TSTP Solution File: ARI259_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI259_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 : n029.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 17:47:28 EDT 2023
% Result : Theorem 12.71s 2.43s
% Output : Proof 26.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI259_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 18:58:12 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.68/0.65 ________ _____
% 0.68/0.65 ___ __ \_________(_)________________________________
% 0.68/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.68/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.68/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.68/0.65
% 0.68/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.68/0.65 (2023-06-19)
% 0.68/0.65
% 0.68/0.65 (c) Philipp Rümmer, 2009-2023
% 0.68/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.68/0.65 Amanda Stjerna.
% 0.68/0.65 Free software under BSD-3-Clause.
% 0.68/0.65
% 0.68/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.68/0.65
% 0.68/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.67 Running up to 7 provers in parallel.
% 0.68/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.69/0.94 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.69/0.94 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.30/1.05 Prover 4: Preprocessing ...
% 2.30/1.05 Prover 1: Preprocessing ...
% 2.81/1.11 Prover 6: Preprocessing ...
% 2.81/1.11 Prover 0: Preprocessing ...
% 3.83/1.28 Prover 5: Preprocessing ...
% 3.83/1.28 Prover 3: Preprocessing ...
% 3.83/1.28 Prover 2: Preprocessing ...
% 6.65/1.69 Prover 6: Constructing countermodel ...
% 7.26/1.69 Prover 1: Constructing countermodel ...
% 7.26/1.73 Prover 4: Constructing countermodel ...
% 7.26/1.74 Prover 0: Proving ...
% 11.18/2.21 Prover 1: gave up
% 11.18/2.21 Prover 6: gave up
% 11.18/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.18/2.22 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 11.18/2.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.18/2.24 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 11.18/2.24 Prover 8: Preprocessing ...
% 11.18/2.27 Prover 7: Preprocessing ...
% 11.83/2.38 Prover 8: Warning: ignoring some quantifiers
% 12.59/2.39 Prover 8: Constructing countermodel ...
% 12.71/2.43 Prover 0: proved (1753ms)
% 12.71/2.43
% 12.71/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.71/2.43
% 12.71/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.71/2.43 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 13.51/2.52 Prover 10: Preprocessing ...
% 14.22/2.65 Prover 8: gave up
% 14.22/2.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.22/2.65 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 14.91/2.69 Prover 11: Preprocessing ...
% 15.93/2.84 Prover 2: Proving ...
% 15.93/2.84 Prover 2: stopped
% 15.93/2.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.93/2.86 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 15.93/2.86 Prover 13: Preprocessing ...
% 15.93/2.91 Prover 3: Constructing countermodel ...
% 16.62/2.95 Prover 3: stopped
% 16.62/2.95 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.62/2.95 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 16.62/2.97 Prover 5: Proving ...
% 16.62/2.98 Prover 5: stopped
% 17.19/2.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 17.19/3.00 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation
% 17.19/3.00 Prover 16: Preprocessing ...
% 17.19/3.00 Prover 13: Warning: ignoring some quantifiers
% 17.19/3.00 Prover 4: Found proof (size 22)
% 17.19/3.00 Prover 4: proved (2317ms)
% 17.19/3.00 Prover 13: Constructing countermodel ...
% 17.19/3.00 Prover 13: stopped
% 17.19/3.03 Prover 19: Preprocessing ...
% 17.84/3.08 Prover 10: stopped
% 18.18/3.14 Prover 7: Warning: ignoring some quantifiers
% 18.18/3.15 Prover 7: Constructing countermodel ...
% 18.18/3.20 Prover 7: stopped
% 20.10/3.43 Prover 11: stopped
% 20.57/3.52 Prover 16: stopped
% 25.12/4.61 Prover 19: Warning: ignoring some quantifiers
% 25.12/4.62 Prover 19: Constructing countermodel ...
% 25.46/4.69 Prover 19: stopped
% 25.46/4.69
% 25.46/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.46/4.69
% 25.46/4.69 % SZS output start Proof for theBenchmark
% 25.46/4.70 Assumptions after simplification:
% 25.46/4.70 ---------------------------------
% 25.46/4.70
% 25.46/4.70 (rat_sum_problem_14)
% 25.46/4.74 ? [v0: $rat] : ( ~ (v0 = rat_23/4) & rat_$sum(rat_17/4, v0) = rat_10)
% 25.46/4.74
% 25.46/4.74 (input)
% 25.93/4.79 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_23/4) & ~
% 25.93/4.79 (rat_very_large = rat_10) & ~ (rat_very_large = rat_17/4) & ~
% 25.93/4.79 (rat_very_large = rat_0) & ~ (rat_very_small = rat_23/4) & ~ (rat_very_small
% 25.93/4.79 = rat_10) & ~ (rat_very_small = rat_17/4) & ~ (rat_very_small = rat_0) &
% 25.93/4.79 ~ (rat_23/4 = rat_10) & ~ (rat_23/4 = rat_17/4) & ~ (rat_23/4 = rat_0) & ~
% 25.93/4.79 (rat_10 = rat_17/4) & ~ (rat_10 = rat_0) & ~ (rat_17/4 = rat_0) &
% 25.93/4.79 rat_$is_int(rat_23/4) = 1 & rat_$is_int(rat_10) = 0 & rat_$is_int(rat_17/4) =
% 25.93/4.79 1 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_23/4) = 0 & rat_$is_rat(rat_10) =
% 25.93/4.79 0 & rat_$is_rat(rat_17/4) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_10) =
% 25.93/4.79 rat_10 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_10) = rat_10 &
% 25.93/4.79 rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_10) = rat_10 &
% 25.93/4.79 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_10) = rat_10 & rat_$round(rat_0)
% 25.93/4.79 = rat_0 & rat_$to_int(rat_23/4) = 5 & rat_$to_int(rat_10) = 10 &
% 25.93/4.79 rat_$to_int(rat_17/4) = 4 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_23/4) =
% 25.93/4.79 rat_23/4 & rat_$to_rat(rat_10) = rat_10 & rat_$to_rat(rat_17/4) = rat_17/4 &
% 25.93/4.79 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_23/4) = real_23/4 &
% 25.93/4.79 rat_$to_real(rat_10) = real_10 & rat_$to_real(rat_17/4) = real_17/4 &
% 25.93/4.79 rat_$to_real(rat_0) = real_0 & int_$to_rat(10) = rat_10 & int_$to_rat(0) =
% 25.93/4.79 rat_0 & rat_$quotient(rat_0, rat_23/4) = rat_0 & rat_$quotient(rat_0, rat_10)
% 25.93/4.79 = rat_0 & rat_$quotient(rat_0, rat_17/4) = rat_0 & rat_$product(rat_23/4,
% 25.93/4.79 rat_0) = rat_0 & rat_$product(rat_10, rat_0) = rat_0 &
% 25.93/4.79 rat_$product(rat_17/4, rat_0) = rat_0 & rat_$product(rat_0, rat_23/4) = rat_0
% 25.93/4.79 & rat_$product(rat_0, rat_10) = rat_0 & rat_$product(rat_0, rat_17/4) = rat_0
% 25.93/4.79 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_23/4, rat_23/4) =
% 25.93/4.79 rat_0 & rat_$difference(rat_23/4, rat_0) = rat_23/4 & rat_$difference(rat_10,
% 25.93/4.80 rat_23/4) = rat_17/4 & rat_$difference(rat_10, rat_10) = rat_0 &
% 25.93/4.80 rat_$difference(rat_10, rat_17/4) = rat_23/4 & rat_$difference(rat_10, rat_0)
% 25.93/4.80 = rat_10 & rat_$difference(rat_17/4, rat_17/4) = rat_0 &
% 25.93/4.80 rat_$difference(rat_17/4, rat_0) = rat_17/4 & rat_$difference(rat_0, rat_0) =
% 25.93/4.80 rat_0 & rat_$uminus(rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 25.93/4.80 rat_very_large) = 1 & rat_$greatereq(rat_23/4, rat_23/4) = 0 &
% 25.93/4.80 rat_$greatereq(rat_23/4, rat_10) = 1 & rat_$greatereq(rat_23/4, rat_17/4) = 0
% 25.93/4.80 & rat_$greatereq(rat_23/4, rat_0) = 0 & rat_$greatereq(rat_10, rat_23/4) = 0 &
% 25.93/4.80 rat_$greatereq(rat_10, rat_10) = 0 & rat_$greatereq(rat_10, rat_17/4) = 0 &
% 25.93/4.80 rat_$greatereq(rat_10, rat_0) = 0 & rat_$greatereq(rat_17/4, rat_23/4) = 1 &
% 25.93/4.80 rat_$greatereq(rat_17/4, rat_10) = 1 & rat_$greatereq(rat_17/4, rat_17/4) = 0
% 25.93/4.80 & rat_$greatereq(rat_17/4, rat_0) = 0 & rat_$greatereq(rat_0, rat_23/4) = 1 &
% 25.93/4.80 rat_$greatereq(rat_0, rat_10) = 1 & rat_$greatereq(rat_0, rat_17/4) = 1 &
% 25.93/4.80 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 25.93/4.80 = 0 & rat_$lesseq(rat_23/4, rat_23/4) = 0 & rat_$lesseq(rat_23/4, rat_10) = 0
% 25.93/4.80 & rat_$lesseq(rat_23/4, rat_17/4) = 1 & rat_$lesseq(rat_23/4, rat_0) = 1 &
% 25.93/4.80 rat_$lesseq(rat_10, rat_23/4) = 1 & rat_$lesseq(rat_10, rat_10) = 0 &
% 25.93/4.80 rat_$lesseq(rat_10, rat_17/4) = 1 & rat_$lesseq(rat_10, rat_0) = 1 &
% 25.93/4.80 rat_$lesseq(rat_17/4, rat_23/4) = 0 & rat_$lesseq(rat_17/4, rat_10) = 0 &
% 25.93/4.80 rat_$lesseq(rat_17/4, rat_17/4) = 0 & rat_$lesseq(rat_17/4, rat_0) = 1 &
% 25.93/4.80 rat_$lesseq(rat_0, rat_23/4) = 0 & rat_$lesseq(rat_0, rat_10) = 0 &
% 25.93/4.80 rat_$lesseq(rat_0, rat_17/4) = 0 & rat_$lesseq(rat_0, rat_0) = 0 &
% 25.93/4.80 rat_$greater(rat_very_large, rat_23/4) = 0 & rat_$greater(rat_very_large,
% 25.93/4.80 rat_10) = 0 & rat_$greater(rat_very_large, rat_17/4) = 0 &
% 25.93/4.80 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 25.93/4.80 rat_very_large) = 1 & rat_$greater(rat_23/4, rat_very_small) = 0 &
% 25.93/4.80 rat_$greater(rat_23/4, rat_23/4) = 1 & rat_$greater(rat_23/4, rat_10) = 1 &
% 25.93/4.80 rat_$greater(rat_23/4, rat_17/4) = 0 & rat_$greater(rat_23/4, rat_0) = 0 &
% 25.93/4.80 rat_$greater(rat_10, rat_very_small) = 0 & rat_$greater(rat_10, rat_23/4) = 0
% 25.93/4.80 & rat_$greater(rat_10, rat_10) = 1 & rat_$greater(rat_10, rat_17/4) = 0 &
% 25.93/4.80 rat_$greater(rat_10, rat_0) = 0 & rat_$greater(rat_17/4, rat_very_small) = 0 &
% 25.93/4.80 rat_$greater(rat_17/4, rat_23/4) = 1 & rat_$greater(rat_17/4, rat_10) = 1 &
% 25.93/4.80 rat_$greater(rat_17/4, rat_17/4) = 1 & rat_$greater(rat_17/4, rat_0) = 0 &
% 25.93/4.80 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_23/4) = 1 &
% 25.93/4.80 rat_$greater(rat_0, rat_10) = 1 & rat_$greater(rat_0, rat_17/4) = 1 &
% 25.93/4.80 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 25.93/4.80 & rat_$less(rat_very_small, rat_23/4) = 0 & rat_$less(rat_very_small, rat_10)
% 25.93/4.80 = 0 & rat_$less(rat_very_small, rat_17/4) = 0 & rat_$less(rat_very_small,
% 25.93/4.80 rat_0) = 0 & rat_$less(rat_23/4, rat_very_large) = 0 & rat_$less(rat_23/4,
% 25.93/4.80 rat_23/4) = 1 & rat_$less(rat_23/4, rat_10) = 0 & rat_$less(rat_23/4,
% 25.93/4.80 rat_17/4) = 1 & rat_$less(rat_23/4, rat_0) = 1 & rat_$less(rat_10,
% 25.93/4.80 rat_very_large) = 0 & rat_$less(rat_10, rat_23/4) = 1 & rat_$less(rat_10,
% 25.93/4.80 rat_10) = 1 & rat_$less(rat_10, rat_17/4) = 1 & rat_$less(rat_10, rat_0) = 1
% 25.93/4.80 & rat_$less(rat_17/4, rat_very_large) = 0 & rat_$less(rat_17/4, rat_23/4) = 0
% 25.93/4.80 & rat_$less(rat_17/4, rat_10) = 0 & rat_$less(rat_17/4, rat_17/4) = 1 &
% 25.93/4.80 rat_$less(rat_17/4, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 25.93/4.80 rat_$less(rat_0, rat_23/4) = 0 & rat_$less(rat_0, rat_10) = 0 &
% 25.93/4.80 rat_$less(rat_0, rat_17/4) = 0 & rat_$less(rat_0, rat_0) = 1 &
% 25.93/4.80 rat_$sum(rat_23/4, rat_17/4) = rat_10 & rat_$sum(rat_23/4, rat_0) = rat_23/4 &
% 25.93/4.80 rat_$sum(rat_10, rat_0) = rat_10 & rat_$sum(rat_17/4, rat_23/4) = rat_10 &
% 25.93/4.80 rat_$sum(rat_17/4, rat_0) = rat_17/4 & rat_$sum(rat_0, rat_23/4) = rat_23/4 &
% 25.93/4.80 rat_$sum(rat_0, rat_10) = rat_10 & rat_$sum(rat_0, rat_17/4) = rat_17/4 &
% 25.93/4.80 rat_$sum(rat_0, rat_0) = rat_0 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 25.93/4.80 : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~
% 25.93/4.80 (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : (rat_$sum(v2, v5) = v4 &
% 25.93/4.80 rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 25.93/4.80 ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1,
% 25.93/4.80 v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) =
% 25.93/4.80 v5)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3
% 25.93/4.80 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v2, v0) = v3) | ? [v4:
% 25.93/4.80 int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1:
% 25.93/4.80 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) =
% 25.93/4.80 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 25.93/4.80 rat_$less(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 25.93/4.80 ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1,
% 25.93/4.80 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & !
% 25.93/4.80 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 25.93/4.80 (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 25.93/4.80 (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 25.93/4.80 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) = 0) | ~
% 25.93/4.80 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0)
% 25.93/4.80 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] :
% 25.93/4.80 (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4:
% 25.93/4.80 int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1:
% 25.93/4.80 $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~ (rat_$uminus(v0) = v2) | ~
% 25.93/4.80 (rat_$sum(v1, v2) = v3) | rat_$difference(v1, v0) = v3) & ! [v0: $rat] : !
% 25.93/4.80 [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (rat_$less(v1, v0) = v2) |
% 25.93/4.80 ? [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 25.93/4.80 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 25.93/4.80 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 25.93/4.80 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 25.93/4.80 int] : ( ~ (v3 = 0) & rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : !
% 25.93/4.80 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3:
% 25.93/4.80 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 25.93/4.80 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3:
% 25.93/4.80 int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1:
% 25.93/4.80 $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int]
% 25.93/4.80 : ( ~ (v3 = 0) & rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat]
% 25.93/4.80 : ! [v2: $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) |
% 25.93/4.80 rat_$quotient(v2, v0) = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 25.93/4.80 : ( ~ (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat]
% 25.93/4.80 : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 25.93/4.80 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 25.93/4.81 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 &
% 25.93/4.81 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 25.93/4.81 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2,
% 25.93/4.81 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 25.93/4.81 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 25.93/4.81 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1,
% 25.93/4.81 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) |
% 25.93/4.81 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 25.93/4.81 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 25.93/4.81 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &
% 25.93/4.81 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & !
% 25.93/4.81 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 25.93/4.81 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1)
% 25.93/4.81 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0)
% 25.93/4.81 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 25.93/4.81 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : !
% 25.93/4.81 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) =
% 25.93/4.81 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 25.93/4.81 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~
% 25.93/4.81 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 =
% 25.93/4.81 rat_0 | ~ (rat_$uminus(v0) = v0))
% 25.93/4.81
% 25.93/4.81 (function-axioms)
% 25.93/4.81 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 25.93/4.81 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 25.93/4.81 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 25.93/4.81 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 25.93/4.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 25.93/4.81 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 25.93/4.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 25.93/4.81 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 25.93/4.81 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.93/4.81 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 25.93/4.81 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 25.93/4.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 25.93/4.81 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 25.93/4.81 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1
% 25.93/4.81 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 25.93/4.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 25.93/4.81 ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0:
% 25.93/4.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 25.93/4.81 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : !
% 25.93/4.81 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 25.93/4.81 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 25.93/4.81 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 25.93/4.81 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 25.93/4.81 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 25.93/4.81 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 25.93/4.81 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 25.93/4.81 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 25.93/4.81 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 25.93/4.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 25.93/4.81 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 25.93/4.81 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 25.93/4.81 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 25.93/4.81 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 25.93/4.81
% 25.93/4.81 Those formulas are unsatisfiable:
% 25.93/4.81 ---------------------------------
% 25.93/4.81
% 25.93/4.81 Begin of proof
% 26.14/4.82 |
% 26.14/4.82 | ALPHA: (function-axioms) implies:
% 26.14/4.82 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~
% 26.14/4.82 | (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 26.14/4.82 | (2) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 =
% 26.14/4.82 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0))
% 26.14/4.82 |
% 26.14/4.82 | ALPHA: (input) implies:
% 26.14/4.82 | (3) rat_$difference(rat_17/4, rat_17/4) = rat_0
% 26.14/4.82 | (4) rat_$difference(rat_10, rat_17/4) = rat_23/4
% 26.14/4.82 | (5) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) =
% 26.14/4.82 | v1))
% 26.14/4.82 | (6) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) =
% 26.14/4.82 | v2) | rat_$sum(v0, v1) = v2)
% 26.14/4.82 | (7) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 26.14/4.82 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) =
% 26.14/4.82 | v3 & rat_$sum(v1, v3) = v2))
% 26.14/4.82 | (8) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 26.14/4.82 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ?
% 26.14/4.82 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5))
% 26.14/4.82 |
% 26.14/4.82 | DELTA: instantiating (rat_sum_problem_14) with fresh symbol all_5_0 gives:
% 26.14/4.82 | (9) ~ (all_5_0 = rat_23/4) & rat_$sum(rat_17/4, all_5_0) = rat_10
% 26.14/4.82 |
% 26.14/4.82 | ALPHA: (9) implies:
% 26.14/4.82 | (10) ~ (all_5_0 = rat_23/4)
% 26.14/4.82 | (11) rat_$sum(rat_17/4, all_5_0) = rat_10
% 26.14/4.82 |
% 26.14/4.82 | GROUND_INST: instantiating (6) with all_5_0, rat_17/4, rat_10, simplifying
% 26.14/4.82 | with (11) gives:
% 26.14/4.82 | (12) rat_$sum(all_5_0, rat_17/4) = rat_10
% 26.14/4.82 |
% 26.14/4.82 | GROUND_INST: instantiating (7) with rat_17/4, rat_17/4, rat_0, simplifying
% 26.14/4.82 | with (3) gives:
% 26.14/4.82 | (13) ? [v0: $rat] : (rat_$uminus(rat_17/4) = v0 & rat_$sum(rat_17/4, v0) =
% 26.14/4.82 | rat_0)
% 26.14/4.82 |
% 26.14/4.82 | GROUND_INST: instantiating (7) with rat_17/4, rat_10, rat_23/4, simplifying
% 26.14/4.82 | with (4) gives:
% 26.14/4.83 | (14) ? [v0: $rat] : (rat_$uminus(rat_17/4) = v0 & rat_$sum(rat_10, v0) =
% 26.14/4.83 | rat_23/4)
% 26.14/4.83 |
% 26.14/4.83 | DELTA: instantiating (13) with fresh symbol all_23_0 gives:
% 26.14/4.83 | (15) rat_$uminus(rat_17/4) = all_23_0 & rat_$sum(rat_17/4, all_23_0) =
% 26.14/4.83 | rat_0
% 26.14/4.83 |
% 26.14/4.83 | ALPHA: (15) implies:
% 26.14/4.83 | (16) rat_$sum(rat_17/4, all_23_0) = rat_0
% 26.14/4.83 | (17) rat_$uminus(rat_17/4) = all_23_0
% 26.14/4.83 |
% 26.14/4.83 | DELTA: instantiating (14) with fresh symbol all_27_0 gives:
% 26.14/4.83 | (18) rat_$uminus(rat_17/4) = all_27_0 & rat_$sum(rat_10, all_27_0) =
% 26.14/4.83 | rat_23/4
% 26.14/4.83 |
% 26.14/4.83 | ALPHA: (18) implies:
% 26.14/4.83 | (19) rat_$sum(rat_10, all_27_0) = rat_23/4
% 26.14/4.83 | (20) rat_$uminus(rat_17/4) = all_27_0
% 26.14/4.83 |
% 26.14/4.83 | GROUND_INST: instantiating (1) with all_23_0, all_27_0, rat_17/4, simplifying
% 26.14/4.83 | with (17), (20) gives:
% 26.14/4.83 | (21) all_27_0 = all_23_0
% 26.14/4.83 |
% 26.14/4.83 | REDUCE: (19), (21) imply:
% 26.14/4.83 | (22) rat_$sum(rat_10, all_23_0) = rat_23/4
% 26.14/4.83 |
% 26.14/4.83 | GROUND_INST: instantiating (8) with all_23_0, rat_17/4, all_5_0, rat_10,
% 26.14/4.83 | rat_23/4, simplifying with (12), (22) gives:
% 26.14/4.83 | (23) ? [v0: $rat] : (rat_$sum(all_5_0, v0) = rat_23/4 & rat_$sum(rat_17/4,
% 26.14/4.83 | all_23_0) = v0)
% 26.14/4.83 |
% 26.14/4.83 | DELTA: instantiating (23) with fresh symbol all_183_0 gives:
% 26.14/4.83 | (24) rat_$sum(all_5_0, all_183_0) = rat_23/4 & rat_$sum(rat_17/4, all_23_0)
% 26.14/4.83 | = all_183_0
% 26.14/4.83 |
% 26.14/4.83 | ALPHA: (24) implies:
% 26.14/4.83 | (25) rat_$sum(rat_17/4, all_23_0) = all_183_0
% 26.14/4.83 | (26) rat_$sum(all_5_0, all_183_0) = rat_23/4
% 26.14/4.83 |
% 26.14/4.83 | GROUND_INST: instantiating (2) with rat_0, all_183_0, all_23_0, rat_17/4,
% 26.14/4.83 | simplifying with (16), (25) gives:
% 26.14/4.83 | (27) all_183_0 = rat_0
% 26.14/4.83 |
% 26.14/4.83 | REDUCE: (26), (27) imply:
% 26.14/4.83 | (28) rat_$sum(all_5_0, rat_0) = rat_23/4
% 26.14/4.83 |
% 26.14/4.83 | GROUND_INST: instantiating (5) with all_5_0, rat_23/4, simplifying with (28)
% 26.14/4.83 | gives:
% 26.14/4.83 | (29) all_5_0 = rat_23/4
% 26.14/4.83 |
% 26.14/4.83 | REDUCE: (10), (29) imply:
% 26.14/4.83 | (30) $false
% 26.14/4.83 |
% 26.14/4.83 | CLOSE: (30) is inconsistent.
% 26.14/4.83 |
% 26.14/4.83 End of proof
% 26.14/4.83 % SZS output end Proof for theBenchmark
% 26.14/4.83
% 26.14/4.83 4183ms
%------------------------------------------------------------------------------