TSTP Solution File: ARI677_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI677_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 17:48:46 EDT 2023
% Result : Theorem 3.79s 1.29s
% Output : Proof 4.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI677_1 : TPTP v8.1.2. Released v6.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.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 17:38:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.66/0.65 ________ _____
% 0.66/0.65 ___ __ \_________(_)________________________________
% 0.66/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.66/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.66/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.66/0.65
% 0.66/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.65 (2023-06-19)
% 0.66/0.65
% 0.66/0.65 (c) Philipp Rümmer, 2009-2023
% 0.66/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.65 Amanda Stjerna.
% 0.66/0.65 Free software under BSD-3-Clause.
% 0.66/0.65
% 0.66/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.65
% 0.66/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.66 Running up to 7 provers in parallel.
% 0.66/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/1.04 Prover 1: Preprocessing ...
% 2.03/1.04 Prover 2: Preprocessing ...
% 2.03/1.04 Prover 5: Preprocessing ...
% 2.03/1.04 Prover 4: Preprocessing ...
% 2.03/1.04 Prover 3: Preprocessing ...
% 2.03/1.04 Prover 0: Preprocessing ...
% 2.03/1.04 Prover 6: Preprocessing ...
% 2.49/1.09 Prover 4: Constructing countermodel ...
% 2.49/1.09 Prover 5: Constructing countermodel ...
% 2.49/1.09 Prover 2: Constructing countermodel ...
% 2.49/1.09 Prover 1: Constructing countermodel ...
% 2.49/1.09 Prover 0: Constructing countermodel ...
% 2.49/1.09 Prover 3: Constructing countermodel ...
% 2.49/1.09 Prover 6: Constructing countermodel ...
% 3.79/1.28 Prover 6: proved (610ms)
% 3.79/1.28 Prover 0: proved (612ms)
% 3.79/1.28 Prover 3: proved (612ms)
% 3.79/1.28 Prover 5: proved (610ms)
% 3.79/1.29
% 3.79/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.29
% 3.79/1.29 Prover 2: proved (611ms)
% 3.79/1.29
% 3.79/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.29
% 3.79/1.29
% 3.79/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.29
% 3.79/1.29
% 3.79/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.29
% 3.79/1.30
% 3.79/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.30
% 3.79/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.79/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.79/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.79/1.30 Prover 7: Preprocessing ...
% 3.79/1.30 Prover 10: Preprocessing ...
% 3.79/1.30 Prover 8: Preprocessing ...
% 3.79/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.79/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.79/1.31 Prover 7: Constructing countermodel ...
% 3.79/1.31 Prover 10: Constructing countermodel ...
% 3.79/1.31 Prover 8: Constructing countermodel ...
% 3.79/1.31 Prover 11: Preprocessing ...
% 3.79/1.31 Prover 13: Preprocessing ...
% 3.79/1.31 Prover 4: Found proof (size 21)
% 3.79/1.31 Prover 4: proved (643ms)
% 3.79/1.31 Prover 1: Found proof (size 21)
% 3.79/1.31 Prover 1: proved (643ms)
% 3.79/1.31 Prover 8: stopped
% 3.79/1.31 Prover 7: stopped
% 3.79/1.31 Prover 10: stopped
% 3.79/1.32 Prover 13: Constructing countermodel ...
% 3.79/1.32 Prover 13: stopped
% 3.79/1.32 Prover 11: Constructing countermodel ...
% 3.79/1.32 Prover 11: stopped
% 3.79/1.32
% 3.79/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.79/1.32
% 3.79/1.33 % SZS output start Proof for theBenchmark
% 3.79/1.33 Assumptions after simplification:
% 3.79/1.33 ---------------------------------
% 3.79/1.33
% 3.79/1.33 (conj)
% 3.79/1.33 ? [v0: int] : ? [v1: int] : ($lesseq(v1, 0)$product(v0, a) = v1 &
% 3.79/1.33 $product(a, a) = v0)
% 3.79/1.33
% 3.79/1.34 (conj_001)
% 3.79/1.34 $lesseq(0, a)
% 3.79/1.34
% 3.79/1.34 (conj_002)
% 3.79/1.34 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & $product(v1, a) =
% 3.79/1.34 v2 & $product(v0, a) = v1 & $product(a, a) = v0)
% 3.79/1.34
% 3.79/1.34 Those formulas are unsatisfiable:
% 3.79/1.34 ---------------------------------
% 3.79/1.34
% 3.79/1.34 Begin of proof
% 3.79/1.34 |
% 3.79/1.34 | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1 gives:
% 3.79/1.34 | (1) $lesseq(all_3_0, 0)$product(all_3_1, a) = all_3_0 & $product(a, a) =
% 3.79/1.34 | all_3_1
% 3.79/1.34 |
% 3.79/1.34 | ALPHA: (1) implies:
% 3.79/1.34 | (2) $lesseq(all_3_0, 0)
% 3.79/1.34 | (3) $product(a, a) = all_3_1
% 3.79/1.34 | (4) $product(all_3_1, a) = all_3_0
% 3.79/1.34 |
% 3.79/1.34 | DELTA: instantiating (conj_002) with fresh symbols all_6_0, all_6_1, all_6_2
% 3.79/1.34 | gives:
% 3.79/1.34 | (5) ~ (all_6_0 = 0) & $product(all_6_1, a) = all_6_0 & $product(all_6_2,
% 3.79/1.34 | a) = all_6_1 & $product(a, a) = all_6_2
% 3.79/1.34 |
% 3.79/1.34 | ALPHA: (5) implies:
% 3.79/1.35 | (6) ~ (all_6_0 = 0)
% 3.79/1.35 | (7) $product(a, a) = all_6_2
% 3.79/1.35 | (8) $product(all_6_2, a) = all_6_1
% 3.79/1.35 | (9) $product(all_6_1, a) = all_6_0
% 3.79/1.35 |
% 3.79/1.35 | THEORY_AXIOM GroebnerMultiplication:
% 3.79/1.35 | (10) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~
% 3.79/1.35 | ($product(v0, v0) = v2) | ~ ($product(v0, v0) = v1))
% 3.79/1.35 |
% 3.79/1.35 | GROUND_INST: instantiating (10) with a, all_3_1, all_6_2, simplifying with
% 3.79/1.35 | (3), (7) gives:
% 3.79/1.35 | (11) all_6_2 = all_3_1
% 3.79/1.35 |
% 3.79/1.35 | THEORY_AXIOM GroebnerMultiplication:
% 3.79/1.35 | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 3.79/1.35 | int] : (v4 = v2 | ~ ($product(v3, v0) = v4) | ~ ($product(v1, v0)
% 3.79/1.35 | = v2) | ~ ($product(v0, v0) = v3) | ~ ($product(v0, v0) = v1))
% 3.79/1.35 |
% 4.17/1.35 | GROUND_INST: instantiating (12) with a, all_3_1, all_3_0, all_6_2, all_6_1,
% 4.17/1.35 | simplifying with (3), (4), (7), (8) gives:
% 4.17/1.35 | (13) all_6_1 = all_3_0
% 4.17/1.35 |
% 4.17/1.35 | REDUCE: (9), (13) imply:
% 4.17/1.35 | (14) $product(all_3_0, a) = all_6_0
% 4.17/1.35 |
% 4.17/1.35 | THEORY_AXIOM GroebnerMultiplication:
% 4.17/1.35 | (15) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = 0 |
% 4.17/1.35 | ~ ($lesseq(v2, 0) | ~ ($lesseq(0, v0)) | ~ ($product(v2, v0) = v3)
% 4.17/1.35 | | ~ ($product(v1, v0) = v2) | ~ ($product(v0, v0) = v1))
% 4.17/1.35 |
% 4.17/1.35 | GROUND_INST: instantiating (15) with a, all_3_1, all_3_0, all_6_0, simplifying
% 4.17/1.35 | with (3), (4), (14) gives:
% 4.17/1.36 | (16) all_6_0 = 0 | ~ ($lesseq(all_3_0, 0) | ~ ($lesseq(0, a))
% 4.17/1.36 |
% 4.17/1.36 | BETA: splitting (16) gives:
% 4.17/1.36 |
% 4.17/1.36 | Case 1:
% 4.17/1.36 | |
% 4.17/1.36 | | (17) $lesseq(1, all_3_0)
% 4.17/1.36 | |
% 4.17/1.36 | | COMBINE_INEQS: (2), (17) imply:
% 4.17/1.36 | | (18) $false
% 4.17/1.36 | |
% 4.17/1.36 | | CLOSE: (18) is inconsistent.
% 4.17/1.36 | |
% 4.17/1.36 | Case 2:
% 4.17/1.36 | |
% 4.17/1.36 | | (19) all_6_0 = 0 | ~ ($lesseq(0, a))
% 4.17/1.36 | |
% 4.17/1.36 | | BETA: splitting (19) gives:
% 4.17/1.36 | |
% 4.17/1.36 | | Case 1:
% 4.17/1.36 | | |
% 4.17/1.36 | | | (20) $lesseq(a, -1)
% 4.17/1.36 | | |
% 4.17/1.36 | | | COMBINE_INEQS: (20), (conj_001) imply:
% 4.17/1.36 | | | (21) $false
% 4.17/1.36 | | |
% 4.17/1.36 | | | CLOSE: (21) is inconsistent.
% 4.17/1.36 | | |
% 4.17/1.36 | | Case 2:
% 4.17/1.36 | | |
% 4.17/1.36 | | | (22) all_6_0 = 0
% 4.17/1.36 | | |
% 4.17/1.36 | | | REDUCE: (6), (22) imply:
% 4.17/1.36 | | | (23) $false
% 4.17/1.36 | | |
% 4.17/1.36 | | | CLOSE: (23) is inconsistent.
% 4.17/1.36 | | |
% 4.17/1.36 | | End of split
% 4.17/1.36 | |
% 4.17/1.36 | End of split
% 4.17/1.36 |
% 4.17/1.36 End of proof
% 4.17/1.36 % SZS output end Proof for theBenchmark
% 4.17/1.36
% 4.17/1.36 708ms
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