TSTP Solution File: ARI342_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI342_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 : n031.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 8.12s 1.82s
% Output : Proof 10.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ARI342_1 : TPTP v8.1.2. Released v5.0.0.
% 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 18:13:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.54/0.60 ________ _____
% 0.54/0.60 ___ __ \_________(_)________________________________
% 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.60 (2023-06-19)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2023
% 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.60 Amanda Stjerna.
% 0.54/0.60 Free software under BSD-3-Clause.
% 0.54/0.60
% 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.60
% 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.61 Running up to 7 provers in parallel.
% 0.64/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.64/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.64/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.64/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.64/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.64/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.64/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.27/0.88 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.27/0.88 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.81/0.96 Prover 1: Preprocessing ...
% 1.81/0.97 Prover 4: Preprocessing ...
% 2.32/1.01 Prover 0: Preprocessing ...
% 2.32/1.01 Prover 2: Preprocessing ...
% 2.32/1.01 Prover 3: Preprocessing ...
% 2.32/1.01 Prover 6: Preprocessing ...
% 2.32/1.01 Prover 5: Preprocessing ...
% 5.35/1.44 Prover 1: Constructing countermodel ...
% 5.67/1.48 Prover 6: Proving ...
% 6.34/1.55 Prover 0: Proving ...
% 6.34/1.56 Prover 4: Constructing countermodel ...
% 6.34/1.57 Prover 3: Constructing countermodel ...
% 6.34/1.58 Prover 2: Proving ...
% 7.19/1.66 Prover 5: Proving ...
% 7.79/1.75 Prover 1: gave up
% 7.79/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.79/1.76 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.12/1.78 Prover 7: Preprocessing ...
% 8.12/1.82 Prover 2: proved (1197ms)
% 8.12/1.82
% 8.12/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.12/1.82
% 8.12/1.83 Prover 5: proved (1195ms)
% 8.12/1.83
% 8.12/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.12/1.83
% 8.12/1.83 Prover 6: stopped
% 8.12/1.83 Prover 0: stopped
% 8.12/1.83 Prover 3: stopped
% 8.12/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.12/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.12/1.83 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.12/1.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.12/1.83 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.12/1.83 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.12/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.55/1.84 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.55/1.85 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.55/1.85 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 8.55/1.85 Prover 11: Preprocessing ...
% 8.55/1.85 Prover 10: Preprocessing ...
% 8.55/1.85 Prover 8: Preprocessing ...
% 8.55/1.85 Prover 13: Preprocessing ...
% 8.55/1.86 Prover 16: Preprocessing ...
% 9.42/1.96 Prover 8: Warning: ignoring some quantifiers
% 9.42/1.98 Prover 8: Constructing countermodel ...
% 9.42/1.99 Prover 7: Warning: ignoring some quantifiers
% 9.42/2.00 Prover 13: Warning: ignoring some quantifiers
% 9.42/2.01 Prover 7: Constructing countermodel ...
% 9.42/2.01 Prover 13: Constructing countermodel ...
% 9.42/2.02 Prover 10: Warning: ignoring some quantifiers
% 9.42/2.03 Prover 10: Constructing countermodel ...
% 9.93/2.06 Prover 16: Warning: ignoring some quantifiers
% 9.93/2.06 Prover 16: Constructing countermodel ...
% 10.28/2.13 Prover 11: Constructing countermodel ...
% 10.79/2.14 Prover 10: Found proof (size 3)
% 10.79/2.14 Prover 10: proved (313ms)
% 10.79/2.14 Prover 7: Found proof (size 3)
% 10.79/2.14 Prover 7: proved (391ms)
% 10.79/2.14 Prover 16: stopped
% 10.79/2.14 Prover 13: stopped
% 10.79/2.14 Prover 8: stopped
% 10.79/2.14 Prover 4: stopped
% 10.79/2.14 Prover 11: stopped
% 10.79/2.14
% 10.79/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.79/2.14
% 10.79/2.15 % SZS output start Proof for theBenchmark
% 10.79/2.15 Assumptions after simplification:
% 10.79/2.15 ---------------------------------
% 10.79/2.15
% 10.79/2.15 (rat_combined_problem_8)
% 10.91/2.17 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$sum(v0, v0) = v1) | ~ rat_$less(v1,
% 10.91/2.17 rat_-13/2))
% 10.91/2.17
% 10.91/2.17 (input)
% 10.91/2.20 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_1) & ~
% 10.91/2.20 (rat_very_large = rat_-2/13) & ~ (rat_very_large = rat_169/4) & ~
% 10.91/2.20 (rat_very_large = rat_-13) & ~ (rat_very_large = rat_13/2) & ~
% 10.91/2.20 (rat_very_large = rat_-13/2) & ~ (rat_very_large = rat_0) & ~
% 10.91/2.20 (rat_very_small = rat_1) & ~ (rat_very_small = rat_-2/13) & ~
% 10.91/2.20 (rat_very_small = rat_169/4) & ~ (rat_very_small = rat_-13) & ~
% 10.91/2.20 (rat_very_small = rat_13/2) & ~ (rat_very_small = rat_-13/2) & ~
% 10.91/2.20 (rat_very_small = rat_0) & ~ (rat_1 = rat_-2/13) & ~ (rat_1 = rat_169/4) &
% 10.91/2.20 ~ (rat_1 = rat_-13) & ~ (rat_1 = rat_13/2) & ~ (rat_1 = rat_-13/2) & ~
% 10.91/2.20 (rat_1 = rat_0) & ~ (rat_-2/13 = rat_169/4) & ~ (rat_-2/13 = rat_-13) & ~
% 10.91/2.20 (rat_-2/13 = rat_13/2) & ~ (rat_-2/13 = rat_-13/2) & ~ (rat_-2/13 = rat_0) &
% 10.91/2.20 ~ (rat_169/4 = rat_-13) & ~ (rat_169/4 = rat_13/2) & ~ (rat_169/4 =
% 10.91/2.20 rat_-13/2) & ~ (rat_169/4 = rat_0) & ~ (rat_-13 = rat_13/2) & ~ (rat_-13
% 10.91/2.20 = rat_-13/2) & ~ (rat_-13 = rat_0) & ~ (rat_13/2 = rat_-13/2) & ~
% 10.91/2.20 (rat_13/2 = rat_0) & ~ (rat_-13/2 = rat_0) & rat_$floor(rat_1) = rat_1 &
% 10.91/2.20 rat_$floor(rat_-13) = rat_-13 & rat_$floor(rat_0) = rat_0 &
% 10.91/2.20 rat_$ceiling(rat_1) = rat_1 & rat_$ceiling(rat_-2/13) = rat_0 &
% 10.91/2.20 rat_$ceiling(rat_-13) = rat_-13 & rat_$ceiling(rat_0) = rat_0 &
% 10.91/2.20 rat_$truncate(rat_1) = rat_1 & rat_$truncate(rat_-2/13) = rat_0 &
% 10.91/2.20 rat_$truncate(rat_-13) = rat_-13 & rat_$truncate(rat_0) = rat_0 &
% 10.91/2.20 rat_$round(rat_1) = rat_1 & rat_$round(rat_-2/13) = rat_0 &
% 10.91/2.20 rat_$round(rat_-13) = rat_-13 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_1)
% 10.91/2.20 = 1 & rat_$to_int(rat_-2/13) = -1 & rat_$to_int(rat_169/4) = 42 &
% 10.91/2.20 rat_$to_int(rat_-13) = -13 & rat_$to_int(rat_13/2) = 6 &
% 10.91/2.20 rat_$to_int(rat_-13/2) = -7 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_1) =
% 10.91/2.20 rat_1 & rat_$to_rat(rat_-2/13) = rat_-2/13 & rat_$to_rat(rat_169/4) =
% 10.91/2.20 rat_169/4 & rat_$to_rat(rat_-13) = rat_-13 & rat_$to_rat(rat_13/2) = rat_13/2
% 10.91/2.20 & rat_$to_rat(rat_-13/2) = rat_-13/2 & rat_$to_rat(rat_0) = rat_0 &
% 10.91/2.20 rat_$to_real(rat_1) = real_1 & rat_$to_real(rat_-2/13) = real_-2/13 &
% 10.91/2.20 rat_$to_real(rat_169/4) = real_169/4 & rat_$to_real(rat_-13) = real_-13 &
% 10.91/2.20 rat_$to_real(rat_13/2) = real_13/2 & rat_$to_real(rat_-13/2) = real_-13/2 &
% 10.91/2.20 rat_$to_real(rat_0) = real_0 & int_$to_rat(-13) = rat_-13 & int_$to_rat(1) =
% 10.91/2.20 rat_1 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_1, rat_1) = rat_1 &
% 10.91/2.20 rat_$quotient(rat_1, rat_-2/13) = rat_-13/2 & rat_$quotient(rat_1, rat_-13/2)
% 10.91/2.20 = rat_-2/13 & rat_$quotient(rat_-2/13, rat_1) = rat_-2/13 &
% 10.91/2.20 rat_$quotient(rat_-2/13, rat_-2/13) = rat_1 & rat_$quotient(rat_169/4, rat_1)
% 10.91/2.20 = rat_169/4 & rat_$quotient(rat_169/4, rat_169/4) = rat_1 &
% 10.91/2.20 rat_$quotient(rat_169/4, rat_13/2) = rat_13/2 & rat_$quotient(rat_169/4,
% 10.91/2.20 rat_-13/2) = rat_-13/2 & rat_$quotient(rat_-13, rat_1) = rat_-13 &
% 10.91/2.20 rat_$quotient(rat_-13, rat_-13) = rat_1 & rat_$quotient(rat_13/2, rat_1) =
% 10.91/2.20 rat_13/2 & rat_$quotient(rat_13/2, rat_13/2) = rat_1 &
% 10.91/2.20 rat_$quotient(rat_-13/2, rat_1) = rat_-13/2 & rat_$quotient(rat_-13/2,
% 10.91/2.20 rat_-2/13) = rat_169/4 & rat_$quotient(rat_-13/2, rat_169/4) = rat_-2/13 &
% 10.91/2.20 rat_$quotient(rat_-13/2, rat_-13/2) = rat_1 & rat_$quotient(rat_0, rat_1) =
% 10.91/2.20 rat_0 & rat_$quotient(rat_0, rat_-2/13) = rat_0 & rat_$quotient(rat_0,
% 10.91/2.20 rat_169/4) = rat_0 & rat_$quotient(rat_0, rat_-13) = rat_0 &
% 10.91/2.20 rat_$quotient(rat_0, rat_13/2) = rat_0 & rat_$quotient(rat_0, rat_-13/2) =
% 10.91/2.20 rat_0 & rat_$product(rat_1, rat_1) = rat_1 & rat_$product(rat_1, rat_-2/13) =
% 10.91/2.20 rat_-2/13 & rat_$product(rat_1, rat_169/4) = rat_169/4 & rat_$product(rat_1,
% 10.91/2.20 rat_-13) = rat_-13 & rat_$product(rat_1, rat_13/2) = rat_13/2 &
% 10.91/2.20 rat_$product(rat_1, rat_-13/2) = rat_-13/2 & rat_$product(rat_1, rat_0) =
% 10.91/2.20 rat_0 & rat_$product(rat_-2/13, rat_1) = rat_-2/13 & rat_$product(rat_-2/13,
% 10.91/2.20 rat_169/4) = rat_-13/2 & rat_$product(rat_-2/13, rat_-13/2) = rat_1 &
% 10.91/2.20 rat_$product(rat_-2/13, rat_0) = rat_0 & rat_$product(rat_169/4, rat_1) =
% 10.91/2.20 rat_169/4 & rat_$product(rat_169/4, rat_-2/13) = rat_-13/2 &
% 10.91/2.20 rat_$product(rat_169/4, rat_0) = rat_0 & rat_$product(rat_-13, rat_1) =
% 10.91/2.20 rat_-13 & rat_$product(rat_-13, rat_0) = rat_0 & rat_$product(rat_13/2, rat_1)
% 10.91/2.20 = rat_13/2 & rat_$product(rat_13/2, rat_13/2) = rat_169/4 &
% 10.91/2.20 rat_$product(rat_13/2, rat_0) = rat_0 & rat_$product(rat_-13/2, rat_1) =
% 10.91/2.20 rat_-13/2 & rat_$product(rat_-13/2, rat_-2/13) = rat_1 &
% 10.91/2.20 rat_$product(rat_-13/2, rat_-13/2) = rat_169/4 & rat_$product(rat_-13/2,
% 10.91/2.20 rat_0) = rat_0 & rat_$product(rat_0, rat_1) = rat_0 & rat_$product(rat_0,
% 10.91/2.20 rat_-2/13) = rat_0 & rat_$product(rat_0, rat_169/4) = rat_0 &
% 10.91/2.20 rat_$product(rat_0, rat_-13) = rat_0 & rat_$product(rat_0, rat_13/2) = rat_0 &
% 10.91/2.20 rat_$product(rat_0, rat_-13/2) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 &
% 10.91/2.20 rat_$difference(rat_1, rat_1) = rat_0 & rat_$difference(rat_1, rat_0) = rat_1
% 10.91/2.20 & rat_$difference(rat_-2/13, rat_-2/13) = rat_0 & rat_$difference(rat_-2/13,
% 10.91/2.20 rat_0) = rat_-2/13 & rat_$difference(rat_169/4, rat_169/4) = rat_0 &
% 10.91/2.20 rat_$difference(rat_169/4, rat_0) = rat_169/4 & rat_$difference(rat_-13,
% 10.91/2.20 rat_-13) = rat_0 & rat_$difference(rat_-13, rat_-13/2) = rat_-13/2 &
% 10.91/2.20 rat_$difference(rat_-13, rat_0) = rat_-13 & rat_$difference(rat_13/2,
% 10.91/2.20 rat_13/2) = rat_0 & rat_$difference(rat_13/2, rat_0) = rat_13/2 &
% 10.91/2.20 rat_$difference(rat_-13/2, rat_-13) = rat_13/2 & rat_$difference(rat_-13/2,
% 10.91/2.20 rat_13/2) = rat_-13 & rat_$difference(rat_-13/2, rat_-13/2) = rat_0 &
% 10.91/2.20 rat_$difference(rat_-13/2, rat_0) = rat_-13/2 & rat_$difference(rat_0,
% 10.91/2.20 rat_13/2) = rat_-13/2 & rat_$difference(rat_0, rat_-13/2) = rat_13/2 &
% 10.91/2.20 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_13/2) = rat_-13/2 &
% 10.91/2.20 rat_$uminus(rat_-13/2) = rat_13/2 & rat_$uminus(rat_0) = rat_0 &
% 10.91/2.20 rat_$sum(rat_1, rat_0) = rat_1 & rat_$sum(rat_-2/13, rat_0) = rat_-2/13 &
% 10.91/2.20 rat_$sum(rat_169/4, rat_0) = rat_169/4 & rat_$sum(rat_-13, rat_13/2) =
% 10.91/2.21 rat_-13/2 & rat_$sum(rat_-13, rat_0) = rat_-13 & rat_$sum(rat_13/2, rat_-13) =
% 10.91/2.21 rat_-13/2 & rat_$sum(rat_13/2, rat_-13/2) = rat_0 & rat_$sum(rat_13/2, rat_0)
% 10.91/2.21 = rat_13/2 & rat_$sum(rat_-13/2, rat_13/2) = rat_0 & rat_$sum(rat_-13/2,
% 10.91/2.21 rat_-13/2) = rat_-13 & rat_$sum(rat_-13/2, rat_0) = rat_-13/2 &
% 10.91/2.21 rat_$sum(rat_0, rat_1) = rat_1 & rat_$sum(rat_0, rat_-2/13) = rat_-2/13 &
% 10.91/2.21 rat_$sum(rat_0, rat_169/4) = rat_169/4 & rat_$sum(rat_0, rat_-13) = rat_-13 &
% 10.91/2.21 rat_$sum(rat_0, rat_13/2) = rat_13/2 & rat_$sum(rat_0, rat_-13/2) = rat_-13/2
% 10.91/2.21 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$is_rat(rat_1) & rat_$is_rat(rat_-2/13)
% 10.91/2.21 & rat_$is_rat(rat_169/4) & rat_$is_rat(rat_-13) & rat_$is_rat(rat_13/2) &
% 10.91/2.21 rat_$is_rat(rat_-13/2) & rat_$is_rat(rat_0) & rat_$is_int(rat_1) &
% 10.91/2.21 rat_$is_int(rat_-13) & rat_$is_int(rat_0) & rat_$greatereq(rat_1, rat_1) &
% 10.91/2.21 rat_$greatereq(rat_1, rat_-2/13) & rat_$greatereq(rat_1, rat_-13) &
% 10.91/2.21 rat_$greatereq(rat_1, rat_-13/2) & rat_$greatereq(rat_1, rat_0) &
% 10.91/2.21 rat_$greatereq(rat_-2/13, rat_-2/13) & rat_$greatereq(rat_-2/13, rat_-13) &
% 10.91/2.21 rat_$greatereq(rat_-2/13, rat_-13/2) & rat_$greatereq(rat_169/4, rat_1) &
% 10.91/2.21 rat_$greatereq(rat_169/4, rat_-2/13) & rat_$greatereq(rat_169/4, rat_169/4) &
% 10.91/2.21 rat_$greatereq(rat_169/4, rat_-13) & rat_$greatereq(rat_169/4, rat_13/2) &
% 10.91/2.21 rat_$greatereq(rat_169/4, rat_-13/2) & rat_$greatereq(rat_169/4, rat_0) &
% 10.91/2.21 rat_$greatereq(rat_-13, rat_-13) & rat_$greatereq(rat_13/2, rat_1) &
% 10.91/2.21 rat_$greatereq(rat_13/2, rat_-2/13) & rat_$greatereq(rat_13/2, rat_-13) &
% 10.91/2.21 rat_$greatereq(rat_13/2, rat_13/2) & rat_$greatereq(rat_13/2, rat_-13/2) &
% 10.91/2.21 rat_$greatereq(rat_13/2, rat_0) & rat_$greatereq(rat_-13/2, rat_-13) &
% 10.91/2.21 rat_$greatereq(rat_-13/2, rat_-13/2) & rat_$greatereq(rat_0, rat_-2/13) &
% 10.91/2.21 rat_$greatereq(rat_0, rat_-13) & rat_$greatereq(rat_0, rat_-13/2) &
% 10.91/2.21 rat_$greatereq(rat_0, rat_0) & rat_$greater(rat_very_large, rat_1) &
% 10.91/2.21 rat_$greater(rat_very_large, rat_-2/13) & rat_$greater(rat_very_large,
% 10.91/2.21 rat_169/4) & rat_$greater(rat_very_large, rat_-13) &
% 10.91/2.21 rat_$greater(rat_very_large, rat_13/2) & rat_$greater(rat_very_large,
% 10.91/2.21 rat_-13/2) & rat_$greater(rat_very_large, rat_0) & rat_$greater(rat_1,
% 10.91/2.21 rat_very_small) & rat_$greater(rat_1, rat_-2/13) & rat_$greater(rat_1,
% 10.91/2.21 rat_-13) & rat_$greater(rat_1, rat_-13/2) & rat_$greater(rat_1, rat_0) &
% 10.91/2.21 rat_$greater(rat_-2/13, rat_very_small) & rat_$greater(rat_-2/13, rat_-13) &
% 10.91/2.21 rat_$greater(rat_-2/13, rat_-13/2) & rat_$greater(rat_169/4, rat_very_small) &
% 10.91/2.21 rat_$greater(rat_169/4, rat_1) & rat_$greater(rat_169/4, rat_-2/13) &
% 10.91/2.21 rat_$greater(rat_169/4, rat_-13) & rat_$greater(rat_169/4, rat_13/2) &
% 10.91/2.21 rat_$greater(rat_169/4, rat_-13/2) & rat_$greater(rat_169/4, rat_0) &
% 10.91/2.21 rat_$greater(rat_-13, rat_very_small) & rat_$greater(rat_13/2, rat_very_small)
% 10.91/2.21 & rat_$greater(rat_13/2, rat_1) & rat_$greater(rat_13/2, rat_-2/13) &
% 10.91/2.21 rat_$greater(rat_13/2, rat_-13) & rat_$greater(rat_13/2, rat_-13/2) &
% 10.91/2.21 rat_$greater(rat_13/2, rat_0) & rat_$greater(rat_-13/2, rat_very_small) &
% 10.91/2.21 rat_$greater(rat_-13/2, rat_-13) & rat_$greater(rat_0, rat_very_small) &
% 10.91/2.21 rat_$greater(rat_0, rat_-2/13) & rat_$greater(rat_0, rat_-13) &
% 10.91/2.21 rat_$greater(rat_0, rat_-13/2) & rat_$lesseq(rat_very_small, rat_very_large) &
% 10.91/2.21 rat_$lesseq(rat_1, rat_1) & rat_$lesseq(rat_1, rat_169/4) & rat_$lesseq(rat_1,
% 10.91/2.21 rat_13/2) & rat_$lesseq(rat_-2/13, rat_1) & rat_$lesseq(rat_-2/13,
% 10.91/2.21 rat_-2/13) & rat_$lesseq(rat_-2/13, rat_169/4) & rat_$lesseq(rat_-2/13,
% 10.91/2.21 rat_13/2) & rat_$lesseq(rat_-2/13, rat_0) & rat_$lesseq(rat_169/4,
% 10.91/2.21 rat_169/4) & rat_$lesseq(rat_-13, rat_1) & rat_$lesseq(rat_-13, rat_-2/13) &
% 10.91/2.21 rat_$lesseq(rat_-13, rat_169/4) & rat_$lesseq(rat_-13, rat_-13) &
% 10.91/2.21 rat_$lesseq(rat_-13, rat_13/2) & rat_$lesseq(rat_-13, rat_-13/2) &
% 10.91/2.21 rat_$lesseq(rat_-13, rat_0) & rat_$lesseq(rat_13/2, rat_169/4) &
% 10.91/2.21 rat_$lesseq(rat_13/2, rat_13/2) & rat_$lesseq(rat_-13/2, rat_1) &
% 10.91/2.21 rat_$lesseq(rat_-13/2, rat_-2/13) & rat_$lesseq(rat_-13/2, rat_169/4) &
% 10.91/2.21 rat_$lesseq(rat_-13/2, rat_13/2) & rat_$lesseq(rat_-13/2, rat_-13/2) &
% 10.91/2.21 rat_$lesseq(rat_-13/2, rat_0) & rat_$lesseq(rat_0, rat_1) & rat_$lesseq(rat_0,
% 10.91/2.21 rat_169/4) & rat_$lesseq(rat_0, rat_13/2) & rat_$lesseq(rat_0, rat_0) &
% 10.91/2.21 rat_$less(rat_very_small, rat_very_large) & rat_$less(rat_very_small, rat_1) &
% 10.91/2.21 rat_$less(rat_very_small, rat_-2/13) & rat_$less(rat_very_small, rat_169/4) &
% 10.91/2.21 rat_$less(rat_very_small, rat_-13) & rat_$less(rat_very_small, rat_13/2) &
% 10.91/2.21 rat_$less(rat_very_small, rat_-13/2) & rat_$less(rat_very_small, rat_0) &
% 10.91/2.21 rat_$less(rat_1, rat_very_large) & rat_$less(rat_1, rat_169/4) &
% 10.91/2.21 rat_$less(rat_1, rat_13/2) & rat_$less(rat_-2/13, rat_very_large) &
% 10.91/2.21 rat_$less(rat_-2/13, rat_1) & rat_$less(rat_-2/13, rat_169/4) &
% 10.91/2.21 rat_$less(rat_-2/13, rat_13/2) & rat_$less(rat_-2/13, rat_0) &
% 10.91/2.21 rat_$less(rat_169/4, rat_very_large) & rat_$less(rat_-13, rat_very_large) &
% 10.91/2.21 rat_$less(rat_-13, rat_1) & rat_$less(rat_-13, rat_-2/13) & rat_$less(rat_-13,
% 10.91/2.21 rat_169/4) & rat_$less(rat_-13, rat_13/2) & rat_$less(rat_-13, rat_-13/2) &
% 10.91/2.21 rat_$less(rat_-13, rat_0) & rat_$less(rat_13/2, rat_very_large) &
% 10.91/2.21 rat_$less(rat_13/2, rat_169/4) & rat_$less(rat_-13/2, rat_very_large) &
% 10.91/2.21 rat_$less(rat_-13/2, rat_1) & rat_$less(rat_-13/2, rat_-2/13) &
% 10.91/2.21 rat_$less(rat_-13/2, rat_169/4) & rat_$less(rat_-13/2, rat_13/2) &
% 10.91/2.21 rat_$less(rat_-13/2, rat_0) & rat_$less(rat_0, rat_very_large) &
% 10.91/2.21 rat_$less(rat_0, rat_1) & rat_$less(rat_0, rat_169/4) & rat_$less(rat_0,
% 10.91/2.21 rat_13/2) & ~ rat_$is_int(rat_-2/13) & ~ rat_$is_int(rat_169/4) & ~
% 10.91/2.21 rat_$is_int(rat_13/2) & ~ rat_$is_int(rat_-13/2) & ~
% 10.91/2.21 rat_$greatereq(rat_very_small, rat_very_large) & ~ rat_$greatereq(rat_1,
% 10.91/2.21 rat_169/4) & ~ rat_$greatereq(rat_1, rat_13/2) & ~
% 10.91/2.21 rat_$greatereq(rat_-2/13, rat_1) & ~ rat_$greatereq(rat_-2/13, rat_169/4) &
% 10.91/2.21 ~ rat_$greatereq(rat_-2/13, rat_13/2) & ~ rat_$greatereq(rat_-2/13, rat_0) &
% 10.91/2.21 ~ rat_$greatereq(rat_-13, rat_1) & ~ rat_$greatereq(rat_-13, rat_-2/13) & ~
% 10.91/2.21 rat_$greatereq(rat_-13, rat_169/4) & ~ rat_$greatereq(rat_-13, rat_13/2) & ~
% 10.91/2.21 rat_$greatereq(rat_-13, rat_-13/2) & ~ rat_$greatereq(rat_-13, rat_0) & ~
% 10.91/2.21 rat_$greatereq(rat_13/2, rat_169/4) & ~ rat_$greatereq(rat_-13/2, rat_1) & ~
% 10.91/2.21 rat_$greatereq(rat_-13/2, rat_-2/13) & ~ rat_$greatereq(rat_-13/2, rat_169/4)
% 10.91/2.21 & ~ rat_$greatereq(rat_-13/2, rat_13/2) & ~ rat_$greatereq(rat_-13/2, rat_0)
% 10.91/2.21 & ~ rat_$greatereq(rat_0, rat_1) & ~ rat_$greatereq(rat_0, rat_169/4) & ~
% 10.91/2.21 rat_$greatereq(rat_0, rat_13/2) & ~ rat_$greater(rat_very_small,
% 10.91/2.21 rat_very_large) & ~ rat_$greater(rat_1, rat_1) & ~ rat_$greater(rat_1,
% 10.91/2.21 rat_169/4) & ~ rat_$greater(rat_1, rat_13/2) & ~ rat_$greater(rat_-2/13,
% 10.91/2.21 rat_1) & ~ rat_$greater(rat_-2/13, rat_-2/13) & ~ rat_$greater(rat_-2/13,
% 10.91/2.21 rat_169/4) & ~ rat_$greater(rat_-2/13, rat_13/2) & ~
% 10.91/2.21 rat_$greater(rat_-2/13, rat_0) & ~ rat_$greater(rat_169/4, rat_169/4) & ~
% 10.91/2.21 rat_$greater(rat_-13, rat_1) & ~ rat_$greater(rat_-13, rat_-2/13) & ~
% 10.91/2.21 rat_$greater(rat_-13, rat_169/4) & ~ rat_$greater(rat_-13, rat_-13) & ~
% 10.91/2.21 rat_$greater(rat_-13, rat_13/2) & ~ rat_$greater(rat_-13, rat_-13/2) & ~
% 10.91/2.21 rat_$greater(rat_-13, rat_0) & ~ rat_$greater(rat_13/2, rat_169/4) & ~
% 10.91/2.21 rat_$greater(rat_13/2, rat_13/2) & ~ rat_$greater(rat_-13/2, rat_1) & ~
% 10.91/2.21 rat_$greater(rat_-13/2, rat_-2/13) & ~ rat_$greater(rat_-13/2, rat_169/4) &
% 10.91/2.21 ~ rat_$greater(rat_-13/2, rat_13/2) & ~ rat_$greater(rat_-13/2, rat_-13/2) &
% 10.91/2.21 ~ rat_$greater(rat_-13/2, rat_0) & ~ rat_$greater(rat_0, rat_1) & ~
% 10.91/2.21 rat_$greater(rat_0, rat_169/4) & ~ rat_$greater(rat_0, rat_13/2) & ~
% 10.91/2.21 rat_$greater(rat_0, rat_0) & ~ rat_$lesseq(rat_1, rat_-2/13) & ~
% 10.91/2.21 rat_$lesseq(rat_1, rat_-13) & ~ rat_$lesseq(rat_1, rat_-13/2) & ~
% 10.91/2.21 rat_$lesseq(rat_1, rat_0) & ~ rat_$lesseq(rat_-2/13, rat_-13) & ~
% 10.91/2.21 rat_$lesseq(rat_-2/13, rat_-13/2) & ~ rat_$lesseq(rat_169/4, rat_1) & ~
% 10.91/2.21 rat_$lesseq(rat_169/4, rat_-2/13) & ~ rat_$lesseq(rat_169/4, rat_-13) & ~
% 10.91/2.21 rat_$lesseq(rat_169/4, rat_13/2) & ~ rat_$lesseq(rat_169/4, rat_-13/2) & ~
% 10.91/2.21 rat_$lesseq(rat_169/4, rat_0) & ~ rat_$lesseq(rat_13/2, rat_1) & ~
% 10.91/2.21 rat_$lesseq(rat_13/2, rat_-2/13) & ~ rat_$lesseq(rat_13/2, rat_-13) & ~
% 10.91/2.21 rat_$lesseq(rat_13/2, rat_-13/2) & ~ rat_$lesseq(rat_13/2, rat_0) & ~
% 10.91/2.21 rat_$lesseq(rat_-13/2, rat_-13) & ~ rat_$lesseq(rat_0, rat_-2/13) & ~
% 10.91/2.21 rat_$lesseq(rat_0, rat_-13) & ~ rat_$lesseq(rat_0, rat_-13/2) & ~
% 10.91/2.21 rat_$less(rat_1, rat_1) & ~ rat_$less(rat_1, rat_-2/13) & ~ rat_$less(rat_1,
% 10.91/2.21 rat_-13) & ~ rat_$less(rat_1, rat_-13/2) & ~ rat_$less(rat_1, rat_0) & ~
% 10.91/2.21 rat_$less(rat_-2/13, rat_-2/13) & ~ rat_$less(rat_-2/13, rat_-13) & ~
% 10.91/2.21 rat_$less(rat_-2/13, rat_-13/2) & ~ rat_$less(rat_169/4, rat_1) & ~
% 10.91/2.21 rat_$less(rat_169/4, rat_-2/13) & ~ rat_$less(rat_169/4, rat_169/4) & ~
% 10.91/2.21 rat_$less(rat_169/4, rat_-13) & ~ rat_$less(rat_169/4, rat_13/2) & ~
% 10.91/2.21 rat_$less(rat_169/4, rat_-13/2) & ~ rat_$less(rat_169/4, rat_0) & ~
% 10.91/2.21 rat_$less(rat_-13, rat_-13) & ~ rat_$less(rat_13/2, rat_1) & ~
% 10.91/2.21 rat_$less(rat_13/2, rat_-2/13) & ~ rat_$less(rat_13/2, rat_-13) & ~
% 10.91/2.21 rat_$less(rat_13/2, rat_13/2) & ~ rat_$less(rat_13/2, rat_-13/2) & ~
% 10.91/2.21 rat_$less(rat_13/2, rat_0) & ~ rat_$less(rat_-13/2, rat_-13) & ~
% 10.91/2.21 rat_$less(rat_-13/2, rat_-13/2) & ~ rat_$less(rat_0, rat_-2/13) & ~
% 10.91/2.21 rat_$less(rat_0, rat_-13) & ~ rat_$less(rat_0, rat_-13/2) & ~
% 10.91/2.21 rat_$less(rat_0, rat_0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : !
% 10.91/2.21 [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2,
% 10.91/2.21 v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) =
% 10.91/2.21 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3
% 10.91/2.21 = v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1,
% 10.91/2.21 v0) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 10.91/2.21 $rat] : ( ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) |
% 10.91/2.21 rat_$difference(v1, v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 10.91/2.21 $rat] : (v2 = rat_0 | ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) =
% 10.91/2.21 v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 10.91/2.21 (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] :
% 10.91/2.21 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0)
% 10.91/2.21 = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ rat_$lesseq(v2,
% 10.91/2.21 v1) | ~ rat_$lesseq(v1, v0) | rat_$lesseq(v2, v0)) & ! [v0: $rat] : !
% 10.91/2.21 [v1: $rat] : ! [v2: $rat] : ( ~ rat_$lesseq(v2, v1) | ~ rat_$less(v1, v0) |
% 10.91/2.21 rat_$less(v2, v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 10.91/2.21 rat_$lesseq(v1, v0) | ~ rat_$less(v2, v1) | rat_$less(v2, v0)) & ! [v0:
% 10.91/2.21 $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0:
% 10.91/2.21 $rat] : ! [v1: $rat] : (v1 = v0 | ~ rat_$lesseq(v1, v0) | rat_$less(v1,
% 10.91/2.21 v0)) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 10.91/2.21 rat_$uminus(v1) = v0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 10.91/2.21 rat_$greatereq(v0, v1) | rat_$lesseq(v1, v0)) & ! [v0: $rat] : ! [v1:
% 10.91/2.21 $rat] : ( ~ rat_$greater(v0, v1) | rat_$less(v1, v0)) & ! [v0: $rat] : !
% 10.91/2.22 [v1: $rat] : ( ~ rat_$lesseq(v1, v0) | rat_$greatereq(v0, v1)) & ! [v0: $rat]
% 10.91/2.22 : ! [v1: $rat] : ( ~ rat_$less(v1, v0) | rat_$greater(v0, v1)) & ! [v0:
% 10.91/2.22 $rat] : ! [v1: $rat] : ( ~ rat_$less(v1, v0) | rat_$lesseq(v1, v0)) & !
% 10.91/2.22 [v0: $rat] : (v0 = rat_0 | ~ (rat_$uminus(v0) = v0)) & ? [v0: $rat] :
% 10.91/2.22 rat_$lesseq(v0, v0)
% 10.91/2.22
% 10.91/2.22 Those formulas are unsatisfiable:
% 10.91/2.22 ---------------------------------
% 10.91/2.22
% 10.91/2.22 Begin of proof
% 10.91/2.22 |
% 10.91/2.22 | ALPHA: (input) implies:
% 10.91/2.22 | (1) rat_$less(rat_-13, rat_-13/2)
% 10.91/2.22 | (2) rat_$sum(rat_-13/2, rat_-13/2) = rat_-13
% 10.91/2.22 |
% 10.91/2.22 | GROUND_INST: instantiating (rat_combined_problem_8) with rat_-13/2, rat_-13,
% 10.91/2.22 | simplifying with (1), (2) gives:
% 10.91/2.22 | (3) $false
% 10.91/2.22 |
% 10.91/2.22 | CLOSE: (3) is inconsistent.
% 10.91/2.22 |
% 10.91/2.22 End of proof
% 10.91/2.22 % SZS output end Proof for theBenchmark
% 10.91/2.22
% 10.91/2.22 1623ms
%------------------------------------------------------------------------------