TSTP Solution File: ARI186_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI186_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 : n027.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 17:47:12 EDT 2023
% Result : Theorem 3.52s 1.39s
% Output : Proof 4.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ARI186_1 : TPTP v8.1.2. Released v5.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 19:00:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.02/1.13 Prover 4: Preprocessing ...
% 2.02/1.13 Prover 1: Preprocessing ...
% 2.58/1.18 Prover 2: Preprocessing ...
% 2.58/1.18 Prover 6: Preprocessing ...
% 2.58/1.18 Prover 5: Preprocessing ...
% 2.58/1.18 Prover 3: Preprocessing ...
% 2.58/1.19 Prover 0: Preprocessing ...
% 3.14/1.26 Prover 3: Constructing countermodel ...
% 3.14/1.26 Prover 1: Constructing countermodel ...
% 3.14/1.26 Prover 4: Constructing countermodel ...
% 3.14/1.27 Prover 6: Proving ...
% 3.14/1.27 Prover 0: Proving ...
% 3.14/1.28 Prover 2: Proving ...
% 3.14/1.28 Prover 5: Proving ...
% 3.52/1.39 Prover 3: proved (717ms)
% 3.52/1.39
% 3.52/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.52/1.39
% 3.52/1.39 Prover 6: stopped
% 4.14/1.39 Prover 0: stopped
% 4.14/1.39 Prover 5: stopped
% 4.14/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.14/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.14/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.14/1.41 Prover 2: stopped
% 4.14/1.41 Prover 8: Preprocessing ...
% 4.14/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.14/1.41 Prover 7: Preprocessing ...
% 4.14/1.41 Prover 10: Preprocessing ...
% 4.14/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.14/1.43 Prover 11: Preprocessing ...
% 4.14/1.43 Prover 13: Preprocessing ...
% 4.14/1.44 Prover 1: Found proof (size 8)
% 4.14/1.44 Prover 1: proved (780ms)
% 4.14/1.44 Prover 4: stopped
% 4.55/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.60/1.45 Prover 8: Constructing countermodel ...
% 4.60/1.46 Prover 8: stopped
% 4.60/1.46 Prover 11: Constructing countermodel ...
% 4.60/1.46 Prover 7: Constructing countermodel ...
% 4.60/1.46 Prover 7: stopped
% 4.60/1.46 Prover 11: stopped
% 4.60/1.46 Prover 10: Constructing countermodel ...
% 4.60/1.46 Prover 10: stopped
% 4.60/1.48 Prover 13: Warning: ignoring some quantifiers
% 4.60/1.49 Prover 13: Constructing countermodel ...
% 4.60/1.49 Prover 13: stopped
% 4.60/1.49
% 4.60/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.60/1.49
% 4.60/1.49 % SZS output start Proof for theBenchmark
% 4.60/1.50 Assumptions after simplification:
% 4.60/1.50 ---------------------------------
% 4.60/1.50
% 4.60/1.50 (co1)
% 4.99/1.56 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & g(3, 5) = v2 &
% 4.99/1.56 g(3, 4) = v0 & g(3, 3) = v0 & g(3, 2) = v1 & ! [v3: int] : ! [v4: int] :
% 4.99/1.56 ! [v5: int] : ( ~ (g(v3, $sum(v4, 2)) = v5) | g(v3, v4) = v5))
% 4.99/1.56
% 4.99/1.56 (function-axioms)
% 4.99/1.56 ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~
% 4.99/1.56 (g(v3, v2) = v1) | ~ (g(v3, v2) = v0))
% 4.99/1.56
% 4.99/1.56 Those formulas are unsatisfiable:
% 4.99/1.56 ---------------------------------
% 4.99/1.56
% 4.99/1.56 Begin of proof
% 4.99/1.56 |
% 4.99/1.56 | DELTA: instantiating (co1) with fresh symbols all_3_0, all_3_1, all_3_2 gives:
% 4.99/1.57 | (1) ~ (all_3_0 = all_3_1) & g(3, 5) = all_3_0 & g(3, 4) = all_3_2 & g(3,
% 4.99/1.57 | 3) = all_3_2 & g(3, 2) = all_3_1 & ! [v0: int] : ! [v1: int] : !
% 4.99/1.57 | [v2: int] : ( ~ (g(v0, $sum(v1, 2)) = v2) | g(v0, v1) = v2)
% 4.99/1.57 |
% 4.99/1.57 | ALPHA: (1) implies:
% 4.99/1.57 | (2) ~ (all_3_0 = all_3_1)
% 4.99/1.57 | (3) g(3, 2) = all_3_1
% 4.99/1.57 | (4) g(3, 3) = all_3_2
% 4.99/1.57 | (5) g(3, 4) = all_3_2
% 4.99/1.57 | (6) g(3, 5) = all_3_0
% 4.99/1.58 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ (g(v0, $sum(v1, 2)) =
% 4.99/1.58 | v2) | g(v0, v1) = v2)
% 4.99/1.58 |
% 4.99/1.58 | GROUND_INST: instantiating (7) with 3, 2, all_3_2, simplifying with (5) gives:
% 4.99/1.58 | (8) g(3, 2) = all_3_2
% 4.99/1.58 |
% 4.99/1.58 | GROUND_INST: instantiating (7) with 3, 3, all_3_0, simplifying with (6) gives:
% 4.99/1.58 | (9) g(3, 3) = all_3_0
% 4.99/1.58 |
% 4.99/1.58 | GROUND_INST: instantiating (function-axioms) with all_3_1, all_3_2, 2, 3,
% 4.99/1.58 | simplifying with (3), (8) gives:
% 4.99/1.58 | (10) all_3_1 = all_3_2
% 4.99/1.58 |
% 4.99/1.58 | GROUND_INST: instantiating (function-axioms) with all_3_2, all_3_0, 3, 3,
% 4.99/1.58 | simplifying with (4), (9) gives:
% 4.99/1.58 | (11) all_3_0 = all_3_2
% 4.99/1.58 |
% 4.99/1.58 | REDUCE: (2), (10), (11) imply:
% 4.99/1.58 | (12) $false
% 4.99/1.58 |
% 4.99/1.58 | CLOSE: (12) is inconsistent.
% 4.99/1.58 |
% 4.99/1.58 End of proof
% 4.99/1.59 % SZS output end Proof for theBenchmark
% 4.99/1.59
% 4.99/1.59 953ms
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