TSTP Solution File: ARI707_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI707_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 : n005.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 17:48:53 EDT 2023

% Result   : Theorem 3.14s 1.30s
% Output   : Proof 3.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ARI707_1 : TPTP v8.1.2. Released v6.3.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n005.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 18:21:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.91/1.07  Prover 1: Preprocessing ...
% 1.91/1.07  Prover 5: Preprocessing ...
% 1.91/1.07  Prover 3: Preprocessing ...
% 1.91/1.07  Prover 4: Preprocessing ...
% 1.91/1.07  Prover 0: Preprocessing ...
% 1.91/1.07  Prover 2: Preprocessing ...
% 1.91/1.07  Prover 6: Preprocessing ...
% 2.64/1.13  Prover 5: Constructing countermodel ...
% 2.64/1.13  Prover 0: Constructing countermodel ...
% 2.64/1.13  Prover 2: Constructing countermodel ...
% 2.64/1.13  Prover 3: Constructing countermodel ...
% 2.64/1.13  Prover 4: Constructing countermodel ...
% 2.64/1.13  Prover 1: Constructing countermodel ...
% 2.64/1.13  Prover 6: Constructing countermodel ...
% 3.14/1.30  Prover 6: proved (656ms)
% 3.14/1.30  Prover 5: proved (657ms)
% 3.14/1.30  Prover 2: proved (659ms)
% 3.14/1.30  Prover 0: proved (660ms)
% 3.14/1.30  
% 3.14/1.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.30  
% 3.14/1.30  
% 3.14/1.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.30  
% 3.14/1.30  
% 3.14/1.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.30  
% 3.14/1.30  Prover 3: proved (660ms)
% 3.14/1.30  
% 3.14/1.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.30  
% 3.14/1.30  
% 3.14/1.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/1.30  
% 3.14/1.32  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.14/1.32  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.14/1.32  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.14/1.32  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.14/1.32  Prover 10: Preprocessing ...
% 3.14/1.32  Prover 8: Preprocessing ...
% 3.14/1.32  Prover 11: Preprocessing ...
% 3.14/1.32  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.14/1.32  Prover 7: Preprocessing ...
% 3.14/1.32  Prover 4: Found proof (size 8)
% 3.14/1.32  Prover 4: proved (681ms)
% 3.14/1.32  Prover 10: Constructing countermodel ...
% 3.14/1.33  Prover 10: stopped
% 3.14/1.33  Prover 1: Found proof (size 8)
% 3.14/1.33  Prover 1: proved (688ms)
% 3.14/1.33  Prover 7: Constructing countermodel ...
% 3.14/1.33  Prover 7: stopped
% 3.14/1.33  Prover 8: Constructing countermodel ...
% 3.14/1.33  Prover 8: stopped
% 3.14/1.33  Prover 11: Constructing countermodel ...
% 3.14/1.33  Prover 11: stopped
% 3.14/1.34  Prover 13: Preprocessing ...
% 3.69/1.35  Prover 13: Constructing countermodel ...
% 3.69/1.35  Prover 13: stopped
% 3.69/1.35  
% 3.69/1.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/1.35  
% 3.69/1.35  % SZS output start Proof for theBenchmark
% 3.69/1.35  Assumptions after simplification:
% 3.69/1.35  ---------------------------------
% 3.69/1.35  
% 3.69/1.35    (conj)
% 3.69/1.36     ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ( ~ (v2 = v1) & $product(v0, d) =
% 3.69/1.36      v1 & $product(c, c) = v2 & $product(c, d) = v0)
% 3.69/1.36  
% 3.69/1.36    (eq)
% 3.69/1.36     ? [v0: int] : ($product($product(2, d), d) = $sum(v0, c) & $product(d, d) =
% 3.69/1.36      v0)
% 3.69/1.36  
% 3.69/1.36  Those formulas are unsatisfiable:
% 3.69/1.36  ---------------------------------
% 3.69/1.36  
% 3.69/1.36  Begin of proof
% 3.69/1.36  | 
% 3.69/1.36  | DELTA: instantiating (eq) with fresh symbol all_2_0 gives:
% 3.69/1.37  |   (1)  $product($product(2, d), d) = $sum(all_2_0, c) & $product(d, d) =
% 3.69/1.37  |        all_2_0
% 3.69/1.37  | 
% 3.69/1.37  | ALPHA: (1) implies:
% 3.69/1.37  |   (2)  $product(d, d) = all_2_0
% 3.69/1.37  |   (3)  $product($product(2, d), d) = $sum(all_2_0, c)
% 3.69/1.37  | 
% 3.69/1.37  | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2
% 3.69/1.37  |        gives:
% 3.69/1.37  |   (4)   ~ (all_4_0 = all_4_1) & $product(all_4_2, d) = all_4_1 & $product(c,
% 3.69/1.37  |          c) = all_4_0 & $product(c, d) = all_4_2
% 3.69/1.37  | 
% 3.69/1.37  | ALPHA: (4) implies:
% 3.69/1.37  |   (5)   ~ (all_4_0 = all_4_1)
% 3.69/1.37  |   (6)  $product(c, d) = all_4_2
% 3.69/1.37  |   (7)  $product(c, c) = all_4_0
% 3.69/1.37  |   (8)  $product(all_4_2, d) = all_4_1
% 3.69/1.37  | 
% 3.69/1.37  | THEORY_AXIOM GroebnerMultiplication: 
% 3.69/1.37  |   (9)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 3.69/1.37  |          int] :  ! [v5: int] : (v5 = v4 |  ~ ($product(v3, v0) = v4) |  ~
% 3.69/1.37  |          ($product(v1, v1) = v5) |  ~ ($product(v1, v0) = v3) |  ~
% 3.69/1.37  |          ($product($product(2, v0), v0) = $sum(v2, v1)) |  ~ ($product(v0, v0)
% 3.69/1.37  |            = v2))
% 3.69/1.37  | 
% 3.69/1.38  | GROUND_INST: instantiating (9) with d, c, all_2_0, all_4_2, all_4_1, all_4_0,
% 3.69/1.38  |              simplifying with (2), (3), (6), (7), (8) gives:
% 3.69/1.38  |   (10)  all_4_0 = all_4_1
% 3.69/1.38  | 
% 3.69/1.38  | REDUCE: (5), (10) imply:
% 3.69/1.38  |   (11)  $false
% 3.69/1.38  | 
% 3.69/1.38  | CLOSE: (11) is inconsistent.
% 3.69/1.38  | 
% 3.69/1.38  End of proof
% 3.69/1.38  % SZS output end Proof for theBenchmark
% 3.69/1.38  
% 3.69/1.38  758ms
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