TSTP Solution File: KRS196+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS196+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n016.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 05:51:37 EDT 2023

% Result   : Theorem 11.10s 2.70s
% Output   : Proof 13.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.55  % Problem  : KRS196+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.06/0.55  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.76  % Computer : n016.cluster.edu
% 0.12/0.76  % Model    : x86_64 x86_64
% 0.12/0.76  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.76  % Memory   : 8042.1875MB
% 0.12/0.76  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.77  % CPULimit : 300
% 0.12/0.77  % WCLimit  : 300
% 0.12/0.77  % DateTime : Mon Aug 28 02:19:14 EDT 2023
% 0.12/0.77  % CPUTime  : 
% 0.19/1.03  ________       _____
% 0.19/1.03  ___  __ \_________(_)________________________________
% 0.19/1.03  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/1.03  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/1.03  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/1.03  
% 0.19/1.03  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/1.03  (2023-06-19)
% 0.19/1.03  
% 0.19/1.03  (c) Philipp Rümmer, 2009-2023
% 0.19/1.03  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/1.03                Amanda Stjerna.
% 0.19/1.03  Free software under BSD-3-Clause.
% 0.19/1.03  
% 0.19/1.03  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/1.03  
% 0.19/1.03  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/1.04  Running up to 7 provers in parallel.
% 0.19/1.06  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/1.06  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/1.06  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/1.06  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/1.06  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/1.06  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/1.06  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.56/1.61  Prover 1: Preprocessing ...
% 2.56/1.62  Prover 4: Preprocessing ...
% 3.84/1.64  Prover 5: Preprocessing ...
% 3.84/1.64  Prover 0: Preprocessing ...
% 3.84/1.65  Prover 6: Preprocessing ...
% 3.84/1.65  Prover 3: Preprocessing ...
% 3.84/1.65  Prover 2: Preprocessing ...
% 8.60/2.32  Prover 5: Proving ...
% 8.60/2.33  Prover 2: Proving ...
% 9.77/2.53  Prover 3: Constructing countermodel ...
% 9.77/2.53  Prover 6: Proving ...
% 10.21/2.55  Prover 1: Constructing countermodel ...
% 10.32/2.58  Prover 0: Proving ...
% 10.32/2.61  Prover 4: Constructing countermodel ...
% 11.10/2.69  Prover 3: proved (1638ms)
% 11.10/2.70  
% 11.10/2.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.10/2.70  
% 11.10/2.70  Prover 2: stopped
% 11.10/2.70  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.10/2.70  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.10/2.71  Prover 5: stopped
% 11.10/2.72  Prover 6: stopped
% 11.10/2.72  Prover 0: stopped
% 11.10/2.73  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.10/2.73  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.10/2.73  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.07/2.78  Prover 7: Preprocessing ...
% 12.07/2.80  Prover 10: Preprocessing ...
% 12.07/2.81  Prover 8: Preprocessing ...
% 12.07/2.81  Prover 13: Preprocessing ...
% 12.07/2.82  Prover 11: Preprocessing ...
% 12.07/2.82  Prover 1: Found proof (size 22)
% 12.07/2.84  Prover 1: proved (1787ms)
% 12.07/2.84  Prover 10: stopped
% 12.07/2.84  Prover 4: stopped
% 12.07/2.89  Prover 13: stopped
% 12.07/2.91  Prover 11: stopped
% 12.07/2.91  Prover 7: Warning: ignoring some quantifiers
% 12.07/2.93  Prover 7: Constructing countermodel ...
% 12.07/2.94  Prover 7: stopped
% 13.37/3.02  Prover 8: Warning: ignoring some quantifiers
% 13.37/3.02  Prover 8: Constructing countermodel ...
% 13.37/3.03  Prover 8: stopped
% 13.37/3.03  
% 13.37/3.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.37/3.03  
% 13.37/3.04  % SZS output start Proof for theBenchmark
% 13.37/3.04  Assumptions after simplification:
% 13.37/3.04  ---------------------------------
% 13.37/3.04  
% 13.37/3.04    (isa)
% 13.70/3.07     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (isa(v0, v1) = v2) | 
% 13.70/3.07      ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: $i] :  ? [v5: int] : ( ~ (v5 =
% 13.70/3.07          0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0 & $i(v4) &
% 13.70/3.07        $i(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (isa(v0, v1) = 0) |  ~ $i(v1) |
% 13.70/3.07       ~ $i(v0) |  ! [v2: $i] :  ! [v3: $i] : ( ~ (status(v2, v3, v0) = 0) |  ~
% 13.70/3.07        $i(v3) |  ~ $i(v2) | status(v2, v3, v1) = 0))
% 13.70/3.07  
% 13.70/3.07    (isa_wca_thm)
% 13.70/3.07    $i(wca) & $i(thm) &  ? [v0: int] : ( ~ (v0 = 0) & isa(wca, thm) = v0)
% 13.70/3.07  
% 13.70/3.07    (thm)
% 13.70/3.07    $i(thm) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (status(v0,
% 13.70/3.07          v1, thm) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : (
% 13.70/3.07        ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) &  ! [v0:
% 13.70/3.07      $i] :  ! [v1: $i] : ( ~ (status(v0, v1, thm) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 13.70/3.07      ! [v2: $i] : ( ~ (model(v2, v0) = 0) |  ~ $i(v2) | model(v2, v1) = 0))
% 13.70/3.07  
% 13.70/3.07    (wca)
% 13.70/3.08    $i(wca) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (status(v0,
% 13.70/3.08          v1, wca) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] : (model(v3, v0) =
% 13.70/3.08        0 & $i(v3)) |  ! [v3: $i] :  ! [v4: int] : (v4 = 0 |  ~ (model(v3, v1) =
% 13.70/3.08          v4) |  ~ $i(v3)) |  ! [v3: $i] : ( ~ (model(v3, v1) = 0) |  ~ $i(v3))) &
% 13.70/3.08     ! [v0: $i] :  ! [v1: $i] : ( ~ (status(v0, v1, wca) = 0) |  ~ $i(v1) |  ~
% 13.70/3.08      $i(v0) | ( ! [v2: $i] : ( ~ (model(v2, v0) = 0) |  ~ $i(v2)) &  ? [v2: $i] :
% 13.70/3.08         ? [v3: int] : ( ~ (v3 = 0) & model(v2, v1) = v3 & $i(v2)) &  ? [v2: $i] :
% 13.70/3.08        (model(v2, v1) = 0 & $i(v2))))
% 13.70/3.08  
% 13.70/3.08  Further assumptions not needed in the proof:
% 13.70/3.08  --------------------------------------------
% 13.70/3.08  cax, completeness, contradiction, csa, eqv, esa, eth, mighta, mixed_pair,
% 13.70/3.08  nevera, noc, non_thm_spt, not, nota, sap, sat, sat_non_taut_pair, satisfiable,
% 13.70/3.08  sca, tac, tau, tautology, tca, unp, uns, wec, wtc, wth, xora
% 13.70/3.08  
% 13.70/3.08  Those formulas are unsatisfiable:
% 13.70/3.08  ---------------------------------
% 13.70/3.08  
% 13.70/3.08  Begin of proof
% 13.70/3.08  | 
% 13.70/3.08  | ALPHA: (thm) implies:
% 13.70/3.08  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (status(v0, v1,
% 13.70/3.08  |              thm) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] :
% 13.70/3.08  |          ( ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3)))
% 13.70/3.08  | 
% 13.70/3.08  | ALPHA: (wca) implies:
% 13.70/3.08  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (status(v0, v1, wca) = 0) |  ~ $i(v1) |
% 13.70/3.08  |           ~ $i(v0) | ( ! [v2: $i] : ( ~ (model(v2, v0) = 0) |  ~ $i(v2)) &  ?
% 13.70/3.08  |            [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) & model(v2, v1) = v3 &
% 13.70/3.08  |              $i(v2)) &  ? [v2: $i] : (model(v2, v1) = 0 & $i(v2))))
% 13.70/3.08  | 
% 13.70/3.08  | ALPHA: (isa) implies:
% 13.70/3.08  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (isa(v0, v1) =
% 13.70/3.08  |            v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 13.70/3.08  |            int] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0)
% 13.70/3.08  |            = 0 & $i(v4) & $i(v3)))
% 13.70/3.08  | 
% 13.70/3.08  | ALPHA: (isa_wca_thm) implies:
% 13.70/3.08  |   (4)  $i(thm)
% 13.70/3.08  |   (5)  $i(wca)
% 13.70/3.09  |   (6)   ? [v0: int] : ( ~ (v0 = 0) & isa(wca, thm) = v0)
% 13.70/3.09  | 
% 13.70/3.09  | DELTA: instantiating (6) with fresh symbol all_30_0 gives:
% 13.70/3.09  |   (7)   ~ (all_30_0 = 0) & isa(wca, thm) = all_30_0
% 13.70/3.09  | 
% 13.70/3.09  | ALPHA: (7) implies:
% 13.70/3.09  |   (8)   ~ (all_30_0 = 0)
% 13.70/3.09  |   (9)  isa(wca, thm) = all_30_0
% 13.70/3.09  | 
% 13.70/3.09  | GROUND_INST: instantiating (3) with wca, thm, all_30_0, simplifying with (4),
% 13.70/3.09  |              (5), (9) gives:
% 13.70/3.09  |   (10)  all_30_0 = 0 |  ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0)
% 13.70/3.09  |           & status(v0, v1, wca) = 0 & status(v0, v1, thm) = v2 & $i(v1) &
% 13.70/3.09  |           $i(v0))
% 13.70/3.09  | 
% 13.70/3.09  | BETA: splitting (10) gives:
% 13.70/3.09  | 
% 13.70/3.09  | Case 1:
% 13.70/3.09  | | 
% 13.70/3.09  | |   (11)  all_30_0 = 0
% 13.70/3.09  | | 
% 13.70/3.09  | | REDUCE: (8), (11) imply:
% 13.70/3.09  | |   (12)  $false
% 13.70/3.09  | | 
% 13.70/3.09  | | CLOSE: (12) is inconsistent.
% 13.70/3.09  | | 
% 13.70/3.09  | Case 2:
% 13.70/3.09  | | 
% 13.70/3.09  | |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) & status(v0,
% 13.70/3.09  | |             v1, wca) = 0 & status(v0, v1, thm) = v2 & $i(v1) & $i(v0))
% 13.70/3.09  | | 
% 13.70/3.09  | | DELTA: instantiating (13) with fresh symbols all_73_0, all_73_1, all_73_2
% 13.70/3.09  | |        gives:
% 13.70/3.09  | |   (14)   ~ (all_73_0 = 0) & status(all_73_2, all_73_1, wca) = 0 &
% 13.70/3.09  | |         status(all_73_2, all_73_1, thm) = all_73_0 & $i(all_73_1) &
% 13.70/3.09  | |         $i(all_73_2)
% 13.70/3.09  | | 
% 13.70/3.09  | | ALPHA: (14) implies:
% 13.70/3.09  | |   (15)   ~ (all_73_0 = 0)
% 13.70/3.09  | |   (16)  $i(all_73_2)
% 13.70/3.09  | |   (17)  $i(all_73_1)
% 13.70/3.09  | |   (18)  status(all_73_2, all_73_1, thm) = all_73_0
% 13.70/3.09  | |   (19)  status(all_73_2, all_73_1, wca) = 0
% 13.70/3.09  | | 
% 13.70/3.09  | | GROUND_INST: instantiating (1) with all_73_2, all_73_1, all_73_0,
% 13.70/3.09  | |              simplifying with (16), (17), (18) gives:
% 13.70/3.09  | |   (20)  all_73_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & model(v0,
% 13.70/3.09  | |             all_73_1) = v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.70/3.09  | | 
% 13.70/3.09  | | GROUND_INST: instantiating (2) with all_73_2, all_73_1, simplifying with
% 13.70/3.09  | |              (16), (17), (19) gives:
% 13.70/3.09  | |   (21)   ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) |  ~ $i(v0)) &  ? [v0:
% 13.70/3.09  | |           $i] :  ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_73_1) = v1 &
% 13.70/3.09  | |           $i(v0)) &  ? [v0: $i] : (model(v0, all_73_1) = 0 & $i(v0))
% 13.70/3.09  | | 
% 13.70/3.09  | | ALPHA: (21) implies:
% 13.70/3.09  | |   (22)   ! [v0: $i] : ( ~ (model(v0, all_73_2) = 0) |  ~ $i(v0))
% 13.70/3.09  | | 
% 13.70/3.09  | | BETA: splitting (20) gives:
% 13.70/3.09  | | 
% 13.70/3.09  | | Case 1:
% 13.70/3.09  | | | 
% 13.70/3.09  | | |   (23)  all_73_0 = 0
% 13.70/3.10  | | | 
% 13.70/3.10  | | | REDUCE: (15), (23) imply:
% 13.70/3.10  | | |   (24)  $false
% 13.70/3.10  | | | 
% 13.70/3.10  | | | CLOSE: (24) is inconsistent.
% 13.70/3.10  | | | 
% 13.70/3.10  | | Case 2:
% 13.70/3.10  | | | 
% 13.70/3.10  | | |   (25)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_73_1) =
% 13.70/3.10  | | |           v1 & model(v0, all_73_2) = 0 & $i(v0))
% 13.70/3.10  | | | 
% 13.70/3.10  | | | DELTA: instantiating (25) with fresh symbols all_89_0, all_89_1 gives:
% 13.70/3.10  | | |   (26)   ~ (all_89_0 = 0) & model(all_89_1, all_73_1) = all_89_0 &
% 13.70/3.10  | | |         model(all_89_1, all_73_2) = 0 & $i(all_89_1)
% 13.70/3.10  | | | 
% 13.70/3.10  | | | ALPHA: (26) implies:
% 13.70/3.10  | | |   (27)  $i(all_89_1)
% 13.70/3.10  | | |   (28)  model(all_89_1, all_73_2) = 0
% 13.70/3.10  | | | 
% 13.70/3.10  | | | GROUND_INST: instantiating (22) with all_89_1, simplifying with (27), (28)
% 13.70/3.10  | | |              gives:
% 13.70/3.10  | | |   (29)  $false
% 13.70/3.10  | | | 
% 13.70/3.10  | | | CLOSE: (29) is inconsistent.
% 13.70/3.10  | | | 
% 13.70/3.10  | | End of split
% 13.70/3.10  | | 
% 13.70/3.10  | End of split
% 13.70/3.10  | 
% 13.70/3.10  End of proof
% 13.70/3.10  % SZS output end Proof for theBenchmark
% 13.70/3.10  
% 13.70/3.10  2065ms
%------------------------------------------------------------------------------