TSTP Solution File: ARI670_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI670_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 : n028.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 17:48:45 EDT 2023
% Result : Theorem 3.29s 1.18s
% Output : Proof 3.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI670_1 : TPTP v8.1.2. Released v6.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n028.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 18:54:26 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.
% 0.52/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.52/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.99/0.98 Prover 1: Preprocessing ...
% 1.99/0.98 Prover 5: Preprocessing ...
% 1.99/0.98 Prover 3: Preprocessing ...
% 1.99/0.98 Prover 2: Preprocessing ...
% 1.99/0.98 Prover 6: Preprocessing ...
% 1.99/0.98 Prover 0: Preprocessing ...
% 1.99/0.98 Prover 4: Preprocessing ...
% 2.40/1.03 Prover 5: Constructing countermodel ...
% 2.40/1.03 Prover 1: Constructing countermodel ...
% 2.40/1.03 Prover 6: Constructing countermodel ...
% 2.40/1.03 Prover 2: Constructing countermodel ...
% 2.40/1.03 Prover 3: Constructing countermodel ...
% 2.40/1.03 Prover 4: Constructing countermodel ...
% 2.40/1.03 Prover 0: Constructing countermodel ...
% 3.29/1.18 Prover 6: proved (544ms)
% 3.29/1.18 Prover 0: proved (552ms)
% 3.29/1.18 Prover 2: proved (549ms)
% 3.29/1.18
% 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.18
% 3.29/1.18 Prover 3: proved (550ms)
% 3.29/1.18
% 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.18
% 3.29/1.18
% 3.29/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.18
% 3.29/1.18
% 3.29/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.19
% 3.29/1.19 Prover 5: proved (547ms)
% 3.29/1.19
% 3.29/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.19
% 3.29/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.29/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.29/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.29/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.29/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.29/1.19 Prover 7: Preprocessing ...
% 3.29/1.19 Prover 8: Preprocessing ...
% 3.29/1.20 Prover 7: Constructing countermodel ...
% 3.29/1.20 Prover 11: Preprocessing ...
% 3.29/1.20 Prover 8: Constructing countermodel ...
% 3.29/1.20 Prover 10: Preprocessing ...
% 3.29/1.20 Prover 13: Preprocessing ...
% 3.29/1.20 Prover 11: Constructing countermodel ...
% 3.29/1.20 Prover 10: Constructing countermodel ...
% 3.29/1.20 Prover 13: Constructing countermodel ...
% 3.29/1.21 Prover 1: Found proof (size 26)
% 3.29/1.21 Prover 1: proved (581ms)
% 3.29/1.21 Prover 7: stopped
% 3.29/1.21 Prover 10: stopped
% 3.29/1.21 Prover 4: Found proof (size 26)
% 3.29/1.21 Prover 4: proved (578ms)
% 3.29/1.21 Prover 11: stopped
% 3.29/1.21 Prover 13: stopped
% 3.29/1.21 Prover 8: stopped
% 3.29/1.21
% 3.29/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.29/1.21
% 3.29/1.22 % SZS output start Proof for theBenchmark
% 3.29/1.22 Assumptions after simplification:
% 3.29/1.22 ---------------------------------
% 3.29/1.22
% 3.29/1.22 (conj)
% 3.29/1.23 ? [v0: int] : ($lesseq(1, $difference(a, v0)) & $product(a, a) = v0)
% 3.29/1.23
% 3.29/1.23 Those formulas are unsatisfiable:
% 3.29/1.23 ---------------------------------
% 3.29/1.23
% 3.29/1.23 Begin of proof
% 3.29/1.23 |
% 3.29/1.23 | DELTA: instantiating (conj) with fresh symbol all_2_0 gives:
% 3.29/1.23 | (1) $lesseq(1, $difference(a, all_2_0)) & $product(a, a) = all_2_0
% 3.29/1.23 |
% 3.29/1.23 | ALPHA: (1) implies:
% 3.29/1.23 | (2) $lesseq(1, $difference(a, all_2_0))
% 3.29/1.24 | (3) $product(a, a) = all_2_0
% 3.29/1.24 |
% 3.29/1.24 | THEORY_AXIOM GroebnerMultiplication:
% 3.29/1.24 | (4) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1))) |
% 3.29/1.24 | ~ ($lesseq(v1, 458328)) | ~ ($product(v0, v0) = v1))
% 3.29/1.24 |
% 3.29/1.24 | GROUND_INST: instantiating (4) with a, all_2_0, simplifying with (3) gives:
% 3.29/1.24 | (5) ~ ($lesseq(1, $difference(a, all_2_0))) | ~ ($lesseq(all_2_0,
% 3.29/1.24 | 458328))
% 3.29/1.24 |
% 3.29/1.24 | BETA: splitting (5) gives:
% 3.29/1.24 |
% 3.29/1.24 | Case 1:
% 3.29/1.24 | |
% 3.29/1.24 | | (6) $lesseq(a, all_2_0)
% 3.29/1.24 | |
% 3.29/1.24 | | COMBINE_INEQS: (2), (6) imply:
% 3.29/1.24 | | (7) $false
% 3.29/1.24 | |
% 3.29/1.24 | | CLOSE: (7) is inconsistent.
% 3.29/1.24 | |
% 3.29/1.24 | Case 2:
% 3.29/1.24 | |
% 3.29/1.24 | | (8) $lesseq(458329, all_2_0)
% 3.29/1.24 | |
% 3.29/1.24 | | COMBINE_INEQS: (2), (8) imply:
% 3.29/1.24 | | (9) $lesseq(458330, a)
% 3.29/1.24 | |
% 3.29/1.24 | | THEORY_AXIOM GroebnerMultiplication:
% 3.29/1.24 | | (10) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(v0, v1)))
% 3.29/1.24 | | | ~ ($lesseq(v1, 999999999999)) | ~ ($lesseq(458330, v0)) | ~
% 3.29/1.24 | | ($product(v0, v0) = v1))
% 3.29/1.24 | |
% 3.29/1.24 | | GROUND_INST: instantiating (10) with a, all_2_0, simplifying with (3) gives:
% 3.29/1.25 | | (11) ~ ($lesseq(1, $difference(a, all_2_0))) | ~ ($lesseq(all_2_0,
% 3.29/1.25 | | 999999999999)) | ~ ($lesseq(458330, a))
% 3.29/1.25 | |
% 3.29/1.25 | | BETA: splitting (11) gives:
% 3.29/1.25 | |
% 3.29/1.25 | | Case 1:
% 3.29/1.25 | | |
% 3.29/1.25 | | | (12) $lesseq(a, all_2_0)
% 3.29/1.25 | | |
% 3.29/1.25 | | | COMBINE_INEQS: (2), (12) imply:
% 3.29/1.25 | | | (13) $false
% 3.29/1.25 | | |
% 3.29/1.25 | | | CLOSE: (13) is inconsistent.
% 3.29/1.25 | | |
% 3.29/1.25 | | Case 2:
% 3.29/1.25 | | |
% 3.29/1.25 | | | (14) ~ ($lesseq(all_2_0, 999999999999)) | ~ ($lesseq(458330, a))
% 3.29/1.25 | | |
% 3.29/1.25 | | | BETA: splitting (14) gives:
% 3.29/1.25 | | |
% 3.29/1.25 | | | Case 1:
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | (15) $lesseq(a, 458329)
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | COMBINE_INEQS: (9), (15) imply:
% 3.29/1.25 | | | | (16) $false
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | CLOSE: (16) is inconsistent.
% 3.29/1.25 | | | |
% 3.29/1.25 | | | Case 2:
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | (17) $lesseq(1000000000000, all_2_0)
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | THEORY_AXIOM GroebnerMultiplication:
% 3.29/1.25 | | | | (18) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(210066388901,
% 3.29/1.25 | | | | $difference($product(916660, v0), v1))) | ~
% 3.29/1.25 | | | | ($lesseq(458330, v0)) | ~ ($product(v0, v0) = v1))
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | GROUND_INST: instantiating (18) with a, all_2_0, simplifying with (3)
% 3.29/1.25 | | | | gives:
% 3.29/1.25 | | | | (19) ~ ($lesseq(210066388901, $difference($product(916660, a),
% 3.29/1.25 | | | | all_2_0))) | ~ ($lesseq(458330, a))
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | BETA: splitting (19) gives:
% 3.29/1.25 | | | |
% 3.29/1.25 | | | | Case 1:
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | (20) $lesseq(a, 458329)
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | COMBINE_INEQS: (9), (20) imply:
% 3.29/1.25 | | | | | (21) $false
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | CLOSE: (21) is inconsistent.
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | Case 2:
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | (22) $lesseq(-210066388900, $difference(all_2_0, $product(916660,
% 3.29/1.25 | | | | | a)))
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | COMBINE_INEQS: (2), (22) imply:
% 3.29/1.25 | | | | | (23) $lesseq(a, 229165)
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | SIMP: (23) implies:
% 3.29/1.25 | | | | | (24) $lesseq(a, 229165)
% 3.29/1.25 | | | | |
% 3.29/1.25 | | | | | COMBINE_INEQS: (2), (17) imply:
% 3.29/1.25 | | | | | (25) $lesseq(1000000000001, a)
% 3.29/1.25 | | | | |
% 3.29/1.26 | | | | | COMBINE_INEQS: (24), (25) imply:
% 3.29/1.26 | | | | | (26) $false
% 3.29/1.26 | | | | |
% 3.29/1.26 | | | | | CLOSE: (26) is inconsistent.
% 3.29/1.26 | | | | |
% 3.29/1.26 | | | | End of split
% 3.29/1.26 | | | |
% 3.29/1.26 | | | End of split
% 3.29/1.26 | | |
% 3.29/1.26 | | End of split
% 3.29/1.26 | |
% 3.29/1.26 | End of split
% 3.29/1.26 |
% 3.29/1.26 End of proof
% 3.29/1.26 % SZS output end Proof for theBenchmark
% 3.29/1.26
% 3.29/1.26 647ms
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