TSTP Solution File: DAT067_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT067_1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 22:19:05 EDT 2023
% Result : Theorem 6.77s 1.75s
% Output : Proof 8.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT067_1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 14:01:32 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.64 Running up to 7 provers in parallel.
% 0.17/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.74/1.18 Prover 1: Preprocessing ...
% 2.74/1.19 Prover 4: Preprocessing ...
% 3.28/1.25 Prover 5: Preprocessing ...
% 3.28/1.25 Prover 6: Preprocessing ...
% 3.28/1.25 Prover 0: Preprocessing ...
% 3.28/1.25 Prover 2: Preprocessing ...
% 3.28/1.25 Prover 3: Preprocessing ...
% 4.32/1.59 Prover 3: Constructing countermodel ...
% 4.32/1.60 Prover 1: Constructing countermodel ...
% 4.32/1.64 Prover 6: Constructing countermodel ...
% 4.32/1.64 Prover 5: Proving ...
% 4.32/1.64 Prover 4: Constructing countermodel ...
% 6.03/1.69 Prover 0: Proving ...
% 6.36/1.70 Prover 2: Proving ...
% 6.77/1.75 Prover 3: proved (1092ms)
% 6.77/1.75
% 6.77/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/1.75
% 6.77/1.75 Prover 6: stopped
% 6.77/1.75 Prover 2: stopped
% 6.77/1.75 Prover 0: stopped
% 6.83/1.75 Prover 5: stopped
% 6.83/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.83/1.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.83/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.83/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.83/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.22/1.81 Prover 7: Preprocessing ...
% 7.22/1.81 Prover 10: Preprocessing ...
% 7.22/1.83 Prover 11: Preprocessing ...
% 7.22/1.84 Prover 8: Preprocessing ...
% 7.57/1.87 Prover 13: Preprocessing ...
% 7.57/1.89 Prover 4: Found proof (size 16)
% 7.57/1.89 Prover 4: proved (1237ms)
% 7.57/1.89 Prover 1: Found proof (size 16)
% 7.57/1.89 Prover 1: proved (1245ms)
% 7.57/1.91 Prover 10: stopped
% 7.57/1.91 Prover 11: stopped
% 7.57/1.94 Prover 7: Constructing countermodel ...
% 7.57/1.94 Prover 13: stopped
% 8.22/1.95 Prover 7: stopped
% 8.22/1.96 Prover 8: Warning: ignoring some quantifiers
% 8.22/1.98 Prover 8: Constructing countermodel ...
% 8.44/1.99 Prover 8: stopped
% 8.44/1.99
% 8.44/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.44/1.99
% 8.44/2.00 % SZS output start Proof for theBenchmark
% 8.44/2.00 Assumptions after simplification:
% 8.44/2.00 ---------------------------------
% 8.44/2.00
% 8.44/2.00 (ax_3)
% 8.69/2.05 ! [v0: int] : ! [v1: heap] : ! [v2: int] : ! [v3: heap] : ! [v4: int] : (
% 8.69/2.05 ~ (app(v1, v0) = v3) | ~ (sel(v3, v2) = v4) | ~ heap(v1) | ? [v5: int] :
% 8.69/2.05 ? [v6: int] : (length(v1) = v5 & sel(v1, v2) = v6 & (v6 = v4 |
% 8.69/2.05 $difference(v5, v2) = -1)))
% 8.69/2.05
% 8.69/2.05 (th_2)
% 8.74/2.05 ? [v0: int] : ? [v1: int] : ? [v2: heap] : ? [v3: heap] : ? [v4: int] :
% 8.74/2.05 ? [v5: int] : ? [v6: int] : ( ~ ($difference(v6, v1) = -1) & ~ (v5 = v4) &
% 8.74/2.05 app(v2, v0) = v3 & length(v2) = v6 & sel(v3, v1) = v4 & sel(v2, v1) = v5 &
% 8.74/2.05 heap(v3) & heap(v2))
% 8.74/2.05
% 8.74/2.05 (function-axioms)
% 8.74/2.06 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: heap] : !
% 8.74/2.06 [v3: heap] : (v1 = v0 | ~ (lsls(v3, v2) = v1) | ~ (lsls(v3, v2) = v0)) & !
% 8.74/2.06 [v0: heap] : ! [v1: heap] : ! [v2: int] : ! [v3: heap] : (v1 = v0 | ~
% 8.74/2.06 (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] :
% 8.74/2.06 ! [v2: int] : ! [v3: heap] : (v1 = v0 | ~ (sel(v3, v2) = v1) | ~ (sel(v3,
% 8.74/2.06 v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: heap] : (v1 = v0 | ~
% 8.74/2.06 (toop(v2) = v1) | ~ (toop(v2) = v0)) & ! [v0: heap] : ! [v1: heap] : !
% 8.74/2.06 [v2: heap] : (v1 = v0 | ~ (get(v2) = v1) | ~ (get(v2) = v0)) & ! [v0: int]
% 8.74/2.06 : ! [v1: int] : ! [v2: heap] : (v1 = v0 | ~ (length(v2) = v1) | ~
% 8.74/2.06 (length(v2) = v0))
% 8.74/2.06
% 8.74/2.06 Further assumptions not needed in the proof:
% 8.74/2.06 --------------------------------------------
% 8.74/2.06 ax_1, ax_2, ax_20, ax_21, ax_22, ax_23, ax_24, ax_25, ax_26, ax_27, ax_28,
% 8.74/2.06 ax_29, ax_30
% 8.74/2.06
% 8.74/2.06 Those formulas are unsatisfiable:
% 8.74/2.06 ---------------------------------
% 8.74/2.06
% 8.74/2.06 Begin of proof
% 8.74/2.06 |
% 8.74/2.06 | ALPHA: (function-axioms) implies:
% 8.74/2.07 | (1) ! [v0: int] : ! [v1: int] : ! [v2: heap] : (v1 = v0 | ~ (length(v2)
% 8.74/2.07 | = v1) | ~ (length(v2) = v0))
% 8.74/2.07 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: heap] : (v1 = v0 |
% 8.74/2.07 | ~ (sel(v3, v2) = v1) | ~ (sel(v3, v2) = v0))
% 8.74/2.07 |
% 8.74/2.07 | DELTA: instantiating (th_2) with fresh symbols all_19_0, all_19_1, all_19_2,
% 8.74/2.07 | all_19_3, all_19_4, all_19_5, all_19_6 gives:
% 8.74/2.07 | (3) ~ ($difference(all_19_0, all_19_5) = -1) & ~ (all_19_1 = all_19_2) &
% 8.74/2.07 | app(all_19_4, all_19_6) = all_19_3 & length(all_19_4) = all_19_0 &
% 8.74/2.07 | sel(all_19_3, all_19_5) = all_19_2 & sel(all_19_4, all_19_5) = all_19_1
% 8.74/2.07 | & heap(all_19_3) & heap(all_19_4)
% 8.74/2.07 |
% 8.74/2.07 | ALPHA: (3) implies:
% 8.74/2.08 | (4) ~ (all_19_1 = all_19_2)
% 8.74/2.08 | (5) ~ ($difference(all_19_0, all_19_5) = -1)
% 8.74/2.08 | (6) heap(all_19_4)
% 8.74/2.08 | (7) sel(all_19_4, all_19_5) = all_19_1
% 8.74/2.08 | (8) sel(all_19_3, all_19_5) = all_19_2
% 8.74/2.08 | (9) length(all_19_4) = all_19_0
% 8.74/2.08 | (10) app(all_19_4, all_19_6) = all_19_3
% 8.74/2.08 |
% 8.74/2.08 | GROUND_INST: instantiating (ax_3) with all_19_6, all_19_4, all_19_5, all_19_3,
% 8.74/2.08 | all_19_2, simplifying with (6), (8), (10) gives:
% 8.74/2.08 | (11) ? [v0: int] : ? [v1: int] : (length(all_19_4) = v0 & sel(all_19_4,
% 8.74/2.08 | all_19_5) = v1 & (v1 = all_19_2 | $difference(v0, all_19_5) = -1))
% 8.74/2.08 |
% 8.74/2.08 | DELTA: instantiating (11) with fresh symbols all_29_0, all_29_1 gives:
% 8.74/2.08 | (12) length(all_19_4) = all_29_1 & sel(all_19_4, all_19_5) = all_29_0 &
% 8.74/2.08 | (all_29_0 = all_19_2 | $difference(all_29_1, all_19_5) = -1)
% 8.74/2.08 |
% 8.74/2.08 | ALPHA: (12) implies:
% 8.74/2.08 | (13) sel(all_19_4, all_19_5) = all_29_0
% 8.74/2.09 | (14) length(all_19_4) = all_29_1
% 8.74/2.09 | (15) all_29_0 = all_19_2 | $difference(all_29_1, all_19_5) = -1
% 8.74/2.09 |
% 8.74/2.09 | GROUND_INST: instantiating (2) with all_19_1, all_29_0, all_19_5, all_19_4,
% 8.74/2.09 | simplifying with (7), (13) gives:
% 8.74/2.09 | (16) all_29_0 = all_19_1
% 8.74/2.09 |
% 8.74/2.09 | GROUND_INST: instantiating (1) with all_19_0, all_29_1, all_19_4, simplifying
% 8.74/2.09 | with (9), (14) gives:
% 8.74/2.09 | (17) all_29_1 = all_19_0
% 8.74/2.09 |
% 8.74/2.09 | BETA: splitting (15) gives:
% 8.74/2.09 |
% 8.74/2.09 | Case 1:
% 8.74/2.09 | |
% 8.74/2.09 | | (18) all_29_0 = all_19_2
% 8.74/2.09 | |
% 8.74/2.09 | | COMBINE_EQS: (16), (18) imply:
% 8.74/2.09 | | (19) all_19_1 = all_19_2
% 8.74/2.09 | |
% 8.74/2.09 | | REDUCE: (4), (19) imply:
% 8.74/2.09 | | (20) $false
% 8.74/2.09 | |
% 8.74/2.09 | | CLOSE: (20) is inconsistent.
% 8.74/2.09 | |
% 8.74/2.09 | Case 2:
% 8.74/2.09 | |
% 8.74/2.09 | | (21) $difference(all_29_1, all_19_5) = -1
% 8.74/2.09 | |
% 8.74/2.09 | | COMBINE_EQS: (17), (21) imply:
% 8.74/2.09 | | (22) $difference(all_19_0, all_19_5) = -1
% 8.74/2.09 | |
% 8.74/2.09 | | SIMP: (22) implies:
% 8.74/2.09 | | (23) $difference(all_19_0, all_19_5) = -1
% 8.74/2.09 | |
% 8.74/2.09 | | REDUCE: (5), (23) imply:
% 8.74/2.09 | | (24) $false
% 8.74/2.09 | |
% 8.74/2.09 | | CLOSE: (24) is inconsistent.
% 8.74/2.09 | |
% 8.74/2.09 | End of split
% 8.74/2.09 |
% 8.74/2.09 End of proof
% 8.74/2.10 % SZS output end Proof for theBenchmark
% 8.74/2.10
% 8.74/2.10 1472ms
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