TSTP Solution File: ARI682_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI682_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 17:48:47 EDT 2023

% Result   : Theorem 3.11s 1.21s
% Output   : Proof 3.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ARI682_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 : n007.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 18:10:14 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.48/0.62  ________       _____
% 0.48/0.62  ___  __ \_________(_)________________________________
% 0.48/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.48/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.48/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.48/0.62  
% 0.48/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.48/0.62  (2023-06-19)
% 0.48/0.62  
% 0.48/0.62  (c) Philipp Rümmer, 2009-2023
% 0.48/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.48/0.62                Amanda Stjerna.
% 0.48/0.62  Free software under BSD-3-Clause.
% 0.48/0.62  
% 0.48/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.48/0.62  
% 0.48/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.48/0.63  Running up to 7 provers in parallel.
% 0.69/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.20/1.02  Prover 4: Preprocessing ...
% 2.20/1.02  Prover 6: Preprocessing ...
% 2.20/1.02  Prover 2: Preprocessing ...
% 2.20/1.02  Prover 5: Preprocessing ...
% 2.20/1.02  Prover 1: Preprocessing ...
% 2.20/1.02  Prover 0: Preprocessing ...
% 2.20/1.02  Prover 3: Preprocessing ...
% 2.65/1.07  Prover 4: Constructing countermodel ...
% 2.65/1.07  Prover 6: Constructing countermodel ...
% 2.65/1.07  Prover 5: Constructing countermodel ...
% 2.65/1.07  Prover 2: Constructing countermodel ...
% 2.65/1.07  Prover 0: Constructing countermodel ...
% 2.65/1.07  Prover 3: Constructing countermodel ...
% 2.65/1.07  Prover 1: Constructing countermodel ...
% 3.11/1.21  Prover 6: proved (567ms)
% 3.11/1.21  Prover 5: proved (569ms)
% 3.11/1.21  Prover 3: proved (571ms)
% 3.11/1.21  Prover 0: proved (571ms)
% 3.11/1.21  
% 3.11/1.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21  
% 3.11/1.21  Prover 2: proved (572ms)
% 3.11/1.21  
% 3.11/1.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21  
% 3.11/1.21  
% 3.11/1.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21  
% 3.11/1.22  
% 3.11/1.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.22  
% 3.11/1.22  
% 3.11/1.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.22  
% 3.11/1.22  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.11/1.22  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.11/1.22  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.11/1.22  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.11/1.22  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.11/1.23  Prover 7: Preprocessing ...
% 3.11/1.23  Prover 8: Preprocessing ...
% 3.62/1.23  Prover 11: Preprocessing ...
% 3.62/1.24  Prover 10: Preprocessing ...
% 3.62/1.24  Prover 8: Constructing countermodel ...
% 3.62/1.24  Prover 7: Constructing countermodel ...
% 3.62/1.24  Prover 11: Constructing countermodel ...
% 3.62/1.24  Prover 13: Preprocessing ...
% 3.62/1.24  Prover 10: Constructing countermodel ...
% 3.62/1.24  Prover 1: Found proof (size 20)
% 3.62/1.24  Prover 1: proved (605ms)
% 3.62/1.25  Prover 10: stopped
% 3.62/1.25  Prover 11: stopped
% 3.62/1.25  Prover 8: stopped
% 3.62/1.25  Prover 7: stopped
% 3.62/1.25  Prover 4: Found proof (size 20)
% 3.62/1.25  Prover 4: proved (607ms)
% 3.62/1.25  Prover 13: Constructing countermodel ...
% 3.62/1.25  Prover 13: stopped
% 3.62/1.25  
% 3.62/1.25  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.25  
% 3.62/1.26  % SZS output start Proof for theBenchmark
% 3.62/1.26  Assumptions after simplification:
% 3.62/1.26  ---------------------------------
% 3.62/1.26  
% 3.62/1.26    (conj)
% 3.62/1.26    $lesseq(1, $difference(b, a))
% 3.62/1.26  
% 3.62/1.26    (conj_001)
% 3.62/1.27    $lesseq(0, a)
% 3.62/1.27  
% 3.62/1.27    (conj_002)
% 3.62/1.27     ? [v0: int] : ($lesseq(b, $difference(a, v0)) & $product(a, b) = v0)
% 3.62/1.27  
% 3.62/1.27  Those formulas are unsatisfiable:
% 3.62/1.27  ---------------------------------
% 3.62/1.27  
% 3.62/1.27  Begin of proof
% 3.62/1.27  | 
% 3.62/1.27  | DELTA: instantiating (conj_002) with fresh symbol all_3_0 gives:
% 3.62/1.27  |   (1)  $lesseq(b, $difference(a, all_3_0)) & $product(a, b) = all_3_0
% 3.62/1.27  | 
% 3.62/1.27  | ALPHA: (1) implies:
% 3.85/1.27  |   (2)  $lesseq(b, $difference(a, all_3_0))
% 3.85/1.28  |   (3)  $product(a, b) = all_3_0
% 3.85/1.28  | 
% 3.85/1.28  | COMBINE_INEQS: (conj), (conj_001) imply:
% 3.85/1.28  |   (4)  $lesseq(1, b)
% 3.85/1.28  | 
% 3.85/1.28  | THEORY_AXIOM GroebnerMultiplication: 
% 3.85/1.28  |   (5)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : ( ~ ($lesseq(v0,
% 3.85/1.28  |              $difference(v1, v2))) |  ~ ($lesseq(v2, 457651)) |  ~ ($lesseq(1,
% 3.85/1.28  |              $difference(v0, v1))) |  ~ ($lesseq(0, v1)) |  ~ ($product(v1,
% 3.85/1.28  |              v0) = v2))
% 3.85/1.28  | 
% 3.85/1.28  | GROUND_INST: instantiating (5) with b, a, all_3_0, simplifying with (3) gives:
% 3.85/1.28  |   (6)   ~ ($lesseq(b, $difference(a, all_3_0))) |  ~ ($lesseq(all_3_0,
% 3.85/1.28  |            457651)) |  ~ ($lesseq(1, $difference(b, a))) |  ~ ($lesseq(0, a))
% 3.85/1.28  | 
% 3.85/1.28  | BETA: splitting (6) gives:
% 3.85/1.28  | 
% 3.85/1.28  | Case 1:
% 3.85/1.28  | | 
% 3.85/1.28  | |   (7)   ~ ($lesseq(b, $difference(a, all_3_0))) |  ~ ($lesseq(1,
% 3.85/1.28  | |            $difference(b, a)))
% 3.85/1.28  | | 
% 3.85/1.28  | | BETA: splitting (7) gives:
% 3.85/1.28  | | 
% 3.85/1.28  | | Case 1:
% 3.85/1.28  | | | 
% 3.85/1.28  | | |   (8)  $lesseq(1, $sum($difference(all_3_0, a), b))
% 3.85/1.28  | | | 
% 3.85/1.28  | | | COMBINE_INEQS: (2), (8) imply:
% 3.85/1.28  | | |   (9)  $false
% 3.85/1.28  | | | 
% 3.85/1.28  | | | CLOSE: (9) is inconsistent.
% 3.85/1.28  | | | 
% 3.85/1.28  | | Case 2:
% 3.85/1.28  | | | 
% 3.85/1.28  | | |   (10)  $lesseq(b, a)
% 3.85/1.28  | | | 
% 3.85/1.29  | | | COMBINE_INEQS: (10), (conj) imply:
% 3.85/1.29  | | |   (11)  $false
% 3.85/1.29  | | | 
% 3.85/1.29  | | | CLOSE: (11) is inconsistent.
% 3.85/1.29  | | | 
% 3.85/1.29  | | End of split
% 3.85/1.29  | | 
% 3.85/1.29  | Case 2:
% 3.85/1.29  | | 
% 3.85/1.29  | |   (12)   ~ ($lesseq(all_3_0, 457651)) |  ~ ($lesseq(0, a)) |  ~ ($lesseq(1,
% 3.85/1.29  | |             b))
% 3.85/1.29  | | 
% 3.85/1.29  | | BETA: splitting (12) gives:
% 3.85/1.29  | | 
% 3.85/1.29  | | Case 1:
% 3.85/1.29  | | | 
% 3.85/1.29  | | |   (13)  $lesseq(a, -1)
% 3.85/1.29  | | | 
% 3.85/1.29  | | | COMBINE_INEQS: (13), (conj_001) imply:
% 3.85/1.29  | | |   (14)  $false
% 3.85/1.29  | | | 
% 3.85/1.29  | | | CLOSE: (14) is inconsistent.
% 3.85/1.29  | | | 
% 3.85/1.29  | | Case 2:
% 3.85/1.29  | | | 
% 3.85/1.29  | | |   (15)   ~ ($lesseq(all_3_0, 457651)) |  ~ ($lesseq(1, b))
% 3.85/1.29  | | | 
% 3.85/1.29  | | | BETA: splitting (15) gives:
% 3.85/1.29  | | | 
% 3.85/1.29  | | | Case 1:
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | |   (16)  $lesseq(b, 0)
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | | COMBINE_INEQS: (4), (16) imply:
% 3.85/1.29  | | | |   (17)  $false
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | | CLOSE: (17) is inconsistent.
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | Case 2:
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | |   (18)  $lesseq(457652, all_3_0)
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | | COMBINE_INEQS: (2), (18) imply:
% 3.85/1.29  | | | |   (19)  $lesseq(457652, $difference(a, b))
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | | COMBINE_INEQS: (19), (conj) imply:
% 3.85/1.29  | | | |   (20)  $false
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | | CLOSE: (20) is inconsistent.
% 3.85/1.29  | | | | 
% 3.85/1.29  | | | End of split
% 3.85/1.29  | | | 
% 3.85/1.29  | | End of split
% 3.85/1.29  | | 
% 3.85/1.29  | End of split
% 3.85/1.29  | 
% 3.85/1.29  End of proof
% 3.85/1.29  % SZS output end Proof for theBenchmark
% 3.85/1.29  
% 3.85/1.29  670ms
%------------------------------------------------------------------------------