TSTP Solution File: ARI341_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI341_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 : n019.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 17:47:41 EDT 2023

% Result   : Theorem 12.57s 2.56s
% Output   : Proof 80.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : ARI341_1 : TPTP v8.1.2. Released v5.0.0.
% 0.09/0.10  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30  % Computer : n019.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue Aug 29 18:39:12 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.58  ________       _____
% 0.15/0.58  ___  __ \_________(_)________________________________
% 0.15/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.15/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.15/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.15/0.58  
% 0.15/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.58  (2023-06-19)
% 0.15/0.58  
% 0.15/0.58  (c) Philipp Rümmer, 2009-2023
% 0.15/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.58                Amanda Stjerna.
% 0.15/0.58  Free software under BSD-3-Clause.
% 0.15/0.58  
% 0.15/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.58  
% 0.15/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.15/0.60  Running up to 7 provers in parallel.
% 0.15/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.47/0.91  Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.47/0.91  Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.80/1.19  Prover 4: Preprocessing ...
% 2.80/1.19  Prover 1: Preprocessing ...
% 2.80/1.26  Prover 0: Preprocessing ...
% 2.80/1.26  Prover 6: Preprocessing ...
% 11.75/2.44  Prover 6: Constructing countermodel ...
% 12.57/2.50  Prover 0: Constructing countermodel ...
% 12.57/2.52  Prover 1: Constructing countermodel ...
% 12.57/2.55  Prover 6: proved (1938ms)
% 12.57/2.55  
% 12.57/2.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.57/2.56  
% 12.57/2.56  Prover 0: proved (1947ms)
% 12.57/2.56  
% 12.57/2.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.57/2.56  
% 12.57/2.57  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.57/2.57  Prover 4: Constructing countermodel ...
% 12.57/2.57  Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 12.57/2.57  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.57/2.57  Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 13.40/2.62  Prover 8: Preprocessing ...
% 17.72/3.25  Prover 8: Warning: ignoring some quantifiers
% 17.72/3.26  Prover 8: Constructing countermodel ...
% 18.77/3.35  Prover 4: Found proof (size 7)
% 18.77/3.35  Prover 4: proved (2744ms)
% 18.77/3.35  Prover 1: stopped
% 18.77/3.35  Prover 8: stopped
% 24.28/4.16  Prover 3: Preprocessing ...
% 24.28/4.16  Prover 5: Preprocessing ...
% 24.28/4.17  Prover 2: Preprocessing ...
% 25.67/4.32  Prover 7: Preprocessing ...
% 55.88/9.00  Prover 7: stopped
% 55.88/9.01  Prover 2: stopped
% 71.04/11.86  Prover 5: Constructing countermodel ...
% 71.04/11.86  Prover 5: stopped
% 79.65/17.45  Prover 3: Constructing countermodel ...
% 79.65/17.46  Prover 3: stopped
% 79.65/17.46  
% 79.65/17.46  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.65/17.46  
% 79.65/17.46  % SZS output start Proof for theBenchmark
% 79.65/17.47  Assumptions after simplification:
% 79.65/17.47  ---------------------------------
% 79.65/17.47  
% 79.65/17.47    (rat_combined_problem_7)
% 79.65/17.50     ? [v0: int] : ( ~ (v0 = 0) & rat_$less(rat_413/25, rat_1203/50) = v0)
% 79.65/17.50  
% 79.65/17.50    (input)
% 80.29/17.59     ~ (rat_very_large = rat_very_small) &  ~ (rat_very_large = rat_1203/50) &  ~
% 80.29/17.59    (rat_very_large = rat_271/10) &  ~ (rat_very_large = rat_-76/25) &  ~
% 80.29/17.59    (rat_very_large = rat_76/25) &  ~ (rat_very_large = rat_413/25) &  ~
% 80.29/17.59    (rat_very_large = rat_-413/10) &  ~ (rat_very_large = rat_569/5) &  ~
% 80.29/17.59    (rat_very_large = rat_145/2) &  ~ (rat_very_large = rat_-2/5) &  ~
% 80.29/17.59    (rat_very_large = rat_0) &  ~ (rat_very_small = rat_1203/50) &  ~
% 80.29/17.59    (rat_very_small = rat_271/10) &  ~ (rat_very_small = rat_-76/25) &  ~
% 80.29/17.59    (rat_very_small = rat_76/25) &  ~ (rat_very_small = rat_413/25) &  ~
% 80.29/17.59    (rat_very_small = rat_-413/10) &  ~ (rat_very_small = rat_569/5) &  ~
% 80.29/17.59    (rat_very_small = rat_145/2) &  ~ (rat_very_small = rat_-2/5) &  ~
% 80.29/17.59    (rat_very_small = rat_0) &  ~ (rat_1203/50 = rat_271/10) &  ~ (rat_1203/50 =
% 80.29/17.59      rat_-76/25) &  ~ (rat_1203/50 = rat_76/25) &  ~ (rat_1203/50 = rat_413/25) &
% 80.29/17.59     ~ (rat_1203/50 = rat_-413/10) &  ~ (rat_1203/50 = rat_569/5) &  ~
% 80.29/17.59    (rat_1203/50 = rat_145/2) &  ~ (rat_1203/50 = rat_-2/5) &  ~ (rat_1203/50 =
% 80.29/17.59      rat_0) &  ~ (rat_271/10 = rat_-76/25) &  ~ (rat_271/10 = rat_76/25) &  ~
% 80.29/17.59    (rat_271/10 = rat_413/25) &  ~ (rat_271/10 = rat_-413/10) &  ~ (rat_271/10 =
% 80.29/17.59      rat_569/5) &  ~ (rat_271/10 = rat_145/2) &  ~ (rat_271/10 = rat_-2/5) &  ~
% 80.29/17.59    (rat_271/10 = rat_0) &  ~ (rat_-76/25 = rat_76/25) &  ~ (rat_-76/25 =
% 80.29/17.59      rat_413/25) &  ~ (rat_-76/25 = rat_-413/10) &  ~ (rat_-76/25 = rat_569/5) & 
% 80.29/17.59    ~ (rat_-76/25 = rat_145/2) &  ~ (rat_-76/25 = rat_-2/5) &  ~ (rat_-76/25 =
% 80.29/17.59      rat_0) &  ~ (rat_76/25 = rat_413/25) &  ~ (rat_76/25 = rat_-413/10) &  ~
% 80.29/17.59    (rat_76/25 = rat_569/5) &  ~ (rat_76/25 = rat_145/2) &  ~ (rat_76/25 =
% 80.29/17.59      rat_-2/5) &  ~ (rat_76/25 = rat_0) &  ~ (rat_413/25 = rat_-413/10) &  ~
% 80.29/17.59    (rat_413/25 = rat_569/5) &  ~ (rat_413/25 = rat_145/2) &  ~ (rat_413/25 =
% 80.29/17.59      rat_-2/5) &  ~ (rat_413/25 = rat_0) &  ~ (rat_-413/10 = rat_569/5) &  ~
% 80.29/17.59    (rat_-413/10 = rat_145/2) &  ~ (rat_-413/10 = rat_-2/5) &  ~ (rat_-413/10 =
% 80.29/17.59      rat_0) &  ~ (rat_569/5 = rat_145/2) &  ~ (rat_569/5 = rat_-2/5) &  ~
% 80.29/17.59    (rat_569/5 = rat_0) &  ~ (rat_145/2 = rat_-2/5) &  ~ (rat_145/2 = rat_0) &  ~
% 80.29/17.59    (rat_-2/5 = rat_0) & rat_$is_int(rat_1203/50) = 1 & rat_$is_int(rat_271/10) =
% 80.29/17.59    1 & rat_$is_int(rat_-76/25) = 1 & rat_$is_int(rat_76/25) = 1 &
% 80.29/17.59    rat_$is_int(rat_413/25) = 1 & rat_$is_int(rat_-413/10) = 1 &
% 80.29/17.59    rat_$is_int(rat_569/5) = 1 & rat_$is_int(rat_145/2) = 1 &
% 80.29/17.59    rat_$is_int(rat_-2/5) = 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_1203/50)
% 80.29/17.59    = 0 & rat_$is_rat(rat_271/10) = 0 & rat_$is_rat(rat_-76/25) = 0 &
% 80.29/17.59    rat_$is_rat(rat_76/25) = 0 & rat_$is_rat(rat_413/25) = 0 &
% 80.29/17.59    rat_$is_rat(rat_-413/10) = 0 & rat_$is_rat(rat_569/5) = 0 &
% 80.29/17.59    rat_$is_rat(rat_145/2) = 0 & rat_$is_rat(rat_-2/5) = 0 & rat_$is_rat(rat_0) =
% 80.29/17.59    0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-2/5) = rat_0 &
% 80.29/17.59    rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_-2/5) = rat_0 &
% 80.29/17.59    rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-2/5) = rat_0 &
% 80.29/17.59    rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1203/50) = 24 &
% 80.29/17.59    rat_$to_int(rat_271/10) = 27 & rat_$to_int(rat_-76/25) = -4 &
% 80.29/17.59    rat_$to_int(rat_76/25) = 3 & rat_$to_int(rat_413/25) = 16 &
% 80.29/17.59    rat_$to_int(rat_-413/10) = -42 & rat_$to_int(rat_569/5) = 113 &
% 80.29/17.59    rat_$to_int(rat_145/2) = 72 & rat_$to_int(rat_-2/5) = -1 & rat_$to_int(rat_0)
% 80.29/17.59    = 0 & rat_$to_rat(rat_1203/50) = rat_1203/50 & rat_$to_rat(rat_271/10) =
% 80.29/17.59    rat_271/10 & rat_$to_rat(rat_-76/25) = rat_-76/25 & rat_$to_rat(rat_76/25) =
% 80.29/17.59    rat_76/25 & rat_$to_rat(rat_413/25) = rat_413/25 & rat_$to_rat(rat_-413/10) =
% 80.29/17.59    rat_-413/10 & rat_$to_rat(rat_569/5) = rat_569/5 & rat_$to_rat(rat_145/2) =
% 80.29/17.59    rat_145/2 & rat_$to_rat(rat_-2/5) = rat_-2/5 & rat_$to_rat(rat_0) = rat_0 &
% 80.29/17.59    rat_$to_real(rat_1203/50) = real_1203/50 & rat_$to_real(rat_271/10) =
% 80.29/17.59    real_271/10 & rat_$to_real(rat_-76/25) = real_-76/25 & rat_$to_real(rat_76/25)
% 80.29/17.59    = real_76/25 & rat_$to_real(rat_413/25) = real_413/25 &
% 80.29/17.59    rat_$to_real(rat_-413/10) = real_-413/10 & rat_$to_real(rat_569/5) =
% 80.29/17.59    real_569/5 & rat_$to_real(rat_145/2) = real_145/2 & rat_$to_real(rat_-2/5) =
% 80.29/17.59    real_-2/5 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 &
% 80.29/17.59    rat_$quotient(rat_413/25, rat_-413/10) = rat_-2/5 & rat_$quotient(rat_413/25,
% 80.29/17.59      rat_-2/5) = rat_-413/10 & rat_$quotient(rat_0, rat_1203/50) = rat_0 &
% 80.29/17.59    rat_$quotient(rat_0, rat_271/10) = rat_0 & rat_$quotient(rat_0, rat_-76/25) =
% 80.29/17.59    rat_0 & rat_$quotient(rat_0, rat_76/25) = rat_0 & rat_$quotient(rat_0,
% 80.29/17.59      rat_413/25) = rat_0 & rat_$quotient(rat_0, rat_-413/10) = rat_0 &
% 80.29/17.59    rat_$quotient(rat_0, rat_569/5) = rat_0 & rat_$quotient(rat_0, rat_145/2) =
% 80.29/17.59    rat_0 & rat_$quotient(rat_0, rat_-2/5) = rat_0 & rat_$product(rat_1203/50,
% 80.29/17.59      rat_0) = rat_0 & rat_$product(rat_271/10, rat_0) = rat_0 &
% 80.29/17.59    rat_$product(rat_-76/25, rat_0) = rat_0 & rat_$product(rat_76/25, rat_0) =
% 80.29/17.59    rat_0 & rat_$product(rat_413/25, rat_0) = rat_0 & rat_$product(rat_-413/10,
% 80.29/17.59      rat_-2/5) = rat_413/25 & rat_$product(rat_-413/10, rat_0) = rat_0 &
% 80.29/17.59    rat_$product(rat_569/5, rat_0) = rat_0 & rat_$product(rat_145/2, rat_0) =
% 80.29/17.59    rat_0 & rat_$product(rat_-2/5, rat_-413/10) = rat_413/25 &
% 80.29/17.59    rat_$product(rat_-2/5, rat_0) = rat_0 & rat_$product(rat_0, rat_1203/50) =
% 80.29/17.59    rat_0 & rat_$product(rat_0, rat_271/10) = rat_0 & rat_$product(rat_0,
% 80.29/17.59      rat_-76/25) = rat_0 & rat_$product(rat_0, rat_76/25) = rat_0 &
% 80.29/17.59    rat_$product(rat_0, rat_413/25) = rat_0 & rat_$product(rat_0, rat_-413/10) =
% 80.29/17.59    rat_0 & rat_$product(rat_0, rat_569/5) = rat_0 & rat_$product(rat_0,
% 80.29/17.59      rat_145/2) = rat_0 & rat_$product(rat_0, rat_-2/5) = rat_0 &
% 80.29/17.59    rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_1203/50, rat_1203/50)
% 80.29/17.59    = rat_0 & rat_$difference(rat_1203/50, rat_271/10) = rat_-76/25 &
% 80.29/17.59    rat_$difference(rat_1203/50, rat_-76/25) = rat_271/10 &
% 80.29/17.59    rat_$difference(rat_1203/50, rat_0) = rat_1203/50 &
% 80.29/17.59    rat_$difference(rat_271/10, rat_1203/50) = rat_76/25 &
% 80.29/17.59    rat_$difference(rat_271/10, rat_271/10) = rat_0 & rat_$difference(rat_271/10,
% 80.29/17.59      rat_76/25) = rat_1203/50 & rat_$difference(rat_271/10, rat_0) = rat_271/10 &
% 80.29/17.59    rat_$difference(rat_-76/25, rat_-76/25) = rat_0 & rat_$difference(rat_-76/25,
% 80.29/17.59      rat_0) = rat_-76/25 & rat_$difference(rat_76/25, rat_76/25) = rat_0 &
% 80.29/17.59    rat_$difference(rat_76/25, rat_0) = rat_76/25 & rat_$difference(rat_413/25,
% 80.29/17.59      rat_413/25) = rat_0 & rat_$difference(rat_413/25, rat_0) = rat_413/25 &
% 80.29/17.59    rat_$difference(rat_-413/10, rat_-413/10) = rat_0 &
% 80.29/17.59    rat_$difference(rat_-413/10, rat_0) = rat_-413/10 & rat_$difference(rat_569/5,
% 80.29/17.59      rat_569/5) = rat_0 & rat_$difference(rat_569/5, rat_0) = rat_569/5 &
% 80.29/17.59    rat_$difference(rat_145/2, rat_-413/10) = rat_569/5 &
% 80.29/17.59    rat_$difference(rat_145/2, rat_569/5) = rat_-413/10 &
% 80.29/17.59    rat_$difference(rat_145/2, rat_145/2) = rat_0 & rat_$difference(rat_145/2,
% 80.29/17.59      rat_0) = rat_145/2 & rat_$difference(rat_-2/5, rat_-2/5) = rat_0 &
% 80.29/17.59    rat_$difference(rat_-2/5, rat_0) = rat_-2/5 & rat_$difference(rat_0,
% 80.29/17.59      rat_-76/25) = rat_76/25 & rat_$difference(rat_0, rat_76/25) = rat_-76/25 &
% 80.29/17.59    rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_-76/25) = rat_76/25 &
% 80.29/17.59    rat_$uminus(rat_76/25) = rat_-76/25 & rat_$uminus(rat_0) = rat_0 &
% 80.29/17.59    rat_$sum(rat_1203/50, rat_76/25) = rat_271/10 & rat_$sum(rat_1203/50, rat_0) =
% 80.29/17.59    rat_1203/50 & rat_$sum(rat_271/10, rat_-76/25) = rat_1203/50 &
% 80.29/17.59    rat_$sum(rat_271/10, rat_0) = rat_271/10 & rat_$sum(rat_-76/25, rat_271/10) =
% 80.29/17.59    rat_1203/50 & rat_$sum(rat_-76/25, rat_76/25) = rat_0 & rat_$sum(rat_-76/25,
% 80.29/17.59      rat_0) = rat_-76/25 & rat_$sum(rat_76/25, rat_1203/50) = rat_271/10 &
% 80.29/17.59    rat_$sum(rat_76/25, rat_-76/25) = rat_0 & rat_$sum(rat_76/25, rat_0) =
% 80.29/17.59    rat_76/25 & rat_$sum(rat_413/25, rat_0) = rat_413/25 & rat_$sum(rat_-413/10,
% 80.29/17.59      rat_569/5) = rat_145/2 & rat_$sum(rat_-413/10, rat_0) = rat_-413/10 &
% 80.29/17.59    rat_$sum(rat_569/5, rat_-413/10) = rat_145/2 & rat_$sum(rat_569/5, rat_0) =
% 80.29/17.59    rat_569/5 & rat_$sum(rat_145/2, rat_0) = rat_145/2 & rat_$sum(rat_-2/5, rat_0)
% 80.29/17.59    = rat_-2/5 & rat_$sum(rat_0, rat_1203/50) = rat_1203/50 & rat_$sum(rat_0,
% 80.29/17.59      rat_271/10) = rat_271/10 & rat_$sum(rat_0, rat_-76/25) = rat_-76/25 &
% 80.29/17.59    rat_$sum(rat_0, rat_76/25) = rat_76/25 & rat_$sum(rat_0, rat_413/25) =
% 80.29/17.59    rat_413/25 & rat_$sum(rat_0, rat_-413/10) = rat_-413/10 & rat_$sum(rat_0,
% 80.29/17.59      rat_569/5) = rat_569/5 & rat_$sum(rat_0, rat_145/2) = rat_145/2 &
% 80.29/17.59    rat_$sum(rat_0, rat_-2/5) = rat_-2/5 & rat_$sum(rat_0, rat_0) = rat_0 &
% 80.29/17.59    rat_$greatereq(rat_very_small, rat_very_large) = 1 &
% 80.29/17.59    rat_$greatereq(rat_1203/50, rat_1203/50) = 0 & rat_$greatereq(rat_1203/50,
% 80.29/17.59      rat_271/10) = 1 & rat_$greatereq(rat_1203/50, rat_-76/25) = 0 &
% 80.29/17.59    rat_$greatereq(rat_1203/50, rat_76/25) = 0 & rat_$greatereq(rat_1203/50,
% 80.29/17.59      rat_413/25) = 0 & rat_$greatereq(rat_1203/50, rat_-413/10) = 0 &
% 80.29/17.59    rat_$greatereq(rat_1203/50, rat_569/5) = 1 & rat_$greatereq(rat_1203/50,
% 80.29/17.59      rat_145/2) = 1 & rat_$greatereq(rat_1203/50, rat_-2/5) = 0 &
% 80.29/17.59    rat_$greatereq(rat_1203/50, rat_0) = 0 & rat_$greatereq(rat_271/10,
% 80.29/17.59      rat_1203/50) = 0 & rat_$greatereq(rat_271/10, rat_271/10) = 0 &
% 80.29/17.59    rat_$greatereq(rat_271/10, rat_-76/25) = 0 & rat_$greatereq(rat_271/10,
% 80.29/17.59      rat_76/25) = 0 & rat_$greatereq(rat_271/10, rat_413/25) = 0 &
% 80.29/17.59    rat_$greatereq(rat_271/10, rat_-413/10) = 0 & rat_$greatereq(rat_271/10,
% 80.29/17.59      rat_569/5) = 1 & rat_$greatereq(rat_271/10, rat_145/2) = 1 &
% 80.29/17.60    rat_$greatereq(rat_271/10, rat_-2/5) = 0 & rat_$greatereq(rat_271/10, rat_0) =
% 80.29/17.60    0 & rat_$greatereq(rat_-76/25, rat_1203/50) = 1 & rat_$greatereq(rat_-76/25,
% 80.29/17.60      rat_271/10) = 1 & rat_$greatereq(rat_-76/25, rat_-76/25) = 0 &
% 80.29/17.60    rat_$greatereq(rat_-76/25, rat_76/25) = 1 & rat_$greatereq(rat_-76/25,
% 80.29/17.60      rat_413/25) = 1 & rat_$greatereq(rat_-76/25, rat_-413/10) = 0 &
% 80.29/17.60    rat_$greatereq(rat_-76/25, rat_569/5) = 1 & rat_$greatereq(rat_-76/25,
% 80.29/17.60      rat_145/2) = 1 & rat_$greatereq(rat_-76/25, rat_-2/5) = 1 &
% 80.29/17.60    rat_$greatereq(rat_-76/25, rat_0) = 1 & rat_$greatereq(rat_76/25, rat_1203/50)
% 80.29/17.60    = 1 & rat_$greatereq(rat_76/25, rat_271/10) = 1 & rat_$greatereq(rat_76/25,
% 80.29/17.60      rat_-76/25) = 0 & rat_$greatereq(rat_76/25, rat_76/25) = 0 &
% 80.29/17.60    rat_$greatereq(rat_76/25, rat_413/25) = 1 & rat_$greatereq(rat_76/25,
% 80.29/17.60      rat_-413/10) = 0 & rat_$greatereq(rat_76/25, rat_569/5) = 1 &
% 80.29/17.60    rat_$greatereq(rat_76/25, rat_145/2) = 1 & rat_$greatereq(rat_76/25, rat_-2/5)
% 80.29/17.60    = 0 & rat_$greatereq(rat_76/25, rat_0) = 0 & rat_$greatereq(rat_413/25,
% 80.29/17.60      rat_1203/50) = 1 & rat_$greatereq(rat_413/25, rat_271/10) = 1 &
% 80.29/17.60    rat_$greatereq(rat_413/25, rat_-76/25) = 0 & rat_$greatereq(rat_413/25,
% 80.29/17.60      rat_76/25) = 0 & rat_$greatereq(rat_413/25, rat_413/25) = 0 &
% 80.29/17.60    rat_$greatereq(rat_413/25, rat_-413/10) = 0 & rat_$greatereq(rat_413/25,
% 80.29/17.60      rat_569/5) = 1 & rat_$greatereq(rat_413/25, rat_145/2) = 1 &
% 80.29/17.60    rat_$greatereq(rat_413/25, rat_-2/5) = 0 & rat_$greatereq(rat_413/25, rat_0) =
% 80.29/17.60    0 & rat_$greatereq(rat_-413/10, rat_1203/50) = 1 & rat_$greatereq(rat_-413/10,
% 80.29/17.60      rat_271/10) = 1 & rat_$greatereq(rat_-413/10, rat_-76/25) = 1 &
% 80.29/17.60    rat_$greatereq(rat_-413/10, rat_76/25) = 1 & rat_$greatereq(rat_-413/10,
% 80.29/17.60      rat_413/25) = 1 & rat_$greatereq(rat_-413/10, rat_-413/10) = 0 &
% 80.29/17.60    rat_$greatereq(rat_-413/10, rat_569/5) = 1 & rat_$greatereq(rat_-413/10,
% 80.29/17.60      rat_145/2) = 1 & rat_$greatereq(rat_-413/10, rat_-2/5) = 1 &
% 80.29/17.60    rat_$greatereq(rat_-413/10, rat_0) = 1 & rat_$greatereq(rat_569/5,
% 80.29/17.60      rat_1203/50) = 0 & rat_$greatereq(rat_569/5, rat_271/10) = 0 &
% 80.29/17.60    rat_$greatereq(rat_569/5, rat_-76/25) = 0 & rat_$greatereq(rat_569/5,
% 80.29/17.60      rat_76/25) = 0 & rat_$greatereq(rat_569/5, rat_413/25) = 0 &
% 80.29/17.60    rat_$greatereq(rat_569/5, rat_-413/10) = 0 & rat_$greatereq(rat_569/5,
% 80.29/17.60      rat_569/5) = 0 & rat_$greatereq(rat_569/5, rat_145/2) = 0 &
% 80.29/17.60    rat_$greatereq(rat_569/5, rat_-2/5) = 0 & rat_$greatereq(rat_569/5, rat_0) = 0
% 80.29/17.60    & rat_$greatereq(rat_145/2, rat_1203/50) = 0 & rat_$greatereq(rat_145/2,
% 80.29/17.60      rat_271/10) = 0 & rat_$greatereq(rat_145/2, rat_-76/25) = 0 &
% 80.29/17.60    rat_$greatereq(rat_145/2, rat_76/25) = 0 & rat_$greatereq(rat_145/2,
% 80.29/17.60      rat_413/25) = 0 & rat_$greatereq(rat_145/2, rat_-413/10) = 0 &
% 80.29/17.60    rat_$greatereq(rat_145/2, rat_569/5) = 1 & rat_$greatereq(rat_145/2,
% 80.29/17.60      rat_145/2) = 0 & rat_$greatereq(rat_145/2, rat_-2/5) = 0 &
% 80.29/17.60    rat_$greatereq(rat_145/2, rat_0) = 0 & rat_$greatereq(rat_-2/5, rat_1203/50) =
% 80.29/17.60    1 & rat_$greatereq(rat_-2/5, rat_271/10) = 1 & rat_$greatereq(rat_-2/5,
% 80.29/17.60      rat_-76/25) = 0 & rat_$greatereq(rat_-2/5, rat_76/25) = 1 &
% 80.29/17.60    rat_$greatereq(rat_-2/5, rat_413/25) = 1 & rat_$greatereq(rat_-2/5,
% 80.29/17.60      rat_-413/10) = 0 & rat_$greatereq(rat_-2/5, rat_569/5) = 1 &
% 80.29/17.60    rat_$greatereq(rat_-2/5, rat_145/2) = 1 & rat_$greatereq(rat_-2/5, rat_-2/5) =
% 80.29/17.60    0 & rat_$greatereq(rat_-2/5, rat_0) = 1 & rat_$greatereq(rat_0, rat_1203/50) =
% 80.29/17.60    1 & rat_$greatereq(rat_0, rat_271/10) = 1 & rat_$greatereq(rat_0, rat_-76/25)
% 80.29/17.60    = 0 & rat_$greatereq(rat_0, rat_76/25) = 1 & rat_$greatereq(rat_0, rat_413/25)
% 80.29/17.60    = 1 & rat_$greatereq(rat_0, rat_-413/10) = 0 & rat_$greatereq(rat_0,
% 80.29/17.60      rat_569/5) = 1 & rat_$greatereq(rat_0, rat_145/2) = 1 &
% 80.29/17.60    rat_$greatereq(rat_0, rat_-2/5) = 0 & rat_$greatereq(rat_0, rat_0) = 0 &
% 80.29/17.60    rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_1203/50,
% 80.29/17.60      rat_1203/50) = 0 & rat_$lesseq(rat_1203/50, rat_271/10) = 0 &
% 80.29/17.60    rat_$lesseq(rat_1203/50, rat_-76/25) = 1 & rat_$lesseq(rat_1203/50, rat_76/25)
% 80.29/17.60    = 1 & rat_$lesseq(rat_1203/50, rat_413/25) = 1 & rat_$lesseq(rat_1203/50,
% 80.29/17.60      rat_-413/10) = 1 & rat_$lesseq(rat_1203/50, rat_569/5) = 0 &
% 80.29/17.60    rat_$lesseq(rat_1203/50, rat_145/2) = 0 & rat_$lesseq(rat_1203/50, rat_-2/5) =
% 80.29/17.60    1 & rat_$lesseq(rat_1203/50, rat_0) = 1 & rat_$lesseq(rat_271/10, rat_1203/50)
% 80.29/17.60    = 1 & rat_$lesseq(rat_271/10, rat_271/10) = 0 & rat_$lesseq(rat_271/10,
% 80.29/17.60      rat_-76/25) = 1 & rat_$lesseq(rat_271/10, rat_76/25) = 1 &
% 80.29/17.60    rat_$lesseq(rat_271/10, rat_413/25) = 1 & rat_$lesseq(rat_271/10, rat_-413/10)
% 80.29/17.60    = 1 & rat_$lesseq(rat_271/10, rat_569/5) = 0 & rat_$lesseq(rat_271/10,
% 80.29/17.60      rat_145/2) = 0 & rat_$lesseq(rat_271/10, rat_-2/5) = 1 &
% 80.29/17.60    rat_$lesseq(rat_271/10, rat_0) = 1 & rat_$lesseq(rat_-76/25, rat_1203/50) = 0
% 80.29/17.60    & rat_$lesseq(rat_-76/25, rat_271/10) = 0 & rat_$lesseq(rat_-76/25,
% 80.29/17.60      rat_-76/25) = 0 & rat_$lesseq(rat_-76/25, rat_76/25) = 0 &
% 80.29/17.60    rat_$lesseq(rat_-76/25, rat_413/25) = 0 & rat_$lesseq(rat_-76/25, rat_-413/10)
% 80.29/17.60    = 1 & rat_$lesseq(rat_-76/25, rat_569/5) = 0 & rat_$lesseq(rat_-76/25,
% 80.29/17.60      rat_145/2) = 0 & rat_$lesseq(rat_-76/25, rat_-2/5) = 0 &
% 80.29/17.60    rat_$lesseq(rat_-76/25, rat_0) = 0 & rat_$lesseq(rat_76/25, rat_1203/50) = 0 &
% 80.29/17.60    rat_$lesseq(rat_76/25, rat_271/10) = 0 & rat_$lesseq(rat_76/25, rat_-76/25) =
% 80.29/17.60    1 & rat_$lesseq(rat_76/25, rat_76/25) = 0 & rat_$lesseq(rat_76/25, rat_413/25)
% 80.29/17.60    = 0 & rat_$lesseq(rat_76/25, rat_-413/10) = 1 & rat_$lesseq(rat_76/25,
% 80.29/17.60      rat_569/5) = 0 & rat_$lesseq(rat_76/25, rat_145/2) = 0 &
% 80.29/17.60    rat_$lesseq(rat_76/25, rat_-2/5) = 1 & rat_$lesseq(rat_76/25, rat_0) = 1 &
% 80.29/17.60    rat_$lesseq(rat_413/25, rat_1203/50) = 0 & rat_$lesseq(rat_413/25, rat_271/10)
% 80.29/17.60    = 0 & rat_$lesseq(rat_413/25, rat_-76/25) = 1 & rat_$lesseq(rat_413/25,
% 80.29/17.60      rat_76/25) = 1 & rat_$lesseq(rat_413/25, rat_413/25) = 0 &
% 80.29/17.60    rat_$lesseq(rat_413/25, rat_-413/10) = 1 & rat_$lesseq(rat_413/25, rat_569/5)
% 80.29/17.60    = 0 & rat_$lesseq(rat_413/25, rat_145/2) = 0 & rat_$lesseq(rat_413/25,
% 80.29/17.60      rat_-2/5) = 1 & rat_$lesseq(rat_413/25, rat_0) = 1 &
% 80.29/17.60    rat_$lesseq(rat_-413/10, rat_1203/50) = 0 & rat_$lesseq(rat_-413/10,
% 80.29/17.60      rat_271/10) = 0 & rat_$lesseq(rat_-413/10, rat_-76/25) = 0 &
% 80.29/17.60    rat_$lesseq(rat_-413/10, rat_76/25) = 0 & rat_$lesseq(rat_-413/10, rat_413/25)
% 80.29/17.60    = 0 & rat_$lesseq(rat_-413/10, rat_-413/10) = 0 & rat_$lesseq(rat_-413/10,
% 80.29/17.60      rat_569/5) = 0 & rat_$lesseq(rat_-413/10, rat_145/2) = 0 &
% 80.29/17.60    rat_$lesseq(rat_-413/10, rat_-2/5) = 0 & rat_$lesseq(rat_-413/10, rat_0) = 0 &
% 80.29/17.60    rat_$lesseq(rat_569/5, rat_1203/50) = 1 & rat_$lesseq(rat_569/5, rat_271/10) =
% 80.29/17.60    1 & rat_$lesseq(rat_569/5, rat_-76/25) = 1 & rat_$lesseq(rat_569/5, rat_76/25)
% 80.29/17.60    = 1 & rat_$lesseq(rat_569/5, rat_413/25) = 1 & rat_$lesseq(rat_569/5,
% 80.29/17.60      rat_-413/10) = 1 & rat_$lesseq(rat_569/5, rat_569/5) = 0 &
% 80.29/17.60    rat_$lesseq(rat_569/5, rat_145/2) = 1 & rat_$lesseq(rat_569/5, rat_-2/5) = 1 &
% 80.29/17.60    rat_$lesseq(rat_569/5, rat_0) = 1 & rat_$lesseq(rat_145/2, rat_1203/50) = 1 &
% 80.29/17.60    rat_$lesseq(rat_145/2, rat_271/10) = 1 & rat_$lesseq(rat_145/2, rat_-76/25) =
% 80.29/17.60    1 & rat_$lesseq(rat_145/2, rat_76/25) = 1 & rat_$lesseq(rat_145/2, rat_413/25)
% 80.29/17.60    = 1 & rat_$lesseq(rat_145/2, rat_-413/10) = 1 & rat_$lesseq(rat_145/2,
% 80.29/17.60      rat_569/5) = 0 & rat_$lesseq(rat_145/2, rat_145/2) = 0 &
% 80.29/17.60    rat_$lesseq(rat_145/2, rat_-2/5) = 1 & rat_$lesseq(rat_145/2, rat_0) = 1 &
% 80.29/17.60    rat_$lesseq(rat_-2/5, rat_1203/50) = 0 & rat_$lesseq(rat_-2/5, rat_271/10) = 0
% 80.29/17.60    & rat_$lesseq(rat_-2/5, rat_-76/25) = 1 & rat_$lesseq(rat_-2/5, rat_76/25) = 0
% 80.29/17.60    & rat_$lesseq(rat_-2/5, rat_413/25) = 0 & rat_$lesseq(rat_-2/5, rat_-413/10) =
% 80.29/17.60    1 & rat_$lesseq(rat_-2/5, rat_569/5) = 0 & rat_$lesseq(rat_-2/5, rat_145/2) =
% 80.29/17.60    0 & rat_$lesseq(rat_-2/5, rat_-2/5) = 0 & rat_$lesseq(rat_-2/5, rat_0) = 0 &
% 80.29/17.60    rat_$lesseq(rat_0, rat_1203/50) = 0 & rat_$lesseq(rat_0, rat_271/10) = 0 &
% 80.29/17.60    rat_$lesseq(rat_0, rat_-76/25) = 1 & rat_$lesseq(rat_0, rat_76/25) = 0 &
% 80.29/17.60    rat_$lesseq(rat_0, rat_413/25) = 0 & rat_$lesseq(rat_0, rat_-413/10) = 1 &
% 80.29/17.60    rat_$lesseq(rat_0, rat_569/5) = 0 & rat_$lesseq(rat_0, rat_145/2) = 0 &
% 80.29/17.60    rat_$lesseq(rat_0, rat_-2/5) = 1 & rat_$lesseq(rat_0, rat_0) = 0 &
% 80.29/17.60    rat_$greater(rat_very_large, rat_1203/50) = 0 & rat_$greater(rat_very_large,
% 80.29/17.60      rat_271/10) = 0 & rat_$greater(rat_very_large, rat_-76/25) = 0 &
% 80.29/17.60    rat_$greater(rat_very_large, rat_76/25) = 0 & rat_$greater(rat_very_large,
% 80.29/17.60      rat_413/25) = 0 & rat_$greater(rat_very_large, rat_-413/10) = 0 &
% 80.29/17.60    rat_$greater(rat_very_large, rat_569/5) = 0 & rat_$greater(rat_very_large,
% 80.29/17.60      rat_145/2) = 0 & rat_$greater(rat_very_large, rat_-2/5) = 0 &
% 80.29/17.60    rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 80.29/17.60      rat_very_large) = 1 & rat_$greater(rat_1203/50, rat_very_small) = 0 &
% 80.29/17.60    rat_$greater(rat_1203/50, rat_1203/50) = 1 & rat_$greater(rat_1203/50,
% 80.29/17.60      rat_271/10) = 1 & rat_$greater(rat_1203/50, rat_-76/25) = 0 &
% 80.29/17.60    rat_$greater(rat_1203/50, rat_76/25) = 0 & rat_$greater(rat_1203/50,
% 80.29/17.60      rat_413/25) = 0 & rat_$greater(rat_1203/50, rat_-413/10) = 0 &
% 80.29/17.60    rat_$greater(rat_1203/50, rat_569/5) = 1 & rat_$greater(rat_1203/50,
% 80.29/17.60      rat_145/2) = 1 & rat_$greater(rat_1203/50, rat_-2/5) = 0 &
% 80.29/17.60    rat_$greater(rat_1203/50, rat_0) = 0 & rat_$greater(rat_271/10,
% 80.29/17.60      rat_very_small) = 0 & rat_$greater(rat_271/10, rat_1203/50) = 0 &
% 80.29/17.60    rat_$greater(rat_271/10, rat_271/10) = 1 & rat_$greater(rat_271/10,
% 80.29/17.60      rat_-76/25) = 0 & rat_$greater(rat_271/10, rat_76/25) = 0 &
% 80.29/17.60    rat_$greater(rat_271/10, rat_413/25) = 0 & rat_$greater(rat_271/10,
% 80.29/17.60      rat_-413/10) = 0 & rat_$greater(rat_271/10, rat_569/5) = 1 &
% 80.29/17.60    rat_$greater(rat_271/10, rat_145/2) = 1 & rat_$greater(rat_271/10, rat_-2/5) =
% 80.29/17.60    0 & rat_$greater(rat_271/10, rat_0) = 0 & rat_$greater(rat_-76/25,
% 80.29/17.60      rat_very_small) = 0 & rat_$greater(rat_-76/25, rat_1203/50) = 1 &
% 80.29/17.60    rat_$greater(rat_-76/25, rat_271/10) = 1 & rat_$greater(rat_-76/25,
% 80.29/17.60      rat_-76/25) = 1 & rat_$greater(rat_-76/25, rat_76/25) = 1 &
% 80.29/17.60    rat_$greater(rat_-76/25, rat_413/25) = 1 & rat_$greater(rat_-76/25,
% 80.29/17.60      rat_-413/10) = 0 & rat_$greater(rat_-76/25, rat_569/5) = 1 &
% 80.29/17.60    rat_$greater(rat_-76/25, rat_145/2) = 1 & rat_$greater(rat_-76/25, rat_-2/5) =
% 80.29/17.60    1 & rat_$greater(rat_-76/25, rat_0) = 1 & rat_$greater(rat_76/25,
% 80.29/17.60      rat_very_small) = 0 & rat_$greater(rat_76/25, rat_1203/50) = 1 &
% 80.29/17.61    rat_$greater(rat_76/25, rat_271/10) = 1 & rat_$greater(rat_76/25, rat_-76/25)
% 80.29/17.61    = 0 & rat_$greater(rat_76/25, rat_76/25) = 1 & rat_$greater(rat_76/25,
% 80.29/17.61      rat_413/25) = 1 & rat_$greater(rat_76/25, rat_-413/10) = 0 &
% 80.29/17.61    rat_$greater(rat_76/25, rat_569/5) = 1 & rat_$greater(rat_76/25, rat_145/2) =
% 80.29/17.61    1 & rat_$greater(rat_76/25, rat_-2/5) = 0 & rat_$greater(rat_76/25, rat_0) = 0
% 80.29/17.61    & rat_$greater(rat_413/25, rat_very_small) = 0 & rat_$greater(rat_413/25,
% 80.29/17.61      rat_1203/50) = 1 & rat_$greater(rat_413/25, rat_271/10) = 1 &
% 80.29/17.61    rat_$greater(rat_413/25, rat_-76/25) = 0 & rat_$greater(rat_413/25, rat_76/25)
% 80.29/17.61    = 0 & rat_$greater(rat_413/25, rat_413/25) = 1 & rat_$greater(rat_413/25,
% 80.29/17.61      rat_-413/10) = 0 & rat_$greater(rat_413/25, rat_569/5) = 1 &
% 80.29/17.61    rat_$greater(rat_413/25, rat_145/2) = 1 & rat_$greater(rat_413/25, rat_-2/5) =
% 80.29/17.61    0 & rat_$greater(rat_413/25, rat_0) = 0 & rat_$greater(rat_-413/10,
% 80.29/17.61      rat_very_small) = 0 & rat_$greater(rat_-413/10, rat_1203/50) = 1 &
% 80.29/17.61    rat_$greater(rat_-413/10, rat_271/10) = 1 & rat_$greater(rat_-413/10,
% 80.29/17.61      rat_-76/25) = 1 & rat_$greater(rat_-413/10, rat_76/25) = 1 &
% 80.29/17.61    rat_$greater(rat_-413/10, rat_413/25) = 1 & rat_$greater(rat_-413/10,
% 80.29/17.61      rat_-413/10) = 1 & rat_$greater(rat_-413/10, rat_569/5) = 1 &
% 80.29/17.61    rat_$greater(rat_-413/10, rat_145/2) = 1 & rat_$greater(rat_-413/10, rat_-2/5)
% 80.29/17.61    = 1 & rat_$greater(rat_-413/10, rat_0) = 1 & rat_$greater(rat_569/5,
% 80.29/17.61      rat_very_small) = 0 & rat_$greater(rat_569/5, rat_1203/50) = 0 &
% 80.29/17.61    rat_$greater(rat_569/5, rat_271/10) = 0 & rat_$greater(rat_569/5, rat_-76/25)
% 80.29/17.61    = 0 & rat_$greater(rat_569/5, rat_76/25) = 0 & rat_$greater(rat_569/5,
% 80.29/17.61      rat_413/25) = 0 & rat_$greater(rat_569/5, rat_-413/10) = 0 &
% 80.29/17.61    rat_$greater(rat_569/5, rat_569/5) = 1 & rat_$greater(rat_569/5, rat_145/2) =
% 80.29/17.61    0 & rat_$greater(rat_569/5, rat_-2/5) = 0 & rat_$greater(rat_569/5, rat_0) = 0
% 80.29/17.61    & rat_$greater(rat_145/2, rat_very_small) = 0 & rat_$greater(rat_145/2,
% 80.29/17.61      rat_1203/50) = 0 & rat_$greater(rat_145/2, rat_271/10) = 0 &
% 80.29/17.61    rat_$greater(rat_145/2, rat_-76/25) = 0 & rat_$greater(rat_145/2, rat_76/25) =
% 80.29/17.61    0 & rat_$greater(rat_145/2, rat_413/25) = 0 & rat_$greater(rat_145/2,
% 80.29/17.61      rat_-413/10) = 0 & rat_$greater(rat_145/2, rat_569/5) = 1 &
% 80.29/17.61    rat_$greater(rat_145/2, rat_145/2) = 1 & rat_$greater(rat_145/2, rat_-2/5) = 0
% 80.29/17.61    & rat_$greater(rat_145/2, rat_0) = 0 & rat_$greater(rat_-2/5, rat_very_small)
% 80.29/17.61    = 0 & rat_$greater(rat_-2/5, rat_1203/50) = 1 & rat_$greater(rat_-2/5,
% 80.29/17.61      rat_271/10) = 1 & rat_$greater(rat_-2/5, rat_-76/25) = 0 &
% 80.29/17.61    rat_$greater(rat_-2/5, rat_76/25) = 1 & rat_$greater(rat_-2/5, rat_413/25) = 1
% 80.29/17.61    & rat_$greater(rat_-2/5, rat_-413/10) = 0 & rat_$greater(rat_-2/5, rat_569/5)
% 80.29/17.61    = 1 & rat_$greater(rat_-2/5, rat_145/2) = 1 & rat_$greater(rat_-2/5, rat_-2/5)
% 80.29/17.61    = 1 & rat_$greater(rat_-2/5, rat_0) = 1 & rat_$greater(rat_0, rat_very_small)
% 80.29/17.61    = 0 & rat_$greater(rat_0, rat_1203/50) = 1 & rat_$greater(rat_0, rat_271/10) =
% 80.29/17.61    1 & rat_$greater(rat_0, rat_-76/25) = 0 & rat_$greater(rat_0, rat_76/25) = 1 &
% 80.29/17.61    rat_$greater(rat_0, rat_413/25) = 1 & rat_$greater(rat_0, rat_-413/10) = 0 &
% 80.29/17.61    rat_$greater(rat_0, rat_569/5) = 1 & rat_$greater(rat_0, rat_145/2) = 1 &
% 80.29/17.61    rat_$greater(rat_0, rat_-2/5) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 80.29/17.61    rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 80.29/17.61      rat_1203/50) = 0 & rat_$less(rat_very_small, rat_271/10) = 0 &
% 80.29/17.61    rat_$less(rat_very_small, rat_-76/25) = 0 & rat_$less(rat_very_small,
% 80.29/17.61      rat_76/25) = 0 & rat_$less(rat_very_small, rat_413/25) = 0 &
% 80.29/17.61    rat_$less(rat_very_small, rat_-413/10) = 0 & rat_$less(rat_very_small,
% 80.29/17.61      rat_569/5) = 0 & rat_$less(rat_very_small, rat_145/2) = 0 &
% 80.29/17.61    rat_$less(rat_very_small, rat_-2/5) = 0 & rat_$less(rat_very_small, rat_0) = 0
% 80.29/17.61    & rat_$less(rat_1203/50, rat_very_large) = 0 & rat_$less(rat_1203/50,
% 80.29/17.61      rat_1203/50) = 1 & rat_$less(rat_1203/50, rat_271/10) = 0 &
% 80.29/17.61    rat_$less(rat_1203/50, rat_-76/25) = 1 & rat_$less(rat_1203/50, rat_76/25) = 1
% 80.29/17.61    & rat_$less(rat_1203/50, rat_413/25) = 1 & rat_$less(rat_1203/50, rat_-413/10)
% 80.29/17.61    = 1 & rat_$less(rat_1203/50, rat_569/5) = 0 & rat_$less(rat_1203/50,
% 80.29/17.61      rat_145/2) = 0 & rat_$less(rat_1203/50, rat_-2/5) = 1 &
% 80.29/17.61    rat_$less(rat_1203/50, rat_0) = 1 & rat_$less(rat_271/10, rat_very_large) = 0
% 80.29/17.61    & rat_$less(rat_271/10, rat_1203/50) = 1 & rat_$less(rat_271/10, rat_271/10) =
% 80.29/17.61    1 & rat_$less(rat_271/10, rat_-76/25) = 1 & rat_$less(rat_271/10, rat_76/25) =
% 80.29/17.61    1 & rat_$less(rat_271/10, rat_413/25) = 1 & rat_$less(rat_271/10, rat_-413/10)
% 80.29/17.61    = 1 & rat_$less(rat_271/10, rat_569/5) = 0 & rat_$less(rat_271/10, rat_145/2)
% 80.29/17.61    = 0 & rat_$less(rat_271/10, rat_-2/5) = 1 & rat_$less(rat_271/10, rat_0) = 1 &
% 80.29/17.61    rat_$less(rat_-76/25, rat_very_large) = 0 & rat_$less(rat_-76/25, rat_1203/50)
% 80.29/17.61    = 0 & rat_$less(rat_-76/25, rat_271/10) = 0 & rat_$less(rat_-76/25,
% 80.29/17.61      rat_-76/25) = 1 & rat_$less(rat_-76/25, rat_76/25) = 0 &
% 80.29/17.61    rat_$less(rat_-76/25, rat_413/25) = 0 & rat_$less(rat_-76/25, rat_-413/10) = 1
% 80.29/17.61    & rat_$less(rat_-76/25, rat_569/5) = 0 & rat_$less(rat_-76/25, rat_145/2) = 0
% 80.29/17.61    & rat_$less(rat_-76/25, rat_-2/5) = 0 & rat_$less(rat_-76/25, rat_0) = 0 &
% 80.29/17.61    rat_$less(rat_76/25, rat_very_large) = 0 & rat_$less(rat_76/25, rat_1203/50) =
% 80.29/17.61    0 & rat_$less(rat_76/25, rat_271/10) = 0 & rat_$less(rat_76/25, rat_-76/25) =
% 80.29/17.61    1 & rat_$less(rat_76/25, rat_76/25) = 1 & rat_$less(rat_76/25, rat_413/25) = 0
% 80.29/17.61    & rat_$less(rat_76/25, rat_-413/10) = 1 & rat_$less(rat_76/25, rat_569/5) = 0
% 80.29/17.61    & rat_$less(rat_76/25, rat_145/2) = 0 & rat_$less(rat_76/25, rat_-2/5) = 1 &
% 80.29/17.61    rat_$less(rat_76/25, rat_0) = 1 & rat_$less(rat_413/25, rat_very_large) = 0 &
% 80.29/17.61    rat_$less(rat_413/25, rat_1203/50) = 0 & rat_$less(rat_413/25, rat_271/10) = 0
% 80.29/17.61    & rat_$less(rat_413/25, rat_-76/25) = 1 & rat_$less(rat_413/25, rat_76/25) = 1
% 80.29/17.61    & rat_$less(rat_413/25, rat_413/25) = 1 & rat_$less(rat_413/25, rat_-413/10) =
% 80.29/17.61    1 & rat_$less(rat_413/25, rat_569/5) = 0 & rat_$less(rat_413/25, rat_145/2) =
% 80.29/17.61    0 & rat_$less(rat_413/25, rat_-2/5) = 1 & rat_$less(rat_413/25, rat_0) = 1 &
% 80.29/17.61    rat_$less(rat_-413/10, rat_very_large) = 0 & rat_$less(rat_-413/10,
% 80.29/17.61      rat_1203/50) = 0 & rat_$less(rat_-413/10, rat_271/10) = 0 &
% 80.29/17.61    rat_$less(rat_-413/10, rat_-76/25) = 0 & rat_$less(rat_-413/10, rat_76/25) = 0
% 80.29/17.61    & rat_$less(rat_-413/10, rat_413/25) = 0 & rat_$less(rat_-413/10, rat_-413/10)
% 80.29/17.61    = 1 & rat_$less(rat_-413/10, rat_569/5) = 0 & rat_$less(rat_-413/10,
% 80.29/17.61      rat_145/2) = 0 & rat_$less(rat_-413/10, rat_-2/5) = 0 &
% 80.29/17.61    rat_$less(rat_-413/10, rat_0) = 0 & rat_$less(rat_569/5, rat_very_large) = 0 &
% 80.29/17.61    rat_$less(rat_569/5, rat_1203/50) = 1 & rat_$less(rat_569/5, rat_271/10) = 1 &
% 80.29/17.61    rat_$less(rat_569/5, rat_-76/25) = 1 & rat_$less(rat_569/5, rat_76/25) = 1 &
% 80.29/17.61    rat_$less(rat_569/5, rat_413/25) = 1 & rat_$less(rat_569/5, rat_-413/10) = 1 &
% 80.29/17.61    rat_$less(rat_569/5, rat_569/5) = 1 & rat_$less(rat_569/5, rat_145/2) = 1 &
% 80.29/17.61    rat_$less(rat_569/5, rat_-2/5) = 1 & rat_$less(rat_569/5, rat_0) = 1 &
% 80.29/17.61    rat_$less(rat_145/2, rat_very_large) = 0 & rat_$less(rat_145/2, rat_1203/50) =
% 80.29/17.61    1 & rat_$less(rat_145/2, rat_271/10) = 1 & rat_$less(rat_145/2, rat_-76/25) =
% 80.29/17.61    1 & rat_$less(rat_145/2, rat_76/25) = 1 & rat_$less(rat_145/2, rat_413/25) = 1
% 80.29/17.61    & rat_$less(rat_145/2, rat_-413/10) = 1 & rat_$less(rat_145/2, rat_569/5) = 0
% 80.29/17.61    & rat_$less(rat_145/2, rat_145/2) = 1 & rat_$less(rat_145/2, rat_-2/5) = 1 &
% 80.29/17.61    rat_$less(rat_145/2, rat_0) = 1 & rat_$less(rat_-2/5, rat_very_large) = 0 &
% 80.29/17.61    rat_$less(rat_-2/5, rat_1203/50) = 0 & rat_$less(rat_-2/5, rat_271/10) = 0 &
% 80.29/17.61    rat_$less(rat_-2/5, rat_-76/25) = 1 & rat_$less(rat_-2/5, rat_76/25) = 0 &
% 80.29/17.61    rat_$less(rat_-2/5, rat_413/25) = 0 & rat_$less(rat_-2/5, rat_-413/10) = 1 &
% 80.29/17.61    rat_$less(rat_-2/5, rat_569/5) = 0 & rat_$less(rat_-2/5, rat_145/2) = 0 &
% 80.29/17.61    rat_$less(rat_-2/5, rat_-2/5) = 1 & rat_$less(rat_-2/5, rat_0) = 0 &
% 80.29/17.61    rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_1203/50) = 0 &
% 80.29/17.61    rat_$less(rat_0, rat_271/10) = 0 & rat_$less(rat_0, rat_-76/25) = 1 &
% 80.29/17.61    rat_$less(rat_0, rat_76/25) = 0 & rat_$less(rat_0, rat_413/25) = 0 &
% 80.29/17.61    rat_$less(rat_0, rat_-413/10) = 1 & rat_$less(rat_0, rat_569/5) = 0 &
% 80.29/17.61    rat_$less(rat_0, rat_145/2) = 0 & rat_$less(rat_0, rat_-2/5) = 1 &
% 80.29/17.61    rat_$less(rat_0, rat_0) = 1 &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : 
% 80.29/17.61    ! [v3: $rat] :  ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) |  ~ (rat_$sum(v2,
% 80.29/17.61          v1) = v3) |  ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) =
% 80.29/17.61        v5)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] :  !
% 80.29/17.61    [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) |  ~ (rat_$sum(v1, v0) = v3) |  ?
% 80.29/17.61      [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5)) &  ! [v0:
% 80.29/17.61      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~
% 80.29/17.61      (rat_$lesseq(v2, v1) = 0) |  ~ (rat_$lesseq(v2, v0) = v3) |  ? [v4: int] : (
% 80.29/17.61        ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] : 
% 80.29/17.61    ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~ (rat_$lesseq(v2, v1) = 0) |  ~
% 80.29/17.61      (rat_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) =
% 80.29/17.61        v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3
% 80.29/17.61      = 0 |  ~ (rat_$lesseq(v2, v0) = v3) |  ~ (rat_$lesseq(v1, v0) = 0) |  ? [v4:
% 80.29/17.61        int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1:
% 80.29/17.61      $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~ (rat_$lesseq(v1, v0) =
% 80.29/17.61        0) |  ~ (rat_$less(v2, v0) = v3) |  ? [v4: int] : ( ~ (v4 = 0) &
% 80.29/17.61        rat_$less(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 80.29/17.61     ! [v3: int] : (v3 = 0 |  ~ (rat_$less(v2, v1) = 0) |  ~ (rat_$less(v2, v0) =
% 80.29/17.61        v3) |  ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) &  ! [v0:
% 80.29/17.61      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: int] : (v3 = 0 |  ~
% 80.29/17.61      (rat_$less(v2, v0) = v3) |  ~ (rat_$less(v1, v0) = 0) |  ? [v4: int] : ( ~
% 80.29/17.61        (v4 = 0) & rat_$lesseq(v2, v1) = v4)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 80.29/17.61    [v2: $rat] :  ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) |  ~ (rat_$sum(v1, v2)
% 80.29/17.61        = v3) | rat_$difference(v1, v0) = v3) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 80.29/17.61    [v2: int] : (v2 = 0 | v1 = v0 |  ~ (rat_$less(v1, v0) = v2) |  ? [v3: int] : (
% 80.29/17.61        ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] : 
% 80.29/17.61    ! [v2: int] : (v2 = 0 |  ~ (rat_$greatereq(v0, v1) = v2) |  ? [v3: int] : ( ~
% 80.29/17.61        (v3 = 0) & rat_$lesseq(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 80.29/17.61    [v2: int] : (v2 = 0 |  ~ (rat_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 80.29/17.61          0) & rat_$greatereq(v0, v1) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 80.29/17.61    [v2: int] : (v2 = 0 |  ~ (rat_$lesseq(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 =
% 80.29/17.61          0) & rat_$less(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 80.29/17.61      int] : (v2 = 0 |  ~ (rat_$greater(v0, v1) = v2) |  ? [v3: int] : ( ~ (v3 =
% 80.29/17.61          0) & rat_$less(v1, v0) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 80.29/17.61      int] : (v2 = 0 |  ~ (rat_$less(v1, v0) = v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 80.29/17.61        rat_$greater(v0, v1) = v3)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 80.29/17.61      $rat] : (v0 = rat_0 |  ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 80.29/17.61      = v1) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~
% 80.29/17.61      (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) &  ! [v0: $rat] : 
% 80.29/17.61    ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 80.29/17.61      rat_$product(v1, v0) = v2) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 80.29/17.61    ( ~ (rat_$difference(v1, v0) = v2) |  ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 80.29/17.61        rat_$sum(v1, v3) = v2)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 80.29/17.61    ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) &  ! [v0: $rat] :  ! [v1:
% 80.29/17.61      $rat] :  ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 80.29/17.61    &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) =
% 80.29/17.61        0) |  ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) &  ! [v0:
% 80.29/17.61      $rat] :  ! [v1: $rat] :  ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) |  ~
% 80.29/17.61      (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) &  ! [v0: $rat] :  ! [v1:
% 80.29/17.61      $rat] :  ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) |  ~ (rat_$less(v2,
% 80.29/17.61          v1) = 0) | rat_$less(v2, v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : (v1
% 80.29/17.61      = v0 |  ~ (rat_$sum(v0, rat_0) = v1)) &  ! [v0: $rat] :  ! [v1: $rat] : (v1
% 80.29/17.61      = v0 |  ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &  ! [v0: $rat]
% 80.29/17.61    :  ! [v1: int] : (v1 = 0 |  ~ (rat_$lesseq(v0, v0) = v1)) &  ! [v0: $rat] :  !
% 80.29/17.61    [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &  ! [v0:
% 80.29/17.61      $rat] :  ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) =
% 80.29/17.62      rat_0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) |
% 80.29/17.62      rat_$lesseq(v1, v0) = 0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~
% 80.29/17.62      (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) &  ! [v0: $rat] :  !
% 80.29/17.62    [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) &  ! [v0:
% 80.29/17.62      $rat] :  ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) =
% 80.29/17.62      0) &  ! [v0: $rat] :  ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 80.29/17.62      rat_$greater(v0, v1) = 0) &  ! [v0: $rat] :  ! [v1: MultipleValueBool] : ( ~
% 80.29/17.62      (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) &  ! [v0: $rat] : (v0 =
% 80.29/17.62      rat_0 |  ~ (rat_$uminus(v0) = v0))
% 80.29/17.62  
% 80.29/17.62    (function-axioms)
% 80.29/17.62     ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$quotient(v3, v2) = v1) |  ~ (rat_$quotient(v3, v2) = v0)) &  ! [v0:
% 80.29/17.62      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$product(v3, v2) = v1) |  ~ (rat_$product(v3, v2) = v0)) &  ! [v0:
% 80.29/17.62      $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$difference(v3, v2) = v1) |  ~ (rat_$difference(v3, v2) = v0)) &  !
% 80.29/17.62    [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$sum(v3, v2) = v1) |  ~ (rat_$sum(v3, v2) = v0)) &  ! [v0:
% 80.29/17.62      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 80.29/17.62      $rat] : (v1 = v0 |  ~ (rat_$greatereq(v3, v2) = v1) |  ~ (rat_$greatereq(v3,
% 80.29/17.62          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 80.29/17.62    ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$lesseq(v3, v2) = v1) |  ~
% 80.29/17.62      (rat_$lesseq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 80.29/17.62      MultipleValueBool] :  ! [v2: $rat] :  ! [v3: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$greater(v3, v2) = v1) |  ~ (rat_$greater(v3, v2) = v0)) &  ! [v0:
% 80.29/17.62      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] :  ! [v3:
% 80.29/17.62      $rat] : (v1 = v0 |  ~ (rat_$less(v3, v2) = v1) |  ~ (rat_$less(v3, v2) =
% 80.29/17.62        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 80.29/17.62      $rat] : (v1 = v0 |  ~ (rat_$is_int(v2) = v1) |  ~ (rat_$is_int(v2) = v0)) & 
% 80.29/17.62    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat] : (v1 =
% 80.29/17.62      v0 |  ~ (rat_$is_rat(v2) = v1) |  ~ (rat_$is_rat(v2) = v0)) &  ! [v0: $rat]
% 80.29/17.62    :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$floor(v2) = v1) |  ~
% 80.29/17.62      (rat_$floor(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1
% 80.29/17.62      = v0 |  ~ (rat_$ceiling(v2) = v1) |  ~ (rat_$ceiling(v2) = v0)) &  ! [v0:
% 80.29/17.62      $rat] :  ! [v1: $rat] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$truncate(v2) =
% 80.29/17.62        v1) |  ~ (rat_$truncate(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  !
% 80.29/17.62    [v2: $rat] : (v1 = v0 |  ~ (rat_$round(v2) = v1) |  ~ (rat_$round(v2) = v0)) &
% 80.29/17.62     ! [v0: int] :  ! [v1: int] :  ! [v2: $rat] : (v1 = v0 |  ~ (rat_$to_int(v2) =
% 80.29/17.62        v1) |  ~ (rat_$to_int(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2:
% 80.29/17.62      $rat] : (v1 = v0 |  ~ (rat_$to_rat(v2) = v1) |  ~ (rat_$to_rat(v2) = v0)) & 
% 80.29/17.62    ! [v0: $real] :  ! [v1: $real] :  ! [v2: $rat] : (v1 = v0 |  ~
% 80.29/17.62      (rat_$to_real(v2) = v1) |  ~ (rat_$to_real(v2) = v0)) &  ! [v0: $rat] :  !
% 80.29/17.62    [v1: $rat] :  ! [v2: int] : (v1 = v0 |  ~ (int_$to_rat(v2) = v1) |  ~
% 80.29/17.62      (int_$to_rat(v2) = v0)) &  ! [v0: $rat] :  ! [v1: $rat] :  ! [v2: $rat] :
% 80.29/17.62    (v1 = v0 |  ~ (rat_$uminus(v2) = v1) |  ~ (rat_$uminus(v2) = v0))
% 80.29/17.62  
% 80.29/17.62  Those formulas are unsatisfiable:
% 80.29/17.62  ---------------------------------
% 80.29/17.62  
% 80.29/17.62  Begin of proof
% 80.29/17.62  | 
% 80.29/17.62  | ALPHA: (function-axioms) implies:
% 80.29/17.62  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $rat]
% 80.29/17.62  |        :  ! [v3: $rat] : (v1 = v0 |  ~ (rat_$less(v3, v2) = v1) |  ~
% 80.29/17.62  |          (rat_$less(v3, v2) = v0))
% 80.29/17.63  | 
% 80.29/17.63  | ALPHA: (input) implies:
% 80.29/17.63  |   (2)  rat_$less(rat_413/25, rat_1203/50) = 0
% 80.29/17.63  | 
% 80.29/17.63  | DELTA: instantiating (rat_combined_problem_7) with fresh symbol all_5_0 gives:
% 80.29/17.63  |   (3)   ~ (all_5_0 = 0) & rat_$less(rat_413/25, rat_1203/50) = all_5_0
% 80.29/17.63  | 
% 80.29/17.63  | ALPHA: (3) implies:
% 80.29/17.63  |   (4)   ~ (all_5_0 = 0)
% 80.29/17.63  |   (5)  rat_$less(rat_413/25, rat_1203/50) = all_5_0
% 80.29/17.63  | 
% 80.29/17.63  | GROUND_INST: instantiating (1) with 0, all_5_0, rat_1203/50, rat_413/25,
% 80.29/17.63  |              simplifying with (2), (5) gives:
% 80.29/17.63  |   (6)  all_5_0 = 0
% 80.29/17.63  | 
% 80.29/17.63  | REDUCE: (4), (6) imply:
% 80.29/17.63  |   (7)  $false
% 80.29/17.63  | 
% 80.29/17.63  | CLOSE: (7) is inconsistent.
% 80.29/17.63  | 
% 80.29/17.63  End of proof
% 80.29/17.63  % SZS output end Proof for theBenchmark
% 80.29/17.63  
% 80.29/17.63  17051ms
%------------------------------------------------------------------------------