TSTP Solution File: ARI697_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI697_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 : n018.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 17:48:51 EDT 2023

% Result   : Theorem 2.93s 1.14s
% Output   : Proof 3.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : ARI697_1 : TPTP v8.1.2. Released v6.3.0.
% 0.08/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n018.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 18:46:18 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 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 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 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
% 2.15/1.01  Prover 3: Preprocessing ...
% 2.15/1.01  Prover 1: Preprocessing ...
% 2.15/1.01  Prover 6: Preprocessing ...
% 2.15/1.01  Prover 5: Preprocessing ...
% 2.15/1.01  Prover 2: Preprocessing ...
% 2.15/1.02  Prover 0: Preprocessing ...
% 2.15/1.02  Prover 4: Preprocessing ...
% 2.71/1.08  Prover 0: Constructing countermodel ...
% 2.71/1.08  Prover 5: Constructing countermodel ...
% 2.71/1.08  Prover 4: Constructing countermodel ...
% 2.71/1.08  Prover 1: Constructing countermodel ...
% 2.71/1.08  Prover 6: Constructing countermodel ...
% 2.71/1.08  Prover 2: Constructing countermodel ...
% 2.71/1.08  Prover 3: Constructing countermodel ...
% 2.93/1.14  Prover 2: proved (499ms)
% 2.93/1.14  Prover 0: proved (500ms)
% 2.93/1.14  
% 2.93/1.14  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/1.14  
% 2.93/1.14  
% 2.93/1.14  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/1.14  
% 3.16/1.14  Prover 3: stopped
% 3.16/1.14  Prover 5: stopped
% 3.16/1.15  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.16/1.15  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.16/1.15  Prover 6: stopped
% 3.16/1.15  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.16/1.15  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.16/1.15  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.16/1.16  Prover 8: Preprocessing ...
% 3.16/1.17  Prover 11: Preprocessing ...
% 3.16/1.17  Prover 10: Preprocessing ...
% 3.16/1.17  Prover 13: Preprocessing ...
% 3.16/1.18  Prover 7: Preprocessing ...
% 3.16/1.18  Prover 11: Constructing countermodel ...
% 3.16/1.19  Prover 13: Constructing countermodel ...
% 3.16/1.19  Prover 10: Constructing countermodel ...
% 3.16/1.19  Prover 7: Constructing countermodel ...
% 3.16/1.20  Prover 8: Constructing countermodel ...
% 3.16/1.22  Prover 13: Found proof (size 39)
% 3.16/1.22  Prover 4: Found proof (size 39)
% 3.16/1.22  Prover 7: Found proof (size 39)
% 3.16/1.22  Prover 13: proved (73ms)
% 3.16/1.22  Prover 4: proved (585ms)
% 3.16/1.22  Prover 7: proved (85ms)
% 3.16/1.22  Prover 10: Found proof (size 39)
% 3.16/1.22  Prover 10: proved (79ms)
% 3.16/1.22  Prover 1: Found proof (size 40)
% 3.16/1.22  Prover 1: proved (589ms)
% 3.16/1.22  Prover 11: Found proof (size 39)
% 3.16/1.22  Prover 11: proved (74ms)
% 3.16/1.22  Prover 8: stopped
% 3.16/1.23  
% 3.16/1.23  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.16/1.23  
% 3.16/1.23  % SZS output start Proof for theBenchmark
% 3.16/1.24  Assumptions after simplification:
% 3.16/1.24  ---------------------------------
% 3.16/1.24  
% 3.16/1.24    (conj)
% 3.16/1.24     ? [v0: int] :  ? [v1: int] : ($sum($product(2, v1), v0) = x5 &  ~ (v0 = 0) &
% 3.16/1.24      $lesseq(v0, 1) & $lesseq(-1, v0) & ( ~ (v0 = 1) |  ~ ($lesseq(x5, 0)) & ( ~
% 3.16/1.24          (v0 = -1) |  ~ ($lesseq(0, x5))))
% 3.16/1.24  
% 3.16/1.25    (eq1)
% 3.16/1.25    $difference($sum($difference(x5, x4), x3), $product(2, x2)) = $product(5, x1)
% 3.16/1.25  
% 3.16/1.25    (eq2)
% 3.16/1.25    $sum($sum($difference($difference($product(101, x5), $product(3, x4)),
% 3.16/1.25          $product(5, x3)), $product(62, x2)), $product(9, x1)) = 0
% 3.16/1.25  
% 3.16/1.25    (eq3)
% 3.16/1.25    $sum($sum($difference($product(98, x5), $product(67, x4)), $product(11, x3)),
% 3.16/1.25      $product(34, x2)) = $product(56, x1)
% 3.16/1.25  
% 3.16/1.25  Those formulas are unsatisfiable:
% 3.16/1.25  ---------------------------------
% 3.16/1.25  
% 3.16/1.25  Begin of proof
% 3.16/1.25  | 
% 3.16/1.25  | COMBINE_EQS: (eq1), (eq3) imply:
% 3.16/1.25  |   (1)  $sum($sum($difference($product(31, x4), $product(87, x3)),
% 3.16/1.25  |            $product(230, x2)), $product(434, x1)) = 0
% 3.16/1.25  | 
% 3.16/1.25  | COMBINE_EQS: (eq1), (eq2) imply:
% 3.16/1.25  |   (2)  $sum($sum($difference($product(49, x4), $product(53, x3)),
% 3.16/1.25  |            $product(132, x2)), $product(257, x1)) = 0
% 3.16/1.25  | 
% 3.16/1.25  | SIMP: (2) implies:
% 3.16/1.25  |   (3)  $sum($sum($difference($product(49, x4), $product(53, x3)),
% 3.16/1.25  |            $product(132, x2)), $product(257, x1)) = 0
% 3.16/1.25  | 
% 3.16/1.25  | COMBINE_EQS: (1), (3) imply:
% 3.16/1.25  |   (4)  $sum($sum($difference(x4, $product(1017, x3)), $product(2786, x2)),
% 3.16/1.25  |          $product(5162, x1)) = 0
% 3.16/1.25  | 
% 3.16/1.25  | COMBINE_EQS: (3), (4) imply:
% 3.16/1.26  |   (5)  $difference($product(2620, x3), $product(7178, x2)) = $product(13299,
% 3.16/1.26  |          x1)
% 3.16/1.26  | 
% 3.16/1.26  | SIMP: (5) implies:
% 3.16/1.26  |   (6)  $difference($product(2620, x3), $product(7178, x2)) = $product(13299,
% 3.16/1.26  |          x1)
% 3.16/1.26  | 
% 3.16/1.26  | COMBINE_EQS: (4), (eq1) imply:
% 3.16/1.26  |   (7)  $sum($sum($difference(x5, $product(1016, x3)), $product(2784, x2)),
% 3.16/1.26  |          $product(5157, x1)) = 0
% 3.16/1.26  | 
% 3.16/1.26  | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1 gives:
% 3.16/1.26  |   (8)  $sum($product(2, all_3_0), all_3_1) = x5 &  ~ (all_3_1 = 0) &
% 3.16/1.26  |        $lesseq(all_3_1, 1) & $lesseq(-1, all_3_1) & ( ~ (all_3_1 = 1) |  ~
% 3.16/1.26  |          ($lesseq(x5, 0)) & ( ~ (all_3_1 = -1) |  ~ ($lesseq(0, x5)))
% 3.16/1.26  | 
% 3.16/1.26  | ALPHA: (8) implies:
% 3.16/1.26  |   (9)  $sum($product(2, all_3_0), all_3_1) = x5
% 3.16/1.26  |   (10)   ~ (all_3_1 = 0)
% 3.16/1.26  |   (11)  $lesseq(-1, all_3_1)
% 3.16/1.26  |   (12)  $lesseq(all_3_1, 1)
% 3.16/1.26  | 
% 3.16/1.26  | COMBINE_EQS: (7), (9) imply:
% 3.16/1.26  |   (13)  $sum($sum($difference($sum($product(2, all_3_0), all_3_1),
% 3.16/1.26  |               $product(1016, x3)), $product(2784, x2)), $product(5157, x1)) =
% 3.16/1.26  |         0
% 3.16/1.26  | 
% 3.16/1.26  | COL_REDUCE: introducing fresh symbol sc_5_0_0 defined by:
% 3.16/1.26  |   (14)  $sum($sum($difference(all_3_0, $product(508, x3)), $product(1392,
% 3.16/1.26  |               x2)), $product(2578, x1)) = sc_5_0_0
% 3.16/1.26  | 
% 3.16/1.26  | COMBINE_EQS: (13), (14) imply:
% 3.16/1.26  |   (15)  $sum($sum(all_3_1, x1), $product(2, sc_5_0_0)) = 0
% 3.16/1.26  | 
% 3.16/1.26  | COL_REDUCE: introducing fresh symbol sc_5_0_1 defined by:
% 3.16/1.26  |   (16)  $difference($difference(x3, $product(3, x2)), $product(5, x1)) =
% 3.16/1.26  |         sc_5_0_1
% 3.16/1.26  | 
% 3.16/1.27  | COMBINE_EQS: (6), (16) imply:
% 3.16/1.27  |   (17)  $sum($difference($product(682, x2), $product(199, x1)), $product(2620,
% 3.16/1.27  |             sc_5_0_1)) = 0
% 3.16/1.27  | 
% 3.16/1.27  | COL_REDUCE: introducing fresh symbol sc_5_0_2 defined by:
% 3.16/1.27  |   (18)  $sum(x2, $product(4, sc_5_0_1)) = sc_5_0_2
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (17), (18) imply:
% 3.16/1.27  |   (19)  $sum($product(199, x1), $product(108, sc_5_0_1)) = $product(682,
% 3.16/1.27  |           sc_5_0_2)
% 3.16/1.27  | 
% 3.16/1.27  | SIMP: (19) implies:
% 3.16/1.27  |   (20)  $sum($product(199, x1), $product(108, sc_5_0_1)) = $product(682,
% 3.16/1.27  |           sc_5_0_2)
% 3.16/1.27  | 
% 3.16/1.27  | COL_REDUCE: introducing fresh symbol sc_5_0_3 defined by:
% 3.16/1.27  |   (21)  $difference($sum(x1, sc_5_0_1), $product(3, sc_5_0_2)) = sc_5_0_3
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (20), (21) imply:
% 3.16/1.27  |   (22)  $sum($product(91, sc_5_0_1), $product(85, sc_5_0_2)) = $product(199,
% 3.16/1.27  |           sc_5_0_3)
% 3.16/1.27  | 
% 3.16/1.27  | SIMP: (22) implies:
% 3.16/1.27  |   (23)  $sum($product(91, sc_5_0_1), $product(85, sc_5_0_2)) = $product(199,
% 3.16/1.27  |           sc_5_0_3)
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (15), (21) imply:
% 3.16/1.27  |   (24)  $sum($sum($sum($difference(all_3_1, sc_5_0_1), $product(3, sc_5_0_2)),
% 3.16/1.27  |             sc_5_0_3), $product(2, sc_5_0_0)) = 0
% 3.16/1.27  | 
% 3.16/1.27  | COL_REDUCE: introducing fresh symbol sc_5_0_4 defined by:
% 3.16/1.27  |   (25)  $difference($sum(sc_5_0_1, sc_5_0_2), $product(2, sc_5_0_3)) =
% 3.16/1.27  |         sc_5_0_4
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (23), (25) imply:
% 3.16/1.27  |   (26)  $sum($product(6, sc_5_0_2), $product(17, sc_5_0_3)) = $product(91,
% 3.16/1.27  |           sc_5_0_4)
% 3.16/1.27  | 
% 3.16/1.27  | SIMP: (26) implies:
% 3.16/1.27  |   (27)  $sum($product(6, sc_5_0_2), $product(17, sc_5_0_3)) = $product(91,
% 3.16/1.27  |           sc_5_0_4)
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (24), (25), (27) imply:
% 3.16/1.27  |   (28)  $sum($sum($difference($difference(all_3_1, $product(2, sc_5_0_2)),
% 3.16/1.27  |               $product(18, sc_5_0_3)), $product(90, sc_5_0_4)), $product(2,
% 3.16/1.27  |             sc_5_0_0)) = 0
% 3.16/1.27  | 
% 3.16/1.27  | COL_REDUCE: introducing fresh symbol sc_5_0_5 defined by:
% 3.16/1.27  |   (29)  $difference($sum(sc_5_0_2, $product(3, sc_5_0_3)), $product(15,
% 3.16/1.27  |             sc_5_0_4)) = sc_5_0_5
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (27), (29) imply:
% 3.16/1.27  |   (30)  $sum(sc_5_0_3, sc_5_0_4) = $product(6, sc_5_0_5)
% 3.16/1.27  | 
% 3.16/1.27  | SIMP: (30) implies:
% 3.16/1.27  |   (31)  $sum(sc_5_0_3, sc_5_0_4) = $product(6, sc_5_0_5)
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (29), (31) imply:
% 3.16/1.27  |   (32)  $sum($difference(sc_5_0_2, $product(18, sc_5_0_4)), $product(17,
% 3.16/1.27  |             sc_5_0_5)) = 0
% 3.16/1.27  | 
% 3.16/1.27  | COMBINE_EQS: (28), (31), (32) imply:
% 3.16/1.27  |   (33)  $sum($difference($sum(all_3_1, $product(72, sc_5_0_4)), $product(74,
% 3.16/1.27  |               sc_5_0_5)), $product(2, sc_5_0_0)) = 0
% 3.16/1.27  | 
% 3.16/1.27  | REDUCE: (12), (33) imply:
% 3.16/1.27  |   (34)  $lesseq(0, $sum($difference($product(36, sc_5_0_4), $product(37,
% 3.16/1.27  |                 sc_5_0_5)), sc_5_0_0))
% 3.16/1.27  | 
% 3.16/1.27  | SIMP: (34) implies:
% 3.16/1.27  |   (35)  $lesseq(0, $sum($difference($product(36, sc_5_0_4), $product(37,
% 3.16/1.27  |                 sc_5_0_5)), sc_5_0_0))
% 3.16/1.27  | 
% 3.16/1.28  | REDUCE: (11), (33) imply:
% 3.16/1.28  |   (36)  $lesseq(sc_5_0_0, $difference($product(37, sc_5_0_5), $product(36,
% 3.16/1.28  |               sc_5_0_4)))
% 3.16/1.28  | 
% 3.16/1.28  | SIMP: (36) implies:
% 3.16/1.28  |   (37)  $lesseq(sc_5_0_0, $difference($product(37, sc_5_0_5), $product(36,
% 3.16/1.28  |               sc_5_0_4)))
% 3.16/1.28  | 
% 3.16/1.28  | REDUCE: (10), (33) imply:
% 3.16/1.28  |   (38)   ~ ($sum($difference($product(36, sc_5_0_4), $product(37, sc_5_0_5)),
% 3.16/1.28  |             sc_5_0_0) = 0)
% 3.16/1.28  | 
% 3.16/1.28  | SIMP: (38) implies:
% 3.16/1.28  |   (39)   ~ ($sum($difference($product(36, sc_5_0_4), $product(37, sc_5_0_5)),
% 3.16/1.28  |             sc_5_0_0) = 0)
% 3.16/1.28  | 
% 3.16/1.28  | STRENGTHEN: (35), (39) imply:
% 3.16/1.28  |   (40)  $lesseq(1, $sum($difference($product(36, sc_5_0_4), $product(37,
% 3.16/1.28  |                 sc_5_0_5)), sc_5_0_0))
% 3.16/1.28  | 
% 3.16/1.28  | COMBINE_INEQS: (37), (40) imply:
% 3.16/1.28  |   (41)  $false
% 3.16/1.28  | 
% 3.16/1.28  | CLOSE: (41) is inconsistent.
% 3.16/1.28  | 
% 3.16/1.28  End of proof
% 3.16/1.28  % SZS output end Proof for theBenchmark
% 3.16/1.28  
% 3.16/1.28  662ms
%------------------------------------------------------------------------------