TSTP Solution File: ARI669_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI669_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 : n014.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 3.56s 1.30s
% Output   : Proof 4.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ARI669_1 : TPTP v8.1.2. Released v6.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n014.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 18:28:30 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  
% 0.20/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64  Running up to 7 provers in parallel.
% 0.20/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.92/1.01  Prover 1: Preprocessing ...
% 1.92/1.01  Prover 6: Preprocessing ...
% 1.92/1.01  Prover 0: Preprocessing ...
% 1.92/1.01  Prover 5: Preprocessing ...
% 1.92/1.01  Prover 4: Preprocessing ...
% 1.92/1.01  Prover 2: Preprocessing ...
% 1.92/1.01  Prover 3: Preprocessing ...
% 2.41/1.07  Prover 5: Constructing countermodel ...
% 2.41/1.07  Prover 6: Constructing countermodel ...
% 2.41/1.07  Prover 4: Constructing countermodel ...
% 2.41/1.07  Prover 2: Constructing countermodel ...
% 2.41/1.07  Prover 0: Constructing countermodel ...
% 2.41/1.07  Prover 3: Constructing countermodel ...
% 2.41/1.07  Prover 1: Constructing countermodel ...
% 3.56/1.30  Prover 3: proved (645ms)
% 3.56/1.30  Prover 2: proved (656ms)
% 3.56/1.30  
% 3.56/1.30  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.30  
% 3.56/1.31  
% 3.56/1.31  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.31  
% 3.56/1.31  Prover 0: stopped
% 3.56/1.31  Prover 5: stopped
% 3.56/1.31  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.56/1.31  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.56/1.31  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.56/1.31  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.56/1.31  Prover 6: stopped
% 3.56/1.32  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.56/1.32  Prover 8: Preprocessing ...
% 3.56/1.32  Prover 10: Preprocessing ...
% 3.56/1.32  Prover 8: Constructing countermodel ...
% 3.56/1.32  Prover 7: Preprocessing ...
% 3.56/1.32  Prover 13: Preprocessing ...
% 3.56/1.33  Prover 10: Constructing countermodel ...
% 4.22/1.33  Prover 7: Constructing countermodel ...
% 4.22/1.33  Prover 13: Constructing countermodel ...
% 4.22/1.34  Prover 11: Preprocessing ...
% 4.22/1.36  Prover 11: Constructing countermodel ...
% 4.22/1.39  Prover 4: Found proof (size 34)
% 4.22/1.39  Prover 4: proved (726ms)
% 4.22/1.39  Prover 13: stopped
% 4.22/1.39  Prover 11: stopped
% 4.22/1.39  Prover 10: stopped
% 4.22/1.39  Prover 8: stopped
% 4.22/1.39  Prover 1: Found proof (size 34)
% 4.22/1.39  Prover 1: proved (743ms)
% 4.22/1.39  Prover 7: stopped
% 4.22/1.39  
% 4.22/1.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.22/1.39  
% 4.22/1.39  % SZS output start Proof for theBenchmark
% 4.22/1.40  Assumptions after simplification:
% 4.22/1.40  ---------------------------------
% 4.22/1.40  
% 4.22/1.40    (conj)
% 4.22/1.41     ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ($product(v1, c) = v2 &
% 4.22/1.41      $product(v0, b) = v1 & $product(a, b) = v0 & ((v2 = 0 &  ~ (c = 0) &  ~ (b =
% 4.22/1.41            0) &  ~ (a = 0)) | ( ~ (v2 = 0) & (c = 0 | b = 0 | a = 0))))
% 4.22/1.41  
% 4.22/1.41  Those formulas are unsatisfiable:
% 4.22/1.41  ---------------------------------
% 4.22/1.41  
% 4.22/1.41  Begin of proof
% 4.22/1.41  | 
% 4.22/1.41  | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1, all_2_2
% 4.22/1.41  |        gives:
% 4.22/1.41  |   (1)  $product(all_2_1, c) = all_2_0 & $product(all_2_2, b) = all_2_1 &
% 4.22/1.41  |        $product(a, b) = all_2_2 & ((all_2_0 = 0 &  ~ (c = 0) &  ~ (b = 0) &  ~
% 4.22/1.41  |            (a = 0)) | ( ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0)))
% 4.22/1.41  | 
% 4.22/1.41  | ALPHA: (1) implies:
% 4.22/1.41  |   (2)  $product(a, b) = all_2_2
% 4.22/1.41  |   (3)  $product(all_2_2, b) = all_2_1
% 4.22/1.41  |   (4)  $product(all_2_1, c) = all_2_0
% 4.22/1.41  |   (5)  (all_2_0 = 0 &  ~ (c = 0) &  ~ (b = 0) &  ~ (a = 0)) | ( ~ (all_2_0 =
% 4.22/1.41  |            0) & (c = 0 | b = 0 | a = 0))
% 4.22/1.41  | 
% 4.22/1.42  | BETA: splitting (5) gives:
% 4.22/1.42  | 
% 4.22/1.42  | Case 1:
% 4.22/1.42  | | 
% 4.22/1.42  | |   (6)  all_2_0 = 0 &  ~ (c = 0) &  ~ (b = 0) &  ~ (a = 0)
% 4.22/1.42  | | 
% 4.22/1.42  | | ALPHA: (6) implies:
% 4.22/1.42  | |   (7)  all_2_0 = 0
% 4.22/1.42  | |   (8)   ~ (a = 0)
% 4.22/1.42  | |   (9)   ~ (b = 0)
% 4.22/1.42  | |   (10)   ~ (c = 0)
% 4.22/1.42  | | 
% 4.22/1.42  | | REDUCE: (4), (7) imply:
% 4.22/1.42  | |   (11)  $product(all_2_1, c) = 0
% 4.22/1.42  | | 
% 4.22/1.42  | | THEORY_AXIOM GroebnerMultiplication: 
% 4.22/1.42  | |   (12)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 4.22/1.42  | |           int] : (v2 = 0 | v1 = 0 | v0 = 0 |  ~ ($product(v4, v2) = 0) |  ~
% 4.22/1.42  | |           ($product(v3, v1) = v4) |  ~ ($product(v0, v1) = v3))
% 4.22/1.42  | | 
% 4.22/1.42  | | GROUND_INST: instantiating (12) with a, b, c, all_2_2, all_2_1, simplifying
% 4.22/1.42  | |              with (2), (3), (11) gives:
% 4.22/1.42  | |   (13)  c = 0 | b = 0 | a = 0
% 4.22/1.42  | | 
% 4.22/1.42  | | BETA: splitting (13) gives:
% 4.22/1.42  | | 
% 4.22/1.42  | | Case 1:
% 4.22/1.42  | | | 
% 4.22/1.42  | | |   (14)  b = 0
% 4.22/1.42  | | | 
% 4.22/1.42  | | | REDUCE: (9), (14) imply:
% 4.22/1.42  | | |   (15)  $false
% 4.22/1.42  | | | 
% 4.22/1.42  | | | CLOSE: (15) is inconsistent.
% 4.22/1.42  | | | 
% 4.22/1.42  | | Case 2:
% 4.22/1.42  | | | 
% 4.22/1.42  | | |   (16)  c = 0 | a = 0
% 4.22/1.42  | | | 
% 4.22/1.42  | | | BETA: splitting (16) gives:
% 4.22/1.42  | | | 
% 4.22/1.42  | | | Case 1:
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | |   (17)  c = 0
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | | REDUCE: (10), (17) imply:
% 4.22/1.42  | | | |   (18)  $false
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | | CLOSE: (18) is inconsistent.
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | Case 2:
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | |   (19)  a = 0
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | | REDUCE: (8), (19) imply:
% 4.22/1.42  | | | |   (20)  $false
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | | CLOSE: (20) is inconsistent.
% 4.22/1.42  | | | | 
% 4.22/1.42  | | | End of split
% 4.22/1.42  | | | 
% 4.22/1.42  | | End of split
% 4.22/1.42  | | 
% 4.22/1.42  | Case 2:
% 4.22/1.42  | | 
% 4.22/1.42  | |   (21)   ~ (all_2_0 = 0) & (c = 0 | b = 0 | a = 0)
% 4.22/1.42  | | 
% 4.22/1.42  | | ALPHA: (21) implies:
% 4.22/1.43  | |   (22)   ~ (all_2_0 = 0)
% 4.22/1.43  | |   (23)  c = 0 | b = 0 | a = 0
% 4.22/1.43  | | 
% 4.22/1.43  | | BETA: splitting (23) gives:
% 4.22/1.43  | | 
% 4.22/1.43  | | Case 1:
% 4.22/1.43  | | | 
% 4.22/1.43  | | |   (24)  b = 0
% 4.22/1.43  | | | 
% 4.22/1.43  | | | REDUCE: (3), (24) imply:
% 4.22/1.43  | | |   (25)  $product(all_2_2, 0) = all_2_1
% 4.22/1.43  | | | 
% 4.22/1.43  | | | THEORY_AXIOM GroebnerMultiplication: 
% 4.22/1.43  | | |   (26)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] : (v3 =
% 4.22/1.43  | | |           0 |  ~ ($product(v2, v0) = v3) |  ~ ($product(v1, 0) = v2))
% 4.22/1.43  | | | 
% 4.22/1.43  | | | GROUND_INST: instantiating (26) with c, all_2_2, all_2_1, all_2_0,
% 4.22/1.43  | | |              simplifying with (4), (25) gives:
% 4.22/1.43  | | |   (27)  all_2_0 = 0
% 4.22/1.43  | | | 
% 4.22/1.43  | | | REDUCE: (22), (27) imply:
% 4.22/1.43  | | |   (28)  $false
% 4.22/1.43  | | | 
% 4.22/1.43  | | | CLOSE: (28) is inconsistent.
% 4.22/1.43  | | | 
% 4.22/1.43  | | Case 2:
% 4.22/1.43  | | | 
% 4.22/1.43  | | |   (29)  c = 0 | a = 0
% 4.22/1.43  | | | 
% 4.22/1.43  | | | BETA: splitting (29) gives:
% 4.22/1.43  | | | 
% 4.22/1.43  | | | Case 1:
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | |   (30)  c = 0
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | REDUCE: (4), (30) imply:
% 4.22/1.43  | | | |   (31)  $product(all_2_1, 0) = all_2_0
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | THEORY_AXIOM GroebnerMultiplication: 
% 4.22/1.43  | | | |   (32)   ! [v0: int] :  ! [v1: int] : (v1 = 0 |  ~ ($product(v0, 0) =
% 4.22/1.43  | | | |             v1))
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | GROUND_INST: instantiating (32) with all_2_1, all_2_0, simplifying with
% 4.22/1.43  | | | |              (31) gives:
% 4.22/1.43  | | | |   (33)  all_2_0 = 0
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | REDUCE: (22), (33) imply:
% 4.22/1.43  | | | |   (34)  $false
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | CLOSE: (34) is inconsistent.
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | Case 2:
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | |   (35)  a = 0
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | REDUCE: (2), (35) imply:
% 4.22/1.43  | | | |   (36)  $product(0, b) = all_2_2
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | THEORY_AXIOM GroebnerMultiplication: 
% 4.22/1.43  | | | |   (37)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  !
% 4.22/1.43  | | | |         [v4: int] : (v4 = 0 |  ~ ($product(v3, v1) = v4) |  ~
% 4.22/1.43  | | | |           ($product(v2, v0) = v3) |  ~ ($product(0, v0) = v2))
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | GROUND_INST: instantiating (37) with b, c, all_2_2, all_2_1, all_2_0,
% 4.22/1.43  | | | |              simplifying with (3), (4), (36) gives:
% 4.22/1.43  | | | |   (38)  all_2_0 = 0
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | REDUCE: (22), (38) imply:
% 4.22/1.43  | | | |   (39)  $false
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | | CLOSE: (39) is inconsistent.
% 4.22/1.43  | | | | 
% 4.22/1.43  | | | End of split
% 4.22/1.43  | | | 
% 4.22/1.43  | | End of split
% 4.22/1.43  | | 
% 4.22/1.43  | End of split
% 4.22/1.43  | 
% 4.22/1.43  End of proof
% 4.22/1.43  % SZS output end Proof for theBenchmark
% 4.22/1.43  
% 4.22/1.43  807ms
%------------------------------------------------------------------------------