TSTP Solution File: ARI307_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI307_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 17:47:39 EDT 2023
% Result : Theorem 14.23s 2.79s
% Output : Proof 21.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI307_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 18:18:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.62/0.90 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.62/0.90 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.62/0.90 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.62/0.90 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.62/0.90 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.65/0.90 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.65/0.90 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.32/1.00 Prover 1: Preprocessing ...
% 2.32/1.04 Prover 4: Preprocessing ...
% 2.32/1.08 Prover 0: Preprocessing ...
% 2.32/1.08 Prover 6: Preprocessing ...
% 2.99/1.11 Prover 2: Preprocessing ...
% 2.99/1.13 Prover 5: Preprocessing ...
% 2.99/1.13 Prover 3: Preprocessing ...
% 6.70/1.62 Prover 1: Constructing countermodel ...
% 6.70/1.62 Prover 4: Constructing countermodel ...
% 6.70/1.65 Prover 6: Proving ...
% 6.70/1.68 Prover 0: Proving ...
% 9.49/2.02 Prover 1: gave up
% 9.49/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.49/2.04 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.49/2.05 Prover 3: Constructing countermodel ...
% 10.16/2.09 Prover 7: Preprocessing ...
% 10.16/2.11 Prover 2: Proving ...
% 11.89/2.35 Prover 5: Proving ...
% 12.57/2.46 Prover 7: Warning: ignoring some quantifiers
% 13.19/2.49 Prover 7: Constructing countermodel ...
% 14.23/2.79 Prover 3: proved (2169ms)
% 14.23/2.79
% 14.23/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.23/2.79
% 14.23/2.79 Prover 6: stopped
% 14.23/2.79 Prover 0: stopped
% 14.23/2.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.23/2.80 Prover 5: stopped
% 14.23/2.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.23/2.82 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 14.23/2.82 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 14.23/2.82 Prover 8: Preprocessing ...
% 14.23/2.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.23/2.82 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 14.23/2.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.23/2.82 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 14.23/2.82 Prover 13: Preprocessing ...
% 14.23/2.83 Prover 10: Preprocessing ...
% 15.23/2.85 Prover 8: Warning: ignoring some quantifiers
% 15.23/2.86 Prover 11: Preprocessing ...
% 15.23/2.86 Prover 8: Constructing countermodel ...
% 15.23/2.90 Prover 13: Warning: ignoring some quantifiers
% 15.23/2.90 Prover 2: stopped
% 15.23/2.90 Prover 13: Constructing countermodel ...
% 15.23/2.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.23/2.91 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 16.53/2.95 Prover 16: Preprocessing ...
% 16.53/2.96 Prover 8: gave up
% 16.53/2.96 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 16.53/2.96 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation
% 16.53/3.00 Prover 19: Preprocessing ...
% 16.53/3.01 Prover 13: gave up
% 18.72/3.22 Prover 10: Warning: ignoring some quantifiers
% 18.85/3.23 Prover 10: Constructing countermodel ...
% 18.85/3.23 Prover 7: Found proof (size 3)
% 18.85/3.23 Prover 7: proved (1209ms)
% 18.85/3.23 Prover 4: stopped
% 18.85/3.23 Prover 16: stopped
% 18.85/3.26 Prover 10: stopped
% 19.38/3.33 Prover 11: Constructing countermodel ...
% 19.38/3.35 Prover 11: stopped
% 20.77/3.65 Prover 19: Warning: ignoring some quantifiers
% 20.85/3.66 Prover 19: Constructing countermodel ...
% 20.85/3.68 Prover 19: stopped
% 20.85/3.68
% 20.85/3.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.85/3.68
% 20.85/3.68 % SZS output start Proof for theBenchmark
% 20.85/3.68 Assumptions after simplification:
% 20.85/3.68 ---------------------------------
% 20.85/3.68
% 20.85/3.68 (rat_product_problem_24)
% 20.85/3.70 ! [v0: $rat] : ~ (rat_$product(v0, rat_-4/5) = rat_3/4)
% 20.85/3.70
% 20.85/3.70 (input)
% 21.31/3.83 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_9/16) & ~
% 21.31/3.83 (rat_very_large = rat_3/2) & ~ (rat_very_large = rat_-16/15) & ~
% 21.31/3.83 (rat_very_large = rat_4/3) & ~ (rat_very_large = rat_31/20) & ~
% 21.31/3.83 (rat_very_large = rat_-3/4) & ~ (rat_very_large = rat_-15/16) & ~
% 21.31/3.83 (rat_very_large = rat_-3/5) & ~ (rat_very_large = rat_-31/20) & ~
% 21.31/3.83 (rat_very_large = rat_-1/20) & ~ (rat_very_large = rat_1) & ~
% 21.31/3.83 (rat_very_large = rat_-5/4) & ~ (rat_very_large = rat_16/25) & ~
% 21.31/3.83 (rat_very_large = rat_-8/5) & ~ (rat_very_large = rat_4/5) & ~
% 21.31/3.83 (rat_very_large = rat_3/4) & ~ (rat_very_large = rat_-4/5) & ~
% 21.31/3.84 (rat_very_large = rat_0) & ~ (rat_very_small = rat_9/16) & ~ (rat_very_small
% 21.31/3.84 = rat_3/2) & ~ (rat_very_small = rat_-16/15) & ~ (rat_very_small =
% 21.31/3.84 rat_4/3) & ~ (rat_very_small = rat_31/20) & ~ (rat_very_small = rat_-3/4)
% 21.31/3.84 & ~ (rat_very_small = rat_-15/16) & ~ (rat_very_small = rat_-3/5) & ~
% 21.31/3.84 (rat_very_small = rat_-31/20) & ~ (rat_very_small = rat_-1/20) & ~
% 21.31/3.84 (rat_very_small = rat_1) & ~ (rat_very_small = rat_-5/4) & ~ (rat_very_small
% 21.31/3.84 = rat_16/25) & ~ (rat_very_small = rat_-8/5) & ~ (rat_very_small =
% 21.31/3.84 rat_4/5) & ~ (rat_very_small = rat_3/4) & ~ (rat_very_small = rat_-4/5) &
% 21.31/3.84 ~ (rat_very_small = rat_0) & ~ (rat_9/16 = rat_3/2) & ~ (rat_9/16 =
% 21.31/3.84 rat_-16/15) & ~ (rat_9/16 = rat_4/3) & ~ (rat_9/16 = rat_31/20) & ~
% 21.31/3.84 (rat_9/16 = rat_-3/4) & ~ (rat_9/16 = rat_-15/16) & ~ (rat_9/16 = rat_-3/5)
% 21.31/3.84 & ~ (rat_9/16 = rat_-31/20) & ~ (rat_9/16 = rat_-1/20) & ~ (rat_9/16 =
% 21.31/3.84 rat_1) & ~ (rat_9/16 = rat_-5/4) & ~ (rat_9/16 = rat_16/25) & ~ (rat_9/16
% 21.31/3.84 = rat_-8/5) & ~ (rat_9/16 = rat_4/5) & ~ (rat_9/16 = rat_3/4) & ~
% 21.31/3.84 (rat_9/16 = rat_-4/5) & ~ (rat_9/16 = rat_0) & ~ (rat_3/2 = rat_-16/15) & ~
% 21.31/3.84 (rat_3/2 = rat_4/3) & ~ (rat_3/2 = rat_31/20) & ~ (rat_3/2 = rat_-3/4) & ~
% 21.31/3.84 (rat_3/2 = rat_-15/16) & ~ (rat_3/2 = rat_-3/5) & ~ (rat_3/2 = rat_-31/20) &
% 21.31/3.84 ~ (rat_3/2 = rat_-1/20) & ~ (rat_3/2 = rat_1) & ~ (rat_3/2 = rat_-5/4) & ~
% 21.31/3.84 (rat_3/2 = rat_16/25) & ~ (rat_3/2 = rat_-8/5) & ~ (rat_3/2 = rat_4/5) & ~
% 21.31/3.84 (rat_3/2 = rat_3/4) & ~ (rat_3/2 = rat_-4/5) & ~ (rat_3/2 = rat_0) & ~
% 21.31/3.84 (rat_-16/15 = rat_4/3) & ~ (rat_-16/15 = rat_31/20) & ~ (rat_-16/15 =
% 21.31/3.84 rat_-3/4) & ~ (rat_-16/15 = rat_-15/16) & ~ (rat_-16/15 = rat_-3/5) & ~
% 21.31/3.84 (rat_-16/15 = rat_-31/20) & ~ (rat_-16/15 = rat_-1/20) & ~ (rat_-16/15 =
% 21.31/3.84 rat_1) & ~ (rat_-16/15 = rat_-5/4) & ~ (rat_-16/15 = rat_16/25) & ~
% 21.31/3.84 (rat_-16/15 = rat_-8/5) & ~ (rat_-16/15 = rat_4/5) & ~ (rat_-16/15 =
% 21.31/3.84 rat_3/4) & ~ (rat_-16/15 = rat_-4/5) & ~ (rat_-16/15 = rat_0) & ~
% 21.31/3.84 (rat_4/3 = rat_31/20) & ~ (rat_4/3 = rat_-3/4) & ~ (rat_4/3 = rat_-15/16) &
% 21.31/3.84 ~ (rat_4/3 = rat_-3/5) & ~ (rat_4/3 = rat_-31/20) & ~ (rat_4/3 = rat_-1/20)
% 21.31/3.84 & ~ (rat_4/3 = rat_1) & ~ (rat_4/3 = rat_-5/4) & ~ (rat_4/3 = rat_16/25) &
% 21.31/3.84 ~ (rat_4/3 = rat_-8/5) & ~ (rat_4/3 = rat_4/5) & ~ (rat_4/3 = rat_3/4) & ~
% 21.31/3.84 (rat_4/3 = rat_-4/5) & ~ (rat_4/3 = rat_0) & ~ (rat_31/20 = rat_-3/4) & ~
% 21.31/3.84 (rat_31/20 = rat_-15/16) & ~ (rat_31/20 = rat_-3/5) & ~ (rat_31/20 =
% 21.31/3.84 rat_-31/20) & ~ (rat_31/20 = rat_-1/20) & ~ (rat_31/20 = rat_1) & ~
% 21.31/3.84 (rat_31/20 = rat_-5/4) & ~ (rat_31/20 = rat_16/25) & ~ (rat_31/20 =
% 21.31/3.84 rat_-8/5) & ~ (rat_31/20 = rat_4/5) & ~ (rat_31/20 = rat_3/4) & ~
% 21.31/3.84 (rat_31/20 = rat_-4/5) & ~ (rat_31/20 = rat_0) & ~ (rat_-3/4 = rat_-15/16) &
% 21.31/3.84 ~ (rat_-3/4 = rat_-3/5) & ~ (rat_-3/4 = rat_-31/20) & ~ (rat_-3/4 =
% 21.31/3.84 rat_-1/20) & ~ (rat_-3/4 = rat_1) & ~ (rat_-3/4 = rat_-5/4) & ~ (rat_-3/4
% 21.31/3.84 = rat_16/25) & ~ (rat_-3/4 = rat_-8/5) & ~ (rat_-3/4 = rat_4/5) & ~
% 21.31/3.84 (rat_-3/4 = rat_3/4) & ~ (rat_-3/4 = rat_-4/5) & ~ (rat_-3/4 = rat_0) & ~
% 21.31/3.84 (rat_-15/16 = rat_-3/5) & ~ (rat_-15/16 = rat_-31/20) & ~ (rat_-15/16 =
% 21.31/3.84 rat_-1/20) & ~ (rat_-15/16 = rat_1) & ~ (rat_-15/16 = rat_-5/4) & ~
% 21.31/3.84 (rat_-15/16 = rat_16/25) & ~ (rat_-15/16 = rat_-8/5) & ~ (rat_-15/16 =
% 21.31/3.84 rat_4/5) & ~ (rat_-15/16 = rat_3/4) & ~ (rat_-15/16 = rat_-4/5) & ~
% 21.31/3.84 (rat_-15/16 = rat_0) & ~ (rat_-3/5 = rat_-31/20) & ~ (rat_-3/5 = rat_-1/20)
% 21.31/3.84 & ~ (rat_-3/5 = rat_1) & ~ (rat_-3/5 = rat_-5/4) & ~ (rat_-3/5 = rat_16/25)
% 21.31/3.84 & ~ (rat_-3/5 = rat_-8/5) & ~ (rat_-3/5 = rat_4/5) & ~ (rat_-3/5 = rat_3/4)
% 21.31/3.84 & ~ (rat_-3/5 = rat_-4/5) & ~ (rat_-3/5 = rat_0) & ~ (rat_-31/20 =
% 21.31/3.84 rat_-1/20) & ~ (rat_-31/20 = rat_1) & ~ (rat_-31/20 = rat_-5/4) & ~
% 21.31/3.84 (rat_-31/20 = rat_16/25) & ~ (rat_-31/20 = rat_-8/5) & ~ (rat_-31/20 =
% 21.31/3.84 rat_4/5) & ~ (rat_-31/20 = rat_3/4) & ~ (rat_-31/20 = rat_-4/5) & ~
% 21.31/3.84 (rat_-31/20 = rat_0) & ~ (rat_-1/20 = rat_1) & ~ (rat_-1/20 = rat_-5/4) & ~
% 21.31/3.84 (rat_-1/20 = rat_16/25) & ~ (rat_-1/20 = rat_-8/5) & ~ (rat_-1/20 = rat_4/5)
% 21.31/3.84 & ~ (rat_-1/20 = rat_3/4) & ~ (rat_-1/20 = rat_-4/5) & ~ (rat_-1/20 =
% 21.31/3.84 rat_0) & ~ (rat_1 = rat_-5/4) & ~ (rat_1 = rat_16/25) & ~ (rat_1 =
% 21.31/3.84 rat_-8/5) & ~ (rat_1 = rat_4/5) & ~ (rat_1 = rat_3/4) & ~ (rat_1 =
% 21.31/3.84 rat_-4/5) & ~ (rat_1 = rat_0) & ~ (rat_-5/4 = rat_16/25) & ~ (rat_-5/4 =
% 21.31/3.84 rat_-8/5) & ~ (rat_-5/4 = rat_4/5) & ~ (rat_-5/4 = rat_3/4) & ~ (rat_-5/4
% 21.31/3.84 = rat_-4/5) & ~ (rat_-5/4 = rat_0) & ~ (rat_16/25 = rat_-8/5) & ~
% 21.31/3.84 (rat_16/25 = rat_4/5) & ~ (rat_16/25 = rat_3/4) & ~ (rat_16/25 = rat_-4/5) &
% 21.31/3.84 ~ (rat_16/25 = rat_0) & ~ (rat_-8/5 = rat_4/5) & ~ (rat_-8/5 = rat_3/4) &
% 21.31/3.84 ~ (rat_-8/5 = rat_-4/5) & ~ (rat_-8/5 = rat_0) & ~ (rat_4/5 = rat_3/4) & ~
% 21.31/3.84 (rat_4/5 = rat_-4/5) & ~ (rat_4/5 = rat_0) & ~ (rat_3/4 = rat_-4/5) & ~
% 21.31/3.84 (rat_3/4 = rat_0) & ~ (rat_-4/5 = rat_0) & rat_$floor(rat_9/16) = rat_0 &
% 21.31/3.84 rat_$floor(rat_3/2) = rat_1 & rat_$floor(rat_4/3) = rat_1 &
% 21.31/3.84 rat_$floor(rat_31/20) = rat_1 & rat_$floor(rat_1) = rat_1 &
% 21.31/3.84 rat_$floor(rat_16/25) = rat_0 & rat_$floor(rat_4/5) = rat_0 &
% 21.31/3.84 rat_$floor(rat_3/4) = rat_0 & rat_$floor(rat_0) = rat_0 &
% 21.31/3.84 rat_$ceiling(rat_9/16) = rat_1 & rat_$ceiling(rat_-3/4) = rat_0 &
% 21.31/3.84 rat_$ceiling(rat_-15/16) = rat_0 & rat_$ceiling(rat_-3/5) = rat_0 &
% 21.31/3.84 rat_$ceiling(rat_-1/20) = rat_0 & rat_$ceiling(rat_1) = rat_1 &
% 21.31/3.84 rat_$ceiling(rat_16/25) = rat_1 & rat_$ceiling(rat_4/5) = rat_1 &
% 21.31/3.84 rat_$ceiling(rat_3/4) = rat_1 & rat_$ceiling(rat_-4/5) = rat_0 &
% 21.31/3.84 rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_9/16) = rat_0 &
% 21.31/3.84 rat_$truncate(rat_3/2) = rat_1 & rat_$truncate(rat_4/3) = rat_1 &
% 21.31/3.84 rat_$truncate(rat_31/20) = rat_1 & rat_$truncate(rat_-3/4) = rat_0 &
% 21.31/3.84 rat_$truncate(rat_-15/16) = rat_0 & rat_$truncate(rat_-3/5) = rat_0 &
% 21.31/3.84 rat_$truncate(rat_-1/20) = rat_0 & rat_$truncate(rat_1) = rat_1 &
% 21.31/3.84 rat_$truncate(rat_16/25) = rat_0 & rat_$truncate(rat_4/5) = rat_0 &
% 21.31/3.84 rat_$truncate(rat_3/4) = rat_0 & rat_$truncate(rat_-4/5) = rat_0 &
% 21.31/3.84 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_9/16) = rat_1 &
% 21.31/3.84 rat_$round(rat_4/3) = rat_1 & rat_$round(rat_-1/20) = rat_0 &
% 21.31/3.84 rat_$round(rat_1) = rat_1 & rat_$round(rat_16/25) = rat_1 &
% 21.31/3.84 rat_$round(rat_4/5) = rat_1 & rat_$round(rat_3/4) = rat_1 & rat_$round(rat_0)
% 21.31/3.84 = rat_0 & rat_$to_int(rat_9/16) = 0 & rat_$to_int(rat_3/2) = 1 &
% 21.31/3.84 rat_$to_int(rat_-16/15) = -2 & rat_$to_int(rat_4/3) = 1 &
% 21.31/3.84 rat_$to_int(rat_31/20) = 1 & rat_$to_int(rat_-3/4) = -1 &
% 21.31/3.84 rat_$to_int(rat_-15/16) = -1 & rat_$to_int(rat_-3/5) = -1 &
% 21.31/3.84 rat_$to_int(rat_-31/20) = -2 & rat_$to_int(rat_-1/20) = -1 &
% 21.31/3.84 rat_$to_int(rat_1) = 1 & rat_$to_int(rat_-5/4) = -2 & rat_$to_int(rat_16/25) =
% 21.31/3.84 0 & rat_$to_int(rat_-8/5) = -2 & rat_$to_int(rat_4/5) = 0 &
% 21.31/3.84 rat_$to_int(rat_3/4) = 0 & rat_$to_int(rat_-4/5) = -1 & rat_$to_int(rat_0) = 0
% 21.31/3.84 & rat_$to_rat(rat_9/16) = rat_9/16 & rat_$to_rat(rat_3/2) = rat_3/2 &
% 21.31/3.84 rat_$to_rat(rat_-16/15) = rat_-16/15 & rat_$to_rat(rat_4/3) = rat_4/3 &
% 21.31/3.84 rat_$to_rat(rat_31/20) = rat_31/20 & rat_$to_rat(rat_-3/4) = rat_-3/4 &
% 21.31/3.84 rat_$to_rat(rat_-15/16) = rat_-15/16 & rat_$to_rat(rat_-3/5) = rat_-3/5 &
% 21.31/3.84 rat_$to_rat(rat_-31/20) = rat_-31/20 & rat_$to_rat(rat_-1/20) = rat_-1/20 &
% 21.31/3.84 rat_$to_rat(rat_1) = rat_1 & rat_$to_rat(rat_-5/4) = rat_-5/4 &
% 21.31/3.84 rat_$to_rat(rat_16/25) = rat_16/25 & rat_$to_rat(rat_-8/5) = rat_-8/5 &
% 21.31/3.84 rat_$to_rat(rat_4/5) = rat_4/5 & rat_$to_rat(rat_3/4) = rat_3/4 &
% 21.31/3.84 rat_$to_rat(rat_-4/5) = rat_-4/5 & rat_$to_rat(rat_0) = rat_0 &
% 21.31/3.84 rat_$to_real(rat_9/16) = real_9/16 & rat_$to_real(rat_3/2) = real_3/2 &
% 21.31/3.84 rat_$to_real(rat_-16/15) = real_-16/15 & rat_$to_real(rat_4/3) = real_4/3 &
% 21.31/3.84 rat_$to_real(rat_31/20) = real_31/20 & rat_$to_real(rat_-3/4) = real_-3/4 &
% 21.31/3.84 rat_$to_real(rat_-15/16) = real_-15/16 & rat_$to_real(rat_-3/5) = real_-3/5 &
% 21.31/3.84 rat_$to_real(rat_-31/20) = real_-31/20 & rat_$to_real(rat_-1/20) = real_-1/20
% 21.31/3.84 & rat_$to_real(rat_1) = real_1 & rat_$to_real(rat_-5/4) = real_-5/4 &
% 21.31/3.84 rat_$to_real(rat_16/25) = real_16/25 & rat_$to_real(rat_-8/5) = real_-8/5 &
% 21.31/3.84 rat_$to_real(rat_4/5) = real_4/5 & rat_$to_real(rat_3/4) = real_3/4 &
% 21.31/3.84 rat_$to_real(rat_-4/5) = real_-4/5 & rat_$to_real(rat_0) = real_0 &
% 21.31/3.84 int_$to_rat(1) = rat_1 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_9/16,
% 21.31/3.84 rat_9/16) = rat_1 & rat_$quotient(rat_9/16, rat_-3/4) = rat_-3/4 &
% 21.31/3.84 rat_$quotient(rat_9/16, rat_-15/16) = rat_-3/5 & rat_$quotient(rat_9/16,
% 21.31/3.84 rat_-3/5) = rat_-15/16 & rat_$quotient(rat_9/16, rat_1) = rat_9/16 &
% 21.31/3.84 rat_$quotient(rat_9/16, rat_3/4) = rat_3/4 & rat_$quotient(rat_3/2, rat_3/2) =
% 21.31/3.84 rat_1 & rat_$quotient(rat_3/2, rat_-15/16) = rat_-8/5 & rat_$quotient(rat_3/2,
% 21.31/3.84 rat_1) = rat_3/2 & rat_$quotient(rat_3/2, rat_-8/5) = rat_-15/16 &
% 21.31/3.84 rat_$quotient(rat_-16/15, rat_-16/15) = rat_1 & rat_$quotient(rat_-16/15,
% 21.31/3.84 rat_4/3) = rat_-4/5 & rat_$quotient(rat_-16/15, rat_1) = rat_-16/15 &
% 21.31/3.84 rat_$quotient(rat_-16/15, rat_-4/5) = rat_4/3 & rat_$quotient(rat_4/3,
% 21.31/3.84 rat_-16/15) = rat_-5/4 & rat_$quotient(rat_4/3, rat_4/3) = rat_1 &
% 21.31/3.84 rat_$quotient(rat_4/3, rat_1) = rat_4/3 & rat_$quotient(rat_4/3, rat_-5/4) =
% 21.31/3.84 rat_-16/15 & rat_$quotient(rat_31/20, rat_31/20) = rat_1 &
% 21.31/3.84 rat_$quotient(rat_31/20, rat_1) = rat_31/20 & rat_$quotient(rat_-3/4,
% 21.31/3.84 rat_-3/4) = rat_1 & rat_$quotient(rat_-3/4, rat_-15/16) = rat_4/5 &
% 21.31/3.84 rat_$quotient(rat_-3/4, rat_1) = rat_-3/4 & rat_$quotient(rat_-3/4, rat_4/5) =
% 21.31/3.84 rat_-15/16 & rat_$quotient(rat_-15/16, rat_-15/16) = rat_1 &
% 21.31/3.84 rat_$quotient(rat_-15/16, rat_1) = rat_-15/16 & rat_$quotient(rat_-15/16,
% 21.31/3.84 rat_-5/4) = rat_3/4 & rat_$quotient(rat_-15/16, rat_3/4) = rat_-5/4 &
% 21.31/3.84 rat_$quotient(rat_-3/5, rat_9/16) = rat_-16/15 & rat_$quotient(rat_-3/5,
% 21.31/3.84 rat_-16/15) = rat_9/16 & rat_$quotient(rat_-3/5, rat_-3/4) = rat_4/5 &
% 21.31/3.84 rat_$quotient(rat_-3/5, rat_-15/16) = rat_16/25 & rat_$quotient(rat_-3/5,
% 21.31/3.84 rat_-3/5) = rat_1 & rat_$quotient(rat_-3/5, rat_1) = rat_-3/5 &
% 21.31/3.84 rat_$quotient(rat_-3/5, rat_16/25) = rat_-15/16 & rat_$quotient(rat_-3/5,
% 21.31/3.84 rat_4/5) = rat_-3/4 & rat_$quotient(rat_-3/5, rat_3/4) = rat_-4/5 &
% 21.31/3.84 rat_$quotient(rat_-3/5, rat_-4/5) = rat_3/4 & rat_$quotient(rat_-31/20,
% 21.31/3.84 rat_-31/20) = rat_1 & rat_$quotient(rat_-31/20, rat_1) = rat_-31/20 &
% 21.31/3.84 rat_$quotient(rat_-1/20, rat_-1/20) = rat_1 & rat_$quotient(rat_-1/20, rat_1)
% 21.31/3.84 = rat_-1/20 & rat_$quotient(rat_1, rat_-16/15) = rat_-15/16 &
% 21.31/3.84 rat_$quotient(rat_1, rat_4/3) = rat_3/4 & rat_$quotient(rat_1, rat_-15/16) =
% 21.31/3.84 rat_-16/15 & rat_$quotient(rat_1, rat_1) = rat_1 & rat_$quotient(rat_1,
% 21.31/3.84 rat_-5/4) = rat_-4/5 & rat_$quotient(rat_1, rat_3/4) = rat_4/3 &
% 21.31/3.84 rat_$quotient(rat_1, rat_-4/5) = rat_-5/4 & rat_$quotient(rat_-5/4, rat_4/3) =
% 21.31/3.84 rat_-15/16 & rat_$quotient(rat_-5/4, rat_-15/16) = rat_4/3 &
% 21.31/3.84 rat_$quotient(rat_-5/4, rat_1) = rat_-5/4 & rat_$quotient(rat_-5/4, rat_-5/4)
% 21.71/3.84 = rat_1 & rat_$quotient(rat_16/25, rat_-16/15) = rat_-3/5 &
% 21.71/3.84 rat_$quotient(rat_16/25, rat_-3/5) = rat_-16/15 & rat_$quotient(rat_16/25,
% 21.71/3.84 rat_1) = rat_16/25 & rat_$quotient(rat_16/25, rat_16/25) = rat_1 &
% 21.71/3.84 rat_$quotient(rat_16/25, rat_4/5) = rat_4/5 & rat_$quotient(rat_16/25,
% 21.71/3.84 rat_-4/5) = rat_-4/5 & rat_$quotient(rat_-8/5, rat_3/2) = rat_-16/15 &
% 21.71/3.84 rat_$quotient(rat_-8/5, rat_-16/15) = rat_3/2 & rat_$quotient(rat_-8/5, rat_1)
% 21.71/3.84 = rat_-8/5 & rat_$quotient(rat_-8/5, rat_-8/5) = rat_1 &
% 21.71/3.84 rat_$quotient(rat_4/5, rat_-16/15) = rat_-3/4 & rat_$quotient(rat_4/5,
% 21.71/3.84 rat_-3/4) = rat_-16/15 & rat_$quotient(rat_4/5, rat_1) = rat_4/5 &
% 21.71/3.84 rat_$quotient(rat_4/5, rat_4/5) = rat_1 & rat_$quotient(rat_3/4, rat_9/16) =
% 21.71/3.84 rat_4/3 & rat_$quotient(rat_3/4, rat_4/3) = rat_9/16 & rat_$quotient(rat_3/4,
% 21.71/3.84 rat_-15/16) = rat_-4/5 & rat_$quotient(rat_3/4, rat_-3/5) = rat_-5/4 &
% 21.71/3.84 rat_$quotient(rat_3/4, rat_1) = rat_3/4 & rat_$quotient(rat_3/4, rat_-5/4) =
% 21.71/3.84 rat_-3/5 & rat_$quotient(rat_3/4, rat_3/4) = rat_1 & rat_$quotient(rat_3/4,
% 21.71/3.84 rat_-4/5) = rat_-15/16 & rat_$quotient(rat_-4/5, rat_-16/15) = rat_3/4 &
% 21.71/3.84 rat_$quotient(rat_-4/5, rat_4/3) = rat_-3/5 & rat_$quotient(rat_-4/5,
% 21.71/3.84 rat_-3/5) = rat_4/3 & rat_$quotient(rat_-4/5, rat_1) = rat_-4/5 &
% 21.71/3.84 rat_$quotient(rat_-4/5, rat_-5/4) = rat_16/25 & rat_$quotient(rat_-4/5,
% 21.71/3.84 rat_16/25) = rat_-5/4 & rat_$quotient(rat_-4/5, rat_3/4) = rat_-16/15 &
% 21.71/3.84 rat_$quotient(rat_-4/5, rat_-4/5) = rat_1 & rat_$quotient(rat_0, rat_9/16) =
% 21.71/3.84 rat_0 & rat_$quotient(rat_0, rat_3/2) = rat_0 & rat_$quotient(rat_0,
% 21.71/3.84 rat_-16/15) = rat_0 & rat_$quotient(rat_0, rat_4/3) = rat_0 &
% 21.71/3.84 rat_$quotient(rat_0, rat_31/20) = rat_0 & rat_$quotient(rat_0, rat_-3/4) =
% 21.71/3.84 rat_0 & rat_$quotient(rat_0, rat_-15/16) = rat_0 & rat_$quotient(rat_0,
% 21.71/3.84 rat_-3/5) = rat_0 & rat_$quotient(rat_0, rat_-31/20) = rat_0 &
% 21.71/3.84 rat_$quotient(rat_0, rat_-1/20) = rat_0 & rat_$quotient(rat_0, rat_1) = rat_0
% 21.71/3.84 & rat_$quotient(rat_0, rat_-5/4) = rat_0 & rat_$quotient(rat_0, rat_16/25) =
% 21.71/3.84 rat_0 & rat_$quotient(rat_0, rat_-8/5) = rat_0 & rat_$quotient(rat_0, rat_4/5)
% 21.71/3.84 = rat_0 & rat_$quotient(rat_0, rat_3/4) = rat_0 & rat_$quotient(rat_0,
% 21.71/3.84 rat_-4/5) = rat_0 & rat_$difference(rat_9/16, rat_9/16) = rat_0 &
% 21.71/3.84 rat_$difference(rat_9/16, rat_3/2) = rat_-15/16 & rat_$difference(rat_9/16,
% 21.71/3.84 rat_-15/16) = rat_3/2 & rat_$difference(rat_9/16, rat_0) = rat_9/16 &
% 21.71/3.84 rat_$difference(rat_3/2, rat_3/2) = rat_0 & rat_$difference(rat_3/2,
% 21.71/3.84 rat_31/20) = rat_-1/20 & rat_$difference(rat_3/2, rat_-1/20) = rat_31/20 &
% 21.71/3.84 rat_$difference(rat_3/2, rat_3/4) = rat_3/4 & rat_$difference(rat_3/2, rat_0)
% 21.71/3.84 = rat_3/2 & rat_$difference(rat_-16/15, rat_-16/15) = rat_0 &
% 21.71/3.84 rat_$difference(rat_-16/15, rat_0) = rat_-16/15 & rat_$difference(rat_4/3,
% 21.71/3.84 rat_4/3) = rat_0 & rat_$difference(rat_4/3, rat_0) = rat_4/3 &
% 21.71/3.84 rat_$difference(rat_31/20, rat_31/20) = rat_0 & rat_$difference(rat_31/20,
% 21.71/3.84 rat_4/5) = rat_3/4 & rat_$difference(rat_31/20, rat_3/4) = rat_4/5 &
% 21.71/3.84 rat_$difference(rat_31/20, rat_0) = rat_31/20 & rat_$difference(rat_-3/4,
% 21.71/3.84 rat_-3/4) = rat_0 & rat_$difference(rat_-3/4, rat_-31/20) = rat_4/5 &
% 21.71/3.84 rat_$difference(rat_-3/4, rat_4/5) = rat_-31/20 & rat_$difference(rat_-3/4,
% 21.71/3.84 rat_0) = rat_-3/4 & rat_$difference(rat_-15/16, rat_-15/16) = rat_0 &
% 21.71/3.84 rat_$difference(rat_-15/16, rat_0) = rat_-15/16 & rat_$difference(rat_-3/5,
% 21.71/3.84 rat_-3/5) = rat_0 & rat_$difference(rat_-3/5, rat_1) = rat_-8/5 &
% 21.71/3.84 rat_$difference(rat_-3/5, rat_-8/5) = rat_1 & rat_$difference(rat_-3/5, rat_0)
% 21.71/3.84 = rat_-3/5 & rat_$difference(rat_-31/20, rat_-3/4) = rat_-4/5 &
% 21.71/3.84 rat_$difference(rat_-31/20, rat_-31/20) = rat_0 & rat_$difference(rat_-31/20,
% 21.71/3.84 rat_-4/5) = rat_-3/4 & rat_$difference(rat_-31/20, rat_0) = rat_-31/20 &
% 21.71/3.84 rat_$difference(rat_-1/20, rat_3/2) = rat_-31/20 & rat_$difference(rat_-1/20,
% 21.71/3.84 rat_31/20) = rat_-8/5 & rat_$difference(rat_-1/20, rat_-31/20) = rat_3/2 &
% 21.71/3.84 rat_$difference(rat_-1/20, rat_-1/20) = rat_0 & rat_$difference(rat_-1/20,
% 21.71/3.84 rat_-8/5) = rat_31/20 & rat_$difference(rat_-1/20, rat_3/4) = rat_-4/5 &
% 21.71/3.84 rat_$difference(rat_-1/20, rat_-4/5) = rat_3/4 & rat_$difference(rat_-1/20,
% 21.71/3.84 rat_0) = rat_-1/20 & rat_$difference(rat_1, rat_1) = rat_0 &
% 21.71/3.84 rat_$difference(rat_1, rat_0) = rat_1 & rat_$difference(rat_-5/4, rat_-5/4) =
% 21.71/3.84 rat_0 & rat_$difference(rat_-5/4, rat_0) = rat_-5/4 &
% 21.71/3.84 rat_$difference(rat_16/25, rat_16/25) = rat_0 & rat_$difference(rat_16/25,
% 21.71/3.84 rat_0) = rat_16/25 & rat_$difference(rat_-8/5, rat_-31/20) = rat_-1/20 &
% 21.71/3.84 rat_$difference(rat_-8/5, rat_-1/20) = rat_-31/20 & rat_$difference(rat_-8/5,
% 21.71/3.84 rat_-8/5) = rat_0 & rat_$difference(rat_-8/5, rat_-4/5) = rat_-4/5 &
% 21.71/3.84 rat_$difference(rat_-8/5, rat_0) = rat_-8/5 & rat_$difference(rat_4/5,
% 21.71/3.84 rat_31/20) = rat_-3/4 & rat_$difference(rat_4/5, rat_-3/4) = rat_31/20 &
% 21.71/3.84 rat_$difference(rat_4/5, rat_4/5) = rat_0 & rat_$difference(rat_4/5, rat_0) =
% 21.71/3.84 rat_4/5 & rat_$difference(rat_3/4, rat_3/2) = rat_-3/4 &
% 21.71/3.84 rat_$difference(rat_3/4, rat_31/20) = rat_-4/5 & rat_$difference(rat_3/4,
% 21.71/3.84 rat_-3/4) = rat_3/2 & rat_$difference(rat_3/4, rat_-1/20) = rat_4/5 &
% 21.71/3.84 rat_$difference(rat_3/4, rat_4/5) = rat_-1/20 & rat_$difference(rat_3/4,
% 21.71/3.84 rat_3/4) = rat_0 & rat_$difference(rat_3/4, rat_-4/5) = rat_31/20 &
% 21.71/3.84 rat_$difference(rat_3/4, rat_0) = rat_3/4 & rat_$difference(rat_-4/5,
% 21.71/3.84 rat_-3/4) = rat_-1/20 & rat_$difference(rat_-4/5, rat_-31/20) = rat_3/4 &
% 21.71/3.84 rat_$difference(rat_-4/5, rat_-1/20) = rat_-3/4 & rat_$difference(rat_-4/5,
% 21.71/3.84 rat_-8/5) = rat_4/5 & rat_$difference(rat_-4/5, rat_4/5) = rat_-8/5 &
% 21.71/3.84 rat_$difference(rat_-4/5, rat_3/4) = rat_-31/20 & rat_$difference(rat_-4/5,
% 21.71/3.84 rat_-4/5) = rat_0 & rat_$difference(rat_-4/5, rat_0) = rat_-4/5 &
% 21.71/3.84 rat_$difference(rat_0, rat_31/20) = rat_-31/20 & rat_$difference(rat_0,
% 21.71/3.84 rat_-3/4) = rat_3/4 & rat_$difference(rat_0, rat_-31/20) = rat_31/20 &
% 21.71/3.84 rat_$difference(rat_0, rat_4/5) = rat_-4/5 & rat_$difference(rat_0, rat_3/4) =
% 21.71/3.84 rat_-3/4 & rat_$difference(rat_0, rat_-4/5) = rat_4/5 & rat_$difference(rat_0,
% 21.71/3.84 rat_0) = rat_0 & rat_$uminus(rat_31/20) = rat_-31/20 & rat_$uminus(rat_-3/4)
% 21.71/3.84 = rat_3/4 & rat_$uminus(rat_-31/20) = rat_31/20 & rat_$uminus(rat_4/5) =
% 21.71/3.84 rat_-4/5 & rat_$uminus(rat_3/4) = rat_-3/4 & rat_$uminus(rat_-4/5) = rat_4/5 &
% 21.71/3.84 rat_$uminus(rat_0) = rat_0 & rat_$sum(rat_9/16, rat_0) = rat_9/16 &
% 21.71/3.84 rat_$sum(rat_3/2, rat_-3/4) = rat_3/4 & rat_$sum(rat_3/2, rat_-15/16) =
% 21.71/3.84 rat_9/16 & rat_$sum(rat_3/2, rat_-31/20) = rat_-1/20 & rat_$sum(rat_3/2,
% 21.71/3.84 rat_0) = rat_3/2 & rat_$sum(rat_-16/15, rat_0) = rat_-16/15 &
% 21.71/3.84 rat_$sum(rat_4/3, rat_0) = rat_4/3 & rat_$sum(rat_31/20, rat_-3/4) = rat_4/5 &
% 21.71/3.84 rat_$sum(rat_31/20, rat_-31/20) = rat_0 & rat_$sum(rat_31/20, rat_-1/20) =
% 21.71/3.84 rat_3/2 & rat_$sum(rat_31/20, rat_-8/5) = rat_-1/20 & rat_$sum(rat_31/20,
% 21.71/3.84 rat_-4/5) = rat_3/4 & rat_$sum(rat_31/20, rat_0) = rat_31/20 &
% 21.71/3.84 rat_$sum(rat_-3/4, rat_3/2) = rat_3/4 & rat_$sum(rat_-3/4, rat_31/20) =
% 21.71/3.84 rat_4/5 & rat_$sum(rat_-3/4, rat_-1/20) = rat_-4/5 & rat_$sum(rat_-3/4,
% 21.71/3.84 rat_3/4) = rat_0 & rat_$sum(rat_-3/4, rat_-4/5) = rat_-31/20 &
% 21.71/3.84 rat_$sum(rat_-3/4, rat_0) = rat_-3/4 & rat_$sum(rat_-15/16, rat_3/2) =
% 21.71/3.84 rat_9/16 & rat_$sum(rat_-15/16, rat_0) = rat_-15/16 & rat_$sum(rat_-3/5,
% 21.71/3.84 rat_0) = rat_-3/5 & rat_$sum(rat_-31/20, rat_3/2) = rat_-1/20 &
% 21.71/3.84 rat_$sum(rat_-31/20, rat_31/20) = rat_0 & rat_$sum(rat_-31/20, rat_-1/20) =
% 21.71/3.84 rat_-8/5 & rat_$sum(rat_-31/20, rat_4/5) = rat_-3/4 & rat_$sum(rat_-31/20,
% 21.71/3.84 rat_3/4) = rat_-4/5 & rat_$sum(rat_-31/20, rat_0) = rat_-31/20 &
% 21.71/3.84 rat_$sum(rat_-1/20, rat_31/20) = rat_3/2 & rat_$sum(rat_-1/20, rat_-3/4) =
% 21.71/3.84 rat_-4/5 & rat_$sum(rat_-1/20, rat_-31/20) = rat_-8/5 & rat_$sum(rat_-1/20,
% 21.71/3.84 rat_4/5) = rat_3/4 & rat_$sum(rat_-1/20, rat_0) = rat_-1/20 &
% 21.71/3.84 rat_$sum(rat_1, rat_-8/5) = rat_-3/5 & rat_$sum(rat_1, rat_0) = rat_1 &
% 21.71/3.84 rat_$sum(rat_-5/4, rat_0) = rat_-5/4 & rat_$sum(rat_16/25, rat_0) = rat_16/25
% 21.71/3.84 & rat_$sum(rat_-8/5, rat_31/20) = rat_-1/20 & rat_$sum(rat_-8/5, rat_1) =
% 21.71/3.84 rat_-3/5 & rat_$sum(rat_-8/5, rat_4/5) = rat_-4/5 & rat_$sum(rat_-8/5, rat_0)
% 21.71/3.84 = rat_-8/5 & rat_$sum(rat_4/5, rat_-31/20) = rat_-3/4 & rat_$sum(rat_4/5,
% 21.71/3.84 rat_-1/20) = rat_3/4 & rat_$sum(rat_4/5, rat_-8/5) = rat_-4/5 &
% 21.71/3.84 rat_$sum(rat_4/5, rat_3/4) = rat_31/20 & rat_$sum(rat_4/5, rat_-4/5) = rat_0 &
% 21.71/3.84 rat_$sum(rat_4/5, rat_0) = rat_4/5 & rat_$sum(rat_3/4, rat_-3/4) = rat_0 &
% 21.71/3.84 rat_$sum(rat_3/4, rat_-31/20) = rat_-4/5 & rat_$sum(rat_3/4, rat_4/5) =
% 21.71/3.84 rat_31/20 & rat_$sum(rat_3/4, rat_3/4) = rat_3/2 & rat_$sum(rat_3/4, rat_-4/5)
% 21.71/3.84 = rat_-1/20 & rat_$sum(rat_3/4, rat_0) = rat_3/4 & rat_$sum(rat_-4/5,
% 21.71/3.84 rat_31/20) = rat_3/4 & rat_$sum(rat_-4/5, rat_-3/4) = rat_-31/20 &
% 21.71/3.84 rat_$sum(rat_-4/5, rat_4/5) = rat_0 & rat_$sum(rat_-4/5, rat_3/4) = rat_-1/20
% 21.71/3.84 & rat_$sum(rat_-4/5, rat_-4/5) = rat_-8/5 & rat_$sum(rat_-4/5, rat_0) =
% 21.71/3.84 rat_-4/5 & rat_$sum(rat_0, rat_9/16) = rat_9/16 & rat_$sum(rat_0, rat_3/2) =
% 21.71/3.84 rat_3/2 & rat_$sum(rat_0, rat_-16/15) = rat_-16/15 & rat_$sum(rat_0, rat_4/3)
% 21.71/3.84 = rat_4/3 & rat_$sum(rat_0, rat_31/20) = rat_31/20 & rat_$sum(rat_0, rat_-3/4)
% 21.71/3.84 = rat_-3/4 & rat_$sum(rat_0, rat_-15/16) = rat_-15/16 & rat_$sum(rat_0,
% 21.71/3.84 rat_-3/5) = rat_-3/5 & rat_$sum(rat_0, rat_-31/20) = rat_-31/20 &
% 21.71/3.84 rat_$sum(rat_0, rat_-1/20) = rat_-1/20 & rat_$sum(rat_0, rat_1) = rat_1 &
% 21.71/3.84 rat_$sum(rat_0, rat_-5/4) = rat_-5/4 & rat_$sum(rat_0, rat_16/25) = rat_16/25
% 21.71/3.84 & rat_$sum(rat_0, rat_-8/5) = rat_-8/5 & rat_$sum(rat_0, rat_4/5) = rat_4/5 &
% 21.71/3.84 rat_$sum(rat_0, rat_3/4) = rat_3/4 & rat_$sum(rat_0, rat_-4/5) = rat_-4/5 &
% 21.71/3.84 rat_$sum(rat_0, rat_0) = rat_0 & rat_$product(rat_9/16, rat_-16/15) = rat_-3/5
% 21.71/3.84 & rat_$product(rat_9/16, rat_4/3) = rat_3/4 & rat_$product(rat_9/16, rat_1) =
% 21.71/3.84 rat_9/16 & rat_$product(rat_9/16, rat_0) = rat_0 & rat_$product(rat_3/2,
% 21.71/3.84 rat_-16/15) = rat_-8/5 & rat_$product(rat_3/2, rat_1) = rat_3/2 &
% 21.71/3.84 rat_$product(rat_3/2, rat_0) = rat_0 & rat_$product(rat_-16/15, rat_9/16) =
% 21.71/3.84 rat_-3/5 & rat_$product(rat_-16/15, rat_3/2) = rat_-8/5 &
% 21.71/3.84 rat_$product(rat_-16/15, rat_-3/4) = rat_4/5 & rat_$product(rat_-16/15,
% 21.71/3.84 rat_-15/16) = rat_1 & rat_$product(rat_-16/15, rat_-3/5) = rat_16/25 &
% 21.71/3.84 rat_$product(rat_-16/15, rat_1) = rat_-16/15 & rat_$product(rat_-16/15,
% 21.71/3.84 rat_-5/4) = rat_4/3 & rat_$product(rat_-16/15, rat_3/4) = rat_-4/5 &
% 21.71/3.84 rat_$product(rat_-16/15, rat_0) = rat_0 & rat_$product(rat_4/3, rat_9/16) =
% 21.71/3.84 rat_3/4 & rat_$product(rat_4/3, rat_-15/16) = rat_-5/4 & rat_$product(rat_4/3,
% 21.71/3.84 rat_-3/5) = rat_-4/5 & rat_$product(rat_4/3, rat_1) = rat_4/3 &
% 21.71/3.84 rat_$product(rat_4/3, rat_3/4) = rat_1 & rat_$product(rat_4/3, rat_-4/5) =
% 21.71/3.84 rat_-16/15 & rat_$product(rat_4/3, rat_0) = rat_0 & rat_$product(rat_31/20,
% 21.71/3.84 rat_1) = rat_31/20 & rat_$product(rat_31/20, rat_0) = rat_0 &
% 21.71/3.84 rat_$product(rat_-3/4, rat_-16/15) = rat_4/5 & rat_$product(rat_-3/4,
% 21.71/3.84 rat_-3/4) = rat_9/16 & rat_$product(rat_-3/4, rat_1) = rat_-3/4 &
% 21.71/3.84 rat_$product(rat_-3/4, rat_4/5) = rat_-3/5 & rat_$product(rat_-3/4, rat_0) =
% 21.71/3.84 rat_0 & rat_$product(rat_-15/16, rat_-16/15) = rat_1 &
% 21.71/3.84 rat_$product(rat_-15/16, rat_4/3) = rat_-5/4 & rat_$product(rat_-15/16,
% 21.71/3.84 rat_-3/5) = rat_9/16 & rat_$product(rat_-15/16, rat_1) = rat_-15/16 &
% 21.71/3.84 rat_$product(rat_-15/16, rat_16/25) = rat_-3/5 & rat_$product(rat_-15/16,
% 21.71/3.84 rat_-8/5) = rat_3/2 & rat_$product(rat_-15/16, rat_4/5) = rat_-3/4 &
% 21.71/3.84 rat_$product(rat_-15/16, rat_-4/5) = rat_3/4 & rat_$product(rat_-15/16, rat_0)
% 21.71/3.84 = rat_0 & rat_$product(rat_-3/5, rat_-16/15) = rat_16/25 &
% 21.71/3.84 rat_$product(rat_-3/5, rat_4/3) = rat_-4/5 & rat_$product(rat_-3/5,
% 21.71/3.84 rat_-15/16) = rat_9/16 & rat_$product(rat_-3/5, rat_1) = rat_-3/5 &
% 21.71/3.84 rat_$product(rat_-3/5, rat_-5/4) = rat_3/4 & rat_$product(rat_-3/5, rat_0) =
% 21.71/3.84 rat_0 & rat_$product(rat_-31/20, rat_1) = rat_-31/20 &
% 21.71/3.84 rat_$product(rat_-31/20, rat_0) = rat_0 & rat_$product(rat_-1/20, rat_1) =
% 21.71/3.84 rat_-1/20 & rat_$product(rat_-1/20, rat_0) = rat_0 & rat_$product(rat_1,
% 21.71/3.84 rat_9/16) = rat_9/16 & rat_$product(rat_1, rat_3/2) = rat_3/2 &
% 21.71/3.84 rat_$product(rat_1, rat_-16/15) = rat_-16/15 & rat_$product(rat_1, rat_4/3) =
% 21.71/3.84 rat_4/3 & rat_$product(rat_1, rat_31/20) = rat_31/20 & rat_$product(rat_1,
% 21.71/3.84 rat_-3/4) = rat_-3/4 & rat_$product(rat_1, rat_-15/16) = rat_-15/16 &
% 21.71/3.84 rat_$product(rat_1, rat_-3/5) = rat_-3/5 & rat_$product(rat_1, rat_-31/20) =
% 21.71/3.84 rat_-31/20 & rat_$product(rat_1, rat_-1/20) = rat_-1/20 & rat_$product(rat_1,
% 21.71/3.84 rat_1) = rat_1 & rat_$product(rat_1, rat_-5/4) = rat_-5/4 &
% 21.71/3.84 rat_$product(rat_1, rat_16/25) = rat_16/25 & rat_$product(rat_1, rat_-8/5) =
% 21.71/3.84 rat_-8/5 & rat_$product(rat_1, rat_4/5) = rat_4/5 & rat_$product(rat_1,
% 21.71/3.84 rat_3/4) = rat_3/4 & rat_$product(rat_1, rat_-4/5) = rat_-4/5 &
% 21.71/3.84 rat_$product(rat_1, rat_0) = rat_0 & rat_$product(rat_-5/4, rat_-16/15) =
% 21.71/3.84 rat_4/3 & rat_$product(rat_-5/4, rat_-3/5) = rat_3/4 & rat_$product(rat_-5/4,
% 21.71/3.84 rat_1) = rat_-5/4 & rat_$product(rat_-5/4, rat_16/25) = rat_-4/5 &
% 21.71/3.84 rat_$product(rat_-5/4, rat_3/4) = rat_-15/16 & rat_$product(rat_-5/4,
% 21.71/3.84 rat_-4/5) = rat_1 & rat_$product(rat_-5/4, rat_0) = rat_0 &
% 21.71/3.84 rat_$product(rat_16/25, rat_-15/16) = rat_-3/5 & rat_$product(rat_16/25,
% 21.71/3.84 rat_1) = rat_16/25 & rat_$product(rat_16/25, rat_-5/4) = rat_-4/5 &
% 21.71/3.84 rat_$product(rat_16/25, rat_0) = rat_0 & rat_$product(rat_-8/5, rat_-15/16) =
% 21.71/3.84 rat_3/2 & rat_$product(rat_-8/5, rat_1) = rat_-8/5 & rat_$product(rat_-8/5,
% 21.71/3.84 rat_0) = rat_0 & rat_$product(rat_4/5, rat_-3/4) = rat_-3/5 &
% 21.71/3.84 rat_$product(rat_4/5, rat_-15/16) = rat_-3/4 & rat_$product(rat_4/5, rat_1) =
% 21.71/3.84 rat_4/5 & rat_$product(rat_4/5, rat_4/5) = rat_16/25 & rat_$product(rat_4/5,
% 21.71/3.84 rat_0) = rat_0 & rat_$product(rat_3/4, rat_-16/15) = rat_-4/5 &
% 21.71/3.84 rat_$product(rat_3/4, rat_4/3) = rat_1 & rat_$product(rat_3/4, rat_1) =
% 21.71/3.84 rat_3/4 & rat_$product(rat_3/4, rat_-5/4) = rat_-15/16 & rat_$product(rat_3/4,
% 21.71/3.84 rat_3/4) = rat_9/16 & rat_$product(rat_3/4, rat_-4/5) = rat_-3/5 &
% 21.71/3.84 rat_$product(rat_3/4, rat_0) = rat_0 & rat_$product(rat_-4/5, rat_4/3) =
% 21.71/3.84 rat_-16/15 & rat_$product(rat_-4/5, rat_-15/16) = rat_3/4 &
% 21.71/3.84 rat_$product(rat_-4/5, rat_1) = rat_-4/5 & rat_$product(rat_-4/5, rat_-5/4) =
% 21.71/3.84 rat_1 & rat_$product(rat_-4/5, rat_3/4) = rat_-3/5 & rat_$product(rat_-4/5,
% 21.71/3.84 rat_-4/5) = rat_16/25 & rat_$product(rat_-4/5, rat_0) = rat_0 &
% 21.71/3.84 rat_$product(rat_0, rat_9/16) = rat_0 & rat_$product(rat_0, rat_3/2) = rat_0 &
% 21.71/3.84 rat_$product(rat_0, rat_-16/15) = rat_0 & rat_$product(rat_0, rat_4/3) = rat_0
% 21.71/3.84 & rat_$product(rat_0, rat_31/20) = rat_0 & rat_$product(rat_0, rat_-3/4) =
% 21.71/3.84 rat_0 & rat_$product(rat_0, rat_-15/16) = rat_0 & rat_$product(rat_0,
% 21.71/3.84 rat_-3/5) = rat_0 & rat_$product(rat_0, rat_-31/20) = rat_0 &
% 21.71/3.84 rat_$product(rat_0, rat_-1/20) = rat_0 & rat_$product(rat_0, rat_1) = rat_0 &
% 21.71/3.84 rat_$product(rat_0, rat_-5/4) = rat_0 & rat_$product(rat_0, rat_16/25) = rat_0
% 21.71/3.84 & rat_$product(rat_0, rat_-8/5) = rat_0 & rat_$product(rat_0, rat_4/5) = rat_0
% 21.71/3.84 & rat_$product(rat_0, rat_3/4) = rat_0 & rat_$product(rat_0, rat_-4/5) = rat_0
% 21.71/3.84 & rat_$product(rat_0, rat_0) = rat_0 & rat_$is_rat(rat_9/16) &
% 21.71/3.84 rat_$is_rat(rat_3/2) & rat_$is_rat(rat_-16/15) & rat_$is_rat(rat_4/3) &
% 21.71/3.84 rat_$is_rat(rat_31/20) & rat_$is_rat(rat_-3/4) & rat_$is_rat(rat_-15/16) &
% 21.71/3.84 rat_$is_rat(rat_-3/5) & rat_$is_rat(rat_-31/20) & rat_$is_rat(rat_-1/20) &
% 21.71/3.84 rat_$is_rat(rat_1) & rat_$is_rat(rat_-5/4) & rat_$is_rat(rat_16/25) &
% 21.71/3.84 rat_$is_rat(rat_-8/5) & rat_$is_rat(rat_4/5) & rat_$is_rat(rat_3/4) &
% 21.71/3.84 rat_$is_rat(rat_-4/5) & rat_$is_rat(rat_0) & rat_$is_int(rat_1) &
% 21.71/3.84 rat_$is_int(rat_0) & rat_$greatereq(rat_9/16, rat_9/16) &
% 21.71/3.84 rat_$greatereq(rat_9/16, rat_-16/15) & rat_$greatereq(rat_9/16, rat_-3/4) &
% 21.71/3.84 rat_$greatereq(rat_9/16, rat_-15/16) & rat_$greatereq(rat_9/16, rat_-3/5) &
% 21.71/3.84 rat_$greatereq(rat_9/16, rat_-31/20) & rat_$greatereq(rat_9/16, rat_-1/20) &
% 21.71/3.84 rat_$greatereq(rat_9/16, rat_-5/4) & rat_$greatereq(rat_9/16, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_9/16, rat_-4/5) & rat_$greatereq(rat_9/16, rat_0) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_9/16) & rat_$greatereq(rat_3/2, rat_3/2) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-16/15) & rat_$greatereq(rat_3/2, rat_4/3) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-3/4) & rat_$greatereq(rat_3/2, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-3/5) & rat_$greatereq(rat_3/2, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-1/20) & rat_$greatereq(rat_3/2, rat_1) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-5/4) & rat_$greatereq(rat_3/2, rat_16/25) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_-8/5) & rat_$greatereq(rat_3/2, rat_4/5) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_3/4) & rat_$greatereq(rat_3/2, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_3/2, rat_0) & rat_$greatereq(rat_-16/15, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_-16/15, rat_-31/20) & rat_$greatereq(rat_-16/15, rat_-5/4)
% 21.71/3.84 & rat_$greatereq(rat_-16/15, rat_-8/5) & rat_$greatereq(rat_4/3, rat_9/16) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-16/15) & rat_$greatereq(rat_4/3, rat_4/3) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-3/4) & rat_$greatereq(rat_4/3, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-3/5) & rat_$greatereq(rat_4/3, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-1/20) & rat_$greatereq(rat_4/3, rat_1) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-5/4) & rat_$greatereq(rat_4/3, rat_16/25) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_-8/5) & rat_$greatereq(rat_4/3, rat_4/5) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_3/4) & rat_$greatereq(rat_4/3, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_4/3, rat_0) & rat_$greatereq(rat_31/20, rat_9/16) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_3/2) & rat_$greatereq(rat_31/20, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_4/3) & rat_$greatereq(rat_31/20, rat_31/20) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_-3/4) & rat_$greatereq(rat_31/20, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_-3/5) & rat_$greatereq(rat_31/20, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_-1/20) & rat_$greatereq(rat_31/20, rat_1) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_-5/4) & rat_$greatereq(rat_31/20, rat_16/25) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_-8/5) & rat_$greatereq(rat_31/20, rat_4/5) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_3/4) & rat_$greatereq(rat_31/20, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_31/20, rat_0) & rat_$greatereq(rat_-3/4, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_-3/4, rat_-3/4) & rat_$greatereq(rat_-3/4, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_-3/4, rat_-31/20) & rat_$greatereq(rat_-3/4, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_-3/4, rat_-8/5) & rat_$greatereq(rat_-3/4, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_-15/16, rat_-16/15) & rat_$greatereq(rat_-15/16,
% 21.71/3.84 rat_-15/16) & rat_$greatereq(rat_-15/16, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_-15/16, rat_-5/4) & rat_$greatereq(rat_-15/16, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_-3/5, rat_-16/15) & rat_$greatereq(rat_-3/5, rat_-3/4) &
% 21.71/3.84 rat_$greatereq(rat_-3/5, rat_-15/16) & rat_$greatereq(rat_-3/5, rat_-3/5) &
% 21.71/3.84 rat_$greatereq(rat_-3/5, rat_-31/20) & rat_$greatereq(rat_-3/5, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_-3/5, rat_-8/5) & rat_$greatereq(rat_-3/5, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_-31/20, rat_-31/20) & rat_$greatereq(rat_-31/20, rat_-8/5)
% 21.71/3.84 & rat_$greatereq(rat_-1/20, rat_-16/15) & rat_$greatereq(rat_-1/20, rat_-3/4)
% 21.71/3.84 & rat_$greatereq(rat_-1/20, rat_-15/16) & rat_$greatereq(rat_-1/20, rat_-3/5)
% 21.71/3.84 & rat_$greatereq(rat_-1/20, rat_-31/20) & rat_$greatereq(rat_-1/20, rat_-1/20)
% 21.71/3.84 & rat_$greatereq(rat_-1/20, rat_-5/4) & rat_$greatereq(rat_-1/20, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_-1/20, rat_-4/5) & rat_$greatereq(rat_1, rat_9/16) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_-16/15) & rat_$greatereq(rat_1, rat_-3/4) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_-15/16) & rat_$greatereq(rat_1, rat_-3/5) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_-31/20) & rat_$greatereq(rat_1, rat_-1/20) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_1) & rat_$greatereq(rat_1, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_16/25) & rat_$greatereq(rat_1, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_4/5) & rat_$greatereq(rat_1, rat_3/4) &
% 21.71/3.84 rat_$greatereq(rat_1, rat_-4/5) & rat_$greatereq(rat_1, rat_0) &
% 21.71/3.84 rat_$greatereq(rat_-5/4, rat_-31/20) & rat_$greatereq(rat_-5/4, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_-5/4, rat_-8/5) & rat_$greatereq(rat_16/25, rat_9/16) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_-16/15) & rat_$greatereq(rat_16/25, rat_-3/4) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_-15/16) & rat_$greatereq(rat_16/25, rat_-3/5) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_-31/20) & rat_$greatereq(rat_16/25, rat_-1/20) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_-5/4) & rat_$greatereq(rat_16/25, rat_16/25) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_-8/5) & rat_$greatereq(rat_16/25, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_16/25, rat_0) & rat_$greatereq(rat_-8/5, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_9/16) & rat_$greatereq(rat_4/5, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_-3/4) & rat_$greatereq(rat_4/5, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_-3/5) & rat_$greatereq(rat_4/5, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_-1/20) & rat_$greatereq(rat_4/5, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_16/25) & rat_$greatereq(rat_4/5, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_4/5) & rat_$greatereq(rat_4/5, rat_3/4) &
% 21.71/3.84 rat_$greatereq(rat_4/5, rat_-4/5) & rat_$greatereq(rat_4/5, rat_0) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_9/16) & rat_$greatereq(rat_3/4, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_-3/4) & rat_$greatereq(rat_3/4, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_-3/5) & rat_$greatereq(rat_3/4, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_-1/20) & rat_$greatereq(rat_3/4, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_16/25) & rat_$greatereq(rat_3/4, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_3/4) & rat_$greatereq(rat_3/4, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_3/4, rat_0) & rat_$greatereq(rat_-4/5, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_-4/5, rat_-15/16) & rat_$greatereq(rat_-4/5, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_-4/5, rat_-5/4) & rat_$greatereq(rat_-4/5, rat_-8/5) &
% 21.71/3.84 rat_$greatereq(rat_-4/5, rat_-4/5) & rat_$greatereq(rat_0, rat_-16/15) &
% 21.71/3.84 rat_$greatereq(rat_0, rat_-3/4) & rat_$greatereq(rat_0, rat_-15/16) &
% 21.71/3.84 rat_$greatereq(rat_0, rat_-3/5) & rat_$greatereq(rat_0, rat_-31/20) &
% 21.71/3.84 rat_$greatereq(rat_0, rat_-1/20) & rat_$greatereq(rat_0, rat_-5/4) &
% 21.71/3.84 rat_$greatereq(rat_0, rat_-8/5) & rat_$greatereq(rat_0, rat_-4/5) &
% 21.71/3.84 rat_$greatereq(rat_0, rat_0) & rat_$greater(rat_very_large, rat_9/16) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_3/2) & rat_$greater(rat_very_large,
% 21.71/3.84 rat_-16/15) & rat_$greater(rat_very_large, rat_4/3) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_31/20) & rat_$greater(rat_very_large,
% 21.71/3.84 rat_-3/4) & rat_$greater(rat_very_large, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_-3/5) & rat_$greater(rat_very_large,
% 21.71/3.84 rat_-31/20) & rat_$greater(rat_very_large, rat_-1/20) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_1) & rat_$greater(rat_very_large, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_16/25) & rat_$greater(rat_very_large,
% 21.71/3.84 rat_-8/5) & rat_$greater(rat_very_large, rat_4/5) &
% 21.71/3.84 rat_$greater(rat_very_large, rat_3/4) & rat_$greater(rat_very_large, rat_-4/5)
% 21.71/3.84 & rat_$greater(rat_very_large, rat_0) & rat_$greater(rat_9/16, rat_very_small)
% 21.71/3.84 & rat_$greater(rat_9/16, rat_-16/15) & rat_$greater(rat_9/16, rat_-3/4) &
% 21.71/3.84 rat_$greater(rat_9/16, rat_-15/16) & rat_$greater(rat_9/16, rat_-3/5) &
% 21.71/3.84 rat_$greater(rat_9/16, rat_-31/20) & rat_$greater(rat_9/16, rat_-1/20) &
% 21.71/3.84 rat_$greater(rat_9/16, rat_-5/4) & rat_$greater(rat_9/16, rat_-8/5) &
% 21.71/3.84 rat_$greater(rat_9/16, rat_-4/5) & rat_$greater(rat_9/16, rat_0) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_very_small) & rat_$greater(rat_3/2, rat_9/16) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-16/15) & rat_$greater(rat_3/2, rat_4/3) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-3/4) & rat_$greater(rat_3/2, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-3/5) & rat_$greater(rat_3/2, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-1/20) & rat_$greater(rat_3/2, rat_1) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-5/4) & rat_$greater(rat_3/2, rat_16/25) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_-8/5) & rat_$greater(rat_3/2, rat_4/5) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_3/4) & rat_$greater(rat_3/2, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_3/2, rat_0) & rat_$greater(rat_-16/15, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_-16/15, rat_-31/20) & rat_$greater(rat_-16/15, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_-16/15, rat_-8/5) & rat_$greater(rat_4/3, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_9/16) & rat_$greater(rat_4/3, rat_-16/15) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_-3/4) & rat_$greater(rat_4/3, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_-3/5) & rat_$greater(rat_4/3, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_-1/20) & rat_$greater(rat_4/3, rat_1) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_-5/4) & rat_$greater(rat_4/3, rat_16/25) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_-8/5) & rat_$greater(rat_4/3, rat_4/5) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_3/4) & rat_$greater(rat_4/3, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_4/3, rat_0) & rat_$greater(rat_31/20, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_9/16) & rat_$greater(rat_31/20, rat_3/2) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-16/15) & rat_$greater(rat_31/20, rat_4/3) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-3/4) & rat_$greater(rat_31/20, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-3/5) & rat_$greater(rat_31/20, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-1/20) & rat_$greater(rat_31/20, rat_1) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-5/4) & rat_$greater(rat_31/20, rat_16/25) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_-8/5) & rat_$greater(rat_31/20, rat_4/5) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_3/4) & rat_$greater(rat_31/20, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_31/20, rat_0) & rat_$greater(rat_-3/4, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_-3/4, rat_-16/15) & rat_$greater(rat_-3/4, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_-3/4, rat_-31/20) & rat_$greater(rat_-3/4, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_-3/4, rat_-8/5) & rat_$greater(rat_-3/4, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_-15/16, rat_very_small) & rat_$greater(rat_-15/16,
% 21.71/3.84 rat_-16/15) & rat_$greater(rat_-15/16, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_-15/16, rat_-5/4) & rat_$greater(rat_-15/16, rat_-8/5) &
% 21.71/3.84 rat_$greater(rat_-3/5, rat_very_small) & rat_$greater(rat_-3/5, rat_-16/15) &
% 21.71/3.84 rat_$greater(rat_-3/5, rat_-3/4) & rat_$greater(rat_-3/5, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_-3/5, rat_-31/20) & rat_$greater(rat_-3/5, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_-3/5, rat_-8/5) & rat_$greater(rat_-3/5, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_-31/20, rat_very_small) & rat_$greater(rat_-31/20, rat_-8/5)
% 21.71/3.84 & rat_$greater(rat_-1/20, rat_very_small) & rat_$greater(rat_-1/20,
% 21.71/3.84 rat_-16/15) & rat_$greater(rat_-1/20, rat_-3/4) & rat_$greater(rat_-1/20,
% 21.71/3.84 rat_-15/16) & rat_$greater(rat_-1/20, rat_-3/5) & rat_$greater(rat_-1/20,
% 21.71/3.84 rat_-31/20) & rat_$greater(rat_-1/20, rat_-5/4) & rat_$greater(rat_-1/20,
% 21.71/3.84 rat_-8/5) & rat_$greater(rat_-1/20, rat_-4/5) & rat_$greater(rat_1,
% 21.71/3.84 rat_very_small) & rat_$greater(rat_1, rat_9/16) & rat_$greater(rat_1,
% 21.71/3.84 rat_-16/15) & rat_$greater(rat_1, rat_-3/4) & rat_$greater(rat_1,
% 21.71/3.84 rat_-15/16) & rat_$greater(rat_1, rat_-3/5) & rat_$greater(rat_1,
% 21.71/3.84 rat_-31/20) & rat_$greater(rat_1, rat_-1/20) & rat_$greater(rat_1, rat_-5/4)
% 21.71/3.84 & rat_$greater(rat_1, rat_16/25) & rat_$greater(rat_1, rat_-8/5) &
% 21.71/3.84 rat_$greater(rat_1, rat_4/5) & rat_$greater(rat_1, rat_3/4) &
% 21.71/3.84 rat_$greater(rat_1, rat_-4/5) & rat_$greater(rat_1, rat_0) &
% 21.71/3.84 rat_$greater(rat_-5/4, rat_very_small) & rat_$greater(rat_-5/4, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_-5/4, rat_-8/5) & rat_$greater(rat_16/25, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_9/16) & rat_$greater(rat_16/25, rat_-16/15) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_-3/4) & rat_$greater(rat_16/25, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_-3/5) & rat_$greater(rat_16/25, rat_-31/20) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_-1/20) & rat_$greater(rat_16/25, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_-8/5) & rat_$greater(rat_16/25, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_16/25, rat_0) & rat_$greater(rat_-8/5, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_very_small) & rat_$greater(rat_4/5, rat_9/16) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-16/15) & rat_$greater(rat_4/5, rat_-3/4) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-15/16) & rat_$greater(rat_4/5, rat_-3/5) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-31/20) & rat_$greater(rat_4/5, rat_-1/20) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-5/4) & rat_$greater(rat_4/5, rat_16/25) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-8/5) & rat_$greater(rat_4/5, rat_3/4) &
% 21.71/3.84 rat_$greater(rat_4/5, rat_-4/5) & rat_$greater(rat_4/5, rat_0) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_very_small) & rat_$greater(rat_3/4, rat_9/16) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_-16/15) & rat_$greater(rat_3/4, rat_-3/4) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_-15/16) & rat_$greater(rat_3/4, rat_-3/5) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_-31/20) & rat_$greater(rat_3/4, rat_-1/20) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_-5/4) & rat_$greater(rat_3/4, rat_16/25) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_-8/5) & rat_$greater(rat_3/4, rat_-4/5) &
% 21.71/3.84 rat_$greater(rat_3/4, rat_0) & rat_$greater(rat_-4/5, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_-4/5, rat_-16/15) & rat_$greater(rat_-4/5, rat_-15/16) &
% 21.71/3.84 rat_$greater(rat_-4/5, rat_-31/20) & rat_$greater(rat_-4/5, rat_-5/4) &
% 21.71/3.84 rat_$greater(rat_-4/5, rat_-8/5) & rat_$greater(rat_0, rat_very_small) &
% 21.71/3.84 rat_$greater(rat_0, rat_-16/15) & rat_$greater(rat_0, rat_-3/4) &
% 21.71/3.84 rat_$greater(rat_0, rat_-15/16) & rat_$greater(rat_0, rat_-3/5) &
% 21.71/3.84 rat_$greater(rat_0, rat_-31/20) & rat_$greater(rat_0, rat_-1/20) &
% 21.71/3.84 rat_$greater(rat_0, rat_-5/4) & rat_$greater(rat_0, rat_-8/5) &
% 21.71/3.84 rat_$greater(rat_0, rat_-4/5) & rat_$lesseq(rat_very_small, rat_very_large) &
% 21.71/3.84 rat_$lesseq(rat_9/16, rat_9/16) & rat_$lesseq(rat_9/16, rat_3/2) &
% 21.71/3.84 rat_$lesseq(rat_9/16, rat_4/3) & rat_$lesseq(rat_9/16, rat_31/20) &
% 21.71/3.84 rat_$lesseq(rat_9/16, rat_1) & rat_$lesseq(rat_9/16, rat_16/25) &
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_4/5) & rat_$lesseq(rat_9/16, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_3/2) & rat_$lesseq(rat_3/2, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_9/16) & rat_$lesseq(rat_-16/15, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_-16/15) & rat_$lesseq(rat_-16/15, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_31/20) & rat_$lesseq(rat_-16/15, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_-15/16) & rat_$lesseq(rat_-16/15, rat_-3/5) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_-1/20) & rat_$lesseq(rat_-16/15, rat_1) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_16/25) & rat_$lesseq(rat_-16/15, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_3/4) & rat_$lesseq(rat_-16/15, rat_-4/5) &
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_0) & rat_$lesseq(rat_4/3, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_4/3) & rat_$lesseq(rat_4/3, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_31/20) & rat_$lesseq(rat_-3/4, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_3/2) & rat_$lesseq(rat_-3/4, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_31/20) & rat_$lesseq(rat_-3/4, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_-3/5) & rat_$lesseq(rat_-3/4, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_1) & rat_$lesseq(rat_-3/4, rat_16/25) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_4/5) & rat_$lesseq(rat_-3/4, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_0) & rat_$lesseq(rat_-15/16, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_3/2) & rat_$lesseq(rat_-15/16, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_31/20) & rat_$lesseq(rat_-15/16, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_-15/16) & rat_$lesseq(rat_-15/16, rat_-3/5) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_-1/20) & rat_$lesseq(rat_-15/16, rat_1) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_16/25) & rat_$lesseq(rat_-15/16, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_3/4) & rat_$lesseq(rat_-15/16, rat_-4/5) &
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_0) & rat_$lesseq(rat_-3/5, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_3/2) & rat_$lesseq(rat_-3/5, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_31/20) & rat_$lesseq(rat_-3/5, rat_-3/5) &
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_-1/20) & rat_$lesseq(rat_-3/5, rat_1) &
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_16/25) & rat_$lesseq(rat_-3/5, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_3/4) & rat_$lesseq(rat_-3/5, rat_0) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_9/16) & rat_$lesseq(rat_-31/20, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_-16/15) & rat_$lesseq(rat_-31/20, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_31/20) & rat_$lesseq(rat_-31/20, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_-15/16) & rat_$lesseq(rat_-31/20, rat_-3/5) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_-31/20) & rat_$lesseq(rat_-31/20, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_1) & rat_$lesseq(rat_-31/20, rat_-5/4) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_16/25) & rat_$lesseq(rat_-31/20, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_3/4) & rat_$lesseq(rat_-31/20, rat_-4/5) &
% 21.71/3.85 rat_$lesseq(rat_-31/20, rat_0) & rat_$lesseq(rat_-1/20, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_3/2) & rat_$lesseq(rat_-1/20, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_31/20) & rat_$lesseq(rat_-1/20, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_1) & rat_$lesseq(rat_-1/20, rat_16/25) &
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_4/5) & rat_$lesseq(rat_-1/20, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_0) & rat_$lesseq(rat_1, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_1, rat_4/3) & rat_$lesseq(rat_1, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_1, rat_1) & rat_$lesseq(rat_-5/4, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_3/2) & rat_$lesseq(rat_-5/4, rat_-16/15) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_4/3) & rat_$lesseq(rat_-5/4, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_-3/4) & rat_$lesseq(rat_-5/4, rat_-15/16) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_-3/5) & rat_$lesseq(rat_-5/4, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_1) & rat_$lesseq(rat_-5/4, rat_-5/4) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_16/25) & rat_$lesseq(rat_-5/4, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_3/4) & rat_$lesseq(rat_-5/4, rat_-4/5) &
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_0) & rat_$lesseq(rat_16/25, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_4/3) & rat_$lesseq(rat_16/25, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_1) & rat_$lesseq(rat_16/25, rat_16/25) &
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_4/5) & rat_$lesseq(rat_16/25, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_9/16) & rat_$lesseq(rat_-8/5, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_-16/15) & rat_$lesseq(rat_-8/5, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_31/20) & rat_$lesseq(rat_-8/5, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_-15/16) & rat_$lesseq(rat_-8/5, rat_-3/5) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_-31/20) & rat_$lesseq(rat_-8/5, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_1) & rat_$lesseq(rat_-8/5, rat_-5/4) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_16/25) & rat_$lesseq(rat_-8/5, rat_-8/5) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_4/5) & rat_$lesseq(rat_-8/5, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_-8/5, rat_-4/5) & rat_$lesseq(rat_-8/5, rat_0) &
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_3/2) & rat_$lesseq(rat_4/5, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_31/20) & rat_$lesseq(rat_4/5, rat_1) &
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_4/5) & rat_$lesseq(rat_3/4, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_4/3) & rat_$lesseq(rat_3/4, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_1) & rat_$lesseq(rat_3/4, rat_4/5) &
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_3/4) & rat_$lesseq(rat_-4/5, rat_9/16) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_3/2) & rat_$lesseq(rat_-4/5, rat_4/3) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_31/20) & rat_$lesseq(rat_-4/5, rat_-3/4) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_-3/5) & rat_$lesseq(rat_-4/5, rat_-1/20) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_1) & rat_$lesseq(rat_-4/5, rat_16/25) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_4/5) & rat_$lesseq(rat_-4/5, rat_3/4) &
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_-4/5) & rat_$lesseq(rat_-4/5, rat_0) &
% 21.71/3.85 rat_$lesseq(rat_0, rat_9/16) & rat_$lesseq(rat_0, rat_3/2) &
% 21.71/3.85 rat_$lesseq(rat_0, rat_4/3) & rat_$lesseq(rat_0, rat_31/20) &
% 21.71/3.85 rat_$lesseq(rat_0, rat_1) & rat_$lesseq(rat_0, rat_16/25) & rat_$lesseq(rat_0,
% 21.71/3.85 rat_4/5) & rat_$lesseq(rat_0, rat_3/4) & rat_$lesseq(rat_0, rat_0) &
% 21.71/3.85 rat_$less(rat_very_small, rat_very_large) & rat_$less(rat_very_small,
% 21.71/3.85 rat_9/16) & rat_$less(rat_very_small, rat_3/2) & rat_$less(rat_very_small,
% 21.71/3.85 rat_-16/15) & rat_$less(rat_very_small, rat_4/3) & rat_$less(rat_very_small,
% 21.71/3.85 rat_31/20) & rat_$less(rat_very_small, rat_-3/4) & rat_$less(rat_very_small,
% 21.71/3.85 rat_-15/16) & rat_$less(rat_very_small, rat_-3/5) &
% 21.71/3.85 rat_$less(rat_very_small, rat_-31/20) & rat_$less(rat_very_small, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_very_small, rat_1) & rat_$less(rat_very_small, rat_-5/4) &
% 21.71/3.85 rat_$less(rat_very_small, rat_16/25) & rat_$less(rat_very_small, rat_-8/5) &
% 21.71/3.85 rat_$less(rat_very_small, rat_4/5) & rat_$less(rat_very_small, rat_3/4) &
% 21.71/3.85 rat_$less(rat_very_small, rat_-4/5) & rat_$less(rat_very_small, rat_0) &
% 21.71/3.85 rat_$less(rat_9/16, rat_very_large) & rat_$less(rat_9/16, rat_3/2) &
% 21.71/3.85 rat_$less(rat_9/16, rat_4/3) & rat_$less(rat_9/16, rat_31/20) &
% 21.71/3.85 rat_$less(rat_9/16, rat_1) & rat_$less(rat_9/16, rat_16/25) &
% 21.71/3.85 rat_$less(rat_9/16, rat_4/5) & rat_$less(rat_9/16, rat_3/4) &
% 21.71/3.85 rat_$less(rat_3/2, rat_very_large) & rat_$less(rat_3/2, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_very_large) & rat_$less(rat_-16/15, rat_9/16) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_3/2) & rat_$less(rat_-16/15, rat_4/3) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_31/20) & rat_$less(rat_-16/15, rat_-3/4) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_-15/16) & rat_$less(rat_-16/15, rat_-3/5) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_-1/20) & rat_$less(rat_-16/15, rat_1) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_16/25) & rat_$less(rat_-16/15, rat_4/5) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_3/4) & rat_$less(rat_-16/15, rat_-4/5) &
% 21.71/3.85 rat_$less(rat_-16/15, rat_0) & rat_$less(rat_4/3, rat_very_large) &
% 21.71/3.85 rat_$less(rat_4/3, rat_3/2) & rat_$less(rat_4/3, rat_31/20) &
% 21.71/3.85 rat_$less(rat_31/20, rat_very_large) & rat_$less(rat_-3/4, rat_very_large) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_9/16) & rat_$less(rat_-3/4, rat_3/2) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_4/3) & rat_$less(rat_-3/4, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_-3/5) & rat_$less(rat_-3/4, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_1) & rat_$less(rat_-3/4, rat_16/25) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_4/5) & rat_$less(rat_-3/4, rat_3/4) &
% 21.71/3.85 rat_$less(rat_-3/4, rat_0) & rat_$less(rat_-15/16, rat_very_large) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_9/16) & rat_$less(rat_-15/16, rat_3/2) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_4/3) & rat_$less(rat_-15/16, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_-3/4) & rat_$less(rat_-15/16, rat_-3/5) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_-1/20) & rat_$less(rat_-15/16, rat_1) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_16/25) & rat_$less(rat_-15/16, rat_4/5) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_3/4) & rat_$less(rat_-15/16, rat_-4/5) &
% 21.71/3.85 rat_$less(rat_-15/16, rat_0) & rat_$less(rat_-3/5, rat_very_large) &
% 21.71/3.85 rat_$less(rat_-3/5, rat_9/16) & rat_$less(rat_-3/5, rat_3/2) &
% 21.71/3.85 rat_$less(rat_-3/5, rat_4/3) & rat_$less(rat_-3/5, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-3/5, rat_-1/20) & rat_$less(rat_-3/5, rat_1) &
% 21.71/3.85 rat_$less(rat_-3/5, rat_16/25) & rat_$less(rat_-3/5, rat_4/5) &
% 21.71/3.85 rat_$less(rat_-3/5, rat_3/4) & rat_$less(rat_-3/5, rat_0) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_very_large) & rat_$less(rat_-31/20, rat_9/16) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_3/2) & rat_$less(rat_-31/20, rat_-16/15) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_4/3) & rat_$less(rat_-31/20, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_-3/4) & rat_$less(rat_-31/20, rat_-15/16) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_-3/5) & rat_$less(rat_-31/20, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_1) & rat_$less(rat_-31/20, rat_-5/4) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_16/25) & rat_$less(rat_-31/20, rat_4/5) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_3/4) & rat_$less(rat_-31/20, rat_-4/5) &
% 21.71/3.85 rat_$less(rat_-31/20, rat_0) & rat_$less(rat_-1/20, rat_very_large) &
% 21.71/3.85 rat_$less(rat_-1/20, rat_9/16) & rat_$less(rat_-1/20, rat_3/2) &
% 21.71/3.85 rat_$less(rat_-1/20, rat_4/3) & rat_$less(rat_-1/20, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-1/20, rat_1) & rat_$less(rat_-1/20, rat_16/25) &
% 21.71/3.85 rat_$less(rat_-1/20, rat_4/5) & rat_$less(rat_-1/20, rat_3/4) &
% 21.71/3.85 rat_$less(rat_-1/20, rat_0) & rat_$less(rat_1, rat_very_large) &
% 21.71/3.85 rat_$less(rat_1, rat_3/2) & rat_$less(rat_1, rat_4/3) & rat_$less(rat_1,
% 21.71/3.85 rat_31/20) & rat_$less(rat_-5/4, rat_very_large) & rat_$less(rat_-5/4,
% 21.71/3.85 rat_9/16) & rat_$less(rat_-5/4, rat_3/2) & rat_$less(rat_-5/4, rat_-16/15) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_4/3) & rat_$less(rat_-5/4, rat_31/20) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_-3/4) & rat_$less(rat_-5/4, rat_-15/16) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_-3/5) & rat_$less(rat_-5/4, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_1) & rat_$less(rat_-5/4, rat_16/25) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_4/5) & rat_$less(rat_-5/4, rat_3/4) &
% 21.71/3.85 rat_$less(rat_-5/4, rat_-4/5) & rat_$less(rat_-5/4, rat_0) &
% 21.71/3.85 rat_$less(rat_16/25, rat_very_large) & rat_$less(rat_16/25, rat_3/2) &
% 21.71/3.85 rat_$less(rat_16/25, rat_4/3) & rat_$less(rat_16/25, rat_31/20) &
% 21.71/3.85 rat_$less(rat_16/25, rat_1) & rat_$less(rat_16/25, rat_4/5) &
% 21.71/3.85 rat_$less(rat_16/25, rat_3/4) & rat_$less(rat_-8/5, rat_very_large) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_9/16) & rat_$less(rat_-8/5, rat_3/2) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_-16/15) & rat_$less(rat_-8/5, rat_4/3) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_31/20) & rat_$less(rat_-8/5, rat_-3/4) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_-15/16) & rat_$less(rat_-8/5, rat_-3/5) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_-31/20) & rat_$less(rat_-8/5, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_1) & rat_$less(rat_-8/5, rat_-5/4) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_16/25) & rat_$less(rat_-8/5, rat_4/5) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_3/4) & rat_$less(rat_-8/5, rat_-4/5) &
% 21.71/3.85 rat_$less(rat_-8/5, rat_0) & rat_$less(rat_4/5, rat_very_large) &
% 21.71/3.85 rat_$less(rat_4/5, rat_3/2) & rat_$less(rat_4/5, rat_4/3) & rat_$less(rat_4/5,
% 21.71/3.85 rat_31/20) & rat_$less(rat_4/5, rat_1) & rat_$less(rat_3/4, rat_very_large)
% 21.71/3.85 & rat_$less(rat_3/4, rat_3/2) & rat_$less(rat_3/4, rat_4/3) &
% 21.71/3.85 rat_$less(rat_3/4, rat_31/20) & rat_$less(rat_3/4, rat_1) & rat_$less(rat_3/4,
% 21.71/3.85 rat_4/5) & rat_$less(rat_-4/5, rat_very_large) & rat_$less(rat_-4/5,
% 21.71/3.85 rat_9/16) & rat_$less(rat_-4/5, rat_3/2) & rat_$less(rat_-4/5, rat_4/3) &
% 21.71/3.85 rat_$less(rat_-4/5, rat_31/20) & rat_$less(rat_-4/5, rat_-3/4) &
% 21.71/3.85 rat_$less(rat_-4/5, rat_-3/5) & rat_$less(rat_-4/5, rat_-1/20) &
% 21.71/3.85 rat_$less(rat_-4/5, rat_1) & rat_$less(rat_-4/5, rat_16/25) &
% 21.71/3.85 rat_$less(rat_-4/5, rat_4/5) & rat_$less(rat_-4/5, rat_3/4) &
% 21.71/3.85 rat_$less(rat_-4/5, rat_0) & rat_$less(rat_0, rat_very_large) &
% 21.71/3.85 rat_$less(rat_0, rat_9/16) & rat_$less(rat_0, rat_3/2) & rat_$less(rat_0,
% 21.71/3.85 rat_4/3) & rat_$less(rat_0, rat_31/20) & rat_$less(rat_0, rat_1) &
% 21.71/3.85 rat_$less(rat_0, rat_16/25) & rat_$less(rat_0, rat_4/5) & rat_$less(rat_0,
% 21.71/3.85 rat_3/4) & ~ rat_$is_int(rat_9/16) & ~ rat_$is_int(rat_3/2) & ~
% 21.71/3.85 rat_$is_int(rat_-16/15) & ~ rat_$is_int(rat_4/3) & ~ rat_$is_int(rat_31/20)
% 21.71/3.85 & ~ rat_$is_int(rat_-3/4) & ~ rat_$is_int(rat_-15/16) & ~
% 21.71/3.85 rat_$is_int(rat_-3/5) & ~ rat_$is_int(rat_-31/20) & ~ rat_$is_int(rat_-1/20)
% 21.71/3.85 & ~ rat_$is_int(rat_-5/4) & ~ rat_$is_int(rat_16/25) & ~
% 21.71/3.85 rat_$is_int(rat_-8/5) & ~ rat_$is_int(rat_4/5) & ~ rat_$is_int(rat_3/4) & ~
% 21.71/3.85 rat_$is_int(rat_-4/5) & ~ rat_$greatereq(rat_very_small, rat_very_large) & ~
% 21.71/3.85 rat_$greatereq(rat_9/16, rat_3/2) & ~ rat_$greatereq(rat_9/16, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_9/16, rat_31/20) & ~ rat_$greatereq(rat_9/16, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_9/16, rat_16/25) & ~ rat_$greatereq(rat_9/16, rat_4/5) &
% 21.71/3.85 ~ rat_$greatereq(rat_9/16, rat_3/4) & ~ rat_$greatereq(rat_3/2, rat_31/20) &
% 21.71/3.85 ~ rat_$greatereq(rat_-16/15, rat_9/16) & ~ rat_$greatereq(rat_-16/15,
% 21.71/3.85 rat_3/2) & ~ rat_$greatereq(rat_-16/15, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_-16/15, rat_31/20) & ~ rat_$greatereq(rat_-16/15,
% 21.71/3.85 rat_-3/4) & ~ rat_$greatereq(rat_-16/15, rat_-15/16) & ~
% 21.71/3.85 rat_$greatereq(rat_-16/15, rat_-3/5) & ~ rat_$greatereq(rat_-16/15,
% 21.71/3.85 rat_-1/20) & ~ rat_$greatereq(rat_-16/15, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_-16/15, rat_16/25) & ~ rat_$greatereq(rat_-16/15, rat_4/5)
% 21.71/3.85 & ~ rat_$greatereq(rat_-16/15, rat_3/4) & ~ rat_$greatereq(rat_-16/15,
% 21.71/3.85 rat_-4/5) & ~ rat_$greatereq(rat_-16/15, rat_0) & ~
% 21.71/3.85 rat_$greatereq(rat_4/3, rat_3/2) & ~ rat_$greatereq(rat_4/3, rat_31/20) & ~
% 21.71/3.85 rat_$greatereq(rat_-3/4, rat_9/16) & ~ rat_$greatereq(rat_-3/4, rat_3/2) & ~
% 21.71/3.85 rat_$greatereq(rat_-3/4, rat_4/3) & ~ rat_$greatereq(rat_-3/4, rat_31/20) &
% 21.71/3.85 ~ rat_$greatereq(rat_-3/4, rat_-3/5) & ~ rat_$greatereq(rat_-3/4, rat_-1/20)
% 21.71/3.85 & ~ rat_$greatereq(rat_-3/4, rat_1) & ~ rat_$greatereq(rat_-3/4, rat_16/25)
% 21.71/3.85 & ~ rat_$greatereq(rat_-3/4, rat_4/5) & ~ rat_$greatereq(rat_-3/4, rat_3/4)
% 21.71/3.85 & ~ rat_$greatereq(rat_-3/4, rat_0) & ~ rat_$greatereq(rat_-15/16, rat_9/16)
% 21.71/3.85 & ~ rat_$greatereq(rat_-15/16, rat_3/2) & ~ rat_$greatereq(rat_-15/16,
% 21.71/3.85 rat_4/3) & ~ rat_$greatereq(rat_-15/16, rat_31/20) & ~
% 21.71/3.85 rat_$greatereq(rat_-15/16, rat_-3/4) & ~ rat_$greatereq(rat_-15/16, rat_-3/5)
% 21.71/3.85 & ~ rat_$greatereq(rat_-15/16, rat_-1/20) & ~ rat_$greatereq(rat_-15/16,
% 21.71/3.85 rat_1) & ~ rat_$greatereq(rat_-15/16, rat_16/25) & ~
% 21.71/3.85 rat_$greatereq(rat_-15/16, rat_4/5) & ~ rat_$greatereq(rat_-15/16, rat_3/4) &
% 21.71/3.85 ~ rat_$greatereq(rat_-15/16, rat_-4/5) & ~ rat_$greatereq(rat_-15/16, rat_0)
% 21.71/3.85 & ~ rat_$greatereq(rat_-3/5, rat_9/16) & ~ rat_$greatereq(rat_-3/5, rat_3/2)
% 21.71/3.85 & ~ rat_$greatereq(rat_-3/5, rat_4/3) & ~ rat_$greatereq(rat_-3/5,
% 21.71/3.85 rat_31/20) & ~ rat_$greatereq(rat_-3/5, rat_-1/20) & ~
% 21.71/3.85 rat_$greatereq(rat_-3/5, rat_1) & ~ rat_$greatereq(rat_-3/5, rat_16/25) & ~
% 21.71/3.85 rat_$greatereq(rat_-3/5, rat_4/5) & ~ rat_$greatereq(rat_-3/5, rat_3/4) & ~
% 21.71/3.85 rat_$greatereq(rat_-3/5, rat_0) & ~ rat_$greatereq(rat_-31/20, rat_9/16) & ~
% 21.71/3.85 rat_$greatereq(rat_-31/20, rat_3/2) & ~ rat_$greatereq(rat_-31/20,
% 21.71/3.85 rat_-16/15) & ~ rat_$greatereq(rat_-31/20, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_-31/20, rat_31/20) & ~ rat_$greatereq(rat_-31/20,
% 21.71/3.85 rat_-3/4) & ~ rat_$greatereq(rat_-31/20, rat_-15/16) & ~
% 21.71/3.85 rat_$greatereq(rat_-31/20, rat_-3/5) & ~ rat_$greatereq(rat_-31/20,
% 21.71/3.85 rat_-1/20) & ~ rat_$greatereq(rat_-31/20, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_-31/20, rat_-5/4) & ~ rat_$greatereq(rat_-31/20,
% 21.71/3.85 rat_16/25) & ~ rat_$greatereq(rat_-31/20, rat_4/5) & ~
% 21.71/3.85 rat_$greatereq(rat_-31/20, rat_3/4) & ~ rat_$greatereq(rat_-31/20, rat_-4/5)
% 21.71/3.85 & ~ rat_$greatereq(rat_-31/20, rat_0) & ~ rat_$greatereq(rat_-1/20,
% 21.71/3.85 rat_9/16) & ~ rat_$greatereq(rat_-1/20, rat_3/2) & ~
% 21.71/3.85 rat_$greatereq(rat_-1/20, rat_4/3) & ~ rat_$greatereq(rat_-1/20, rat_31/20) &
% 21.71/3.85 ~ rat_$greatereq(rat_-1/20, rat_1) & ~ rat_$greatereq(rat_-1/20, rat_16/25)
% 21.71/3.85 & ~ rat_$greatereq(rat_-1/20, rat_4/5) & ~ rat_$greatereq(rat_-1/20,
% 21.71/3.85 rat_3/4) & ~ rat_$greatereq(rat_-1/20, rat_0) & ~ rat_$greatereq(rat_1,
% 21.71/3.85 rat_3/2) & ~ rat_$greatereq(rat_1, rat_4/3) & ~ rat_$greatereq(rat_1,
% 21.71/3.85 rat_31/20) & ~ rat_$greatereq(rat_-5/4, rat_9/16) & ~
% 21.71/3.85 rat_$greatereq(rat_-5/4, rat_3/2) & ~ rat_$greatereq(rat_-5/4, rat_-16/15) &
% 21.71/3.85 ~ rat_$greatereq(rat_-5/4, rat_4/3) & ~ rat_$greatereq(rat_-5/4, rat_31/20) &
% 21.71/3.85 ~ rat_$greatereq(rat_-5/4, rat_-3/4) & ~ rat_$greatereq(rat_-5/4,
% 21.71/3.85 rat_-15/16) & ~ rat_$greatereq(rat_-5/4, rat_-3/5) & ~
% 21.71/3.85 rat_$greatereq(rat_-5/4, rat_-1/20) & ~ rat_$greatereq(rat_-5/4, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_-5/4, rat_16/25) & ~ rat_$greatereq(rat_-5/4, rat_4/5) &
% 21.71/3.85 ~ rat_$greatereq(rat_-5/4, rat_3/4) & ~ rat_$greatereq(rat_-5/4, rat_-4/5) &
% 21.71/3.85 ~ rat_$greatereq(rat_-5/4, rat_0) & ~ rat_$greatereq(rat_16/25, rat_3/2) & ~
% 21.71/3.85 rat_$greatereq(rat_16/25, rat_4/3) & ~ rat_$greatereq(rat_16/25, rat_31/20) &
% 21.71/3.85 ~ rat_$greatereq(rat_16/25, rat_1) & ~ rat_$greatereq(rat_16/25, rat_4/5) &
% 21.71/3.85 ~ rat_$greatereq(rat_16/25, rat_3/4) & ~ rat_$greatereq(rat_-8/5, rat_9/16) &
% 21.71/3.85 ~ rat_$greatereq(rat_-8/5, rat_3/2) & ~ rat_$greatereq(rat_-8/5, rat_-16/15)
% 21.71/3.85 & ~ rat_$greatereq(rat_-8/5, rat_4/3) & ~ rat_$greatereq(rat_-8/5,
% 21.71/3.85 rat_31/20) & ~ rat_$greatereq(rat_-8/5, rat_-3/4) & ~
% 21.71/3.85 rat_$greatereq(rat_-8/5, rat_-15/16) & ~ rat_$greatereq(rat_-8/5, rat_-3/5) &
% 21.71/3.85 ~ rat_$greatereq(rat_-8/5, rat_-31/20) & ~ rat_$greatereq(rat_-8/5,
% 21.71/3.85 rat_-1/20) & ~ rat_$greatereq(rat_-8/5, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_-8/5, rat_-5/4) & ~ rat_$greatereq(rat_-8/5, rat_16/25) &
% 21.71/3.85 ~ rat_$greatereq(rat_-8/5, rat_4/5) & ~ rat_$greatereq(rat_-8/5, rat_3/4) &
% 21.71/3.85 ~ rat_$greatereq(rat_-8/5, rat_-4/5) & ~ rat_$greatereq(rat_-8/5, rat_0) & ~
% 21.71/3.85 rat_$greatereq(rat_4/5, rat_3/2) & ~ rat_$greatereq(rat_4/5, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_4/5, rat_31/20) & ~ rat_$greatereq(rat_4/5, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_3/4, rat_3/2) & ~ rat_$greatereq(rat_3/4, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_3/4, rat_31/20) & ~ rat_$greatereq(rat_3/4, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_3/4, rat_4/5) & ~ rat_$greatereq(rat_-4/5, rat_9/16) & ~
% 21.71/3.85 rat_$greatereq(rat_-4/5, rat_3/2) & ~ rat_$greatereq(rat_-4/5, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_-4/5, rat_31/20) & ~ rat_$greatereq(rat_-4/5, rat_-3/4) &
% 21.71/3.85 ~ rat_$greatereq(rat_-4/5, rat_-3/5) & ~ rat_$greatereq(rat_-4/5, rat_-1/20)
% 21.71/3.85 & ~ rat_$greatereq(rat_-4/5, rat_1) & ~ rat_$greatereq(rat_-4/5, rat_16/25)
% 21.71/3.85 & ~ rat_$greatereq(rat_-4/5, rat_4/5) & ~ rat_$greatereq(rat_-4/5, rat_3/4)
% 21.71/3.85 & ~ rat_$greatereq(rat_-4/5, rat_0) & ~ rat_$greatereq(rat_0, rat_9/16) & ~
% 21.71/3.85 rat_$greatereq(rat_0, rat_3/2) & ~ rat_$greatereq(rat_0, rat_4/3) & ~
% 21.71/3.85 rat_$greatereq(rat_0, rat_31/20) & ~ rat_$greatereq(rat_0, rat_1) & ~
% 21.71/3.85 rat_$greatereq(rat_0, rat_16/25) & ~ rat_$greatereq(rat_0, rat_4/5) & ~
% 21.71/3.85 rat_$greatereq(rat_0, rat_3/4) & ~ rat_$greater(rat_very_small,
% 21.71/3.85 rat_very_large) & ~ rat_$greater(rat_9/16, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_9/16, rat_3/2) & ~ rat_$greater(rat_9/16, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_9/16, rat_31/20) & ~ rat_$greater(rat_9/16, rat_1) & ~
% 21.71/3.85 rat_$greater(rat_9/16, rat_16/25) & ~ rat_$greater(rat_9/16, rat_4/5) & ~
% 21.71/3.85 rat_$greater(rat_9/16, rat_3/4) & ~ rat_$greater(rat_3/2, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_3/2, rat_31/20) & ~ rat_$greater(rat_-16/15, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-16/15, rat_3/2) & ~ rat_$greater(rat_-16/15, rat_-16/15) &
% 21.71/3.85 ~ rat_$greater(rat_-16/15, rat_4/3) & ~ rat_$greater(rat_-16/15, rat_31/20) &
% 21.71/3.85 ~ rat_$greater(rat_-16/15, rat_-3/4) & ~ rat_$greater(rat_-16/15,
% 21.71/3.85 rat_-15/16) & ~ rat_$greater(rat_-16/15, rat_-3/5) & ~
% 21.71/3.85 rat_$greater(rat_-16/15, rat_-1/20) & ~ rat_$greater(rat_-16/15, rat_1) & ~
% 21.71/3.85 rat_$greater(rat_-16/15, rat_16/25) & ~ rat_$greater(rat_-16/15, rat_4/5) &
% 21.71/3.85 ~ rat_$greater(rat_-16/15, rat_3/4) & ~ rat_$greater(rat_-16/15, rat_-4/5) &
% 21.71/3.85 ~ rat_$greater(rat_-16/15, rat_0) & ~ rat_$greater(rat_4/3, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_4/3, rat_4/3) & ~ rat_$greater(rat_4/3, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_31/20, rat_31/20) & ~ rat_$greater(rat_-3/4, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_3/2) & ~ rat_$greater(rat_-3/4, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_31/20) & ~ rat_$greater(rat_-3/4, rat_-3/4) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_-3/5) & ~ rat_$greater(rat_-3/4, rat_-1/20) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_1) & ~ rat_$greater(rat_-3/4, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_4/5) & ~ rat_$greater(rat_-3/4, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-3/4, rat_0) & ~ rat_$greater(rat_-15/16, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-15/16, rat_3/2) & ~ rat_$greater(rat_-15/16, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_-15/16, rat_31/20) & ~ rat_$greater(rat_-15/16, rat_-3/4) &
% 21.71/3.85 ~ rat_$greater(rat_-15/16, rat_-15/16) & ~ rat_$greater(rat_-15/16, rat_-3/5)
% 21.71/3.85 & ~ rat_$greater(rat_-15/16, rat_-1/20) & ~ rat_$greater(rat_-15/16, rat_1)
% 21.71/3.85 & ~ rat_$greater(rat_-15/16, rat_16/25) & ~ rat_$greater(rat_-15/16,
% 21.71/3.85 rat_4/5) & ~ rat_$greater(rat_-15/16, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-15/16, rat_-4/5) & ~ rat_$greater(rat_-15/16, rat_0) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_9/16) & ~ rat_$greater(rat_-3/5, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_4/3) & ~ rat_$greater(rat_-3/5, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_-3/5) & ~ rat_$greater(rat_-3/5, rat_-1/20) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_1) & ~ rat_$greater(rat_-3/5, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_4/5) & ~ rat_$greater(rat_-3/5, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-3/5, rat_0) & ~ rat_$greater(rat_-31/20, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-31/20, rat_3/2) & ~ rat_$greater(rat_-31/20, rat_-16/15) &
% 21.71/3.85 ~ rat_$greater(rat_-31/20, rat_4/3) & ~ rat_$greater(rat_-31/20, rat_31/20) &
% 21.71/3.85 ~ rat_$greater(rat_-31/20, rat_-3/4) & ~ rat_$greater(rat_-31/20,
% 21.71/3.85 rat_-15/16) & ~ rat_$greater(rat_-31/20, rat_-3/5) & ~
% 21.71/3.85 rat_$greater(rat_-31/20, rat_-31/20) & ~ rat_$greater(rat_-31/20, rat_-1/20)
% 21.71/3.85 & ~ rat_$greater(rat_-31/20, rat_1) & ~ rat_$greater(rat_-31/20, rat_-5/4) &
% 21.71/3.85 ~ rat_$greater(rat_-31/20, rat_16/25) & ~ rat_$greater(rat_-31/20, rat_4/5)
% 21.71/3.85 & ~ rat_$greater(rat_-31/20, rat_3/4) & ~ rat_$greater(rat_-31/20, rat_-4/5)
% 21.71/3.85 & ~ rat_$greater(rat_-31/20, rat_0) & ~ rat_$greater(rat_-1/20, rat_9/16) &
% 21.71/3.85 ~ rat_$greater(rat_-1/20, rat_3/2) & ~ rat_$greater(rat_-1/20, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_-1/20, rat_31/20) & ~ rat_$greater(rat_-1/20, rat_-1/20) &
% 21.71/3.85 ~ rat_$greater(rat_-1/20, rat_1) & ~ rat_$greater(rat_-1/20, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_-1/20, rat_4/5) & ~ rat_$greater(rat_-1/20, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-1/20, rat_0) & ~ rat_$greater(rat_1, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_1, rat_4/3) & ~ rat_$greater(rat_1, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_1, rat_1) & ~ rat_$greater(rat_-5/4, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_3/2) & ~ rat_$greater(rat_-5/4, rat_-16/15) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_4/3) & ~ rat_$greater(rat_-5/4, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_-3/4) & ~ rat_$greater(rat_-5/4, rat_-15/16) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_-3/5) & ~ rat_$greater(rat_-5/4, rat_-1/20) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_1) & ~ rat_$greater(rat_-5/4, rat_-5/4) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_16/25) & ~ rat_$greater(rat_-5/4, rat_4/5) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_3/4) & ~ rat_$greater(rat_-5/4, rat_-4/5) & ~
% 21.71/3.85 rat_$greater(rat_-5/4, rat_0) & ~ rat_$greater(rat_16/25, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_16/25, rat_4/3) & ~ rat_$greater(rat_16/25, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_16/25, rat_1) & ~ rat_$greater(rat_16/25, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_16/25, rat_4/5) & ~ rat_$greater(rat_16/25, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_9/16) & ~ rat_$greater(rat_-8/5, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_-16/15) & ~ rat_$greater(rat_-8/5, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_31/20) & ~ rat_$greater(rat_-8/5, rat_-3/4) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_-15/16) & ~ rat_$greater(rat_-8/5, rat_-3/5) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_-31/20) & ~ rat_$greater(rat_-8/5, rat_-1/20) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_1) & ~ rat_$greater(rat_-8/5, rat_-5/4) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_16/25) & ~ rat_$greater(rat_-8/5, rat_-8/5) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_4/5) & ~ rat_$greater(rat_-8/5, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-8/5, rat_-4/5) & ~ rat_$greater(rat_-8/5, rat_0) & ~
% 21.71/3.85 rat_$greater(rat_4/5, rat_3/2) & ~ rat_$greater(rat_4/5, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_4/5, rat_31/20) & ~ rat_$greater(rat_4/5, rat_1) & ~
% 21.71/3.85 rat_$greater(rat_4/5, rat_4/5) & ~ rat_$greater(rat_3/4, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_3/4, rat_4/3) & ~ rat_$greater(rat_3/4, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_3/4, rat_1) & ~ rat_$greater(rat_3/4, rat_4/5) & ~
% 21.71/3.85 rat_$greater(rat_3/4, rat_3/4) & ~ rat_$greater(rat_-4/5, rat_9/16) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_3/2) & ~ rat_$greater(rat_-4/5, rat_4/3) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_31/20) & ~ rat_$greater(rat_-4/5, rat_-3/4) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_-3/5) & ~ rat_$greater(rat_-4/5, rat_-1/20) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_1) & ~ rat_$greater(rat_-4/5, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_4/5) & ~ rat_$greater(rat_-4/5, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_-4/5, rat_-4/5) & ~ rat_$greater(rat_-4/5, rat_0) & ~
% 21.71/3.85 rat_$greater(rat_0, rat_9/16) & ~ rat_$greater(rat_0, rat_3/2) & ~
% 21.71/3.85 rat_$greater(rat_0, rat_4/3) & ~ rat_$greater(rat_0, rat_31/20) & ~
% 21.71/3.85 rat_$greater(rat_0, rat_1) & ~ rat_$greater(rat_0, rat_16/25) & ~
% 21.71/3.85 rat_$greater(rat_0, rat_4/5) & ~ rat_$greater(rat_0, rat_3/4) & ~
% 21.71/3.85 rat_$greater(rat_0, rat_0) & ~ rat_$lesseq(rat_9/16, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_-3/4) & ~ rat_$lesseq(rat_9/16, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_-3/5) & ~ rat_$lesseq(rat_9/16, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_-1/20) & ~ rat_$lesseq(rat_9/16, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_-8/5) & ~ rat_$lesseq(rat_9/16, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_9/16, rat_0) & ~ rat_$lesseq(rat_3/2, rat_9/16) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-16/15) & ~ rat_$lesseq(rat_3/2, rat_4/3) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-3/4) & ~ rat_$lesseq(rat_3/2, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-3/5) & ~ rat_$lesseq(rat_3/2, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-1/20) & ~ rat_$lesseq(rat_3/2, rat_1) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-5/4) & ~ rat_$lesseq(rat_3/2, rat_16/25) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_-8/5) & ~ rat_$lesseq(rat_3/2, rat_4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_3/4) & ~ rat_$lesseq(rat_3/2, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_3/2, rat_0) & ~ rat_$lesseq(rat_-16/15, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_-16/15, rat_-5/4) & ~ rat_$lesseq(rat_-16/15, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_9/16) & ~ rat_$lesseq(rat_4/3, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_-3/4) & ~ rat_$lesseq(rat_4/3, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_-3/5) & ~ rat_$lesseq(rat_4/3, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_-1/20) & ~ rat_$lesseq(rat_4/3, rat_1) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_-5/4) & ~ rat_$lesseq(rat_4/3, rat_16/25) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_-8/5) & ~ rat_$lesseq(rat_4/3, rat_4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_3/4) & ~ rat_$lesseq(rat_4/3, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_4/3, rat_0) & ~ rat_$lesseq(rat_31/20, rat_9/16) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_3/2) & ~ rat_$lesseq(rat_31/20, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_4/3) & ~ rat_$lesseq(rat_31/20, rat_-3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_-15/16) & ~ rat_$lesseq(rat_31/20, rat_-3/5) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_-31/20) & ~ rat_$lesseq(rat_31/20, rat_-1/20) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_1) & ~ rat_$lesseq(rat_31/20, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_16/25) & ~ rat_$lesseq(rat_31/20, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_4/5) & ~ rat_$lesseq(rat_31/20, rat_3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_31/20, rat_-4/5) & ~ rat_$lesseq(rat_31/20, rat_0) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_-16/15) & ~ rat_$lesseq(rat_-3/4, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_-31/20) & ~ rat_$lesseq(rat_-3/4, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/4, rat_-8/5) & ~ rat_$lesseq(rat_-3/4, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_-15/16, rat_-16/15) & ~ rat_$lesseq(rat_-15/16, rat_-31/20) &
% 21.71/3.85 ~ rat_$lesseq(rat_-15/16, rat_-5/4) & ~ rat_$lesseq(rat_-15/16, rat_-8/5) &
% 21.71/3.85 ~ rat_$lesseq(rat_-3/5, rat_-16/15) & ~ rat_$lesseq(rat_-3/5, rat_-3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_-15/16) & ~ rat_$lesseq(rat_-3/5, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_-5/4) & ~ rat_$lesseq(rat_-3/5, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_-3/5, rat_-4/5) & ~ rat_$lesseq(rat_-31/20, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_-16/15) & ~ rat_$lesseq(rat_-1/20, rat_-3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_-15/16) & ~ rat_$lesseq(rat_-1/20, rat_-3/5) & ~
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_-31/20) & ~ rat_$lesseq(rat_-1/20, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_-1/20, rat_-8/5) & ~ rat_$lesseq(rat_-1/20, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_9/16) & ~ rat_$lesseq(rat_1, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_-3/4) & ~ rat_$lesseq(rat_1, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_-3/5) & ~ rat_$lesseq(rat_1, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_-1/20) & ~ rat_$lesseq(rat_1, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_16/25) & ~ rat_$lesseq(rat_1, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_4/5) & ~ rat_$lesseq(rat_1, rat_3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_1, rat_-4/5) & ~ rat_$lesseq(rat_1, rat_0) & ~
% 21.71/3.85 rat_$lesseq(rat_-5/4, rat_-31/20) & ~ rat_$lesseq(rat_-5/4, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_9/16) & ~ rat_$lesseq(rat_16/25, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_-3/4) & ~ rat_$lesseq(rat_16/25, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_-3/5) & ~ rat_$lesseq(rat_16/25, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_-1/20) & ~ rat_$lesseq(rat_16/25, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_-8/5) & ~ rat_$lesseq(rat_16/25, rat_-4/5) & ~
% 21.71/3.85 rat_$lesseq(rat_16/25, rat_0) & ~ rat_$lesseq(rat_4/5, rat_9/16) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-16/15) & ~ rat_$lesseq(rat_4/5, rat_-3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-15/16) & ~ rat_$lesseq(rat_4/5, rat_-3/5) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-31/20) & ~ rat_$lesseq(rat_4/5, rat_-1/20) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-5/4) & ~ rat_$lesseq(rat_4/5, rat_16/25) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-8/5) & ~ rat_$lesseq(rat_4/5, rat_3/4) & ~
% 21.71/3.85 rat_$lesseq(rat_4/5, rat_-4/5) & ~ rat_$lesseq(rat_4/5, rat_0) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_9/16) & ~ rat_$lesseq(rat_3/4, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_-3/4) & ~ rat_$lesseq(rat_3/4, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_-3/5) & ~ rat_$lesseq(rat_3/4, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_-1/20) & ~ rat_$lesseq(rat_3/4, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_16/25) & ~ rat_$lesseq(rat_3/4, rat_-8/5) & ~
% 21.71/3.85 rat_$lesseq(rat_3/4, rat_-4/5) & ~ rat_$lesseq(rat_3/4, rat_0) & ~
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_-16/15) & ~ rat_$lesseq(rat_-4/5, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_-31/20) & ~ rat_$lesseq(rat_-4/5, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_-4/5, rat_-8/5) & ~ rat_$lesseq(rat_0, rat_-16/15) & ~
% 21.71/3.85 rat_$lesseq(rat_0, rat_-3/4) & ~ rat_$lesseq(rat_0, rat_-15/16) & ~
% 21.71/3.85 rat_$lesseq(rat_0, rat_-3/5) & ~ rat_$lesseq(rat_0, rat_-31/20) & ~
% 21.71/3.85 rat_$lesseq(rat_0, rat_-1/20) & ~ rat_$lesseq(rat_0, rat_-5/4) & ~
% 21.71/3.85 rat_$lesseq(rat_0, rat_-8/5) & ~ rat_$lesseq(rat_0, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_9/16) & ~ rat_$less(rat_9/16, rat_-16/15) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_-3/4) & ~ rat_$less(rat_9/16, rat_-15/16) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_-3/5) & ~ rat_$less(rat_9/16, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_-1/20) & ~ rat_$less(rat_9/16, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_-8/5) & ~ rat_$less(rat_9/16, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_9/16, rat_0) & ~ rat_$less(rat_3/2, rat_9/16) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_3/2) & ~ rat_$less(rat_3/2, rat_-16/15) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_4/3) & ~ rat_$less(rat_3/2, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_-15/16) & ~ rat_$less(rat_3/2, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_-31/20) & ~ rat_$less(rat_3/2, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_1) & ~ rat_$less(rat_3/2, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_16/25) & ~ rat_$less(rat_3/2, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_4/5) & ~ rat_$less(rat_3/2, rat_3/4) & ~
% 21.71/3.85 rat_$less(rat_3/2, rat_-4/5) & ~ rat_$less(rat_3/2, rat_0) & ~
% 21.71/3.85 rat_$less(rat_-16/15, rat_-16/15) & ~ rat_$less(rat_-16/15, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_-16/15, rat_-5/4) & ~ rat_$less(rat_-16/15, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_9/16) & ~ rat_$less(rat_4/3, rat_-16/15) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_4/3) & ~ rat_$less(rat_4/3, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_-15/16) & ~ rat_$less(rat_4/3, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_-31/20) & ~ rat_$less(rat_4/3, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_1) & ~ rat_$less(rat_4/3, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_16/25) & ~ rat_$less(rat_4/3, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_4/5) & ~ rat_$less(rat_4/3, rat_3/4) & ~
% 21.71/3.85 rat_$less(rat_4/3, rat_-4/5) & ~ rat_$less(rat_4/3, rat_0) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_9/16) & ~ rat_$less(rat_31/20, rat_3/2) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_-16/15) & ~ rat_$less(rat_31/20, rat_4/3) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_31/20) & ~ rat_$less(rat_31/20, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_-15/16) & ~ rat_$less(rat_31/20, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_-31/20) & ~ rat_$less(rat_31/20, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_1) & ~ rat_$less(rat_31/20, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_16/25) & ~ rat_$less(rat_31/20, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_4/5) & ~ rat_$less(rat_31/20, rat_3/4) & ~
% 21.71/3.85 rat_$less(rat_31/20, rat_-4/5) & ~ rat_$less(rat_31/20, rat_0) & ~
% 21.71/3.85 rat_$less(rat_-3/4, rat_-16/15) & ~ rat_$less(rat_-3/4, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_-3/4, rat_-15/16) & ~ rat_$less(rat_-3/4, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_-3/4, rat_-5/4) & ~ rat_$less(rat_-3/4, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_-3/4, rat_-4/5) & ~ rat_$less(rat_-15/16, rat_-16/15) & ~
% 21.71/3.85 rat_$less(rat_-15/16, rat_-15/16) & ~ rat_$less(rat_-15/16, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_-15/16, rat_-5/4) & ~ rat_$less(rat_-15/16, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_-3/5, rat_-16/15) & ~ rat_$less(rat_-3/5, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_-3/5, rat_-15/16) & ~ rat_$less(rat_-3/5, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_-3/5, rat_-31/20) & ~ rat_$less(rat_-3/5, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_-3/5, rat_-8/5) & ~ rat_$less(rat_-3/5, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_-31/20, rat_-31/20) & ~ rat_$less(rat_-31/20, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_-1/20, rat_-16/15) & ~ rat_$less(rat_-1/20, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_-1/20, rat_-15/16) & ~ rat_$less(rat_-1/20, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_-1/20, rat_-31/20) & ~ rat_$less(rat_-1/20, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_-1/20, rat_-5/4) & ~ rat_$less(rat_-1/20, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_-1/20, rat_-4/5) & ~ rat_$less(rat_1, rat_9/16) & ~
% 21.71/3.85 rat_$less(rat_1, rat_-16/15) & ~ rat_$less(rat_1, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_1, rat_-15/16) & ~ rat_$less(rat_1, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_1, rat_-31/20) & ~ rat_$less(rat_1, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_1, rat_1) & ~ rat_$less(rat_1, rat_-5/4) & ~ rat_$less(rat_1,
% 21.71/3.85 rat_16/25) & ~ rat_$less(rat_1, rat_-8/5) & ~ rat_$less(rat_1, rat_4/5) &
% 21.71/3.85 ~ rat_$less(rat_1, rat_3/4) & ~ rat_$less(rat_1, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_1, rat_0) & ~ rat_$less(rat_-5/4, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_-5/4, rat_-5/4) & ~ rat_$less(rat_-5/4, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_9/16) & ~ rat_$less(rat_16/25, rat_-16/15) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_-3/4) & ~ rat_$less(rat_16/25, rat_-15/16) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_-3/5) & ~ rat_$less(rat_16/25, rat_-31/20) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_-1/20) & ~ rat_$less(rat_16/25, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_16/25) & ~ rat_$less(rat_16/25, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_16/25, rat_-4/5) & ~ rat_$less(rat_16/25, rat_0) & ~
% 21.71/3.85 rat_$less(rat_-8/5, rat_-8/5) & ~ rat_$less(rat_4/5, rat_9/16) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_-16/15) & ~ rat_$less(rat_4/5, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_-15/16) & ~ rat_$less(rat_4/5, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_-31/20) & ~ rat_$less(rat_4/5, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_-5/4) & ~ rat_$less(rat_4/5, rat_16/25) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_-8/5) & ~ rat_$less(rat_4/5, rat_4/5) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_3/4) & ~ rat_$less(rat_4/5, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_4/5, rat_0) & ~ rat_$less(rat_3/4, rat_9/16) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-16/15) & ~ rat_$less(rat_3/4, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-15/16) & ~ rat_$less(rat_3/4, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-31/20) & ~ rat_$less(rat_3/4, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-5/4) & ~ rat_$less(rat_3/4, rat_16/25) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-8/5) & ~ rat_$less(rat_3/4, rat_3/4) & ~
% 21.71/3.85 rat_$less(rat_3/4, rat_-4/5) & ~ rat_$less(rat_3/4, rat_0) & ~
% 21.71/3.85 rat_$less(rat_-4/5, rat_-16/15) & ~ rat_$less(rat_-4/5, rat_-15/16) & ~
% 21.71/3.85 rat_$less(rat_-4/5, rat_-31/20) & ~ rat_$less(rat_-4/5, rat_-5/4) & ~
% 21.71/3.85 rat_$less(rat_-4/5, rat_-8/5) & ~ rat_$less(rat_-4/5, rat_-4/5) & ~
% 21.71/3.85 rat_$less(rat_0, rat_-16/15) & ~ rat_$less(rat_0, rat_-3/4) & ~
% 21.71/3.85 rat_$less(rat_0, rat_-15/16) & ~ rat_$less(rat_0, rat_-3/5) & ~
% 21.71/3.85 rat_$less(rat_0, rat_-31/20) & ~ rat_$less(rat_0, rat_-1/20) & ~
% 21.71/3.85 rat_$less(rat_0, rat_-5/4) & ~ rat_$less(rat_0, rat_-8/5) & ~
% 21.71/3.85 rat_$less(rat_0, rat_-4/5) & ~ rat_$less(rat_0, rat_0) & ! [v0: $rat] : !
% 21.71/3.85 [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3,
% 21.71/3.85 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2,
% 21.71/3.85 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 21.71/3.85 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~
% 21.71/3.85 (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 &
% 21.71/3.85 rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 21.71/3.85 ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) |
% 21.71/3.85 rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 21.71/3.85 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 21.71/3.85 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 21.71/3.85 (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 21.71/3.85 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 21.71/3.85 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1:
% 21.71/3.85 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 21.71/3.85 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v1, v0) =
% 21.71/3.85 v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 21.71/3.85 $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & !
% 21.71/3.85 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ rat_$lesseq(v2, v1) | ~
% 21.71/3.85 rat_$lesseq(v1, v0) | rat_$lesseq(v2, v0)) & ! [v0: $rat] : ! [v1: $rat] :
% 21.71/3.85 ! [v2: $rat] : ( ~ rat_$lesseq(v2, v1) | ~ rat_$less(v1, v0) | rat_$less(v2,
% 21.71/3.85 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ rat_$lesseq(v1,
% 21.71/3.85 v0) | ~ rat_$less(v2, v1) | rat_$less(v2, v0)) & ! [v0: $rat] : ! [v1:
% 21.71/3.85 $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1:
% 21.71/3.85 $rat] : (v1 = v0 | ~ rat_$lesseq(v1, v0) | rat_$less(v1, v0)) & ! [v0:
% 21.71/3.85 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 21.71/3.85 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1)
% 21.71/3.85 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ rat_$greatereq(v0, v1) |
% 21.71/3.85 rat_$lesseq(v1, v0)) & ! [v0: $rat] : ! [v1: $rat] : ( ~ rat_$greater(v0,
% 21.71/3.85 v1) | rat_$less(v1, v0)) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 21.71/3.85 rat_$lesseq(v1, v0) | rat_$greatereq(v0, v1)) & ! [v0: $rat] : ! [v1:
% 21.71/3.85 $rat] : ( ~ rat_$less(v1, v0) | rat_$greater(v0, v1)) & ! [v0: $rat] : !
% 21.71/3.85 [v1: $rat] : ( ~ rat_$less(v1, v0) | rat_$lesseq(v1, v0)) & ! [v0: $rat] :
% 21.71/3.85 (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) & ? [v0: $rat] : rat_$lesseq(v0, v0)
% 21.71/3.85
% 21.71/3.85 Those formulas are unsatisfiable:
% 21.71/3.85 ---------------------------------
% 21.71/3.85
% 21.71/3.85 Begin of proof
% 21.71/3.85 |
% 21.71/3.86 | ALPHA: (input) implies:
% 21.71/3.86 | (1) rat_$product(rat_-15/16, rat_-4/5) = rat_3/4
% 21.71/3.86 |
% 21.71/3.86 | GROUND_INST: instantiating (rat_product_problem_24) with rat_-15/16,
% 21.71/3.86 | simplifying with (1) gives:
% 21.71/3.86 | (2) $false
% 21.71/3.86 |
% 21.71/3.86 | CLOSE: (2) is inconsistent.
% 21.71/3.86 |
% 21.71/3.86 End of proof
% 21.71/3.86 % SZS output end Proof for theBenchmark
% 21.71/3.86
% 21.71/3.86 3271ms
%------------------------------------------------------------------------------