TSTP Solution File: ARI341_1 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------