TSTP Solution File: ARI526_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI526_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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:48:16 EDT 2023
% Result : Theorem 9.15s 1.97s
% Output : Proof 51.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI526_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 18:27:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 1.75/0.97 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.97 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.97 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.97 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.97 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.98 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.98 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.75/0.99 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.75/0.99 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.95/1.11 Prover 4: Preprocessing ...
% 2.95/1.12 Prover 1: Preprocessing ...
% 3.21/1.17 Prover 0: Preprocessing ...
% 3.21/1.17 Prover 6: Preprocessing ...
% 7.86/1.77 Prover 2: Preprocessing ...
% 7.86/1.78 Prover 3: Preprocessing ...
% 7.86/1.79 Prover 5: Preprocessing ...
% 9.15/1.95 Prover 6: Constructing countermodel ...
% 9.15/1.97 Prover 6: proved (1325ms)
% 9.15/1.97
% 9.15/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.15/1.97
% 9.15/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.15/1.98 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 9.15/1.99 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.78/2.03 Prover 0: Constructing countermodel ...
% 9.78/2.03 Prover 0: stopped
% 9.78/2.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.78/2.04 Prover 1: Constructing countermodel ...
% 9.78/2.04 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 9.78/2.05 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.78/2.06 Prover 8: Preprocessing ...
% 9.78/2.06 Prover 4: Constructing countermodel ...
% 12.08/2.39 Prover 7: Preprocessing ...
% 12.75/2.47 Prover 8: Warning: ignoring some quantifiers
% 12.75/2.50 Prover 8: Constructing countermodel ...
% 13.75/2.55 Prover 4: Found proof (size 7)
% 13.75/2.55 Prover 4: proved (1907ms)
% 13.75/2.55 Prover 1: Found proof (size 7)
% 13.75/2.55 Prover 1: proved (1912ms)
% 13.75/2.55 Prover 8: stopped
% 29.30/4.73 Prover 2: stopped
% 30.19/4.87 Prover 7: stopped
% 45.76/7.80 Prover 5: Constructing countermodel ...
% 45.76/7.81 Prover 5: stopped
% 50.80/11.41 Prover 3: Constructing countermodel ...
% 50.80/11.41 Prover 3: stopped
% 50.80/11.41
% 50.80/11.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.80/11.41
% 50.80/11.42 % SZS output start Proof for theBenchmark
% 50.80/11.42 Assumptions after simplification:
% 50.80/11.42 ---------------------------------
% 50.80/11.42
% 50.80/11.42 (mixed_types_problem_31)
% 51.09/11.47 ? [v0: int] : ( ~ (v0 = 5) & rat_$to_int(rat_5) = v0)
% 51.09/11.47
% 51.09/11.47 (input)
% 51.47/11.61 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_5) & ~
% 51.47/11.61 (real_very_large = real_53/20) & ~ (real_very_large = real_153/20) & ~
% 51.47/11.61 (real_very_large = real_18/5) & ~ (real_very_large = real_81/20) & ~
% 51.47/11.61 (real_very_large = real_0) & ~ (real_very_small = real_5) & ~
% 51.47/11.61 (real_very_small = real_53/20) & ~ (real_very_small = real_153/20) & ~
% 51.47/11.61 (real_very_small = real_18/5) & ~ (real_very_small = real_81/20) & ~
% 51.47/11.61 (real_very_small = real_0) & ~ (rat_very_large = rat_very_small) & ~
% 51.47/11.61 (rat_very_large = rat_5) & ~ (rat_very_large = rat_53/20) & ~
% 51.47/11.61 (rat_very_large = rat_153/20) & ~ (rat_very_large = rat_18/5) & ~
% 51.47/11.61 (rat_very_large = rat_81/20) & ~ (rat_very_large = rat_0) & ~
% 51.47/11.61 (rat_very_small = rat_5) & ~ (rat_very_small = rat_53/20) & ~
% 51.47/11.61 (rat_very_small = rat_153/20) & ~ (rat_very_small = rat_18/5) & ~
% 51.47/11.61 (rat_very_small = rat_81/20) & ~ (rat_very_small = rat_0) & ~ (real_5 =
% 51.47/11.61 real_53/20) & ~ (real_5 = real_153/20) & ~ (real_5 = real_18/5) & ~
% 51.47/11.61 (real_5 = real_81/20) & ~ (real_5 = real_0) & ~ (rat_5 = rat_53/20) & ~
% 51.47/11.61 (rat_5 = rat_153/20) & ~ (rat_5 = rat_18/5) & ~ (rat_5 = rat_81/20) & ~
% 51.47/11.61 (rat_5 = rat_0) & ~ (real_53/20 = real_153/20) & ~ (real_53/20 = real_18/5)
% 51.47/11.61 & ~ (real_53/20 = real_81/20) & ~ (real_53/20 = real_0) & ~ (rat_53/20 =
% 51.47/11.61 rat_153/20) & ~ (rat_53/20 = rat_18/5) & ~ (rat_53/20 = rat_81/20) & ~
% 51.47/11.61 (rat_53/20 = rat_0) & ~ (real_153/20 = real_18/5) & ~ (real_153/20 =
% 51.47/11.61 real_81/20) & ~ (real_153/20 = real_0) & ~ (rat_153/20 = rat_18/5) & ~
% 51.47/11.61 (rat_153/20 = rat_81/20) & ~ (rat_153/20 = rat_0) & ~ (real_18/5 =
% 51.47/11.61 real_81/20) & ~ (real_18/5 = real_0) & ~ (rat_18/5 = rat_81/20) & ~
% 51.47/11.61 (rat_18/5 = rat_0) & ~ (real_81/20 = real_0) & ~ (rat_81/20 = rat_0) &
% 51.47/11.61 rat_$is_int(rat_5) = 0 & rat_$is_int(rat_53/20) = 1 & rat_$is_int(rat_153/20)
% 51.47/11.61 = 1 & rat_$is_int(rat_18/5) = 1 & rat_$is_int(rat_81/20) = 1 &
% 51.47/11.62 rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_5) = 0 & rat_$is_rat(rat_53/20) = 0 &
% 51.47/11.62 rat_$is_rat(rat_153/20) = 0 & rat_$is_rat(rat_18/5) = 0 &
% 51.47/11.62 rat_$is_rat(rat_81/20) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_5) =
% 51.47/11.62 rat_5 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_5) = rat_5 &
% 51.47/11.62 rat_$ceiling(rat_81/20) = rat_5 & rat_$ceiling(rat_0) = rat_0 &
% 51.47/11.62 rat_$truncate(rat_5) = rat_5 & rat_$truncate(rat_0) = rat_0 &
% 51.47/11.62 rat_$round(rat_5) = rat_5 & rat_$round(rat_0) = rat_0 & rat_$to_rat(rat_5) =
% 51.47/11.62 rat_5 & rat_$to_rat(rat_53/20) = rat_53/20 & rat_$to_rat(rat_153/20) =
% 51.47/11.62 rat_153/20 & rat_$to_rat(rat_18/5) = rat_18/5 & rat_$to_rat(rat_81/20) =
% 51.47/11.62 rat_81/20 & rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_5) = real_5 &
% 51.47/11.62 rat_$to_real(rat_53/20) = real_53/20 & rat_$to_real(rat_153/20) = real_153/20
% 51.47/11.62 & rat_$to_real(rat_18/5) = real_18/5 & rat_$to_real(rat_81/20) = real_81/20 &
% 51.47/11.62 rat_$to_real(rat_0) = real_0 & int_$to_rat(5) = rat_5 & int_$to_rat(0) = rat_0
% 51.47/11.62 & real_$is_int(real_5) = 0 & real_$is_int(real_53/20) = 1 &
% 51.47/11.62 real_$is_int(real_153/20) = 1 & real_$is_int(real_18/5) = 1 &
% 51.47/11.62 real_$is_int(real_81/20) = 1 & real_$is_int(real_0) = 0 & real_$is_rat(real_5)
% 51.47/11.62 = 0 & real_$is_rat(real_53/20) = 0 & real_$is_rat(real_153/20) = 0 &
% 51.47/11.62 real_$is_rat(real_18/5) = 0 & real_$is_rat(real_81/20) = 0 &
% 51.47/11.62 real_$is_rat(real_0) = 0 & real_$floor(real_5) = real_5 & real_$floor(real_0)
% 51.47/11.62 = real_0 & real_$ceiling(real_5) = real_5 & real_$ceiling(real_81/20) = real_5
% 51.47/11.62 & real_$ceiling(real_0) = real_0 & real_$truncate(real_5) = real_5 &
% 51.47/11.62 real_$truncate(real_0) = real_0 & real_$round(real_5) = real_5 &
% 51.47/11.62 real_$round(real_0) = real_0 & real_$to_int(real_5) = 5 &
% 51.47/11.62 real_$to_int(real_53/20) = 2 & real_$to_int(real_153/20) = 7 &
% 51.47/11.62 real_$to_int(real_18/5) = 3 & real_$to_int(real_81/20) = 4 &
% 51.47/11.62 real_$to_int(real_0) = 0 & real_$to_rat(real_5) = rat_5 &
% 51.47/11.62 real_$to_rat(real_53/20) = rat_53/20 & real_$to_rat(real_153/20) = rat_153/20
% 51.47/11.62 & real_$to_rat(real_18/5) = rat_18/5 & real_$to_rat(real_81/20) = rat_81/20 &
% 51.47/11.62 real_$to_rat(real_0) = rat_0 & real_$to_real(real_5) = real_5 &
% 51.47/11.62 real_$to_real(real_53/20) = real_53/20 & real_$to_real(real_153/20) =
% 51.47/11.62 real_153/20 & real_$to_real(real_18/5) = real_18/5 & real_$to_real(real_81/20)
% 51.47/11.62 = real_81/20 & real_$to_real(real_0) = real_0 & int_$to_real(5) = real_5 &
% 51.47/11.62 int_$to_real(0) = real_0 & real_$quotient(real_0, real_5) = real_0 &
% 51.47/11.62 real_$quotient(real_0, real_53/20) = real_0 & real_$quotient(real_0,
% 51.47/11.62 real_153/20) = real_0 & real_$quotient(real_0, real_18/5) = real_0 &
% 51.47/11.62 real_$quotient(real_0, real_81/20) = real_0 & real_$product(real_5, real_0) =
% 51.47/11.62 real_0 & real_$product(real_53/20, real_0) = real_0 &
% 51.47/11.62 real_$product(real_153/20, real_0) = real_0 & real_$product(real_18/5, real_0)
% 51.47/11.62 = real_0 & real_$product(real_81/20, real_0) = real_0 & real_$product(real_0,
% 51.47/11.62 real_5) = real_0 & real_$product(real_0, real_53/20) = real_0 &
% 51.47/11.62 real_$product(real_0, real_153/20) = real_0 & real_$product(real_0, real_18/5)
% 51.47/11.62 = real_0 & real_$product(real_0, real_81/20) = real_0 & real_$product(real_0,
% 51.47/11.62 real_0) = real_0 & real_$difference(real_5, real_5) = real_0 &
% 51.47/11.62 real_$difference(real_5, real_0) = real_5 & real_$difference(real_53/20,
% 51.47/11.62 real_53/20) = real_0 & real_$difference(real_53/20, real_0) = real_53/20 &
% 51.47/11.62 real_$difference(real_153/20, real_5) = real_53/20 &
% 51.47/11.62 real_$difference(real_153/20, real_53/20) = real_5 &
% 51.47/11.62 real_$difference(real_153/20, real_153/20) = real_0 &
% 51.47/11.62 real_$difference(real_153/20, real_18/5) = real_81/20 &
% 51.47/11.62 real_$difference(real_153/20, real_81/20) = real_18/5 &
% 51.47/11.62 real_$difference(real_153/20, real_0) = real_153/20 &
% 51.47/11.62 real_$difference(real_18/5, real_18/5) = real_0 & real_$difference(real_18/5,
% 51.47/11.62 real_0) = real_18/5 & real_$difference(real_81/20, real_81/20) = real_0 &
% 51.47/11.62 real_$difference(real_81/20, real_0) = real_81/20 & real_$difference(real_0,
% 51.47/11.62 real_0) = real_0 & real_$uminus(real_0) = real_0 & real_$sum(real_5,
% 51.47/11.62 real_53/20) = real_153/20 & real_$sum(real_5, real_0) = real_5 &
% 51.47/11.62 real_$sum(real_53/20, real_5) = real_153/20 & real_$sum(real_53/20, real_0) =
% 51.47/11.62 real_53/20 & real_$sum(real_153/20, real_0) = real_153/20 &
% 51.47/11.62 real_$sum(real_18/5, real_81/20) = real_153/20 & real_$sum(real_18/5, real_0)
% 51.47/11.62 = real_18/5 & real_$sum(real_81/20, real_18/5) = real_153/20 &
% 51.47/11.62 real_$sum(real_81/20, real_0) = real_81/20 & real_$sum(real_0, real_5) =
% 51.47/11.62 real_5 & real_$sum(real_0, real_53/20) = real_53/20 & real_$sum(real_0,
% 51.47/11.62 real_153/20) = real_153/20 & real_$sum(real_0, real_18/5) = real_18/5 &
% 51.47/11.62 real_$sum(real_0, real_81/20) = real_81/20 & real_$sum(real_0, real_0) =
% 51.47/11.62 real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 51.47/11.62 real_$greatereq(real_5, real_5) = 0 & real_$greatereq(real_5, real_53/20) = 0
% 51.47/11.62 & real_$greatereq(real_5, real_153/20) = 1 & real_$greatereq(real_5,
% 51.47/11.62 real_18/5) = 0 & real_$greatereq(real_5, real_81/20) = 0 &
% 51.47/11.62 real_$greatereq(real_5, real_0) = 0 & real_$greatereq(real_53/20, real_5) = 1
% 51.47/11.62 & real_$greatereq(real_53/20, real_53/20) = 0 & real_$greatereq(real_53/20,
% 51.47/11.62 real_153/20) = 1 & real_$greatereq(real_53/20, real_18/5) = 1 &
% 51.47/11.62 real_$greatereq(real_53/20, real_81/20) = 1 & real_$greatereq(real_53/20,
% 51.47/11.62 real_0) = 0 & real_$greatereq(real_153/20, real_5) = 0 &
% 51.47/11.62 real_$greatereq(real_153/20, real_53/20) = 0 & real_$greatereq(real_153/20,
% 51.47/11.62 real_153/20) = 0 & real_$greatereq(real_153/20, real_18/5) = 0 &
% 51.47/11.62 real_$greatereq(real_153/20, real_81/20) = 0 & real_$greatereq(real_153/20,
% 51.47/11.62 real_0) = 0 & real_$greatereq(real_18/5, real_5) = 1 &
% 51.47/11.62 real_$greatereq(real_18/5, real_53/20) = 0 & real_$greatereq(real_18/5,
% 51.47/11.62 real_153/20) = 1 & real_$greatereq(real_18/5, real_18/5) = 0 &
% 51.47/11.62 real_$greatereq(real_18/5, real_81/20) = 1 & real_$greatereq(real_18/5,
% 51.47/11.62 real_0) = 0 & real_$greatereq(real_81/20, real_5) = 1 &
% 51.47/11.62 real_$greatereq(real_81/20, real_53/20) = 0 & real_$greatereq(real_81/20,
% 51.47/11.62 real_153/20) = 1 & real_$greatereq(real_81/20, real_18/5) = 0 &
% 51.47/11.62 real_$greatereq(real_81/20, real_81/20) = 0 & real_$greatereq(real_81/20,
% 51.47/11.62 real_0) = 0 & real_$greatereq(real_0, real_5) = 1 & real_$greatereq(real_0,
% 51.47/11.62 real_53/20) = 1 & real_$greatereq(real_0, real_153/20) = 1 &
% 51.47/11.62 real_$greatereq(real_0, real_18/5) = 1 & real_$greatereq(real_0, real_81/20) =
% 51.47/11.62 1 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 51.47/11.62 real_very_large) = 0 & real_$lesseq(real_5, real_5) = 0 &
% 51.47/11.62 real_$lesseq(real_5, real_53/20) = 1 & real_$lesseq(real_5, real_153/20) = 0 &
% 51.47/11.62 real_$lesseq(real_5, real_18/5) = 1 & real_$lesseq(real_5, real_81/20) = 1 &
% 51.47/11.62 real_$lesseq(real_5, real_0) = 1 & real_$lesseq(real_53/20, real_5) = 0 &
% 51.47/11.62 real_$lesseq(real_53/20, real_53/20) = 0 & real_$lesseq(real_53/20,
% 51.47/11.62 real_153/20) = 0 & real_$lesseq(real_53/20, real_18/5) = 0 &
% 51.47/11.62 real_$lesseq(real_53/20, real_81/20) = 0 & real_$lesseq(real_53/20, real_0) =
% 51.47/11.62 1 & real_$lesseq(real_153/20, real_5) = 1 & real_$lesseq(real_153/20,
% 51.47/11.62 real_53/20) = 1 & real_$lesseq(real_153/20, real_153/20) = 0 &
% 51.47/11.62 real_$lesseq(real_153/20, real_18/5) = 1 & real_$lesseq(real_153/20,
% 51.47/11.62 real_81/20) = 1 & real_$lesseq(real_153/20, real_0) = 1 &
% 51.47/11.62 real_$lesseq(real_18/5, real_5) = 0 & real_$lesseq(real_18/5, real_53/20) = 1
% 51.47/11.62 & real_$lesseq(real_18/5, real_153/20) = 0 & real_$lesseq(real_18/5,
% 51.47/11.62 real_18/5) = 0 & real_$lesseq(real_18/5, real_81/20) = 0 &
% 51.47/11.62 real_$lesseq(real_18/5, real_0) = 1 & real_$lesseq(real_81/20, real_5) = 0 &
% 51.47/11.62 real_$lesseq(real_81/20, real_53/20) = 1 & real_$lesseq(real_81/20,
% 51.47/11.62 real_153/20) = 0 & real_$lesseq(real_81/20, real_18/5) = 1 &
% 51.47/11.62 real_$lesseq(real_81/20, real_81/20) = 0 & real_$lesseq(real_81/20, real_0) =
% 51.47/11.62 1 & real_$lesseq(real_0, real_5) = 0 & real_$lesseq(real_0, real_53/20) = 0 &
% 51.47/11.62 real_$lesseq(real_0, real_153/20) = 0 & real_$lesseq(real_0, real_18/5) = 0 &
% 51.47/11.62 real_$lesseq(real_0, real_81/20) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 51.47/11.62 real_$greater(real_very_large, real_5) = 0 & real_$greater(real_very_large,
% 51.47/11.62 real_53/20) = 0 & real_$greater(real_very_large, real_153/20) = 0 &
% 51.47/11.62 real_$greater(real_very_large, real_18/5) = 0 & real_$greater(real_very_large,
% 51.47/11.62 real_81/20) = 0 & real_$greater(real_very_large, real_0) = 0 &
% 51.47/11.62 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_5,
% 51.47/11.62 real_very_small) = 0 & real_$greater(real_5, real_5) = 1 &
% 51.47/11.62 real_$greater(real_5, real_53/20) = 0 & real_$greater(real_5, real_153/20) = 1
% 51.47/11.62 & real_$greater(real_5, real_18/5) = 0 & real_$greater(real_5, real_81/20) = 0
% 51.47/11.62 & real_$greater(real_5, real_0) = 0 & real_$greater(real_53/20,
% 51.47/11.62 real_very_small) = 0 & real_$greater(real_53/20, real_5) = 1 &
% 51.47/11.62 real_$greater(real_53/20, real_53/20) = 1 & real_$greater(real_53/20,
% 51.47/11.62 real_153/20) = 1 & real_$greater(real_53/20, real_18/5) = 1 &
% 51.47/11.62 real_$greater(real_53/20, real_81/20) = 1 & real_$greater(real_53/20, real_0)
% 51.47/11.62 = 0 & real_$greater(real_153/20, real_very_small) = 0 &
% 51.47/11.62 real_$greater(real_153/20, real_5) = 0 & real_$greater(real_153/20,
% 51.47/11.62 real_53/20) = 0 & real_$greater(real_153/20, real_153/20) = 1 &
% 51.47/11.62 real_$greater(real_153/20, real_18/5) = 0 & real_$greater(real_153/20,
% 51.47/11.62 real_81/20) = 0 & real_$greater(real_153/20, real_0) = 0 &
% 51.47/11.62 real_$greater(real_18/5, real_very_small) = 0 & real_$greater(real_18/5,
% 51.47/11.62 real_5) = 1 & real_$greater(real_18/5, real_53/20) = 0 &
% 51.47/11.62 real_$greater(real_18/5, real_153/20) = 1 & real_$greater(real_18/5,
% 51.47/11.62 real_18/5) = 1 & real_$greater(real_18/5, real_81/20) = 1 &
% 51.47/11.62 real_$greater(real_18/5, real_0) = 0 & real_$greater(real_81/20,
% 51.47/11.62 real_very_small) = 0 & real_$greater(real_81/20, real_5) = 1 &
% 51.47/11.62 real_$greater(real_81/20, real_53/20) = 0 & real_$greater(real_81/20,
% 51.47/11.62 real_153/20) = 1 & real_$greater(real_81/20, real_18/5) = 0 &
% 51.47/11.62 real_$greater(real_81/20, real_81/20) = 1 & real_$greater(real_81/20, real_0)
% 51.47/11.62 = 0 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 51.47/11.62 real_5) = 1 & real_$greater(real_0, real_53/20) = 1 & real_$greater(real_0,
% 51.47/11.62 real_153/20) = 1 & real_$greater(real_0, real_18/5) = 1 &
% 51.47/11.62 real_$greater(real_0, real_81/20) = 1 & real_$greater(real_0, real_0) = 1 &
% 51.47/11.62 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small,
% 51.47/11.62 real_5) = 0 & real_$less(real_very_small, real_53/20) = 0 &
% 51.47/11.62 real_$less(real_very_small, real_153/20) = 0 & real_$less(real_very_small,
% 51.47/11.62 real_18/5) = 0 & real_$less(real_very_small, real_81/20) = 0 &
% 51.47/11.62 real_$less(real_very_small, real_0) = 0 & real_$less(real_5, real_very_large)
% 51.47/11.62 = 0 & real_$less(real_5, real_5) = 1 & real_$less(real_5, real_53/20) = 1 &
% 51.47/11.62 real_$less(real_5, real_153/20) = 0 & real_$less(real_5, real_18/5) = 1 &
% 51.47/11.62 real_$less(real_5, real_81/20) = 1 & real_$less(real_5, real_0) = 1 &
% 51.47/11.62 real_$less(real_53/20, real_very_large) = 0 & real_$less(real_53/20, real_5) =
% 51.47/11.62 0 & real_$less(real_53/20, real_53/20) = 1 & real_$less(real_53/20,
% 51.47/11.62 real_153/20) = 0 & real_$less(real_53/20, real_18/5) = 0 &
% 51.47/11.62 real_$less(real_53/20, real_81/20) = 0 & real_$less(real_53/20, real_0) = 1 &
% 51.47/11.62 real_$less(real_153/20, real_very_large) = 0 & real_$less(real_153/20, real_5)
% 51.47/11.62 = 1 & real_$less(real_153/20, real_53/20) = 1 & real_$less(real_153/20,
% 51.47/11.62 real_153/20) = 1 & real_$less(real_153/20, real_18/5) = 1 &
% 51.47/11.62 real_$less(real_153/20, real_81/20) = 1 & real_$less(real_153/20, real_0) = 1
% 51.47/11.62 & real_$less(real_18/5, real_very_large) = 0 & real_$less(real_18/5, real_5) =
% 51.47/11.62 0 & real_$less(real_18/5, real_53/20) = 1 & real_$less(real_18/5, real_153/20)
% 51.47/11.62 = 0 & real_$less(real_18/5, real_18/5) = 1 & real_$less(real_18/5, real_81/20)
% 51.47/11.62 = 0 & real_$less(real_18/5, real_0) = 1 & real_$less(real_81/20,
% 51.47/11.62 real_very_large) = 0 & real_$less(real_81/20, real_5) = 0 &
% 51.47/11.62 real_$less(real_81/20, real_53/20) = 1 & real_$less(real_81/20, real_153/20) =
% 51.47/11.62 0 & real_$less(real_81/20, real_18/5) = 1 & real_$less(real_81/20, real_81/20)
% 51.47/11.62 = 1 & real_$less(real_81/20, real_0) = 1 & real_$less(real_0, real_very_large)
% 51.47/11.62 = 0 & real_$less(real_0, real_5) = 0 & real_$less(real_0, real_53/20) = 0 &
% 51.47/11.62 real_$less(real_0, real_153/20) = 0 & real_$less(real_0, real_18/5) = 0 &
% 51.47/11.62 real_$less(real_0, real_81/20) = 0 & real_$less(real_0, real_0) = 1 &
% 51.47/11.62 rat_$quotient(rat_0, rat_5) = rat_0 & rat_$quotient(rat_0, rat_53/20) = rat_0
% 51.47/11.62 & rat_$quotient(rat_0, rat_153/20) = rat_0 & rat_$quotient(rat_0, rat_18/5) =
% 51.47/11.62 rat_0 & rat_$quotient(rat_0, rat_81/20) = rat_0 & rat_$product(rat_5, rat_0) =
% 51.47/11.62 rat_0 & rat_$product(rat_53/20, rat_0) = rat_0 & rat_$product(rat_153/20,
% 51.47/11.62 rat_0) = rat_0 & rat_$product(rat_18/5, rat_0) = rat_0 &
% 51.47/11.62 rat_$product(rat_81/20, rat_0) = rat_0 & rat_$product(rat_0, rat_5) = rat_0 &
% 51.47/11.62 rat_$product(rat_0, rat_53/20) = rat_0 & rat_$product(rat_0, rat_153/20) =
% 51.47/11.62 rat_0 & rat_$product(rat_0, rat_18/5) = rat_0 & rat_$product(rat_0, rat_81/20)
% 51.47/11.62 = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_5, rat_5) =
% 51.47/11.62 rat_0 & rat_$difference(rat_5, rat_0) = rat_5 & rat_$difference(rat_53/20,
% 51.47/11.62 rat_53/20) = rat_0 & rat_$difference(rat_53/20, rat_0) = rat_53/20 &
% 51.47/11.62 rat_$difference(rat_153/20, rat_5) = rat_53/20 & rat_$difference(rat_153/20,
% 51.47/11.62 rat_53/20) = rat_5 & rat_$difference(rat_153/20, rat_153/20) = rat_0 &
% 51.47/11.62 rat_$difference(rat_153/20, rat_18/5) = rat_81/20 &
% 51.47/11.62 rat_$difference(rat_153/20, rat_81/20) = rat_18/5 &
% 51.47/11.62 rat_$difference(rat_153/20, rat_0) = rat_153/20 & rat_$difference(rat_18/5,
% 51.47/11.62 rat_18/5) = rat_0 & rat_$difference(rat_18/5, rat_0) = rat_18/5 &
% 51.47/11.62 rat_$difference(rat_81/20, rat_81/20) = rat_0 & rat_$difference(rat_81/20,
% 51.47/11.62 rat_0) = rat_81/20 & rat_$difference(rat_0, rat_0) = rat_0 &
% 51.47/11.62 rat_$uminus(rat_0) = rat_0 & rat_$sum(rat_5, rat_53/20) = rat_153/20 &
% 51.47/11.62 rat_$sum(rat_5, rat_0) = rat_5 & rat_$sum(rat_53/20, rat_5) = rat_153/20 &
% 51.47/11.62 rat_$sum(rat_53/20, rat_0) = rat_53/20 & rat_$sum(rat_153/20, rat_0) =
% 51.47/11.62 rat_153/20 & rat_$sum(rat_18/5, rat_81/20) = rat_153/20 & rat_$sum(rat_18/5,
% 51.47/11.62 rat_0) = rat_18/5 & rat_$sum(rat_81/20, rat_18/5) = rat_153/20 &
% 51.47/11.62 rat_$sum(rat_81/20, rat_0) = rat_81/20 & rat_$sum(rat_0, rat_5) = rat_5 &
% 51.47/11.62 rat_$sum(rat_0, rat_53/20) = rat_53/20 & rat_$sum(rat_0, rat_153/20) =
% 51.47/11.62 rat_153/20 & rat_$sum(rat_0, rat_18/5) = rat_18/5 & rat_$sum(rat_0, rat_81/20)
% 51.47/11.62 = rat_81/20 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 51.47/11.62 rat_very_large) = 1 & rat_$greatereq(rat_5, rat_5) = 0 &
% 51.47/11.62 rat_$greatereq(rat_5, rat_53/20) = 0 & rat_$greatereq(rat_5, rat_153/20) = 1 &
% 51.47/11.62 rat_$greatereq(rat_5, rat_18/5) = 0 & rat_$greatereq(rat_5, rat_81/20) = 0 &
% 51.47/11.62 rat_$greatereq(rat_5, rat_0) = 0 & rat_$greatereq(rat_53/20, rat_5) = 1 &
% 51.47/11.62 rat_$greatereq(rat_53/20, rat_53/20) = 0 & rat_$greatereq(rat_53/20,
% 51.47/11.62 rat_153/20) = 1 & rat_$greatereq(rat_53/20, rat_18/5) = 1 &
% 51.47/11.62 rat_$greatereq(rat_53/20, rat_81/20) = 1 & rat_$greatereq(rat_53/20, rat_0) =
% 51.47/11.62 0 & rat_$greatereq(rat_153/20, rat_5) = 0 & rat_$greatereq(rat_153/20,
% 51.47/11.62 rat_53/20) = 0 & rat_$greatereq(rat_153/20, rat_153/20) = 0 &
% 51.47/11.62 rat_$greatereq(rat_153/20, rat_18/5) = 0 & rat_$greatereq(rat_153/20,
% 51.47/11.62 rat_81/20) = 0 & rat_$greatereq(rat_153/20, rat_0) = 0 &
% 51.47/11.62 rat_$greatereq(rat_18/5, rat_5) = 1 & rat_$greatereq(rat_18/5, rat_53/20) = 0
% 51.47/11.62 & rat_$greatereq(rat_18/5, rat_153/20) = 1 & rat_$greatereq(rat_18/5,
% 51.47/11.62 rat_18/5) = 0 & rat_$greatereq(rat_18/5, rat_81/20) = 1 &
% 51.47/11.62 rat_$greatereq(rat_18/5, rat_0) = 0 & rat_$greatereq(rat_81/20, rat_5) = 1 &
% 51.47/11.62 rat_$greatereq(rat_81/20, rat_53/20) = 0 & rat_$greatereq(rat_81/20,
% 51.47/11.62 rat_153/20) = 1 & rat_$greatereq(rat_81/20, rat_18/5) = 0 &
% 51.47/11.62 rat_$greatereq(rat_81/20, rat_81/20) = 0 & rat_$greatereq(rat_81/20, rat_0) =
% 51.47/11.62 0 & rat_$greatereq(rat_0, rat_5) = 1 & rat_$greatereq(rat_0, rat_53/20) = 1 &
% 51.47/11.62 rat_$greatereq(rat_0, rat_153/20) = 1 & rat_$greatereq(rat_0, rat_18/5) = 1 &
% 51.47/11.62 rat_$greatereq(rat_0, rat_81/20) = 1 & rat_$greatereq(rat_0, rat_0) = 0 &
% 51.47/11.62 rat_$lesseq(rat_very_small, rat_very_large) = 0 & rat_$lesseq(rat_5, rat_5) =
% 51.47/11.62 0 & rat_$lesseq(rat_5, rat_53/20) = 1 & rat_$lesseq(rat_5, rat_153/20) = 0 &
% 51.47/11.62 rat_$lesseq(rat_5, rat_18/5) = 1 & rat_$lesseq(rat_5, rat_81/20) = 1 &
% 51.47/11.62 rat_$lesseq(rat_5, rat_0) = 1 & rat_$lesseq(rat_53/20, rat_5) = 0 &
% 51.47/11.62 rat_$lesseq(rat_53/20, rat_53/20) = 0 & rat_$lesseq(rat_53/20, rat_153/20) = 0
% 51.47/11.62 & rat_$lesseq(rat_53/20, rat_18/5) = 0 & rat_$lesseq(rat_53/20, rat_81/20) = 0
% 51.47/11.62 & rat_$lesseq(rat_53/20, rat_0) = 1 & rat_$lesseq(rat_153/20, rat_5) = 1 &
% 51.47/11.62 rat_$lesseq(rat_153/20, rat_53/20) = 1 & rat_$lesseq(rat_153/20, rat_153/20) =
% 51.47/11.62 0 & rat_$lesseq(rat_153/20, rat_18/5) = 1 & rat_$lesseq(rat_153/20, rat_81/20)
% 51.47/11.62 = 1 & rat_$lesseq(rat_153/20, rat_0) = 1 & rat_$lesseq(rat_18/5, rat_5) = 0 &
% 51.47/11.62 rat_$lesseq(rat_18/5, rat_53/20) = 1 & rat_$lesseq(rat_18/5, rat_153/20) = 0 &
% 51.47/11.62 rat_$lesseq(rat_18/5, rat_18/5) = 0 & rat_$lesseq(rat_18/5, rat_81/20) = 0 &
% 51.47/11.62 rat_$lesseq(rat_18/5, rat_0) = 1 & rat_$lesseq(rat_81/20, rat_5) = 0 &
% 51.47/11.62 rat_$lesseq(rat_81/20, rat_53/20) = 1 & rat_$lesseq(rat_81/20, rat_153/20) = 0
% 51.47/11.62 & rat_$lesseq(rat_81/20, rat_18/5) = 1 & rat_$lesseq(rat_81/20, rat_81/20) = 0
% 51.47/11.62 & rat_$lesseq(rat_81/20, rat_0) = 1 & rat_$lesseq(rat_0, rat_5) = 0 &
% 51.47/11.62 rat_$lesseq(rat_0, rat_53/20) = 0 & rat_$lesseq(rat_0, rat_153/20) = 0 &
% 51.47/11.62 rat_$lesseq(rat_0, rat_18/5) = 0 & rat_$lesseq(rat_0, rat_81/20) = 0 &
% 51.47/11.62 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_5) = 0 &
% 51.47/11.62 rat_$greater(rat_very_large, rat_53/20) = 0 & rat_$greater(rat_very_large,
% 51.47/11.62 rat_153/20) = 0 & rat_$greater(rat_very_large, rat_18/5) = 0 &
% 51.47/11.62 rat_$greater(rat_very_large, rat_81/20) = 0 & rat_$greater(rat_very_large,
% 51.47/11.62 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 &
% 51.47/11.62 rat_$greater(rat_5, rat_very_small) = 0 & rat_$greater(rat_5, rat_5) = 1 &
% 51.47/11.62 rat_$greater(rat_5, rat_53/20) = 0 & rat_$greater(rat_5, rat_153/20) = 1 &
% 51.47/11.62 rat_$greater(rat_5, rat_18/5) = 0 & rat_$greater(rat_5, rat_81/20) = 0 &
% 51.47/11.62 rat_$greater(rat_5, rat_0) = 0 & rat_$greater(rat_53/20, rat_very_small) = 0 &
% 51.47/11.62 rat_$greater(rat_53/20, rat_5) = 1 & rat_$greater(rat_53/20, rat_53/20) = 1 &
% 51.47/11.62 rat_$greater(rat_53/20, rat_153/20) = 1 & rat_$greater(rat_53/20, rat_18/5) =
% 51.47/11.62 1 & rat_$greater(rat_53/20, rat_81/20) = 1 & rat_$greater(rat_53/20, rat_0) =
% 51.47/11.62 0 & rat_$greater(rat_153/20, rat_very_small) = 0 & rat_$greater(rat_153/20,
% 51.47/11.62 rat_5) = 0 & rat_$greater(rat_153/20, rat_53/20) = 0 &
% 51.47/11.62 rat_$greater(rat_153/20, rat_153/20) = 1 & rat_$greater(rat_153/20, rat_18/5)
% 51.47/11.62 = 0 & rat_$greater(rat_153/20, rat_81/20) = 0 & rat_$greater(rat_153/20,
% 51.47/11.62 rat_0) = 0 & rat_$greater(rat_18/5, rat_very_small) = 0 &
% 51.47/11.62 rat_$greater(rat_18/5, rat_5) = 1 & rat_$greater(rat_18/5, rat_53/20) = 0 &
% 51.47/11.62 rat_$greater(rat_18/5, rat_153/20) = 1 & rat_$greater(rat_18/5, rat_18/5) = 1
% 51.47/11.62 & rat_$greater(rat_18/5, rat_81/20) = 1 & rat_$greater(rat_18/5, rat_0) = 0 &
% 51.47/11.62 rat_$greater(rat_81/20, rat_very_small) = 0 & rat_$greater(rat_81/20, rat_5) =
% 51.47/11.62 1 & rat_$greater(rat_81/20, rat_53/20) = 0 & rat_$greater(rat_81/20,
% 51.47/11.62 rat_153/20) = 1 & rat_$greater(rat_81/20, rat_18/5) = 0 &
% 51.47/11.62 rat_$greater(rat_81/20, rat_81/20) = 1 & rat_$greater(rat_81/20, rat_0) = 0 &
% 51.47/11.62 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_5) = 1 &
% 51.47/11.62 rat_$greater(rat_0, rat_53/20) = 1 & rat_$greater(rat_0, rat_153/20) = 1 &
% 51.47/11.62 rat_$greater(rat_0, rat_18/5) = 1 & rat_$greater(rat_0, rat_81/20) = 1 &
% 51.47/11.62 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 51.47/11.62 & rat_$less(rat_very_small, rat_5) = 0 & rat_$less(rat_very_small, rat_53/20)
% 51.47/11.62 = 0 & rat_$less(rat_very_small, rat_153/20) = 0 & rat_$less(rat_very_small,
% 51.47/11.62 rat_18/5) = 0 & rat_$less(rat_very_small, rat_81/20) = 0 &
% 51.47/11.62 rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_5, rat_very_large) = 0 &
% 51.47/11.62 rat_$less(rat_5, rat_5) = 1 & rat_$less(rat_5, rat_53/20) = 1 &
% 51.47/11.62 rat_$less(rat_5, rat_153/20) = 0 & rat_$less(rat_5, rat_18/5) = 1 &
% 51.47/11.62 rat_$less(rat_5, rat_81/20) = 1 & rat_$less(rat_5, rat_0) = 1 &
% 51.47/11.62 rat_$less(rat_53/20, rat_very_large) = 0 & rat_$less(rat_53/20, rat_5) = 0 &
% 51.47/11.62 rat_$less(rat_53/20, rat_53/20) = 1 & rat_$less(rat_53/20, rat_153/20) = 0 &
% 51.47/11.62 rat_$less(rat_53/20, rat_18/5) = 0 & rat_$less(rat_53/20, rat_81/20) = 0 &
% 51.47/11.62 rat_$less(rat_53/20, rat_0) = 1 & rat_$less(rat_153/20, rat_very_large) = 0 &
% 51.47/11.62 rat_$less(rat_153/20, rat_5) = 1 & rat_$less(rat_153/20, rat_53/20) = 1 &
% 51.47/11.62 rat_$less(rat_153/20, rat_153/20) = 1 & rat_$less(rat_153/20, rat_18/5) = 1 &
% 51.47/11.62 rat_$less(rat_153/20, rat_81/20) = 1 & rat_$less(rat_153/20, rat_0) = 1 &
% 51.47/11.62 rat_$less(rat_18/5, rat_very_large) = 0 & rat_$less(rat_18/5, rat_5) = 0 &
% 51.47/11.62 rat_$less(rat_18/5, rat_53/20) = 1 & rat_$less(rat_18/5, rat_153/20) = 0 &
% 51.47/11.62 rat_$less(rat_18/5, rat_18/5) = 1 & rat_$less(rat_18/5, rat_81/20) = 0 &
% 51.47/11.62 rat_$less(rat_18/5, rat_0) = 1 & rat_$less(rat_81/20, rat_very_large) = 0 &
% 51.47/11.62 rat_$less(rat_81/20, rat_5) = 0 & rat_$less(rat_81/20, rat_53/20) = 1 &
% 51.47/11.62 rat_$less(rat_81/20, rat_153/20) = 0 & rat_$less(rat_81/20, rat_18/5) = 1 &
% 51.47/11.62 rat_$less(rat_81/20, rat_81/20) = 1 & rat_$less(rat_81/20, rat_0) = 1 &
% 51.47/11.62 rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_5) = 0 &
% 51.47/11.62 rat_$less(rat_0, rat_53/20) = 0 & rat_$less(rat_0, rat_153/20) = 0 &
% 51.47/11.62 rat_$less(rat_0, rat_18/5) = 0 & rat_$less(rat_0, rat_81/20) = 0 &
% 51.47/11.62 rat_$less(rat_0, rat_0) = 1 & rat_$to_int(rat_5) = 5 & rat_$to_int(rat_53/20)
% 51.47/11.62 = 2 & rat_$to_int(rat_153/20) = 7 & rat_$to_int(rat_18/5) = 3 &
% 51.47/11.62 rat_$to_int(rat_81/20) = 4 & rat_$to_int(rat_0) = 0 & ! [v0: $real] : ! [v1:
% 51.47/11.62 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 51.47/11.62 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] :
% 51.47/11.62 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : !
% 51.47/11.62 [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~
% 51.47/11.62 (real_$sum(v2, v3) = v4) | ~ (real_$sum(v1, v0) = v3) | ? [v5: $real] :
% 51.47/11.62 (real_$sum(v5, v0) = v4 & real_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1:
% 51.47/11.62 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3,
% 51.47/11.62 v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2,
% 51.47/11.62 v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 51.47/11.62 [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~
% 51.89/11.62 (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 &
% 51.89/11.62 rat_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 51.89/11.62 : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~
% 51.89/11.62 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1,
% 51.89/11.62 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 51.89/11.62 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v2, v0) =
% 51.89/11.62 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0:
% 51.89/11.62 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~
% 51.89/11.62 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] :
% 51.89/11.62 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real]
% 51.89/11.62 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~
% 51.89/11.62 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1)
% 51.89/11.62 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] :
% 51.89/11.63 (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4:
% 51.89/11.63 int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : !
% 51.89/11.63 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0)
% 51.89/11.63 = v3) | ~ (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 51.89/11.63 real_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 51.89/11.63 $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~
% 51.89/11.63 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1,
% 51.89/11.63 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 51.89/11.63 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3)
% 51.89/11.63 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] :
% 51.89/11.63 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 51.89/11.63 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 51.89/11.63 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 51.89/11.63 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 51.89/11.63 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 51.89/11.63 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 51.89/11.63 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 51.89/11.63 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 51.89/11.63 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~
% 51.89/11.63 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1)
% 51.89/11.63 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real]
% 51.89/11.63 : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) |
% 51.89/11.63 real_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 51.89/11.63 $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) =
% 51.89/11.63 v3) | rat_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : !
% 51.89/11.63 [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2) | ? [v3: int] :
% 51.89/11.63 ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] :
% 51.89/11.63 ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int]
% 51.89/11.63 : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1:
% 51.89/11.63 $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ?
% 51.89/11.63 [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : !
% 51.89/11.63 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 51.89/11.63 [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] :
% 51.89/11.63 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ?
% 51.89/11.63 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 51.89/11.63 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 51.89/11.63 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 51.89/11.63 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3:
% 51.89/11.63 int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $rat] : !
% 51.89/11.63 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 51.89/11.63 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 51.89/11.63 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 51.89/11.63 int] : ( ~ (v3 = 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : !
% 51.89/11.63 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 51.89/11.63 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 51.89/11.63 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3:
% 51.89/11.63 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 51.89/11.63 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int]
% 51.89/11.63 : ( ~ (v3 = 0) & rat_$greater(v0, v1) = v3)) & ! [v0: $real] : ! [v1:
% 51.89/11.63 $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) |
% 51.89/11.63 real_$quotient(v2, v0) = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 51.89/11.63 : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) = v1) &
% 51.89/11.63 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v1, v0)
% 51.89/11.63 = v2) | real_$product(v0, v1) = v2) & ! [v0: $real] : ! [v1: $real] : !
% 51.89/11.63 [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) &
% 51.89/11.63 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$difference(v1,
% 51.89/11.63 v0) = v2) | ? [v3: $real] : (real_$uminus(v0) = v3 & real_$sum(v1, v3)
% 51.89/11.63 = v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 51.89/11.63 (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = v2) & ! [v0: $real] : !
% 51.89/11.63 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1,
% 51.89/11.63 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 51.89/11.63 (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) |
% 51.89/11.63 real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 51.89/11.63 : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) |
% 51.89/11.63 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 51.89/11.63 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2,
% 51.89/11.63 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 51.89/11.63 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] :
% 51.89/11.63 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 51.89/11.63 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 51.89/11.63 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 51.89/11.63 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 51.89/11.63 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1:
% 51.89/11.63 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2)
% 51.89/11.63 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) =
% 51.89/11.63 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0:
% 51.89/11.63 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~
% 51.89/11.63 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1:
% 51.89/11.63 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 51.89/11.63 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] :
% 51.89/11.63 (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real]
% 51.89/11.63 : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0:
% 51.89/11.63 $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0:
% 51.89/11.63 $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) |
% 51.89/11.63 rat_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: int] : (v1 = 0 | ~
% 51.89/11.63 (real_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! [v1: int] : (v1 = 0 | ~
% 51.89/11.63 (rat_$lesseq(v0, v0) = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~
% 51.89/11.63 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1:
% 51.89/11.63 $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! [v0:
% 51.89/11.63 $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) |
% 51.89/11.63 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 51.89/11.63 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] :
% 51.89/11.63 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 51.89/11.63 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) |
% 51.89/11.63 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 51.89/11.63 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : !
% 51.89/11.63 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0)
% 51.89/11.63 = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 51.89/11.63 rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0)
% 51.89/11.63 = v1) | rat_$sum(v0, v1) = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 51.89/11.63 (rat_$greatereq(v0, v1) = 0) | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : !
% 51.89/11.63 [v1: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & !
% 51.89/11.63 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1,
% 51.89/11.63 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 51.89/11.63 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 51.89/11.63 (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0: $rat] : !
% 51.89/11.63 [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) =
% 51.89/11.63 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & ! [v0:
% 51.89/11.63 $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 51.89/11.63
% 51.89/11.63 (function-axioms)
% 51.89/11.64 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 51.89/11.64 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & !
% 51.89/11.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 51.89/11.64 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 51.89/11.64 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 51.89/11.64 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 51.89/11.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 51.89/11.64 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 51.89/11.64 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 51.89/11.64 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 51.89/11.64 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 51.89/11.64 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 51.89/11.64 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 51.89/11.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 51.89/11.64 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 51.89/11.64 (real_$less(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 51.89/11.64 ! [v3: $rat] : (v1 = v0 | ~ (rat_$quotient(v3, v2) = v1) | ~
% 51.89/11.64 (rat_$quotient(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 51.89/11.64 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$product(v3, v2) = v1) | ~
% 51.89/11.64 (rat_$product(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 51.89/11.64 : ! [v3: $rat] : (v1 = v0 | ~ (rat_$difference(v3, v2) = v1) | ~
% 51.89/11.64 (rat_$difference(v3, v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 51.89/11.64 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~
% 51.89/11.64 (rat_$sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 51.89/11.64 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 51.89/11.64 (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3, v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 51.89/11.64 $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~ (rat_$lesseq(v3, v2) =
% 51.89/11.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 51.89/11.64 $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$greater(v3, v2) = v1) | ~
% 51.89/11.64 (rat_$greater(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 51.89/11.64 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 51.89/11.64 (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 51.89/11.64 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 51.89/11.64 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : !
% 51.89/11.64 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 51.89/11.64 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 51.89/11.64 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 51.89/11.64 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 51.89/11.64 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 51.89/11.64 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 51.89/11.64 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_rat(v2)
% 51.89/11.64 = v1) | ~ (rat_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 51.89/11.64 [v2: $rat] : (v1 = v0 | ~ (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) =
% 51.89/11.64 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v1 = v0 | ~
% 51.89/11.64 (int_$to_rat(v2) = v1) | ~ (int_$to_rat(v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 51.89/11.64 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0:
% 51.89/11.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 51.89/11.64 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real]
% 51.89/11.64 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 51.89/11.64 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 51.89/11.64 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & !
% 51.89/11.64 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 51.89/11.64 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] :
% 51.89/11.64 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~
% 51.89/11.64 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1
% 51.89/11.64 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0:
% 51.89/11.64 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) =
% 51.89/11.64 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 51.89/11.64 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) =
% 51.89/11.64 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~
% 51.89/11.64 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : !
% 51.89/11.64 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~
% 51.89/11.64 (real_$uminus(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 51.89/11.64 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0)) & ! [v0:
% 51.89/11.64 int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) = v1) |
% 51.89/11.64 ~ (rat_$to_int(v2) = v0))
% 51.89/11.64
% 51.89/11.64 Those formulas are unsatisfiable:
% 51.89/11.64 ---------------------------------
% 51.89/11.64
% 51.89/11.64 Begin of proof
% 51.89/11.64 |
% 51.89/11.64 | ALPHA: (function-axioms) implies:
% 51.89/11.64 | (1) ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~
% 51.89/11.64 | (rat_$to_int(v2) = v1) | ~ (rat_$to_int(v2) = v0))
% 51.89/11.64 |
% 51.89/11.64 | ALPHA: (input) implies:
% 51.89/11.64 | (2) rat_$to_int(rat_5) = 5
% 51.89/11.64 |
% 51.89/11.65 | DELTA: instantiating (mixed_types_problem_31) with fresh symbol all_5_0 gives:
% 51.89/11.65 | (3) ~ (all_5_0 = 5) & rat_$to_int(rat_5) = all_5_0
% 51.89/11.65 |
% 51.89/11.65 | ALPHA: (3) implies:
% 51.89/11.65 | (4) ~ (all_5_0 = 5)
% 51.89/11.65 | (5) rat_$to_int(rat_5) = all_5_0
% 51.89/11.65 |
% 51.89/11.65 | GROUND_INST: instantiating (1) with 5, all_5_0, rat_5, simplifying with (2),
% 51.89/11.65 | (5) gives:
% 51.89/11.65 | (6) all_5_0 = 5
% 51.89/11.65 |
% 51.89/11.65 | REDUCE: (4), (6) imply:
% 51.89/11.65 | (7) $false
% 51.89/11.65 |
% 51.89/11.65 | CLOSE: (7) is inconsistent.
% 51.89/11.65 |
% 51.89/11.65 End of proof
% 51.89/11.65 % SZS output end Proof for theBenchmark
% 51.89/11.65
% 51.89/11.65 11032ms
%------------------------------------------------------------------------------