TSTP Solution File: PUZ061+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : PUZ061+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n029.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 : Thu Aug 31 13:22:59 EDT 2023

% Result   : Theorem 4.02s 1.33s
% Output   : Proof 5.74s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : PUZ061+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.15  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.20/0.37  % Computer : n029.cluster.edu
% 0.20/0.37  % Model    : x86_64 x86_64
% 0.20/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.37  % Memory   : 8042.1875MB
% 0.20/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.37  % CPULimit : 300
% 0.20/0.37  % WCLimit  : 300
% 0.20/0.37  % DateTime : Sat Aug 26 22:26:40 EDT 2023
% 0.23/0.37  % CPUTime  : 
% 0.24/0.62  ________       _____
% 0.24/0.62  ___  __ \_________(_)________________________________
% 0.24/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.24/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.24/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.24/0.62  
% 0.24/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.24/0.62  (2023-06-19)
% 0.24/0.62  
% 0.24/0.62  (c) Philipp Rümmer, 2009-2023
% 0.24/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.24/0.62                Amanda Stjerna.
% 0.24/0.62  Free software under BSD-3-Clause.
% 0.24/0.62  
% 0.24/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.24/0.62  
% 0.24/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.24/0.63  Running up to 7 provers in parallel.
% 0.24/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.24/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.24/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.24/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.24/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.24/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.24/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/1.01  Prover 4: Preprocessing ...
% 1.97/1.01  Prover 1: Preprocessing ...
% 2.36/1.05  Prover 2: Preprocessing ...
% 2.36/1.05  Prover 0: Preprocessing ...
% 2.36/1.05  Prover 3: Preprocessing ...
% 2.36/1.06  Prover 5: Preprocessing ...
% 2.36/1.06  Prover 6: Preprocessing ...
% 3.04/1.16  Prover 2: Proving ...
% 3.04/1.17  Prover 5: Proving ...
% 3.04/1.19  Prover 3: Constructing countermodel ...
% 3.04/1.19  Prover 1: Constructing countermodel ...
% 3.04/1.19  Prover 6: Proving ...
% 3.04/1.19  Prover 4: Constructing countermodel ...
% 3.04/1.21  Prover 0: Proving ...
% 4.02/1.31  Prover 3: gave up
% 4.02/1.33  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.02/1.33  Prover 2: proved (695ms)
% 4.02/1.33  
% 4.02/1.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/1.33  
% 4.02/1.34  Prover 6: stopped
% 4.02/1.34  Prover 5: stopped
% 4.02/1.34  Prover 0: stopped
% 4.02/1.35  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.02/1.35  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.02/1.35  Prover 7: Preprocessing ...
% 4.48/1.35  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.48/1.35  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.48/1.36  Prover 10: Preprocessing ...
% 4.48/1.36  Prover 8: Preprocessing ...
% 4.48/1.36  Prover 7: Warning: ignoring some quantifiers
% 4.48/1.36  Prover 7: Constructing countermodel ...
% 4.48/1.36  Prover 13: Preprocessing ...
% 4.48/1.38  Prover 13: Warning: ignoring some quantifiers
% 4.48/1.38  Prover 13: Constructing countermodel ...
% 4.48/1.38  Prover 10: Warning: ignoring some quantifiers
% 4.48/1.39  Prover 10: Constructing countermodel ...
% 4.48/1.39  Prover 1: gave up
% 4.48/1.39  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.48/1.39  Prover 11: Preprocessing ...
% 4.48/1.40  Prover 16: Preprocessing ...
% 4.48/1.40  Prover 13: gave up
% 4.48/1.41  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.48/1.41  Prover 4: Found proof (size 18)
% 4.48/1.41  Prover 4: proved (771ms)
% 4.48/1.41  Prover 10: stopped
% 4.48/1.41  Prover 7: stopped
% 4.48/1.42  Prover 19: Preprocessing ...
% 4.48/1.43  Prover 8: Warning: ignoring some quantifiers
% 4.48/1.43  Prover 16: Warning: ignoring some quantifiers
% 4.48/1.43  Prover 16: Constructing countermodel ...
% 4.48/1.44  Prover 16: stopped
% 4.48/1.44  Prover 8: Constructing countermodel ...
% 4.48/1.44  Prover 8: stopped
% 4.48/1.46  Prover 11: Constructing countermodel ...
% 4.48/1.46  Prover 11: stopped
% 5.28/1.50  Prover 19: Warning: ignoring some quantifiers
% 5.28/1.51  Prover 19: Constructing countermodel ...
% 5.28/1.51  Prover 19: stopped
% 5.28/1.51  
% 5.28/1.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.28/1.51  
% 5.28/1.51  % SZS output start Proof for theBenchmark
% 5.28/1.52  Assumptions after simplification:
% 5.28/1.52  ---------------------------------
% 5.28/1.52  
% 5.28/1.52    (prove_this)
% 5.56/1.55     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 5.56/1.56      $i] :  ? [v6: int] : ( ~ (v6 = 0) & food(v5) = 0 & food(v4) = 0 & likes(v1,
% 5.56/1.56        v0) = v6 & alive(v2) = 0 & eats(v2, v0) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 5.56/1.56      $i(v2) & $i(v1) & $i(v0) &  ! [v7: $i] :  ! [v8: $i] :  ! [v9: int] : (v9 =
% 5.56/1.56        0 |  ~ (not_killed_by(v7, v8) = v9) |  ~ (alive(v7) = 0) |  ~ $i(v8) |  ~
% 5.56/1.56        $i(v7)) &  ! [v7: $i] :  ! [v8: $i] :  ! [v9: int] : (v9 = 0 |  ~
% 5.56/1.56        (likes(v8, v7) = v9) |  ~ $i(v8) |  ~ $i(v7) |  ? [v10: any] :  ? [v11:
% 5.56/1.56          any] : (alive(v8) = v10 & eats(v8, v5) = v11 & ( ~ (v11 = 0) |  ~ (v10 =
% 5.56/1.56              0)))) &  ! [v7: $i] :  ! [v8: int] :  ! [v9: $i] : (v8 = 0 |  ~
% 5.56/1.56        (not_killed_by(v9, v7) = 0) |  ~ (food(v7) = v8) |  ~ $i(v9) |  ~ $i(v7) |
% 5.56/1.56         ? [v10: int] : ( ~ (v10 = 0) & eats(v9, v7) = v10)) &  ! [v7: $i] :  !
% 5.56/1.56      [v8: int] :  ! [v9: $i] : (v8 = 0 |  ~ (food(v7) = v8) |  ~ (eats(v9, v7) =
% 5.56/1.56          0) |  ~ $i(v9) |  ~ $i(v7) |  ? [v10: int] : ( ~ (v10 = 0) &
% 5.56/1.56          not_killed_by(v9, v7) = v10)) &  ! [v7: $i] :  ! [v8: int] : (v8 = 0 | 
% 5.56/1.56        ~ (likes(v1, v7) = v8) |  ~ $i(v7) |  ? [v9: int] : ( ~ (v9 = 0) &
% 5.56/1.56          food(v7) = v9)) &  ! [v7: $i] :  ! [v8: int] : (v8 = 0 |  ~ (eats(v3,
% 5.56/1.56            v7) = v8) |  ~ $i(v7) |  ? [v9: int] : ( ~ (v9 = 0) & eats(v2, v7) =
% 5.56/1.56          v9)) &  ! [v7: $i] : ( ~ (food(v7) = 0) |  ~ $i(v7) | likes(v1, v7) = 0)
% 5.56/1.56      &  ! [v7: $i] : ( ~ (eats(v2, v7) = 0) |  ~ $i(v7) | eats(v3, v7) = 0))
% 5.56/1.56  
% 5.56/1.56  Those formulas are unsatisfiable:
% 5.56/1.56  ---------------------------------
% 5.56/1.56  
% 5.56/1.56  Begin of proof
% 5.56/1.56  | 
% 5.56/1.56  | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 5.56/1.56  |        all_3_2, all_3_3, all_3_4, all_3_5, all_3_6 gives:
% 5.56/1.57  |   (1)   ~ (all_3_0 = 0) & food(all_3_1) = 0 & food(all_3_2) = 0 &
% 5.56/1.57  |        likes(all_3_5, all_3_6) = all_3_0 & alive(all_3_4) = 0 & eats(all_3_4,
% 5.56/1.57  |          all_3_6) = 0 & $i(all_3_1) & $i(all_3_2) & $i(all_3_3) & $i(all_3_4)
% 5.56/1.57  |        & $i(all_3_5) & $i(all_3_6) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int]
% 5.56/1.57  |        : (v2 = 0 |  ~ (not_killed_by(v0, v1) = v2) |  ~ (alive(v0) = 0) |  ~
% 5.56/1.57  |          $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2
% 5.56/1.57  |          = 0 |  ~ (likes(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any]
% 5.56/1.57  |          :  ? [v4: any] : (alive(v1) = v3 & eats(v1, all_3_1) = v4 & ( ~ (v4 =
% 5.56/1.57  |                0) |  ~ (v3 = 0)))) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i]
% 5.56/1.57  |        : (v1 = 0 |  ~ (not_killed_by(v2, v0) = 0) |  ~ (food(v0) = v1) |  ~
% 5.56/1.57  |          $i(v2) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & eats(v2, v0) =
% 5.56/1.57  |            v3)) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] : (v1 = 0 |  ~
% 5.56/1.57  |          (food(v0) = v1) |  ~ (eats(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v0) |  ?
% 5.56/1.57  |          [v3: int] : ( ~ (v3 = 0) & not_killed_by(v2, v0) = v3)) &  ! [v0: $i]
% 5.56/1.57  |        :  ! [v1: int] : (v1 = 0 |  ~ (likes(all_3_5, v0) = v1) |  ~ $i(v0) | 
% 5.56/1.57  |          ? [v2: int] : ( ~ (v2 = 0) & food(v0) = v2)) &  ! [v0: $i] :  ! [v1:
% 5.56/1.57  |          int] : (v1 = 0 |  ~ (eats(all_3_3, v0) = v1) |  ~ $i(v0) |  ? [v2:
% 5.56/1.57  |            int] : ( ~ (v2 = 0) & eats(all_3_4, v0) = v2)) &  ! [v0: $i] : ( ~
% 5.56/1.57  |          (food(v0) = 0) |  ~ $i(v0) | likes(all_3_5, v0) = 0) &  ! [v0: $i] :
% 5.56/1.57  |        ( ~ (eats(all_3_4, v0) = 0) |  ~ $i(v0) | eats(all_3_3, v0) = 0)
% 5.56/1.57  | 
% 5.56/1.57  | ALPHA: (1) implies:
% 5.74/1.57  |   (2)   ~ (all_3_0 = 0)
% 5.74/1.57  |   (3)  $i(all_3_6)
% 5.74/1.57  |   (4)  $i(all_3_4)
% 5.74/1.57  |   (5)  eats(all_3_4, all_3_6) = 0
% 5.74/1.57  |   (6)  alive(all_3_4) = 0
% 5.74/1.57  |   (7)  likes(all_3_5, all_3_6) = all_3_0
% 5.74/1.57  |   (8)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (likes(all_3_5, v0) = v1) | 
% 5.74/1.57  |          ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & food(v0) = v2))
% 5.74/1.58  |   (9)   ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] : (v1 = 0 |  ~ (food(v0) = v1)
% 5.74/1.58  |          |  ~ (eats(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v0) |  ? [v3: int] : ( ~
% 5.74/1.58  |            (v3 = 0) & not_killed_by(v2, v0) = v3))
% 5.74/1.58  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 5.74/1.58  |           (not_killed_by(v0, v1) = v2) |  ~ (alive(v0) = 0) |  ~ $i(v1) |  ~
% 5.74/1.58  |           $i(v0))
% 5.74/1.58  | 
% 5.74/1.58  | GROUND_INST: instantiating (8) with all_3_6, all_3_0, simplifying with (3),
% 5.74/1.58  |              (7) gives:
% 5.74/1.58  |   (11)  all_3_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & food(all_3_6) = v0)
% 5.74/1.58  | 
% 5.74/1.58  | BETA: splitting (11) gives:
% 5.74/1.58  | 
% 5.74/1.58  | Case 1:
% 5.74/1.58  | | 
% 5.74/1.58  | |   (12)  all_3_0 = 0
% 5.74/1.58  | | 
% 5.74/1.58  | | REDUCE: (2), (12) imply:
% 5.74/1.58  | |   (13)  $false
% 5.74/1.58  | | 
% 5.74/1.58  | | CLOSE: (13) is inconsistent.
% 5.74/1.58  | | 
% 5.74/1.58  | Case 2:
% 5.74/1.58  | | 
% 5.74/1.58  | |   (14)   ? [v0: int] : ( ~ (v0 = 0) & food(all_3_6) = v0)
% 5.74/1.58  | | 
% 5.74/1.58  | | DELTA: instantiating (14) with fresh symbol all_16_0 gives:
% 5.74/1.58  | |   (15)   ~ (all_16_0 = 0) & food(all_3_6) = all_16_0
% 5.74/1.58  | | 
% 5.74/1.58  | | ALPHA: (15) implies:
% 5.74/1.58  | |   (16)   ~ (all_16_0 = 0)
% 5.74/1.58  | |   (17)  food(all_3_6) = all_16_0
% 5.74/1.58  | | 
% 5.74/1.58  | | GROUND_INST: instantiating (9) with all_3_6, all_16_0, all_3_4, simplifying
% 5.74/1.58  | |              with (3), (4), (5), (17) gives:
% 5.74/1.58  | |   (18)  all_16_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & not_killed_by(all_3_4,
% 5.74/1.58  | |             all_3_6) = v0)
% 5.74/1.58  | | 
% 5.74/1.58  | | BETA: splitting (18) gives:
% 5.74/1.58  | | 
% 5.74/1.58  | | Case 1:
% 5.74/1.58  | | | 
% 5.74/1.58  | | |   (19)  all_16_0 = 0
% 5.74/1.58  | | | 
% 5.74/1.58  | | | REDUCE: (16), (19) imply:
% 5.74/1.58  | | |   (20)  $false
% 5.74/1.58  | | | 
% 5.74/1.58  | | | CLOSE: (20) is inconsistent.
% 5.74/1.58  | | | 
% 5.74/1.58  | | Case 2:
% 5.74/1.58  | | | 
% 5.74/1.58  | | |   (21)   ? [v0: int] : ( ~ (v0 = 0) & not_killed_by(all_3_4, all_3_6) =
% 5.74/1.58  | | |           v0)
% 5.74/1.58  | | | 
% 5.74/1.58  | | | DELTA: instantiating (21) with fresh symbol all_39_0 gives:
% 5.74/1.58  | | |   (22)   ~ (all_39_0 = 0) & not_killed_by(all_3_4, all_3_6) = all_39_0
% 5.74/1.58  | | | 
% 5.74/1.58  | | | ALPHA: (22) implies:
% 5.74/1.59  | | |   (23)   ~ (all_39_0 = 0)
% 5.74/1.59  | | |   (24)  not_killed_by(all_3_4, all_3_6) = all_39_0
% 5.74/1.59  | | | 
% 5.74/1.59  | | | GROUND_INST: instantiating (10) with all_3_4, all_3_6, all_39_0,
% 5.74/1.59  | | |              simplifying with (3), (4), (6), (24) gives:
% 5.74/1.59  | | |   (25)  all_39_0 = 0
% 5.74/1.59  | | | 
% 5.74/1.59  | | | REDUCE: (23), (25) imply:
% 5.74/1.59  | | |   (26)  $false
% 5.74/1.59  | | | 
% 5.74/1.59  | | | CLOSE: (26) is inconsistent.
% 5.74/1.59  | | | 
% 5.74/1.59  | | End of split
% 5.74/1.59  | | 
% 5.74/1.59  | End of split
% 5.74/1.59  | 
% 5.74/1.59  End of proof
% 5.74/1.59  % SZS output end Proof for theBenchmark
% 5.74/1.59  
% 5.74/1.59  967ms
%------------------------------------------------------------------------------