatereq(real_9/100, real_0) &
% 63.67/9.54 real_$greatereq(real_-5/3, real_-5/3) & real_$greatereq(real_-5/3, real_-10/3)
% 63.67/9.54 & real_$greatereq(real_-10/3, real_-10/3) & real_$greatereq(real_-4/5,
% 63.67/9.54 real_-5/3) & real_$greatereq(real_-4/5, real_-10/3) &
% 63.67/9.54 real_$greatereq(real_-4/5, real_-4/5) & real_$greatereq(real_3/10, real_9/100)
% 63.67/9.54 & real_$greatereq(real_3/10, real_-5/3) & real_$greatereq(real_3/10,
% 63.67/9.54 real_-10/3) & real_$greatereq(real_3/10, real_-4/5) &
% 63.67/9.54 real_$greatereq(real_3/10, real_3/10) & real_$greatereq(real_3/10, real_-3/5)
% 63.67/9.54 & real_$greatereq(real_3/10, real_-3/20) & real_$greatereq(real_3/10,
% 63.67/9.54 real_1/5) & real_$greatereq(real_3/10, real_1/4) &
% 63.67/9.54 real_$greatereq(real_3/10, real_-1/2) & real_$greatereq(real_3/10, real_-3/10)
% 63.67/9.54 & real_$greatereq(real_3/10, real_0) & real_$greatereq(real_-3/5, real_-5/3) &
% 63.67/9.54 real_$greatereq(real_-3/5, real_-10/3) & real_$greatereq(real_-3/5, real_-4/5)
% 63.67/9.55 & real_$greatereq(real_-3/5, real_-3/5) & real_$greatereq(real_-3/20,
% 63.67/9.55 real_-5/3) & real_$greatereq(real_-3/20, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_-3/20, real_-4/5) & real_$greatereq(real_-3/20,
% 63.67/9.55 real_-3/5) & real_$greatereq(real_-3/20, real_-3/20) &
% 63.67/9.55 real_$greatereq(real_-3/20, real_-1/2) & real_$greatereq(real_-3/20,
% 63.67/9.55 real_-3/10) & real_$greatereq(real_4/5, real_9/100) &
% 63.67/9.55 real_$greatereq(real_4/5, real_-5/3) & real_$greatereq(real_4/5, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_4/5, real_-4/5) & real_$greatereq(real_4/5, real_3/10) &
% 63.67/9.55 real_$greatereq(real_4/5, real_-3/5) & real_$greatereq(real_4/5, real_-3/20) &
% 63.67/9.55 real_$greatereq(real_4/5, real_4/5) & real_$greatereq(real_4/5, real_1/5) &
% 63.67/9.55 real_$greatereq(real_4/5, real_1/4) & real_$greatereq(real_4/5, real_-1/2) &
% 63.67/9.55 real_$greatereq(real_4/5, real_-3/10) & real_$greatereq(real_4/5, real_1/2) &
% 63.67/9.55 real_$greatereq(real_4/5, real_0) & real_$greatereq(real_1/5, real_9/100) &
% 63.67/9.55 real_$greatereq(real_1/5, real_-5/3) & real_$greatereq(real_1/5, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_1/5, real_-4/5) & real_$greatereq(real_1/5, real_-3/5) &
% 63.67/9.55 real_$greatereq(real_1/5, real_-3/20) & real_$greatereq(real_1/5, real_1/5) &
% 63.67/9.55 real_$greatereq(real_1/5, real_-1/2) & real_$greatereq(real_1/5, real_-3/10) &
% 63.67/9.55 real_$greatereq(real_1/5, real_0) & real_$greatereq(real_2, real_9/100) &
% 63.67/9.55 real_$greatereq(real_2, real_-5/3) & real_$greatereq(real_2, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_2, real_-4/5) & real_$greatereq(real_2, real_3/10) &
% 63.67/9.55 real_$greatereq(real_2, real_-3/5) & real_$greatereq(real_2, real_-3/20) &
% 63.67/9.55 real_$greatereq(real_2, real_4/5) & real_$greatereq(real_2, real_1/5) &
% 63.67/9.55 real_$greatereq(real_2, real_2) & real_$greatereq(real_2, real_1/4) &
% 63.67/9.55 real_$greatereq(real_2, real_1) & real_$greatereq(real_2, real_-1/2) &
% 63.67/9.55 real_$greatereq(real_2, real_-3/10) & real_$greatereq(real_2, real_1/2) &
% 63.67/9.55 real_$greatereq(real_2, real_0) & real_$greatereq(real_1/4, real_9/100) &
% 63.67/9.55 real_$greatereq(real_1/4, real_-5/3) & real_$greatereq(real_1/4, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_1/4, real_-4/5) & real_$greatereq(real_1/4, real_-3/5) &
% 63.67/9.55 real_$greatereq(real_1/4, real_-3/20) & real_$greatereq(real_1/4, real_1/5) &
% 63.67/9.55 real_$greatereq(real_1/4, real_1/4) & real_$greatereq(real_1/4, real_-1/2) &
% 63.67/9.55 real_$greatereq(real_1/4, real_-3/10) & real_$greatereq(real_1/4, real_0) &
% 63.67/9.55 real_$greatereq(real_1, real_9/100) & real_$greatereq(real_1, real_-5/3) &
% 63.67/9.55 real_$greatereq(real_1, real_-10/3) & real_$greatereq(real_1, real_-4/5) &
% 63.67/9.55 real_$greatereq(real_1, real_3/10) & real_$greatereq(real_1, real_-3/5) &
% 63.67/9.55 real_$greatereq(real_1, real_-3/20) & real_$greatereq(real_1, real_4/5) &
% 63.67/9.55 real_$greatereq(real_1, real_1/5) & real_$greatereq(real_1, real_1/4) &
% 63.67/9.55 real_$greatereq(real_1, real_1) & real_$greatereq(real_1, real_-1/2) &
% 63.67/9.55 real_$greatereq(real_1, real_-3/10) & real_$greatereq(real_1, real_1/2) &
% 63.67/9.55 real_$greatereq(real_1, real_0) & real_$greatereq(real_-1/2, real_-5/3) &
% 63.67/9.55 real_$greatereq(real_-1/2, real_-10/3) & real_$greatereq(real_-1/2, real_-4/5)
% 63.67/9.55 & real_$greatereq(real_-1/2, real_-3/5) & real_$greatereq(real_-1/2,
% 63.67/9.55 real_-1/2) & real_$greatereq(real_-3/10, real_-5/3) &
% 63.67/9.55 real_$greatereq(real_-3/10, real_-10/3) & real_$greatereq(real_-3/10,
% 63.67/9.55 real_-4/5) & real_$greatereq(real_-3/10, real_-3/5) &
% 63.67/9.55 real_$greatereq(real_-3/10, real_-1/2) & real_$greatereq(real_-3/10,
% 63.67/9.55 real_-3/10) & real_$greatereq(real_1/2, real_9/100) &
% 63.67/9.55 real_$greatereq(real_1/2, real_-5/3) & real_$greatereq(real_1/2, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_1/2, real_-4/5) & real_$greatereq(real_1/2, real_3/10) &
% 63.67/9.55 real_$greatereq(real_1/2, real_-3/5) & real_$greatereq(real_1/2, real_-3/20) &
% 63.67/9.55 real_$greatereq(real_1/2, real_1/5) & real_$greatereq(real_1/2, real_1/4) &
% 63.67/9.55 real_$greatereq(real_1/2, real_-1/2) & real_$greatereq(real_1/2, real_-3/10) &
% 63.67/9.55 real_$greatereq(real_1/2, real_1/2) & real_$greatereq(real_1/2, real_0) &
% 63.67/9.55 real_$greatereq(real_0, real_-5/3) & real_$greatereq(real_0, real_-10/3) &
% 63.67/9.55 real_$greatereq(real_0, real_-4/5) & real_$greatereq(real_0, real_-3/5) &
% 63.67/9.55 real_$greatereq(real_0, real_-3/20) & real_$greatereq(real_0, real_-1/2) &
% 63.67/9.55 real_$greatereq(real_0, real_-3/10) & real_$greatereq(real_0, real_0) &
% 63.67/9.55 real_$greater(real_very_large, real_9/100) & real_$greater(real_very_large,
% 63.67/9.55 real_-5/3) & real_$greater(real_very_large, real_-10/3) &
% 63.67/9.55 real_$greater(real_very_large, real_-4/5) & real_$greater(real_very_large,
% 63.67/9.55 real_3/10) & real_$greater(real_very_large, real_-3/5) &
% 63.67/9.55 real_$greater(real_very_large, real_-3/20) & real_$greater(real_very_large,
% 63.67/9.55 real_4/5) & real_$greater(real_very_large, real_1/5) &
% 63.67/9.55 real_$greater(real_very_large, real_2) & real_$greater(real_very_large,
% 63.67/9.55 real_1/4) & real_$greater(real_very_large, real_1) &
% 63.67/9.55 real_$greater(real_very_large, real_-1/2) & real_$greater(real_very_large,
% 63.67/9.55 real_-3/10) & real_$greater(real_very_large, real_1/2) &
% 63.67/9.55 real_$greater(real_very_large, real_0) & real_$greater(real_9/100,
% 63.67/9.55 real_very_small) & real_$greater(real_9/100, real_-5/3) &
% 63.67/9.55 real_$greater(real_9/100, real_-10/3) & real_$greater(real_9/100, real_-4/5) &
% 63.67/9.55 real_$greater(real_9/100, real_-3/5) & real_$greater(real_9/100, real_-3/20) &
% 63.67/9.55 real_$greater(real_9/100, real_-1/2) & real_$greater(real_9/100, real_-3/10) &
% 63.67/9.55 real_$greater(real_9/100, real_0) & real_$greater(real_-5/3, real_very_small)
% 63.67/9.55 & real_$greater(real_-5/3, real_-10/3) & real_$greater(real_-10/3,
% 63.67/9.55 real_very_small) & real_$greater(real_-4/5, real_very_small) &
% 63.67/9.55 real_$greater(real_-4/5, real_-5/3) & real_$greater(real_-4/5, real_-10/3) &
% 63.67/9.55 real_$greater(real_3/10, real_very_small) & real_$greater(real_3/10,
% 63.67/9.55 real_9/100) & real_$greater(real_3/10, real_-5/3) & real_$greater(real_3/10,
% 63.67/9.55 real_-10/3) & real_$greater(real_3/10, real_-4/5) & real_$greater(real_3/10,
% 63.67/9.55 real_-3/5) & real_$greater(real_3/10, real_-3/20) & real_$greater(real_3/10,
% 63.67/9.55 real_1/5) & real_$greater(real_3/10, real_1/4) & real_$greater(real_3/10,
% 63.67/9.55 real_-1/2) & real_$greater(real_3/10, real_-3/10) & real_$greater(real_3/10,
% 63.67/9.55 real_0) & real_$greater(real_-3/5, real_very_small) &
% 63.67/9.55 real_$greater(real_-3/5, real_-5/3) & real_$greater(real_-3/5, real_-10/3) &
% 63.67/9.55 real_$greater(real_-3/5, real_-4/5) & real_$greater(real_-3/20,
% 63.67/9.55 real_very_small) & real_$greater(real_-3/20, real_-5/3) &
% 63.67/9.55 real_$greater(real_-3/20, real_-10/3) & real_$greater(real_-3/20, real_-4/5) &
% 63.67/9.55 real_$greater(real_-3/20, real_-3/5) & real_$greater(real_-3/20, real_-1/2) &
% 63.67/9.55 real_$greater(real_-3/20, real_-3/10) & real_$greater(real_4/5,
% 63.67/9.55 real_very_small) & real_$greater(real_4/5, real_9/100) &
% 63.67/9.55 real_$greater(real_4/5, real_-5/3) & real_$greater(real_4/5, real_-10/3) &
% 63.67/9.55 real_$greater(real_4/5, real_-4/5) & real_$greater(real_4/5, real_3/10) &
% 63.67/9.55 real_$greater(real_4/5, real_-3/5) & real_$greater(real_4/5, real_-3/20) &
% 63.67/9.55 real_$greater(real_4/5, real_1/5) & real_$greater(real_4/5, real_1/4) &
% 63.67/9.55 real_$greater(real_4/5, real_-1/2) & real_$greater(real_4/5, real_-3/10) &
% 63.67/9.55 real_$greater(real_4/5, real_1/2) & real_$greater(real_4/5, real_0) &
% 63.67/9.55 real_$greater(real_1/5, real_very_small) & real_$greater(real_1/5, real_9/100)
% 63.67/9.55 & real_$greater(real_1/5, real_-5/3) & real_$greater(real_1/5, real_-10/3) &
% 63.67/9.55 real_$greater(real_1/5, real_-4/5) & real_$greater(real_1/5, real_-3/5) &
% 63.67/9.55 real_$greater(real_1/5, real_-3/20) & real_$greater(real_1/5, real_-1/2) &
% 63.67/9.55 real_$greater(real_1/5, real_-3/10) & real_$greater(real_1/5, real_0) &
% 63.67/9.55 real_$greater(real_2, real_very_small) & real_$greater(real_2, real_9/100) &
% 63.67/9.55 real_$greater(real_2, real_-5/3) & real_$greater(real_2, real_-10/3) &
% 63.67/9.55 real_$greater(real_2, real_-4/5) & real_$greater(real_2, real_3/10) &
% 63.67/9.55 real_$greater(real_2, real_-3/5) & real_$greater(real_2, real_-3/20) &
% 63.67/9.55 real_$greater(real_2, real_4/5) & real_$greater(real_2, real_1/5) &
% 63.67/9.55 real_$greater(real_2, real_1/4) & real_$greater(real_2, real_1) &
% 63.67/9.55 real_$greater(real_2, real_-1/2) & real_$greater(real_2, real_-3/10) &
% 63.67/9.55 real_$greater(real_2, real_1/2) & real_$greater(real_2, real_0) &
% 63.67/9.55 real_$greater(real_1/4, real_very_small) & real_$greater(real_1/4, real_9/100)
% 63.67/9.55 & real_$greater(real_1/4, real_-5/3) & real_$greater(real_1/4, real_-10/3) &
% 63.67/9.55 real_$greater(real_1/4, real_-4/5) & real_$greater(real_1/4, real_-3/5) &
% 63.67/9.55 real_$greater(real_1/4, real_-3/20) & real_$greater(real_1/4, real_1/5) &
% 63.67/9.55 real_$greater(real_1/4, real_-1/2) & real_$greater(real_1/4, real_-3/10) &
% 63.67/9.55 real_$greater(real_1/4, real_0) & real_$greater(real_1, real_very_small) &
% 63.67/9.55 real_$greater(real_1, real_9/100) & real_$greater(real_1, real_-5/3) &
% 63.67/9.55 real_$greater(real_1, real_-10/3) & real_$greater(real_1, real_-4/5) &
% 63.67/9.55 real_$greater(real_1, real_3/10) & real_$greater(real_1, real_-3/5) &
% 63.67/9.55 real_$greater(real_1, real_-3/20) & real_$greater(real_1, real_4/5) &
% 63.67/9.55 real_$greater(real_1, real_1/5) & real_$greater(real_1, real_1/4) &
% 63.67/9.55 real_$greater(real_1, real_-1/2) & real_$greater(real_1, real_-3/10) &
% 63.67/9.55 real_$greater(real_1, real_1/2) & real_$greater(real_1, real_0) &
% 63.67/9.55 real_$greater(real_-1/2, real_very_small) & real_$greater(real_-1/2,
% 63.67/9.55 real_-5/3) & real_$greater(real_-1/2, real_-10/3) & real_$greater(real_-1/2,
% 63.67/9.55 real_-4/5) & real_$greater(real_-1/2, real_-3/5) & real_$greater(real_-3/10,
% 63.67/9.55 real_very_small) & real_$greater(real_-3/10, real_-5/3) &
% 63.67/9.55 real_$greater(real_-3/10, real_-10/3) & real_$greater(real_-3/10, real_-4/5) &
% 63.67/9.55 real_$greater(real_-3/10, real_-3/5) & real_$greater(real_-3/10, real_-1/2) &
% 63.67/9.55 real_$greater(real_1/2, real_very_small) & real_$greater(real_1/2, real_9/100)
% 63.67/9.55 & real_$greater(real_1/2, real_-5/3) & real_$greater(real_1/2, real_-10/3) &
% 63.67/9.55 real_$greater(real_1/2, real_-4/5) & real_$greater(real_1/2, real_3/10) &
% 63.67/9.55 real_$greater(real_1/2, real_-3/5) & real_$greater(real_1/2, real_-3/20) &
% 63.67/9.55 real_$greater(real_1/2, real_1/5) & real_$greater(real_1/2, real_1/4) &
% 63.67/9.55 real_$greater(real_1/2, real_-1/2) & real_$greater(real_1/2, real_-3/10) &
% 63.67/9.55 real_$greater(real_1/2, real_0) & real_$greater(real_0, real_very_small) &
% 63.67/9.55 real_$greater(real_0, real_-5/3) & real_$greater(real_0, real_-10/3) &
% 63.67/9.55 real_$greater(real_0, real_-4/5) & real_$greater(real_0, real_-3/5) &
% 63.67/9.55 real_$greater(real_0, real_-3/20) & real_$greater(real_0, real_-1/2) &
% 63.67/9.55 real_$greater(real_0, real_-3/10) & real_$lesseq(real_very_small,
% 63.67/9.55 real_very_large) & real_$lesseq(real_9/100, real_9/100) &
% 63.67/9.55 real_$lesseq(real_9/100, real_3/10) & real_$lesseq(real_9/100, real_4/5) &
% 63.67/9.55 real_$lesseq(real_9/100, real_1/5) & real_$lesseq(real_9/100, real_2) &
% 63.67/9.56 real_$lesseq(real_9/100, real_1/4) & real_$lesseq(real_9/100, real_1) &
% 63.67/9.56 real_$lesseq(real_9/100, real_1/2) & real_$lesseq(real_-5/3, real_9/100) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_-5/3) & real_$lesseq(real_-5/3, real_-4/5) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_3/10) & real_$lesseq(real_-5/3, real_-3/5) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_-3/20) & real_$lesseq(real_-5/3, real_4/5) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_1/5) & real_$lesseq(real_-5/3, real_2) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_1/4) & real_$lesseq(real_-5/3, real_1) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_-1/2) & real_$lesseq(real_-5/3, real_-3/10) &
% 63.67/9.56 real_$lesseq(real_-5/3, real_1/2) & real_$lesseq(real_-5/3, real_0) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_9/100) & real_$lesseq(real_-10/3, real_-5/3) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_-10/3) & real_$lesseq(real_-10/3, real_-4/5) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_3/10) & real_$lesseq(real_-10/3, real_-3/5) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_-3/20) & real_$lesseq(real_-10/3, real_4/5) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_1/5) & real_$lesseq(real_-10/3, real_2) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_1/4) & real_$lesseq(real_-10/3, real_1) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_-1/2) & real_$lesseq(real_-10/3, real_-3/10) &
% 63.67/9.56 real_$lesseq(real_-10/3, real_1/2) & real_$lesseq(real_-10/3, real_0) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_9/100) & real_$lesseq(real_-4/5, real_-4/5) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_3/10) & real_$lesseq(real_-4/5, real_-3/5) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_-3/20) & real_$lesseq(real_-4/5, real_4/5) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_1/5) & real_$lesseq(real_-4/5, real_2) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_1/4) & real_$lesseq(real_-4/5, real_1) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_-1/2) & real_$lesseq(real_-4/5, real_-3/10) &
% 63.67/9.56 real_$lesseq(real_-4/5, real_1/2) & real_$lesseq(real_-4/5, real_0) &
% 63.67/9.56 real_$lesseq(real_3/10, real_3/10) & real_$lesseq(real_3/10, real_4/5) &
% 63.67/9.56 real_$lesseq(real_3/10, real_2) & real_$lesseq(real_3/10, real_1) &
% 63.67/9.56 real_$lesseq(real_3/10, real_1/2) & real_$lesseq(real_-3/5, real_9/100) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_3/10) & real_$lesseq(real_-3/5, real_-3/5) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_-3/20) & real_$lesseq(real_-3/5, real_4/5) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_1/5) & real_$lesseq(real_-3/5, real_2) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_1/4) & real_$lesseq(real_-3/5, real_1) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_-1/2) & real_$lesseq(real_-3/5, real_-3/10) &
% 63.67/9.56 real_$lesseq(real_-3/5, real_1/2) & real_$lesseq(real_-3/5, real_0) &
% 63.67/9.56 real_$lesseq(real_-3/20, real_9/100) & real_$lesseq(real_-3/20, real_3/10) &
% 63.67/9.56 real_$lesseq(real_-3/20, real_-3/20) & real_$lesseq(real_-3/20, real_4/5) &
% 63.67/9.56 real_$lesseq(real_-3/20, real_1/5) & real_$lesseq(real_-3/20, real_2) &
% 63.67/9.56 real_$lesseq(real_-3/20, real_1/4) & real_$lesseq(real_-3/20, real_1) &
% 63.67/9.56 real_$lesseq(real_-3/20, real_1/2) & real_$lesseq(real_-3/20, real_0) &
% 63.67/9.56 real_$lesseq(real_4/5, real_4/5) & real_$lesseq(real_4/5, real_2) &
% 63.67/9.56 real_$lesseq(real_4/5, real_1) & real_$lesseq(real_1/5, real_3/10) &
% 63.67/9.56 real_$lesseq(real_1/5, real_4/5) & real_$lesseq(real_1/5, real_1/5) &
% 63.67/9.56 real_$lesseq(real_1/5, real_2) & real_$lesseq(real_1/5, real_1/4) &
% 63.67/9.56 real_$lesseq(real_1/5, real_1) & real_$lesseq(real_1/5, real_1/2) &
% 63.67/9.56 real_$lesseq(real_2, real_2) & real_$lesseq(real_1/4, real_3/10) &
% 63.67/9.56 real_$lesseq(real_1/4, real_4/5) & real_$lesseq(real_1/4, real_2) &
% 63.67/9.56 real_$lesseq(real_1/4, real_1/4) & real_$lesseq(real_1/4, real_1) &
% 63.67/9.56 real_$lesseq(real_1/4, real_1/2) & real_$lesseq(real_1, real_2) &
% 63.67/9.56 real_$lesseq(real_1, real_1) & real_$lesseq(real_-1/2, real_9/100) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_3/10) & real_$lesseq(real_-1/2, real_-3/20) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_4/5) & real_$lesseq(real_-1/2, real_1/5) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_2) & real_$lesseq(real_-1/2, real_1/4) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_1) & real_$lesseq(real_-1/2, real_-1/2) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_-3/10) & real_$lesseq(real_-1/2, real_1/2) &
% 63.67/9.56 real_$lesseq(real_-1/2, real_0) & real_$lesseq(real_-3/10, real_9/100) &
% 63.67/9.56 real_$lesseq(real_-3/10, real_3/10) & real_$lesseq(real_-3/10, real_-3/20) &
% 63.67/9.56 real_$lesseq(real_-3/10, real_4/5) & real_$lesseq(real_-3/10, real_1/5) &
% 63.67/9.56 real_$lesseq(real_-3/10, real_2) & real_$lesseq(real_-3/10, real_1/4) &
% 63.67/9.56 real_$lesseq(real_-3/10, real_1) & real_$lesseq(real_-3/10, real_-3/10) &
% 63.67/9.56 real_$lesseq(real_-3/10, real_1/2) & real_$lesseq(real_-3/10, real_0) &
% 63.67/9.56 real_$lesseq(real_1/2, real_4/5) & real_$lesseq(real_1/2, real_2) &
% 63.67/9.56 real_$lesseq(real_1/2, real_1) & real_$lesseq(real_1/2, real_1/2) &
% 63.67/9.56 real_$lesseq(real_0, real_9/100) & real_$lesseq(real_0, real_3/10) &
% 63.67/9.56 real_$lesseq(real_0, real_4/5) & real_$lesseq(real_0, real_1/5) &
% 63.67/9.56 real_$lesseq(real_0, real_2) & real_$lesseq(real_0, real_1/4) &
% 63.67/9.56 real_$lesseq(real_0, real_1) & real_$lesseq(real_0, real_1/2) &
% 63.67/9.56 real_$lesseq(real_0, real_0) & real_$less(real_very_small, real_very_large) &
% 63.67/9.56 real_$less(real_very_small, real_9/100) & real_$less(real_very_small,
% 63.67/9.56 real_-5/3) & real_$less(real_very_small, real_-10/3) &
% 63.67/9.56 real_$less(real_very_small, real_-4/5) & real_$less(real_very_small,
% 63.67/9.56 real_3/10) & real_$less(real_very_small, real_-3/5) &
% 63.67/9.56 real_$less(real_very_small, real_-3/20) & real_$less(real_very_small,
% 63.67/9.56 real_4/5) & real_$less(real_very_small, real_1/5) &
% 63.67/9.56 real_$less(real_very_small, real_2) & real_$less(real_very_small, real_1/4) &
% 63.67/9.56 real_$less(real_very_small, real_1) & real_$less(real_very_small, real_-1/2) &
% 63.67/9.56 real_$less(real_very_small, real_-3/10) & real_$less(real_very_small,
% 63.67/9.56 real_1/2) & real_$less(real_very_small, real_0) & real_$less(real_9/100,
% 63.67/9.56 real_very_large) & real_$less(real_9/100, real_3/10) &
% 63.67/9.56 real_$less(real_9/100, real_4/5) & real_$less(real_9/100, real_1/5) &
% 63.67/9.56 real_$less(real_9/100, real_2) & real_$less(real_9/100, real_1/4) &
% 63.67/9.56 real_$less(real_9/100, real_1) & real_$less(real_9/100, real_1/2) &
% 63.67/9.56 real_$less(real_-5/3, real_very_large) & real_$less(real_-5/3, real_9/100) &
% 63.67/9.56 real_$less(real_-5/3, real_-4/5) & real_$less(real_-5/3, real_3/10) &
% 63.67/9.56 real_$less(real_-5/3, real_-3/5) & real_$less(real_-5/3, real_-3/20) &
% 63.67/9.56 real_$less(real_-5/3, real_4/5) & real_$less(real_-5/3, real_1/5) &
% 63.67/9.56 real_$less(real_-5/3, real_2) & real_$less(real_-5/3, real_1/4) &
% 63.67/9.56 real_$less(real_-5/3, real_1) & real_$less(real_-5/3, real_-1/2) &
% 63.67/9.56 real_$less(real_-5/3, real_-3/10) & real_$less(real_-5/3, real_1/2) &
% 63.67/9.56 real_$less(real_-5/3, real_0) & real_$less(real_-10/3, real_very_large) &
% 63.67/9.56 real_$less(real_-10/3, real_9/100) & real_$less(real_-10/3, real_-5/3) &
% 63.67/9.56 real_$less(real_-10/3, real_-4/5) & real_$less(real_-10/3, real_3/10) &
% 63.67/9.56 real_$less(real_-10/3, real_-3/5) & real_$less(real_-10/3, real_-3/20) &
% 63.67/9.56 real_$less(real_-10/3, real_4/5) & real_$less(real_-10/3, real_1/5) &
% 63.67/9.56 real_$less(real_-10/3, real_2) & real_$less(real_-10/3, real_1/4) &
% 63.67/9.56 real_$less(real_-10/3, real_1) & real_$less(real_-10/3, real_-1/2) &
% 63.67/9.56 real_$less(real_-10/3, real_-3/10) & real_$less(real_-10/3, real_1/2) &
% 63.67/9.56 real_$less(real_-10/3, real_0) & real_$less(real_-4/5, real_very_large) &
% 63.67/9.56 real_$less(real_-4/5, real_9/100) & real_$less(real_-4/5, real_3/10) &
% 63.67/9.56 real_$less(real_-4/5, real_-3/5) & real_$less(real_-4/5, real_-3/20) &
% 63.67/9.56 real_$less(real_-4/5, real_4/5) & real_$less(real_-4/5, real_1/5) &
% 63.67/9.56 real_$less(real_-4/5, real_2) & real_$less(real_-4/5, real_1/4) &
% 63.67/9.56 real_$less(real_-4/5, real_1) & real_$less(real_-4/5, real_-1/2) &
% 63.67/9.56 real_$less(real_-4/5, real_-3/10) & real_$less(real_-4/5, real_1/2) &
% 63.67/9.56 real_$less(real_-4/5, real_0) & real_$less(real_3/10, real_very_large) &
% 63.67/9.56 real_$less(real_3/10, real_4/5) & real_$less(real_3/10, real_2) &
% 63.67/9.56 real_$less(real_3/10, real_1) & real_$less(real_3/10, real_1/2) &
% 63.67/9.56 real_$less(real_-3/5, real_very_large) & real_$less(real_-3/5, real_9/100) &
% 63.67/9.56 real_$less(real_-3/5, real_3/10) & real_$less(real_-3/5, real_-3/20) &
% 63.67/9.56 real_$less(real_-3/5, real_4/5) & real_$less(real_-3/5, real_1/5) &
% 63.67/9.56 real_$less(real_-3/5, real_2) & real_$less(real_-3/5, real_1/4) &
% 63.67/9.56 real_$less(real_-3/5, real_1) & real_$less(real_-3/5, real_-1/2) &
% 63.67/9.56 real_$less(real_-3/5, real_-3/10) & real_$less(real_-3/5, real_1/2) &
% 63.67/9.56 real_$less(real_-3/5, real_0) & real_$less(real_-3/20, real_very_large) &
% 63.67/9.56 real_$less(real_-3/20, real_9/100) & real_$less(real_-3/20, real_3/10) &
% 63.67/9.56 real_$less(real_-3/20, real_4/5) & real_$less(real_-3/20, real_1/5) &
% 63.67/9.56 real_$less(real_-3/20, real_2) & real_$less(real_-3/20, real_1/4) &
% 63.67/9.56 real_$less(real_-3/20, real_1) & real_$less(real_-3/20, real_1/2) &
% 63.67/9.56 real_$less(real_-3/20, real_0) & real_$less(real_4/5, real_very_large) &
% 63.67/9.56 real_$less(real_4/5, real_2) & real_$less(real_4/5, real_1) &
% 63.67/9.56 real_$less(real_1/5, real_very_large) & real_$less(real_1/5, real_3/10) &
% 63.67/9.56 real_$less(real_1/5, real_4/5) & real_$less(real_1/5, real_2) &
% 63.67/9.56 real_$less(real_1/5, real_1/4) & real_$less(real_1/5, real_1) &
% 63.67/9.56 real_$less(real_1/5, real_1/2) & real_$less(real_2, real_very_large) &
% 63.67/9.56 real_$less(real_1/4, real_very_large) & real_$less(real_1/4, real_3/10) &
% 63.67/9.56 real_$less(real_1/4, real_4/5) & real_$less(real_1/4, real_2) &
% 63.67/9.56 real_$less(real_1/4, real_1) & real_$less(real_1/4, real_1/2) &
% 63.67/9.56 real_$less(real_1, real_very_large) & real_$less(real_1, real_2) &
% 63.67/9.56 real_$less(real_-1/2, real_very_large) & real_$less(real_-1/2, real_9/100) &
% 63.67/9.56 real_$less(real_-1/2, real_3/10) & real_$less(real_-1/2, real_-3/20) &
% 63.67/9.56 real_$less(real_-1/2, real_4/5) & real_$less(real_-1/2, real_1/5) &
% 63.67/9.56 real_$less(real_-1/2, real_2) & real_$less(real_-1/2, real_1/4) &
% 63.67/9.56 real_$less(real_-1/2, real_1) & real_$less(real_-1/2, real_-3/10) &
% 63.67/9.56 real_$less(real_-1/2, real_1/2) & real_$less(real_-1/2, real_0) &
% 63.67/9.56 real_$less(real_-3/10, real_very_large) & real_$less(real_-3/10, real_9/100) &
% 63.67/9.56 real_$less(real_-3/10, real_3/10) & real_$less(real_-3/10, real_-3/20) &
% 63.67/9.56 real_$less(real_-3/10, real_4/5) & real_$less(real_-3/10, real_1/5) &
% 63.67/9.56 real_$less(real_-3/10, real_2) & real_$less(real_-3/10, real_1/4) &
% 63.67/9.56 real_$less(real_-3/10, real_1) & real_$less(real_-3/10, real_1/2) &
% 63.67/9.56 real_$less(real_-3/10, real_0) & real_$less(real_1/2, real_very_large) &
% 63.67/9.56 real_$less(real_1/2, real_4/5) & real_$less(real_1/2, real_2) &
% 63.67/9.56 real_$less(real_1/2, real_1) & real_$less(real_0, real_very_large) &
% 63.67/9.56 real_$less(real_0, real_9/100) & real_$less(real_0, real_3/10) &
% 63.67/9.56 real_$less(real_0, real_4/5) & real_$less(real_0, real_1/5) &
% 63.67/9.56 real_$less(real_0, real_2) & real_$less(real_0, real_1/4) & real_$less(real_0,
% 63.67/9.56 real_1) & real_$less(real_0, real_1/2) & ~ real_$is_int(real_9/100) & ~
% 63.67/9.56 real_$is_int(real_-5/3) & ~ real_$is_int(real_-10/3) & ~
% 63.67/9.56 real_$is_int(real_-4/5) & ~ real_$is_int(real_3/10) & ~
% 63.67/9.56 real_$is_int(real_-3/5) & ~ real_$is_int(real_-3/20) & ~
% 63.67/9.56 real_$is_int(real_4/5) & ~ real_$is_int(real_1/5) & ~ real_$is_int(real_1/4)
% 63.67/9.56 & ~ real_$is_int(real_-1/2) & ~ real_$is_int(real_-3/10) & ~
% 63.67/9.56 real_$is_int(real_1/2) & ~ real_$greatereq(real_very_small, real_very_large)
% 63.67/9.56 & ~ real_$greatereq(real_9/100, real_3/10) & ~ real_$greatereq(real_9/100,
% 63.67/9.56 real_4/5) & ~ real_$greatereq(real_9/100, real_1/5) & ~
% 63.67/9.56 real_$greatereq(real_9/100, real_2) & ~ real_$greatereq(real_9/100, real_1/4)
% 63.67/9.56 & ~ real_$greatereq(real_9/100, real_1) & ~ real_$greatereq(real_9/100,
% 63.67/9.56 real_1/2) & ~ real_$greatereq(real_-5/3, real_9/100) & ~
% 63.67/9.56 real_$greatereq(real_-5/3, real_-4/5) & ~ real_$greatereq(real_-5/3,
% 63.67/9.56 real_3/10) & ~ real_$greatereq(real_-5/3, real_-3/5) & ~
% 63.67/9.56 real_$greatereq(real_-5/3, real_-3/20) & ~ real_$greatereq(real_-5/3,
% 63.67/9.56 real_4/5) & ~ real_$greatereq(real_-5/3, real_1/5) & ~
% 63.67/9.56 real_$greatereq(real_-5/3, real_2) & ~ real_$greatereq(real_-5/3, real_1/4) &
% 63.67/9.56 ~ real_$greatereq(real_-5/3, real_1) & ~ real_$greatereq(real_-5/3,
% 63.67/9.56 real_-1/2) & ~ real_$greatereq(real_-5/3, real_-3/10) & ~
% 63.67/9.56 real_$greatereq(real_-5/3, real_1/2) & ~ real_$greatereq(real_-5/3, real_0) &
% 63.67/9.56 ~ real_$greatereq(real_-10/3, real_9/100) & ~ real_$greatereq(real_-10/3,
% 63.67/9.56 real_-5/3) & ~ real_$greatereq(real_-10/3, real_-4/5) & ~
% 63.67/9.56 real_$greatereq(real_-10/3, real_3/10) & ~ real_$greatereq(real_-10/3,
% 63.67/9.56 real_-3/5) & ~ real_$greatereq(real_-10/3, real_-3/20) & ~
% 63.67/9.56 real_$greatereq(real_-10/3, real_4/5) & ~ real_$greatereq(real_-10/3,
% 63.67/9.56 real_1/5) & ~ real_$greatereq(real_-10/3, real_2) & ~
% 63.67/9.56 real_$greatereq(real_-10/3, real_1/4) & ~ real_$greatereq(real_-10/3, real_1)
% 63.67/9.56 & ~ real_$greatereq(real_-10/3, real_-1/2) & ~ real_$greatereq(real_-10/3,
% 63.67/9.56 real_-3/10) & ~ real_$greatereq(real_-10/3, real_1/2) & ~
% 63.67/9.56 real_$greatereq(real_-10/3, real_0) & ~ real_$greatereq(real_-4/5,
% 63.67/9.56 real_9/100) & ~ real_$greatereq(real_-4/5, real_3/10) & ~
% 63.67/9.56 real_$greatereq(real_-4/5, real_-3/5) & ~ real_$greatereq(real_-4/5,
% 63.67/9.56 real_-3/20) & ~ real_$greatereq(real_-4/5, real_4/5) & ~
% 63.67/9.56 real_$greatereq(real_-4/5, real_1/5) & ~ real_$greatereq(real_-4/5, real_2) &
% 63.67/9.56 ~ real_$greatereq(real_-4/5, real_1/4) & ~ real_$greatereq(real_-4/5,
% 63.67/9.56 real_1) & ~ real_$greatereq(real_-4/5, real_-1/2) & ~
% 63.67/9.56 real_$greatereq(real_-4/5, real_-3/10) & ~ real_$greatereq(real_-4/5,
% 63.67/9.56 real_1/2) & ~ real_$greatereq(real_-4/5, real_0) & ~
% 63.67/9.56 real_$greatereq(real_3/10, real_4/5) & ~ real_$greatereq(real_3/10, real_2) &
% 63.67/9.56 ~ real_$greatereq(real_3/10, real_1) & ~ real_$greatereq(real_3/10,
% 63.67/9.56 real_1/2) & ~ real_$greatereq(real_-3/5, real_9/100) & ~
% 63.67/9.56 real_$greatereq(real_-3/5, real_3/10) & ~ real_$greatereq(real_-3/5,
% 63.67/9.56 real_-3/20) & ~ real_$greatereq(real_-3/5, real_4/5) & ~
% 63.67/9.56 real_$greatereq(real_-3/5, real_1/5) & ~ real_$greatereq(real_-3/5, real_2) &
% 63.67/9.56 ~ real_$greatereq(real_-3/5, real_1/4) & ~ real_$greatereq(real_-3/5,
% 63.67/9.56 real_1) & ~ real_$greatereq(real_-3/5, real_-1/2) & ~
% 63.67/9.56 real_$greatereq(real_-3/5, real_-3/10) & ~ real_$greatereq(real_-3/5,
% 63.67/9.56 real_1/2) & ~ real_$greatereq(real_-3/5, real_0) & ~
% 63.67/9.56 real_$greatereq(real_-3/20, real_9/100) & ~ real_$greatereq(real_-3/20,
% 63.67/9.56 real_3/10) & ~ real_$greatereq(real_-3/20, real_4/5) & ~
% 63.67/9.56 real_$greatereq(real_-3/20, real_1/5) & ~ real_$greatereq(real_-3/20, real_2)
% 63.67/9.56 & ~ real_$greatereq(real_-3/20, real_1/4) & ~ real_$greatereq(real_-3/20,
% 63.67/9.56 real_1) & ~ real_$greatereq(real_-3/20, real_1/2) & ~
% 63.67/9.56 real_$greatereq(real_-3/20, real_0) & ~ real_$greatereq(real_4/5, real_2) &
% 63.67/9.56 ~ real_$greatereq(real_4/5, real_1) & ~ real_$greatereq(real_1/5, real_3/10)
% 63.67/9.56 & ~ real_$greatereq(real_1/5, real_4/5) & ~ real_$greatereq(real_1/5,
% 63.67/9.56 real_2) & ~ real_$greatereq(real_1/5, real_1/4) & ~
% 63.67/9.56 real_$greatereq(real_1/5, real_1) & ~ real_$greatereq(real_1/5, real_1/2) &
% 63.67/9.56 ~ real_$greatereq(real_1/4, real_3/10) & ~ real_$greatereq(real_1/4,
% 63.67/9.56 real_4/5) & ~ real_$greatereq(real_1/4, real_2) & ~
% 63.67/9.56 real_$greatereq(real_1/4, real_1) & ~ real_$greatereq(real_1/4, real_1/2) &
% 63.67/9.56 ~ real_$greatereq(real_1, real_2) & ~ real_$greatereq(real_-1/2, real_9/100)
% 63.67/9.56 & ~ real_$greatereq(real_-1/2, real_3/10) & ~ real_$greatereq(real_-1/2,
% 63.67/9.56 real_-3/20) & ~ real_$greatereq(real_-1/2, real_4/5) & ~
% 63.67/9.56 real_$greatereq(real_-1/2, real_1/5) & ~ real_$greatereq(real_-1/2, real_2) &
% 63.67/9.56 ~ real_$greatereq(real_-1/2, real_1/4) & ~ real_$greatereq(real_-1/2,
% 63.67/9.56 real_1) & ~ real_$greatereq(real_-1/2, real_-3/10) & ~
% 63.67/9.56 real_$greatereq(real_-1/2, real_1/2) & ~ real_$greatereq(real_-1/2, real_0) &
% 63.67/9.56 ~ real_$greatereq(real_-3/10, real_9/100) & ~ real_$greatereq(real_-3/10,
% 63.67/9.56 real_3/10) & ~ real_$greatereq(real_-3/10, real_-3/20) & ~
% 63.67/9.56 real_$greatereq(real_-3/10, real_4/5) & ~ real_$greatereq(real_-3/10,
% 63.67/9.56 real_1/5) & ~ real_$greatereq(real_-3/10, real_2) & ~
% 63.67/9.56 real_$greatereq(real_-3/10, real_1/4) & ~ real_$greatereq(real_-3/10, real_1)
% 63.67/9.56 & ~ real_$greatereq(real_-3/10, real_1/2) & ~ real_$greatereq(real_-3/10,
% 63.67/9.56 real_0) & ~ real_$greatereq(real_1/2, real_4/5) & ~
% 63.67/9.56 real_$greatereq(real_1/2, real_2) & ~ real_$greatereq(real_1/2, real_1) & ~
% 63.67/9.56 real_$greatereq(real_0, real_9/100) & ~ real_$greatereq(real_0, real_3/10) &
% 63.67/9.56 ~ real_$greatereq(real_0, real_4/5) & ~ real_$greatereq(real_0, real_1/5) &
% 63.67/9.56 ~ real_$greatereq(real_0, real_2) & ~ real_$greatereq(real_0, real_1/4) & ~
% 63.67/9.56 real_$greatereq(real_0, real_1) & ~ real_$greatereq(real_0, real_1/2) & ~
% 63.67/9.56 real_$greater(real_very_small, real_very_large) & ~ real_$greater(real_9/100,
% 63.67/9.56 real_9/100) & ~ real_$greater(real_9/100, real_3/10) & ~
% 63.67/9.56 real_$greater(real_9/100, real_4/5) & ~ real_$greater(real_9/100, real_1/5) &
% 63.67/9.56 ~ real_$greater(real_9/100, real_2) & ~ real_$greater(real_9/100, real_1/4)
% 63.67/9.56 & ~ real_$greater(real_9/100, real_1) & ~ real_$greater(real_9/100,
% 63.67/9.56 real_1/2) & ~ real_$greater(real_-5/3, real_9/100) & ~
% 63.67/9.56 real_$greater(real_-5/3, real_-5/3) & ~ real_$greater(real_-5/3, real_-4/5) &
% 63.67/9.56 ~ real_$greater(real_-5/3, real_3/10) & ~ real_$greater(real_-5/3,
% 63.67/9.56 real_-3/5) & ~ real_$greater(real_-5/3, real_-3/20) & ~
% 63.67/9.56 real_$greater(real_-5/3, real_4/5) & ~ real_$greater(real_-5/3, real_1/5) &
% 63.67/9.56 ~ real_$greater(real_-5/3, real_2) & ~ real_$greater(real_-5/3, real_1/4) &
% 63.67/9.56 ~ real_$greater(real_-5/3, real_1) & ~ real_$greater(real_-5/3, real_-1/2) &
% 63.67/9.56 ~ real_$greater(real_-5/3, real_-3/10) & ~ real_$greater(real_-5/3, real_1/2)
% 63.67/9.56 & ~ real_$greater(real_-5/3, real_0) & ~ real_$greater(real_-10/3,
% 63.67/9.56 real_9/100) & ~ real_$greater(real_-10/3, real_-5/3) & ~
% 63.67/9.56 real_$greater(real_-10/3, real_-10/3) & ~ real_$greater(real_-10/3,
% 63.67/9.56 real_-4/5) & ~ real_$greater(real_-10/3, real_3/10) & ~
% 63.67/9.56 real_$greater(real_-10/3, real_-3/5) & ~ real_$greater(real_-10/3,
% 63.67/9.56 real_-3/20) & ~ real_$greater(real_-10/3, real_4/5) & ~
% 63.67/9.56 real_$greater(real_-10/3, real_1/5) & ~ real_$greater(real_-10/3, real_2) &
% 63.67/9.56 ~ real_$greater(real_-10/3, real_1/4) & ~ real_$greater(real_-10/3, real_1) &
% 63.67/9.56 ~ real_$greater(real_-10/3, real_-1/2) & ~ real_$greater(real_-10/3,
% 63.67/9.56 real_-3/10) & ~ real_$greater(real_-10/3, real_1/2) & ~
% 63.67/9.56 real_$greater(real_-10/3, real_0) & ~ real_$greater(real_-4/5, real_9/100) &
% 63.67/9.56 ~ real_$greater(real_-4/5, real_-4/5) & ~ real_$greater(real_-4/5, real_3/10)
% 63.67/9.56 & ~ real_$greater(real_-4/5, real_-3/5) & ~ real_$greater(real_-4/5,
% 63.67/9.56 real_-3/20) & ~ real_$greater(real_-4/5, real_4/5) & ~
% 63.67/9.56 real_$greater(real_-4/5, real_1/5) & ~ real_$greater(real_-4/5, real_2) & ~
% 63.67/9.56 real_$greater(real_-4/5, real_1/4) & ~ real_$greater(real_-4/5, real_1) & ~
% 63.67/9.56 real_$greater(real_-4/5, real_-1/2) & ~ real_$greater(real_-4/5, real_-3/10)
% 63.67/9.56 & ~ real_$greater(real_-4/5, real_1/2) & ~ real_$greater(real_-4/5, real_0)
% 63.67/9.56 & ~ real_$greater(real_3/10, real_3/10) & ~ real_$greater(real_3/10,
% 63.67/9.56 real_4/5) & ~ real_$greater(real_3/10, real_2) & ~
% 63.67/9.56 real_$greater(real_3/10, real_1) & ~ real_$greater(real_3/10, real_1/2) & ~
% 63.67/9.56 real_$greater(real_-3/5, real_9/100) & ~ real_$greater(real_-3/5, real_3/10)
% 63.67/9.56 & ~ real_$greater(real_-3/5, real_-3/5) & ~ real_$greater(real_-3/5,
% 63.67/9.56 real_-3/20) & ~ real_$greater(real_-3/5, real_4/5) & ~
% 63.67/9.56 real_$greater(real_-3/5, real_1/5) & ~ real_$greater(real_-3/5, real_2) & ~
% 63.67/9.56 real_$greater(real_-3/5, real_1/4) & ~ real_$greater(real_-3/5, real_1) & ~
% 63.67/9.56 real_$greater(real_-3/5, real_-1/2) & ~ real_$greater(real_-3/5, real_-3/10)
% 63.67/9.56 & ~ real_$greater(real_-3/5, real_1/2) & ~ real_$greater(real_-3/5, real_0)
% 63.67/9.56 & ~ real_$greater(real_-3/20, real_9/100) & ~ real_$greater(real_-3/20,
% 63.67/9.56 real_3/10) & ~ real_$greater(real_-3/20, real_-3/20) & ~
% 63.67/9.56 real_$greater(real_-3/20, real_4/5) & ~ real_$greater(real_-3/20, real_1/5) &
% 63.67/9.56 ~ real_$greater(real_-3/20, real_2) & ~ real_$greater(real_-3/20, real_1/4)
% 63.67/9.56 & ~ real_$greater(real_-3/20, real_1) & ~ real_$greater(real_-3/20,
% 63.67/9.57 real_1/2) & ~ real_$greater(real_-3/20, real_0) & ~
% 63.67/9.57 real_$greater(real_4/5, real_4/5) & ~ real_$greater(real_4/5, real_2) & ~
% 63.67/9.57 real_$greater(real_4/5, real_1) & ~ real_$greater(real_1/5, real_3/10) & ~
% 63.67/9.57 real_$greater(real_1/5, real_4/5) & ~ real_$greater(real_1/5, real_1/5) & ~
% 63.67/9.57 real_$greater(real_1/5, real_2) & ~ real_$greater(real_1/5, real_1/4) & ~
% 63.67/9.57 real_$greater(real_1/5, real_1) & ~ real_$greater(real_1/5, real_1/2) & ~
% 63.67/9.57 real_$greater(real_2, real_2) & ~ real_$greater(real_1/4, real_3/10) & ~
% 63.67/9.57 real_$greater(real_1/4, real_4/5) & ~ real_$greater(real_1/4, real_2) & ~
% 63.67/9.57 real_$greater(real_1/4, real_1/4) & ~ real_$greater(real_1/4, real_1) & ~
% 63.67/9.57 real_$greater(real_1/4, real_1/2) & ~ real_$greater(real_1, real_2) & ~
% 63.67/9.57 real_$greater(real_1, real_1) & ~ real_$greater(real_-1/2, real_9/100) & ~
% 63.67/9.57 real_$greater(real_-1/2, real_3/10) & ~ real_$greater(real_-1/2, real_-3/20)
% 63.67/9.57 & ~ real_$greater(real_-1/2, real_4/5) & ~ real_$greater(real_-1/2,
% 63.67/9.57 real_1/5) & ~ real_$greater(real_-1/2, real_2) & ~
% 63.67/9.57 real_$greater(real_-1/2, real_1/4) & ~ real_$greater(real_-1/2, real_1) & ~
% 63.67/9.57 real_$greater(real_-1/2, real_-1/2) & ~ real_$greater(real_-1/2, real_-3/10)
% 63.67/9.57 & ~ real_$greater(real_-1/2, real_1/2) & ~ real_$greater(real_-1/2, real_0)
% 63.67/9.57 & ~ real_$greater(real_-3/10, real_9/100) & ~ real_$greater(real_-3/10,
% 63.67/9.57 real_3/10) & ~ real_$greater(real_-3/10, real_-3/20) & ~
% 63.67/9.57 real_$greater(real_-3/10, real_4/5) & ~ real_$greater(real_-3/10, real_1/5) &
% 63.67/9.57 ~ real_$greater(real_-3/10, real_2) & ~ real_$greater(real_-3/10, real_1/4)
% 63.67/9.57 & ~ real_$greater(real_-3/10, real_1) & ~ real_$greater(real_-3/10,
% 63.67/9.57 real_-3/10) & ~ real_$greater(real_-3/10, real_1/2) & ~
% 63.67/9.57 real_$greater(real_-3/10, real_0) & ~ real_$greater(real_1/2, real_4/5) & ~
% 63.67/9.57 real_$greater(real_1/2, real_2) & ~ real_$greater(real_1/2, real_1) & ~
% 63.67/9.57 real_$greater(real_1/2, real_1/2) & ~ real_$greater(real_0, real_9/100) & ~
% 63.67/9.57 real_$greater(real_0, real_3/10) & ~ real_$greater(real_0, real_4/5) & ~
% 63.67/9.57 real_$greater(real_0, real_1/5) & ~ real_$greater(real_0, real_2) & ~
% 63.67/9.57 real_$greater(real_0, real_1/4) & ~ real_$greater(real_0, real_1) & ~
% 63.67/9.57 real_$greater(real_0, real_1/2) & ~ real_$greater(real_0, real_0) & ~
% 63.67/9.57 real_$lesseq(real_9/100, real_-5/3) & ~ real_$lesseq(real_9/100, real_-10/3)
% 63.67/9.57 & ~ real_$lesseq(real_9/100, real_-4/5) & ~ real_$lesseq(real_9/100,
% 63.67/9.57 real_-3/5) & ~ real_$lesseq(real_9/100, real_-3/20) & ~
% 63.67/9.57 real_$lesseq(real_9/100, real_-1/2) & ~ real_$lesseq(real_9/100, real_-3/10)
% 63.67/9.57 & ~ real_$lesseq(real_9/100, real_0) & ~ real_$lesseq(real_-5/3, real_-10/3)
% 63.67/9.57 & ~ real_$lesseq(real_-4/5, real_-5/3) & ~ real_$lesseq(real_-4/5,
% 63.67/9.57 real_-10/3) & ~ real_$lesseq(real_3/10, real_9/100) & ~
% 63.67/9.57 real_$lesseq(real_3/10, real_-5/3) & ~ real_$lesseq(real_3/10, real_-10/3) &
% 63.67/9.57 ~ real_$lesseq(real_3/10, real_-4/5) & ~ real_$lesseq(real_3/10, real_-3/5) &
% 63.67/9.57 ~ real_$lesseq(real_3/10, real_-3/20) & ~ real_$lesseq(real_3/10, real_1/5)
% 63.67/9.57 & ~ real_$lesseq(real_3/10, real_1/4) & ~ real_$lesseq(real_3/10, real_-1/2)
% 63.67/9.57 & ~ real_$lesseq(real_3/10, real_-3/10) & ~ real_$lesseq(real_3/10, real_0)
% 63.67/9.57 & ~ real_$lesseq(real_-3/5, real_-5/3) & ~ real_$lesseq(real_-3/5,
% 63.67/9.57 real_-10/3) & ~ real_$lesseq(real_-3/5, real_-4/5) & ~
% 63.67/9.57 real_$lesseq(real_-3/20, real_-5/3) & ~ real_$lesseq(real_-3/20, real_-10/3)
% 63.67/9.57 & ~ real_$lesseq(real_-3/20, real_-4/5) & ~ real_$lesseq(real_-3/20,
% 63.67/9.57 real_-3/5) & ~ real_$lesseq(real_-3/20, real_-1/2) & ~
% 63.67/9.57 real_$lesseq(real_-3/20, real_-3/10) & ~ real_$lesseq(real_4/5, real_9/100) &
% 63.67/9.57 ~ real_$lesseq(real_4/5, real_-5/3) & ~ real_$lesseq(real_4/5, real_-10/3) &
% 63.67/9.57 ~ real_$lesseq(real_4/5, real_-4/5) & ~ real_$lesseq(real_4/5, real_3/10) &
% 63.67/9.57 ~ real_$lesseq(real_4/5, real_-3/5) & ~ real_$lesseq(real_4/5, real_-3/20) &
% 63.67/9.57 ~ real_$lesseq(real_4/5, real_1/5) & ~ real_$lesseq(real_4/5, real_1/4) & ~
% 63.67/9.57 real_$lesseq(real_4/5, real_-1/2) & ~ real_$lesseq(real_4/5, real_-3/10) & ~
% 63.67/9.57 real_$lesseq(real_4/5, real_1/2) & ~ real_$lesseq(real_4/5, real_0) & ~
% 63.67/9.57 real_$lesseq(real_1/5, real_9/100) & ~ real_$lesseq(real_1/5, real_-5/3) & ~
% 63.67/9.57 real_$lesseq(real_1/5, real_-10/3) & ~ real_$lesseq(real_1/5, real_-4/5) & ~
% 63.67/9.57 real_$lesseq(real_1/5, real_-3/5) & ~ real_$lesseq(real_1/5, real_-3/20) & ~
% 63.67/9.57 real_$lesseq(real_1/5, real_-1/2) & ~ real_$lesseq(real_1/5, real_-3/10) & ~
% 63.67/9.57 real_$lesseq(real_1/5, real_0) & ~ real_$lesseq(real_2, real_9/100) & ~
% 63.67/9.57 real_$lesseq(real_2, real_-5/3) & ~ real_$lesseq(real_2, real_-10/3) & ~
% 63.67/9.57 real_$lesseq(real_2, real_-4/5) & ~ real_$lesseq(real_2, real_3/10) & ~
% 63.67/9.57 real_$lesseq(real_2, real_-3/5) & ~ real_$lesseq(real_2, real_-3/20) & ~
% 63.67/9.57 real_$lesseq(real_2, real_4/5) & ~ real_$lesseq(real_2, real_1/5) & ~
% 63.67/9.57 real_$lesseq(real_2, real_1/4) & ~ real_$lesseq(real_2, real_1) & ~
% 63.67/9.57 real_$lesseq(real_2, real_-1/2) & ~ real_$lesseq(real_2, real_-3/10) & ~
% 63.67/9.57 real_$lesseq(real_2, real_1/2) & ~ real_$lesseq(real_2, real_0) & ~
% 63.67/9.57 real_$lesseq(real_1/4, real_9/100) & ~ real_$lesseq(real_1/4, real_-5/3) & ~
% 63.67/9.57 real_$lesseq(real_1/4, real_-10/3) & ~ real_$lesseq(real_1/4, real_-4/5) & ~
% 63.67/9.57 real_$lesseq(real_1/4, real_-3/5) & ~ real_$lesseq(real_1/4, real_-3/20) & ~
% 63.67/9.57 real_$lesseq(real_1/4, real_1/5) & ~ real_$lesseq(real_1/4, real_-1/2) & ~
% 63.67/9.57 real_$lesseq(real_1/4, real_-3/10) & ~ real_$lesseq(real_1/4, real_0) & ~
% 63.67/9.57 real_$lesseq(real_1, real_9/100) & ~ real_$lesseq(real_1, real_-5/3) & ~
% 63.67/9.57 real_$lesseq(real_1, real_-10/3) & ~ real_$lesseq(real_1, real_-4/5) & ~
% 63.67/9.57 real_$lesseq(real_1, real_3/10) & ~ real_$lesseq(real_1, real_-3/5) & ~
% 63.67/9.57 real_$lesseq(real_1, real_-3/20) & ~ real_$lesseq(real_1, real_4/5) & ~
% 63.67/9.57 real_$lesseq(real_1, real_1/5) & ~ real_$lesseq(real_1, real_1/4) & ~
% 63.67/9.57 real_$lesseq(real_1, real_-1/2) & ~ real_$lesseq(real_1, real_-3/10) & ~
% 63.67/9.57 real_$lesseq(real_1, real_1/2) & ~ real_$lesseq(real_1, real_0) & ~
% 63.67/9.57 real_$lesseq(real_-1/2, real_-5/3) & ~ real_$lesseq(real_-1/2, real_-10/3) &
% 63.67/9.57 ~ real_$lesseq(real_-1/2, real_-4/5) & ~ real_$lesseq(real_-1/2, real_-3/5) &
% 63.67/9.57 ~ real_$lesseq(real_-3/10, real_-5/3) & ~ real_$lesseq(real_-3/10,
% 63.67/9.57 real_-10/3) & ~ real_$lesseq(real_-3/10, real_-4/5) & ~
% 63.67/9.57 real_$lesseq(real_-3/10, real_-3/5) & ~ real_$lesseq(real_-3/10, real_-1/2) &
% 63.67/9.57 ~ real_$lesseq(real_1/2, real_9/100) & ~ real_$lesseq(real_1/2, real_-5/3) &
% 63.67/9.57 ~ real_$lesseq(real_1/2, real_-10/3) & ~ real_$lesseq(real_1/2, real_-4/5) &
% 63.67/9.57 ~ real_$lesseq(real_1/2, real_3/10) & ~ real_$lesseq(real_1/2, real_-3/5) &
% 63.67/9.57 ~ real_$lesseq(real_1/2, real_-3/20) & ~ real_$lesseq(real_1/2, real_1/5) &
% 63.67/9.57 ~ real_$lesseq(real_1/2, real_1/4) & ~ real_$lesseq(real_1/2, real_-1/2) & ~
% 63.67/9.57 real_$lesseq(real_1/2, real_-3/10) & ~ real_$lesseq(real_1/2, real_0) & ~
% 63.67/9.57 real_$lesseq(real_0, real_-5/3) & ~ real_$lesseq(real_0, real_-10/3) & ~
% 63.67/9.57 real_$lesseq(real_0, real_-4/5) & ~ real_$lesseq(real_0, real_-3/5) & ~
% 63.67/9.57 real_$lesseq(real_0, real_-3/20) & ~ real_$lesseq(real_0, real_-1/2) & ~
% 63.67/9.57 real_$lesseq(real_0, real_-3/10) & ~ real_$less(real_9/100, real_9/100) & ~
% 63.67/9.57 real_$less(real_9/100, real_-5/3) & ~ real_$less(real_9/100, real_-10/3) & ~
% 63.67/9.57 real_$less(real_9/100, real_-4/5) & ~ real_$less(real_9/100, real_-3/5) & ~
% 63.67/9.57 real_$less(real_9/100, real_-3/20) & ~ real_$less(real_9/100, real_-1/2) & ~
% 63.67/9.57 real_$less(real_9/100, real_-3/10) & ~ real_$less(real_9/100, real_0) & ~
% 63.67/9.57 real_$less(real_-5/3, real_-5/3) & ~ real_$less(real_-5/3, real_-10/3) & ~
% 63.67/9.57 real_$less(real_-10/3, real_-10/3) & ~ real_$less(real_-4/5, real_-5/3) & ~
% 63.67/9.57 real_$less(real_-4/5, real_-10/3) & ~ real_$less(real_-4/5, real_-4/5) & ~
% 63.67/9.57 real_$less(real_3/10, real_9/100) & ~ real_$less(real_3/10, real_-5/3) & ~
% 63.67/9.57 real_$less(real_3/10, real_-10/3) & ~ real_$less(real_3/10, real_-4/5) & ~
% 63.67/9.57 real_$less(real_3/10, real_3/10) & ~ real_$less(real_3/10, real_-3/5) & ~
% 63.67/9.57 real_$less(real_3/10, real_-3/20) & ~ real_$less(real_3/10, real_1/5) & ~
% 63.67/9.57 real_$less(real_3/10, real_1/4) & ~ real_$less(real_3/10, real_-1/2) & ~
% 63.67/9.57 real_$less(real_3/10, real_-3/10) & ~ real_$less(real_3/10, real_0) & ~
% 63.67/9.57 real_$less(real_-3/5, real_-5/3) & ~ real_$less(real_-3/5, real_-10/3) & ~
% 63.67/9.57 real_$less(real_-3/5, real_-4/5) & ~ real_$less(real_-3/5, real_-3/5) & ~
% 63.67/9.57 real_$less(real_-3/20, real_-5/3) & ~ real_$less(real_-3/20, real_-10/3) & ~
% 63.67/9.57 real_$less(real_-3/20, real_-4/5) & ~ real_$less(real_-3/20, real_-3/5) & ~
% 63.67/9.57 real_$less(real_-3/20, real_-3/20) & ~ real_$less(real_-3/20, real_-1/2) & ~
% 63.67/9.57 real_$less(real_-3/20, real_-3/10) & ~ real_$less(real_4/5, real_9/100) & ~
% 63.67/9.57 real_$less(real_4/5, real_-5/3) & ~ real_$less(real_4/5, real_-10/3) & ~
% 63.67/9.57 real_$less(real_4/5, real_-4/5) & ~ real_$less(real_4/5, real_3/10) & ~
% 63.67/9.57 real_$less(real_4/5, real_-3/5) & ~ real_$less(real_4/5, real_-3/20) & ~
% 63.67/9.57 real_$less(real_4/5, real_4/5) & ~ real_$less(real_4/5, real_1/5) & ~
% 63.67/9.57 real_$less(real_4/5, real_1/4) & ~ real_$less(real_4/5, real_-1/2) & ~
% 63.67/9.57 real_$less(real_4/5, real_-3/10) & ~ real_$less(real_4/5, real_1/2) & ~
% 63.67/9.57 real_$less(real_4/5, real_0) & ~ real_$less(real_1/5, real_9/100) & ~
% 63.67/9.57 real_$less(real_1/5, real_-5/3) & ~ real_$less(real_1/5, real_-10/3) & ~
% 63.67/9.57 real_$less(real_1/5, real_-4/5) & ~ real_$less(real_1/5, real_-3/5) & ~
% 63.67/9.57 real_$less(real_1/5, real_-3/20) & ~ real_$less(real_1/5, real_1/5) & ~
% 63.67/9.57 real_$less(real_1/5, real_-1/2) & ~ real_$less(real_1/5, real_-3/10) & ~
% 63.67/9.57 real_$less(real_1/5, real_0) & ~ real_$less(real_2, real_9/100) & ~
% 63.67/9.57 real_$less(real_2, real_-5/3) & ~ real_$less(real_2, real_-10/3) & ~
% 63.67/9.57 real_$less(real_2, real_-4/5) & ~ real_$less(real_2, real_3/10) & ~
% 63.67/9.57 real_$less(real_2, real_-3/5) & ~ real_$less(real_2, real_-3/20) & ~
% 63.67/9.57 real_$less(real_2, real_4/5) & ~ real_$less(real_2, real_1/5) & ~
% 63.67/9.57 real_$less(real_2, real_2) & ~ real_$less(real_2, real_1/4) & ~
% 63.67/9.57 real_$less(real_2, real_1) & ~ real_$less(real_2, real_-1/2) & ~
% 63.67/9.57 real_$less(real_2, real_-3/10) & ~ real_$less(real_2, real_1/2) & ~
% 63.67/9.57 real_$less(real_2, real_0) & ~ real_$less(real_1/4, real_9/100) & ~
% 63.67/9.57 real_$less(real_1/4, real_-5/3) & ~ real_$less(real_1/4, real_-10/3) & ~
% 63.67/9.57 real_$less(real_1/4, real_-4/5) & ~ real_$less(real_1/4, real_-3/5) & ~
% 63.67/9.57 real_$less(real_1/4, real_-3/20) & ~ real_$less(real_1/4, real_1/5) & ~
% 63.67/9.57 real_$less(real_1/4, real_1/4) & ~ real_$less(real_1/4, real_-1/2) & ~
% 63.67/9.57 real_$less(real_1/4, real_-3/10) & ~ real_$less(real_1/4, real_0) & ~
% 63.67/9.57 real_$less(real_1, real_9/100) & ~ real_$less(real_1, real_-5/3) & ~
% 63.67/9.57 real_$less(real_1, real_-10/3) & ~ real_$less(real_1, real_-4/5) & ~
% 63.67/9.57 real_$less(real_1, real_3/10) & ~ real_$less(real_1, real_-3/5) & ~
% 63.67/9.57 real_$less(real_1, real_-3/20) & ~ real_$less(real_1, real_4/5) & ~
% 63.67/9.57 real_$less(real_1, real_1/5) & ~ real_$less(real_1, real_1/4) & ~
% 63.67/9.57 real_$less(real_1, real_1) & ~ real_$less(real_1, real_-1/2) & ~
% 63.67/9.57 real_$less(real_1, real_-3/10) & ~ real_$less(real_1, real_1/2) & ~
% 63.67/9.57 real_$less(real_1, real_0) & ~ real_$less(real_-1/2, real_-5/3) & ~
% 63.67/9.57 real_$less(real_-1/2, real_-10/3) & ~ real_$less(real_-1/2, real_-4/5) & ~
% 63.67/9.57 real_$less(real_-1/2, real_-3/5) & ~ real_$less(real_-1/2, real_-1/2) & ~
% 63.67/9.57 real_$less(real_-3/10, real_-5/3) & ~ real_$less(real_-3/10, real_-10/3) & ~
% 63.67/9.57 real_$less(real_-3/10, real_-4/5) & ~ real_$less(real_-3/10, real_-3/5) & ~
% 63.67/9.57 real_$less(real_-3/10, real_-1/2) & ~ real_$less(real_-3/10, real_-3/10) & ~
% 63.67/9.57 real_$less(real_1/2, real_9/100) & ~ real_$less(real_1/2, real_-5/3) & ~
% 63.67/9.57 real_$less(real_1/2, real_-10/3) & ~ real_$less(real_1/2, real_-4/5) & ~
% 63.67/9.57 real_$less(real_1/2, real_3/10) & ~ real_$less(real_1/2, real_-3/5) & ~
% 63.67/9.57 real_$less(real_1/2, real_-3/20) & ~ real_$less(real_1/2, real_1/5) & ~
% 63.67/9.57 real_$less(real_1/2, real_1/4) & ~ real_$less(real_1/2, real_-1/2) & ~
% 63.67/9.57 real_$less(real_1/2, real_-3/10) & ~ real_$less(real_1/2, real_1/2) & ~
% 63.67/9.57 real_$less(real_1/2, real_0) & ~ real_$less(real_0, real_-5/3) & ~
% 63.67/9.57 real_$less(real_0, real_-10/3) & ~ real_$less(real_0, real_-4/5) & ~
% 63.67/9.57 real_$less(real_0, real_-3/5) & ~ real_$less(real_0, real_-3/20) & ~
% 63.67/9.57 real_$less(real_0, real_-1/2) & ~ real_$less(real_0, real_-3/10) & ~
% 63.67/9.57 real_$less(real_0, real_0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 63.67/9.57 : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = v2)) &
% 63.67/9.57 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~
% 63.67/9.57 (real_$product(v1, v0) = v2) | real_$quotient(v2, v0) = v1) & ! [v0: $real]
% 63.67/9.57 : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) |
% 63.67/9.57 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 63.67/9.57 ( ~ real_$lesseq(v2, v1) | ~ real_$lesseq(v1, v0) | real_$lesseq(v2, v0)) &
% 63.67/9.57 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ real_$lesseq(v2, v1) |
% 63.67/9.57 ~ real_$less(v1, v0) | real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real]
% 63.67/9.57 : ! [v2: $real] : ( ~ real_$lesseq(v1, v0) | ~ real_$less(v2, v1) |
% 63.67/9.57 real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~
% 63.67/9.57 (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 |
% 63.67/9.57 ~ real_$lesseq(v1, v0) | real_$less(v1, v0)) & ! [v0: $real] : ! [v1:
% 63.67/9.57 $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0:
% 63.67/9.57 $real] : ! [v1: $real] : ( ~ real_$greatereq(v0, v1) | real_$lesseq(v1,
% 63.67/9.57 v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ real_$greater(v0, v1) |
% 63.67/9.57 real_$less(v1, v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ real_$lesseq(v1,
% 63.67/9.57 v0) | real_$greatereq(v0, v1)) & ! [v0: $real] : ! [v1: $real] : ( ~
% 63.67/9.57 real_$less(v1, v0) | real_$greater(v0, v1)) & ! [v0: $real] : ! [v1:
% 63.67/9.57 $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, v0)) & ! [v0: $real] :
% 63.67/9.57 (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & ? [v0: $real] : ? [v1: $real] :
% 63.67/9.57 ? [v2: $real] : ? [v3: $real] : ? [v4: $real] : ? [v5: $real] :
% 63.67/9.57 (real_$sum(v5, v0) = v4 & real_$sum(v2, v3) = v4 & real_$sum(v2, v1) = v5 &
% 63.67/9.57 real_$sum(v1, v0) = v3) & ? [v0: $real] : ? [v1: $real] : ? [v2: $real] :
% 63.67/9.57 ? [v3: $real] : (real_$difference(v1, v0) = v3 & real_$uminus(v0) = v2 &
% 63.67/9.57 real_$sum(v1, v2) = v3) & ? [v0: $real] : ? [v1: $real] : ? [v2: $real] :
% 63.67/9.57 (real_$product(v1, v0) = v2 & real_$product(v0, v1) = v2) & ? [v0: $real] :
% 63.67/9.57 real_$lesseq(v0, v0)
% 63.67/9.57
% 63.67/9.57 (function-axioms)
% 63.83/9.58 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 63.83/9.58 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 63.83/9.58 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 63.83/9.58 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 63.83/9.58 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 63.83/9.58 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 63.83/9.58 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 63.83/9.58 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $real] :
% 63.83/9.58 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~
% 63.83/9.58 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 63.83/9.58 : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & !
% 63.83/9.58 [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2)
% 63.83/9.58 = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 63.83/9.58 [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) =
% 63.83/9.58 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 63.83/9.58 (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & ! [v0: $real] : !
% 63.83/9.58 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~
% 63.83/9.58 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 63.83/9.58 $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) =
% 63.83/9.58 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 63.83/9.58 (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: $real] : !
% 63.83/9.58 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 63.83/9.58 (real_$floor(v2) = v0))
% 63.83/9.58
% 63.83/9.58 Those formulas are unsatisfiable:
% 63.83/9.58 ---------------------------------
% 63.83/9.58
% 63.83/9.58 Begin of proof
% 63.83/9.58 |
% 63.83/9.58 | ALPHA: (function-axioms) implies:
% 63.83/9.58 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 63.83/9.58 | (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0))
% 63.83/9.58 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1
% 63.83/9.58 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0))
% 63.83/9.58 |
% 63.83/9.59 | ALPHA: (input) implies:
% 63.83/9.59 | (3) real_$floor(real_0) = real_0
% 63.83/9.59 | (4) real_$floor(real_1/5) = real_0
% 63.83/9.59 | (5) real_$floor(real_4/5) = real_0
% 63.83/9.59 | (6) real_$sum(real_-3/10, real_1/2) = real_1/5
% 63.83/9.59 | (7) real_$sum(real_-3/10, real_-3/10) = real_-3/5
% 63.83/9.59 | (8) real_$sum(real_3/10, real_1/2) = real_4/5
% 63.83/9.59 | (9) real_$sum(real_3/10, real_-3/10) = real_0
% 63.83/9.59 |
% 63.83/9.59 | GROUND_INST: instantiating (prove) with real_-3/10, real_-3/5, simplifying
% 63.83/9.59 | with (7) gives:
% 63.83/9.59 | (10) ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : ( ~ (v2 = v1) &
% 63.83/9.59 | real_$sum(real_-3/10, real_1/2) = v0 & real_$floor(v0) = v1 &
% 63.83/9.59 | real_$floor(real_-3/5) = v2)
% 63.83/9.59 |
% 63.83/9.59 | GROUND_INST: instantiating (prove) with real_3/10, real_0, simplifying with
% 63.83/9.59 | (9) gives:
% 63.83/9.59 | (11) ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : ( ~ (v2 = v1) &
% 63.83/9.59 | real_$sum(real_3/10, real_1/2) = v0 & real_$floor(v0) = v1 &
% 63.83/9.59 | real_$floor(real_0) = v2)
% 63.83/9.59 |
% 63.83/9.59 | DELTA: instantiating (11) with fresh symbols all_20_0, all_20_1, all_20_2
% 63.83/9.59 | gives:
% 63.83/9.59 | (12) ~ (all_20_0 = all_20_1) & real_$sum(real_3/10, real_1/2) = all_20_2 &
% 63.83/9.59 | real_$floor(all_20_2) = all_20_1 & real_$floor(real_0) = all_20_0
% 63.83/9.59 |
% 63.83/9.59 | ALPHA: (12) implies:
% 63.83/9.59 | (13) ~ (all_20_0 = all_20_1)
% 63.83/9.59 | (14) real_$floor(real_0) = all_20_0
% 63.83/9.59 | (15) real_$floor(all_20_2) = all_20_1
% 63.83/9.59 | (16) real_$sum(real_3/10, real_1/2) = all_20_2
% 63.83/9.59 |
% 63.83/9.60 | DELTA: instantiating (10) with fresh symbols all_28_0, all_28_1, all_28_2
% 63.83/9.60 | gives:
% 63.83/9.60 | (17) ~ (all_28_0 = all_28_1) & real_$sum(real_-3/10, real_1/2) = all_28_2
% 63.83/9.60 | & real_$floor(all_28_2) = all_28_1 & real_$floor(real_-3/5) = all_28_0
% 63.83/9.60 |
% 63.83/9.60 | ALPHA: (17) implies:
% 63.83/9.60 | (18) real_$floor(all_28_2) = all_28_1
% 63.83/9.60 | (19) real_$sum(real_-3/10, real_1/2) = all_28_2
% 63.83/9.60 |
% 63.83/9.60 | GROUND_INST: instantiating (1) with real_0, all_20_0, real_0, simplifying with
% 63.83/9.60 | (3), (14) gives:
% 63.83/9.60 | (20) all_20_0 = real_0
% 63.83/9.60 |
% 63.83/9.60 | GROUND_INST: instantiating (1) with real_0, all_28_1, real_1/5, simplifying
% 63.83/9.60 | with (4) gives:
% 63.83/9.60 | (21) all_28_1 = real_0 | ~ (real_$floor(real_1/5) = all_28_1)
% 63.83/9.60 |
% 63.83/9.60 | GROUND_INST: instantiating (1) with all_20_1, all_28_1, all_20_2, simplifying
% 63.83/9.60 | with (15) gives:
% 63.83/9.60 | (22) all_28_1 = all_20_1 | ~ (real_$floor(all_20_2) = all_28_1)
% 63.83/9.60 |
% 63.83/9.60 | GROUND_INST: instantiating (2) with real_1/5, all_28_2, real_1/2, real_-3/10,
% 63.83/9.60 | simplifying with (6), (19) gives:
% 63.83/9.60 | (23) all_28_2 = real_1/5
% 63.83/9.60 |
% 63.83/9.60 | GROUND_INST: instantiating (2) with real_4/5, all_20_2, real_1/2, real_3/10,
% 63.83/9.60 | simplifying with (8), (16) gives:
% 63.83/9.60 | (24) all_20_2 = real_4/5
% 63.83/9.60 |
% 63.83/9.60 | REDUCE: (13), (20) imply:
% 63.83/9.60 | (25) ~ (all_20_1 = real_0)
% 63.83/9.60 |
% 63.83/9.60 | SIMP: (25) implies:
% 63.83/9.60 | (26) ~ (all_20_1 = real_0)
% 63.83/9.60 |
% 63.83/9.60 | REDUCE: (18), (23) imply:
% 63.83/9.60 | (27) real_$floor(real_1/5) = all_28_1
% 63.83/9.60 |
% 63.83/9.60 | BETA: splitting (21) gives:
% 63.83/9.60 |
% 63.83/9.60 | Case 1:
% 63.83/9.60 | |
% 63.83/9.60 | | (28) ~ (real_$floor(real_1/5) = all_28_1)
% 63.83/9.60 | |
% 63.83/9.60 | | PRED_UNIFY: (27), (28) imply:
% 63.83/9.60 | | (29) $false
% 63.83/9.60 | |
% 63.83/9.60 | | CLOSE: (29) is inconsistent.
% 63.83/9.60 | |
% 63.83/9.60 | Case 2:
% 63.83/9.60 | |
% 63.83/9.60 | | (30) all_28_1 = real_0
% 63.83/9.60 | |
% 63.83/9.60 | | BETA: splitting (22) gives:
% 63.83/9.60 | |
% 63.83/9.60 | | Case 1:
% 63.83/9.60 | | |
% 63.83/9.60 | | | (31) ~ (real_$floor(all_20_2) = all_28_1)
% 63.83/9.60 | | |
% 63.83/9.60 | | | REDUCE: (24), (30), (31) imply:
% 63.83/9.60 | | | (32) ~ (real_$floor(real_4/5) = real_0)
% 63.83/9.60 | | |
% 63.83/9.60 | | | PRED_UNIFY: (5), (32) imply:
% 63.83/9.60 | | | (33) $false
% 63.83/9.60 | | |
% 63.83/9.60 | | | CLOSE: (33) is inconsistent.
% 63.83/9.60 | | |
% 63.83/9.60 | | Case 2:
% 63.83/9.60 | | |
% 63.83/9.60 | | | (34) all_28_1 = all_20_1
% 63.83/9.60 | | |
% 63.83/9.60 | | | COMBINE_EQS: (30), (34) imply:
% 63.83/9.60 | | | (35) all_20_1 = real_0
% 63.83/9.60 | | |
% 63.83/9.60 | | | SIMP: (35) implies:
% 63.83/9.60 | | | (36) all_20_1 = real_0
% 63.83/9.61 | | |
% 63.83/9.61 | | | REDUCE: (26), (36) imply:
% 63.83/9.61 | | | (37) $false
% 63.83/9.61 | | |
% 63.83/9.61 | | | CLOSE: (37) is inconsistent.
% 63.83/9.61 | | |
% 63.83/9.61 | | End of split
% 63.83/9.61 | |
% 63.83/9.61 | End of split
% 63.83/9.61 |
% 63.83/9.61 End of proof
% 63.83/9.61 % SZS output end Proof for theBenchmark
% 63.83/9.61
% 63.83/9.61 9039ms
%------------------------------------------------------------------------------