TSTP Solution File: MSC017+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MSC017+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 : Thu Aug 31 09:26:47 EDT 2023
% Result : Theorem 3.95s 1.40s
% Output : Proof 7.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MSC017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n001.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 : Thu Aug 24 14:21:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 1.86/0.97 Prover 4: Preprocessing ...
% 1.86/0.97 Prover 1: Preprocessing ...
% 2.43/1.02 Prover 3: Preprocessing ...
% 2.43/1.02 Prover 2: Preprocessing ...
% 2.43/1.02 Prover 5: Preprocessing ...
% 2.43/1.02 Prover 6: Preprocessing ...
% 2.43/1.03 Prover 0: Preprocessing ...
% 3.95/1.25 Prover 1: Constructing countermodel ...
% 3.95/1.25 Prover 3: Constructing countermodel ...
% 3.95/1.26 Prover 5: Constructing countermodel ...
% 3.95/1.27 Prover 6: Proving ...
% 3.95/1.27 Prover 2: Proving ...
% 3.95/1.28 Prover 4: Constructing countermodel ...
% 3.95/1.39 Prover 3: gave up
% 3.95/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.95/1.40 Prover 5: proved (760ms)
% 3.95/1.40
% 3.95/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/1.40
% 3.95/1.41 Prover 2: proved (771ms)
% 3.95/1.41
% 3.95/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/1.41
% 4.91/1.41 Prover 0: Proving ...
% 4.91/1.41 Prover 6: stopped
% 4.91/1.42 Prover 0: stopped
% 4.91/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.91/1.44 Prover 7: Preprocessing ...
% 4.91/1.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.91/1.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.91/1.44 Prover 8: Preprocessing ...
% 4.91/1.44 Prover 10: Preprocessing ...
% 4.91/1.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.91/1.45 Prover 11: Preprocessing ...
% 4.91/1.46 Prover 13: Preprocessing ...
% 4.91/1.48 Prover 1: gave up
% 4.91/1.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.83/1.50 Prover 7: Constructing countermodel ...
% 5.83/1.50 Prover 10: Constructing countermodel ...
% 5.83/1.51 Prover 8: Warning: ignoring some quantifiers
% 5.83/1.51 Prover 16: Preprocessing ...
% 5.83/1.53 Prover 13: Constructing countermodel ...
% 5.83/1.53 Prover 7: gave up
% 5.83/1.54 Prover 8: Constructing countermodel ...
% 5.83/1.54 Prover 10: gave up
% 5.83/1.54 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.83/1.55 Prover 16: Constructing countermodel ...
% 5.83/1.55 Prover 19: Preprocessing ...
% 6.52/1.59 Prover 11: Constructing countermodel ...
% 6.57/1.59 Prover 4: Found proof (size 65)
% 6.57/1.59 Prover 4: proved (959ms)
% 6.57/1.59 Prover 13: stopped
% 6.57/1.59 Prover 16: stopped
% 6.57/1.59 Prover 8: stopped
% 6.57/1.60 Prover 11: stopped
% 6.65/1.61 Prover 19: Warning: ignoring some quantifiers
% 6.65/1.62 Prover 19: Constructing countermodel ...
% 6.65/1.62 Prover 19: stopped
% 6.65/1.62
% 6.65/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.65/1.62
% 6.65/1.64 % SZS output start Proof for theBenchmark
% 6.65/1.64 Assumptions after simplification:
% 6.65/1.64 ---------------------------------
% 6.65/1.64
% 6.65/1.64 (dci_is_the_only_bad_outcome)
% 6.65/1.67 $i(dci) & ! [v0: $i] : ! [v1: $i] : (v1 = dci | ~ (bad(v1) = 0) | ~
% 6.65/1.67 (dive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 6.65/1.67 outcome(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (v1 = dci | ~
% 6.65/1.67 (outcome(v0, v1) = 0) | ~ (dive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 6.65/1.67 int] : ( ~ (v2 = 0) & bad(v1) = v2))
% 6.65/1.67
% 6.65/1.67 (depth_and_time_and_nitrogen)
% 6.65/1.69 $i(nitrogen_limit) & $i(time_limit) & $i(depth_limit) & ! [v0: $i] : ! [v1:
% 6.65/1.69 $i] : ( ~ (depth(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 6.65/1.69 [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : (greater(v6,
% 6.65/1.69 nitrogen_limit) = v7 & greater(v4, time_limit) = v5 & greater(v1,
% 6.65/1.69 depth_limit) = v3 & dive(v0) = v2 & nitrogen(v0) = v6 & time(v0) = v4 &
% 6.65/1.69 $i(v6) & $i(v4) & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v5 = 0 | v3 = 0) & (v7 =
% 6.65/1.69 0 | ( ~ (v5 = 0) & ~ (v3 = 0))))))) & ! [v0: $i] : ! [v1: $i] : (
% 6.65/1.69 ~ (nitrogen(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4:
% 6.65/1.69 any] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : (greater(v5,
% 6.65/1.69 time_limit) = v6 & greater(v3, depth_limit) = v4 & greater(v1,
% 6.65/1.69 nitrogen_limit) = v7 & depth(v0) = v3 & dive(v0) = v2 & time(v0) = v5 &
% 6.65/1.69 $i(v5) & $i(v3) & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v6 = 0 | v4 = 0) & (v7 =
% 6.65/1.69 0 | ( ~ (v6 = 0) & ~ (v4 = 0))))))) & ! [v0: $i] : ! [v1: $i] : (
% 6.65/1.69 ~ (time(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 6.65/1.69 ? [v5: any] : ? [v6: $i] : ? [v7: any] : (greater(v6, nitrogen_limit) = v7
% 6.65/1.69 & greater(v3, depth_limit) = v4 & greater(v1, time_limit) = v5 & depth(v0)
% 6.65/1.69 = v3 & dive(v0) = v2 & nitrogen(v0) = v6 & $i(v6) & $i(v3) & ( ~ (v2 = 0)
% 6.65/1.69 | (( ~ (v7 = 0) | v5 = 0 | v4 = 0) & (v7 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 6.65/1.69 0))))))) & ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ?
% 6.65/1.69 [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6:
% 6.65/1.69 any] : (greater(v5, nitrogen_limit) = v6 & greater(v3, time_limit) = v4 &
% 6.65/1.69 greater(v1, depth_limit) = v2 & depth(v0) = v1 & nitrogen(v0) = v5 &
% 6.65/1.69 time(v0) = v3 & $i(v5) & $i(v3) & $i(v1) & ( ~ (v6 = 0) | v4 = 0 | v2 = 0)
% 6.65/1.69 & (v6 = 0 | ( ~ (v4 = 0) & ~ (v2 = 0)))))
% 6.65/1.69
% 6.65/1.69 (dive_nitrogen)
% 6.65/1.70 ! [v0: $i] : ! [v1: $i] : ( ~ (depth(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 6.65/1.70 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (dive(v0) = v2 & nitrogen(v0) = v3
% 6.65/1.70 & time(v0) = v4 & padi(v1, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 =
% 6.65/1.70 0) | v5 = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (nitrogen(v0) = v1)
% 6.65/1.70 | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 6.65/1.70 (depth(v0) = v3 & dive(v0) = v2 & time(v0) = v4 & padi(v3, v4) = v5 & $i(v5)
% 6.65/1.70 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v1))) & ! [v0: $i] : ! [v1: $i]
% 6.65/1.70 : ( ~ (time(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 6.65/1.70 ? [v5: $i] : (depth(v0) = v4 & dive(v0) = v2 & nitrogen(v0) = v3 & padi(v4,
% 6.65/1.70 v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & !
% 6.65/1.70 [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 6.65/1.70 [v3: $i] : (depth(v0) = v2 & nitrogen(v0) = v1 & time(v0) = v3 & padi(v2,
% 6.65/1.70 v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 6.65/1.70
% 6.65/1.70 (no_bad)
% 6.65/1.70 ? [v0: $i] : ? [v1: $i] : (bad(v1) = 0 & outcome(v0, v1) = 0 & dive(v0) = 0
% 6.65/1.70 & $i(v1) & $i(v0))
% 6.65/1.70
% 6.65/1.70 (no_deep_long)
% 7.12/1.70 $i(time_limit) & $i(depth_limit) & ! [v0: $i] : ! [v1: $i] : ( ~ (depth(v0)
% 7.12/1.70 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 7.12/1.70 any] : (greater(v4, time_limit) = v5 & greater(v1, depth_limit) = v3 &
% 7.12/1.70 dive(v0) = v2 & time(v0) = v4 & $i(v4) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & ~
% 7.12/1.70 (v3 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (time(v0) = v1) | ~
% 7.12/1.70 $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 7.12/1.70 (greater(v3, depth_limit) = v4 & greater(v1, time_limit) = v5 & depth(v0) =
% 7.12/1.70 v3 & dive(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v5 = 0) & ~ (v4 =
% 7.12/1.70 0))))) & ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 7.12/1.70 : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v2 = 0) &
% 7.12/1.70 greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 & depth(v0) =
% 7.12/1.70 v1 & time(v0) = v3 & $i(v3) & $i(v1)))
% 7.12/1.70
% 7.12/1.70 (too_much_nitrogen)
% 7.12/1.71 $i(dci) & $i(nitrogen_limit) & ! [v0: $i] : ! [v1: any] : ( ~ (outcome(v0,
% 7.12/1.71 dci) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 7.12/1.71 (greater(v3, nitrogen_limit) = v4 & dive(v0) = v2 & nitrogen(v0) = v3 &
% 7.12/1.71 $i(v3) & ( ~ (v2 = 0) | (( ~ (v4 = 0) | v1 = 0) & ( ~ (v1 = 0) | v4 =
% 7.12/1.71 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (nitrogen(v0) = v1) | ~
% 7.12/1.71 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (outcome(v0, dci) = v4
% 7.12/1.71 & greater(v1, nitrogen_limit) = v3 & dive(v0) = v2 & ( ~ (v2 = 0) | (( ~
% 7.12/1.71 (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) | v4 = 0))))) & ! [v0: $i] : ( ~
% 7.12/1.71 (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 7.12/1.71 (outcome(v0, dci) = v3 & greater(v1, nitrogen_limit) = v2 & nitrogen(v0) =
% 7.12/1.71 v1 & $i(v1) & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 7.12/1.71
% 7.12/1.71 (function-axioms)
% 7.12/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.12/1.71 [v3: $i] : (v1 = v0 | ~ (outcome(v3, v2) = v1) | ~ (outcome(v3, v2) = v0)) &
% 7.12/1.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.12/1.71 [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) &
% 7.12/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.12/1.71 (padi(v3, v2) = v1) | ~ (padi(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 7.12/1.71 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (bad(v2) = v1) | ~
% 7.12/1.71 (bad(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 7.12/1.71 (depth(v2) = v1) | ~ (depth(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.12/1.71 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (dive(v2) = v1) | ~
% 7.12/1.71 (dive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 7.12/1.71 (nitrogen(v2) = v1) | ~ (nitrogen(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 7.12/1.71 ! [v2: $i] : (v1 = v0 | ~ (time(v2) = v1) | ~ (time(v2) = v0))
% 7.12/1.71
% 7.12/1.71 Further assumptions not needed in the proof:
% 7.12/1.71 --------------------------------------------
% 7.12/1.71 bad_dci
% 7.12/1.71
% 7.12/1.71 Those formulas are unsatisfiable:
% 7.12/1.71 ---------------------------------
% 7.12/1.71
% 7.12/1.71 Begin of proof
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (dive_nitrogen) implies:
% 7.12/1.72 | (1) ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 7.12/1.72 | $i] : ? [v3: $i] : (depth(v0) = v2 & nitrogen(v0) = v1 & time(v0)
% 7.12/1.72 | = v3 & padi(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (depth_and_time_and_nitrogen) implies:
% 7.12/1.72 | (2) ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 7.12/1.72 | any] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 7.12/1.72 | (greater(v5, nitrogen_limit) = v6 & greater(v3, time_limit) = v4 &
% 7.12/1.72 | greater(v1, depth_limit) = v2 & depth(v0) = v1 & nitrogen(v0) = v5
% 7.12/1.72 | & time(v0) = v3 & $i(v5) & $i(v3) & $i(v1) & ( ~ (v6 = 0) | v4 = 0
% 7.12/1.72 | | v2 = 0) & (v6 = 0 | ( ~ (v4 = 0) & ~ (v2 = 0)))))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (too_much_nitrogen) implies:
% 7.12/1.72 | (3) ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 7.12/1.72 | any] : ? [v3: any] : (outcome(v0, dci) = v3 & greater(v1,
% 7.12/1.72 | nitrogen_limit) = v2 & nitrogen(v0) = v1 & $i(v1) & ( ~ (v3 = 0)
% 7.12/1.72 | | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (dci_is_the_only_bad_outcome) implies:
% 7.12/1.72 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = dci | ~ (bad(v1) = 0) | ~ (dive(v0)
% 7.12/1.72 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 7.12/1.72 | outcome(v0, v1) = v2))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (no_deep_long) implies:
% 7.12/1.72 | (5) ! [v0: $i] : ( ~ (dive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 7.12/1.72 | int] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v2 = 0) &
% 7.12/1.72 | greater(v3, time_limit) = v4 & greater(v1, depth_limit) = v2 &
% 7.12/1.72 | depth(v0) = v1 & time(v0) = v3 & $i(v3) & $i(v1)))
% 7.12/1.72 |
% 7.12/1.72 | ALPHA: (function-axioms) implies:
% 7.12/1.73 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (time(v2) = v1)
% 7.12/1.73 | | ~ (time(v2) = v0))
% 7.12/1.73 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (nitrogen(v2) =
% 7.12/1.73 | v1) | ~ (nitrogen(v2) = v0))
% 7.12/1.73 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (depth(v2) =
% 7.12/1.73 | v1) | ~ (depth(v2) = v0))
% 7.12/1.73 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.12/1.73 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 7.12/1.73 | v2) = v0))
% 7.12/1.73 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.12/1.73 | : ! [v3: $i] : (v1 = v0 | ~ (outcome(v3, v2) = v1) | ~ (outcome(v3,
% 7.12/1.73 | v2) = v0))
% 7.12/1.73 |
% 7.12/1.73 | DELTA: instantiating (no_bad) with fresh symbols all_9_0, all_9_1 gives:
% 7.12/1.73 | (11) bad(all_9_0) = 0 & outcome(all_9_1, all_9_0) = 0 & dive(all_9_1) = 0 &
% 7.12/1.73 | $i(all_9_0) & $i(all_9_1)
% 7.12/1.73 |
% 7.12/1.73 | ALPHA: (11) implies:
% 7.12/1.73 | (12) $i(all_9_1)
% 7.12/1.73 | (13) $i(all_9_0)
% 7.12/1.73 | (14) dive(all_9_1) = 0
% 7.12/1.73 | (15) outcome(all_9_1, all_9_0) = 0
% 7.12/1.73 | (16) bad(all_9_0) = 0
% 7.12/1.73 |
% 7.12/1.73 | GROUND_INST: instantiating (2) with all_9_1, simplifying with (12), (14)
% 7.12/1.73 | gives:
% 7.12/1.73 | (17) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 7.12/1.73 | : ? [v5: any] : (greater(v4, nitrogen_limit) = v5 & greater(v2,
% 7.12/1.73 | time_limit) = v3 & greater(v0, depth_limit) = v1 & depth(all_9_1)
% 7.12/1.73 | = v0 & nitrogen(all_9_1) = v4 & time(all_9_1) = v2 & $i(v4) & $i(v2)
% 7.12/1.73 | & $i(v0) & ( ~ (v5 = 0) | v3 = 0 | v1 = 0) & (v5 = 0 | ( ~ (v3 = 0)
% 7.12/1.73 | & ~ (v1 = 0))))
% 7.12/1.73 |
% 7.12/1.73 | GROUND_INST: instantiating (5) with all_9_1, simplifying with (12), (14)
% 7.12/1.74 | gives:
% 7.12/1.74 | (18) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 7.12/1.74 | & ~ (v1 = 0) & greater(v2, time_limit) = v3 & greater(v0,
% 7.12/1.74 | depth_limit) = v1 & depth(all_9_1) = v0 & time(all_9_1) = v2 &
% 7.12/1.74 | $i(v2) & $i(v0))
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (3) with all_9_1, simplifying with (12), (14)
% 7.12/1.74 | gives:
% 7.12/1.74 | (19) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (outcome(all_9_1, dci) =
% 7.12/1.74 | v2 & greater(v0, nitrogen_limit) = v1 & nitrogen(all_9_1) = v0 &
% 7.12/1.74 | $i(v0) & ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (1) with all_9_1, simplifying with (12), (14)
% 7.12/1.74 | gives:
% 7.12/1.74 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (depth(all_9_1) = v1 &
% 7.12/1.74 | nitrogen(all_9_1) = v0 & time(all_9_1) = v2 & padi(v1, v2) = v0 &
% 7.12/1.74 | $i(v2) & $i(v1) & $i(v0))
% 7.12/1.74 |
% 7.12/1.74 | GROUND_INST: instantiating (4) with all_9_1, all_9_0, simplifying with (12),
% 7.12/1.74 | (13), (14), (16) gives:
% 7.12/1.74 | (21) all_9_0 = dci | ? [v0: int] : ( ~ (v0 = 0) & outcome(all_9_1,
% 7.12/1.74 | all_9_0) = v0)
% 7.12/1.74 |
% 7.12/1.74 | DELTA: instantiating (20) with fresh symbols all_16_0, all_16_1, all_16_2
% 7.12/1.74 | gives:
% 7.12/1.74 | (22) depth(all_9_1) = all_16_1 & nitrogen(all_9_1) = all_16_2 &
% 7.12/1.74 | time(all_9_1) = all_16_0 & padi(all_16_1, all_16_0) = all_16_2 &
% 7.12/1.74 | $i(all_16_0) & $i(all_16_1) & $i(all_16_2)
% 7.12/1.74 |
% 7.12/1.74 | ALPHA: (22) implies:
% 7.12/1.74 | (23) time(all_9_1) = all_16_0
% 7.12/1.74 | (24) nitrogen(all_9_1) = all_16_2
% 7.12/1.74 | (25) depth(all_9_1) = all_16_1
% 7.12/1.74 |
% 7.12/1.74 | DELTA: instantiating (19) with fresh symbols all_18_0, all_18_1, all_18_2
% 7.12/1.74 | gives:
% 7.12/1.74 | (26) outcome(all_9_1, dci) = all_18_0 & greater(all_18_2, nitrogen_limit) =
% 7.12/1.74 | all_18_1 & nitrogen(all_9_1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_0
% 7.12/1.74 | = 0) | all_18_1 = 0) & ( ~ (all_18_1 = 0) | all_18_0 = 0)
% 7.12/1.74 |
% 7.12/1.74 | ALPHA: (26) implies:
% 7.12/1.74 | (27) nitrogen(all_9_1) = all_18_2
% 7.12/1.74 | (28) greater(all_18_2, nitrogen_limit) = all_18_1
% 7.12/1.74 | (29) outcome(all_9_1, dci) = all_18_0
% 7.12/1.74 | (30) ~ (all_18_0 = 0) | all_18_1 = 0
% 7.12/1.74 |
% 7.12/1.74 | DELTA: instantiating (18) with fresh symbols all_20_0, all_20_1, all_20_2,
% 7.12/1.74 | all_20_3 gives:
% 7.12/1.75 | (31) ~ (all_20_0 = 0) & ~ (all_20_2 = 0) & greater(all_20_1, time_limit)
% 7.12/1.75 | = all_20_0 & greater(all_20_3, depth_limit) = all_20_2 &
% 7.12/1.75 | depth(all_9_1) = all_20_3 & time(all_9_1) = all_20_1 & $i(all_20_1) &
% 7.12/1.75 | $i(all_20_3)
% 7.12/1.75 |
% 7.12/1.75 | ALPHA: (31) implies:
% 7.12/1.75 | (32) ~ (all_20_2 = 0)
% 7.12/1.75 | (33) ~ (all_20_0 = 0)
% 7.12/1.75 | (34) time(all_9_1) = all_20_1
% 7.12/1.75 | (35) depth(all_9_1) = all_20_3
% 7.12/1.75 | (36) greater(all_20_3, depth_limit) = all_20_2
% 7.12/1.75 | (37) greater(all_20_1, time_limit) = all_20_0
% 7.12/1.75 |
% 7.12/1.75 | DELTA: instantiating (17) with fresh symbols all_22_0, all_22_1, all_22_2,
% 7.12/1.75 | all_22_3, all_22_4, all_22_5 gives:
% 7.12/1.75 | (38) greater(all_22_1, nitrogen_limit) = all_22_0 & greater(all_22_3,
% 7.12/1.75 | time_limit) = all_22_2 & greater(all_22_5, depth_limit) = all_22_4 &
% 7.12/1.75 | depth(all_9_1) = all_22_5 & nitrogen(all_9_1) = all_22_1 &
% 7.12/1.75 | time(all_9_1) = all_22_3 & $i(all_22_1) & $i(all_22_3) & $i(all_22_5)
% 7.12/1.75 | & ( ~ (all_22_0 = 0) | all_22_2 = 0 | all_22_4 = 0) & (all_22_0 = 0 |
% 7.12/1.75 | ( ~ (all_22_2 = 0) & ~ (all_22_4 = 0)))
% 7.12/1.75 |
% 7.12/1.75 | ALPHA: (38) implies:
% 7.12/1.75 | (39) time(all_9_1) = all_22_3
% 7.12/1.75 | (40) nitrogen(all_9_1) = all_22_1
% 7.12/1.75 | (41) depth(all_9_1) = all_22_5
% 7.12/1.75 | (42) greater(all_22_5, depth_limit) = all_22_4
% 7.12/1.75 | (43) greater(all_22_3, time_limit) = all_22_2
% 7.12/1.75 | (44) greater(all_22_1, nitrogen_limit) = all_22_0
% 7.12/1.75 | (45) ~ (all_22_0 = 0) | all_22_2 = 0 | all_22_4 = 0
% 7.12/1.75 |
% 7.12/1.75 | BETA: splitting (21) gives:
% 7.12/1.75 |
% 7.12/1.75 | Case 1:
% 7.12/1.75 | |
% 7.12/1.75 | | (46) all_9_0 = dci
% 7.12/1.75 | |
% 7.12/1.75 | | REDUCE: (15), (46) imply:
% 7.12/1.75 | | (47) outcome(all_9_1, dci) = 0
% 7.12/1.75 | |
% 7.12/1.75 | | GROUND_INST: instantiating (6) with all_20_1, all_22_3, all_9_1, simplifying
% 7.12/1.75 | | with (34), (39) gives:
% 7.12/1.75 | | (48) all_22_3 = all_20_1
% 7.12/1.75 | |
% 7.12/1.75 | | GROUND_INST: instantiating (6) with all_16_0, all_22_3, all_9_1, simplifying
% 7.12/1.75 | | with (23), (39) gives:
% 7.12/1.75 | | (49) all_22_3 = all_16_0
% 7.12/1.75 | |
% 7.12/1.75 | | GROUND_INST: instantiating (7) with all_18_2, all_22_1, all_9_1, simplifying
% 7.12/1.75 | | with (27), (40) gives:
% 7.12/1.75 | | (50) all_22_1 = all_18_2
% 7.12/1.75 | |
% 7.12/1.75 | | GROUND_INST: instantiating (7) with all_16_2, all_22_1, all_9_1, simplifying
% 7.12/1.75 | | with (24), (40) gives:
% 7.12/1.75 | | (51) all_22_1 = all_16_2
% 7.12/1.75 | |
% 7.12/1.75 | | GROUND_INST: instantiating (8) with all_20_3, all_22_5, all_9_1, simplifying
% 7.12/1.75 | | with (35), (41) gives:
% 7.12/1.75 | | (52) all_22_5 = all_20_3
% 7.12/1.75 | |
% 7.12/1.76 | | GROUND_INST: instantiating (8) with all_16_1, all_22_5, all_9_1, simplifying
% 7.12/1.76 | | with (25), (41) gives:
% 7.12/1.76 | | (53) all_22_5 = all_16_1
% 7.12/1.76 | |
% 7.12/1.76 | | GROUND_INST: instantiating (10) with 0, all_18_0, dci, all_9_1, simplifying
% 7.12/1.76 | | with (29), (47) gives:
% 7.12/1.76 | | (54) all_18_0 = 0
% 7.12/1.76 | |
% 7.12/1.76 | | COMBINE_EQS: (50), (51) imply:
% 7.12/1.76 | | (55) all_18_2 = all_16_2
% 7.12/1.76 | |
% 7.12/1.76 | | SIMP: (55) implies:
% 7.12/1.76 | | (56) all_18_2 = all_16_2
% 7.12/1.76 | |
% 7.12/1.76 | | COMBINE_EQS: (48), (49) imply:
% 7.12/1.76 | | (57) all_20_1 = all_16_0
% 7.12/1.76 | |
% 7.12/1.76 | | SIMP: (57) implies:
% 7.12/1.76 | | (58) all_20_1 = all_16_0
% 7.12/1.76 | |
% 7.12/1.76 | | COMBINE_EQS: (52), (53) imply:
% 7.12/1.76 | | (59) all_20_3 = all_16_1
% 7.12/1.76 | |
% 7.12/1.76 | | SIMP: (59) implies:
% 7.12/1.76 | | (60) all_20_3 = all_16_1
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (44), (51) imply:
% 7.12/1.76 | | (61) greater(all_16_2, nitrogen_limit) = all_22_0
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (43), (49) imply:
% 7.12/1.76 | | (62) greater(all_16_0, time_limit) = all_22_2
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (42), (53) imply:
% 7.12/1.76 | | (63) greater(all_16_1, depth_limit) = all_22_4
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (37), (58) imply:
% 7.12/1.76 | | (64) greater(all_16_0, time_limit) = all_20_0
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (36), (60) imply:
% 7.12/1.76 | | (65) greater(all_16_1, depth_limit) = all_20_2
% 7.12/1.76 | |
% 7.12/1.76 | | REDUCE: (28), (56) imply:
% 7.12/1.76 | | (66) greater(all_16_2, nitrogen_limit) = all_18_1
% 7.12/1.76 | |
% 7.12/1.76 | | BETA: splitting (30) gives:
% 7.12/1.76 | |
% 7.12/1.76 | | Case 1:
% 7.12/1.76 | | |
% 7.12/1.76 | | | (67) ~ (all_18_0 = 0)
% 7.12/1.76 | | |
% 7.12/1.76 | | | REDUCE: (54), (67) imply:
% 7.12/1.76 | | | (68) $false
% 7.12/1.76 | | |
% 7.12/1.76 | | | CLOSE: (68) is inconsistent.
% 7.12/1.76 | | |
% 7.12/1.76 | | Case 2:
% 7.12/1.76 | | |
% 7.12/1.76 | | | (69) all_18_1 = 0
% 7.12/1.76 | | |
% 7.12/1.76 | | | REDUCE: (66), (69) imply:
% 7.12/1.76 | | | (70) greater(all_16_2, nitrogen_limit) = 0
% 7.12/1.76 | | |
% 7.12/1.76 | | | GROUND_INST: instantiating (9) with 0, all_22_0, nitrogen_limit, all_16_2,
% 7.12/1.76 | | | simplifying with (61), (70) gives:
% 7.12/1.76 | | | (71) all_22_0 = 0
% 7.12/1.76 | | |
% 7.12/1.76 | | | GROUND_INST: instantiating (9) with all_20_2, all_22_4, depth_limit,
% 7.12/1.76 | | | all_16_1, simplifying with (63), (65) gives:
% 7.12/1.76 | | | (72) all_22_4 = all_20_2
% 7.12/1.76 | | |
% 7.12/1.76 | | | GROUND_INST: instantiating (9) with all_20_0, all_22_2, time_limit,
% 7.12/1.76 | | | all_16_0, simplifying with (62), (64) gives:
% 7.12/1.76 | | | (73) all_22_2 = all_20_0
% 7.12/1.76 | | |
% 7.12/1.76 | | | BETA: splitting (45) gives:
% 7.12/1.76 | | |
% 7.12/1.76 | | | Case 1:
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | (74) ~ (all_22_0 = 0)
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | REDUCE: (71), (74) imply:
% 7.12/1.76 | | | | (75) $false
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | CLOSE: (75) is inconsistent.
% 7.12/1.76 | | | |
% 7.12/1.76 | | | Case 2:
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | (76) all_22_2 = 0 | all_22_4 = 0
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | BETA: splitting (76) gives:
% 7.12/1.76 | | | |
% 7.12/1.76 | | | | Case 1:
% 7.12/1.76 | | | | |
% 7.12/1.76 | | | | | (77) all_22_2 = 0
% 7.12/1.76 | | | | |
% 7.12/1.77 | | | | | COMBINE_EQS: (73), (77) imply:
% 7.12/1.77 | | | | | (78) all_20_0 = 0
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | REDUCE: (33), (78) imply:
% 7.12/1.77 | | | | | (79) $false
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | CLOSE: (79) is inconsistent.
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | Case 2:
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | (80) all_22_4 = 0
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | COMBINE_EQS: (72), (80) imply:
% 7.12/1.77 | | | | | (81) all_20_2 = 0
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | REDUCE: (32), (81) imply:
% 7.12/1.77 | | | | | (82) $false
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | | CLOSE: (82) is inconsistent.
% 7.12/1.77 | | | | |
% 7.12/1.77 | | | | End of split
% 7.12/1.77 | | | |
% 7.12/1.77 | | | End of split
% 7.12/1.77 | | |
% 7.12/1.77 | | End of split
% 7.12/1.77 | |
% 7.12/1.77 | Case 2:
% 7.12/1.77 | |
% 7.12/1.77 | | (83) ? [v0: int] : ( ~ (v0 = 0) & outcome(all_9_1, all_9_0) = v0)
% 7.12/1.77 | |
% 7.12/1.77 | | DELTA: instantiating (83) with fresh symbol all_28_0 gives:
% 7.12/1.77 | | (84) ~ (all_28_0 = 0) & outcome(all_9_1, all_9_0) = all_28_0
% 7.12/1.77 | |
% 7.12/1.77 | | ALPHA: (84) implies:
% 7.12/1.77 | | (85) ~ (all_28_0 = 0)
% 7.12/1.77 | | (86) outcome(all_9_1, all_9_0) = all_28_0
% 7.12/1.77 | |
% 7.12/1.77 | | GROUND_INST: instantiating (10) with 0, all_28_0, all_9_0, all_9_1,
% 7.12/1.77 | | simplifying with (15), (86) gives:
% 7.12/1.77 | | (87) all_28_0 = 0
% 7.12/1.77 | |
% 7.12/1.77 | | REDUCE: (85), (87) imply:
% 7.12/1.77 | | (88) $false
% 7.12/1.77 | |
% 7.12/1.77 | | CLOSE: (88) is inconsistent.
% 7.12/1.77 | |
% 7.12/1.77 | End of split
% 7.12/1.77 |
% 7.12/1.77 End of proof
% 7.12/1.77 % SZS output end Proof for theBenchmark
% 7.12/1.77
% 7.12/1.77 1157ms
%------------------------------------------------------------------------------