TSTP Solution File: KRS124+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS124+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 : n008.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 05:51:20 EDT 2023

% Result   : Unsatisfiable 4.85s 1.54s
% Output   : Proof 6.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS124+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Aug 28 01:26:32 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.20/0.59  ________       _____
% 0.20/0.59  ___  __ \_________(_)________________________________
% 0.20/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59  (2023-06-19)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2023
% 0.20/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59                Amanda Stjerna.
% 0.20/0.59  Free software under BSD-3-Clause.
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.72/0.99  Prover 1: Preprocessing ...
% 1.72/0.99  Prover 4: Preprocessing ...
% 2.34/1.04  Prover 6: Preprocessing ...
% 2.34/1.04  Prover 5: Preprocessing ...
% 2.34/1.05  Prover 0: Preprocessing ...
% 2.34/1.05  Prover 3: Preprocessing ...
% 2.34/1.05  Prover 2: Preprocessing ...
% 4.23/1.32  Prover 2: Proving ...
% 4.23/1.33  Prover 5: Proving ...
% 4.23/1.36  Prover 6: Proving ...
% 4.23/1.37  Prover 1: Constructing countermodel ...
% 4.23/1.38  Prover 3: Constructing countermodel ...
% 4.85/1.39  Prover 4: Constructing countermodel ...
% 4.85/1.47  Prover 0: Proving ...
% 4.85/1.53  Prover 1: gave up
% 4.85/1.54  Prover 5: proved (907ms)
% 4.85/1.54  
% 4.85/1.54  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.85/1.54  
% 4.85/1.54  Prover 3: stopped
% 4.85/1.54  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.85/1.54  Prover 6: stopped
% 4.85/1.54  Prover 2: stopped
% 4.85/1.54  Prover 0: stopped
% 4.85/1.54  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.85/1.54  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.85/1.54  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.85/1.55  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.48/1.55  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.01/1.57  Prover 8: Preprocessing ...
% 6.01/1.58  Prover 10: Preprocessing ...
% 6.01/1.58  Prover 7: Preprocessing ...
% 6.01/1.59  Prover 13: Preprocessing ...
% 6.01/1.60  Prover 16: Preprocessing ...
% 6.01/1.60  Prover 11: Preprocessing ...
% 6.28/1.61  Prover 4: Found proof (size 18)
% 6.28/1.61  Prover 4: proved (985ms)
% 6.28/1.62  Prover 13: stopped
% 6.28/1.62  Prover 16: stopped
% 6.28/1.63  Prover 10: Warning: ignoring some quantifiers
% 6.47/1.63  Prover 7: Warning: ignoring some quantifiers
% 6.47/1.64  Prover 11: stopped
% 6.47/1.64  Prover 7: Constructing countermodel ...
% 6.47/1.64  Prover 10: Constructing countermodel ...
% 6.47/1.64  Prover 7: stopped
% 6.47/1.65  Prover 10: stopped
% 6.47/1.66  Prover 8: Warning: ignoring some quantifiers
% 6.47/1.67  Prover 8: Constructing countermodel ...
% 6.47/1.67  Prover 8: stopped
% 6.47/1.67  
% 6.47/1.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.47/1.67  
% 6.47/1.68  % SZS output start Proof for theBenchmark
% 6.47/1.68  Assumptions after simplification:
% 6.47/1.68  ---------------------------------
% 6.47/1.68  
% 6.47/1.68    (axiom_12)
% 6.47/1.71     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (ca_Ax3(v0) = v1) |  ~ $i(v0) |  ?
% 6.47/1.71      [v2: any] :  ? [v3: any] : (cd(v0) = v2 & cc(v0) = v3 & ( ~ (v3 = 0) |  ~
% 6.47/1.71          (v2 = 0)))) &  ! [v0: $i] :  ! [v1: any] : ( ~ (cd(v0) = v1) |  ~ $i(v0)
% 6.47/1.71      |  ? [v2: any] :  ? [v3: any] : (cc(v0) = v3 & ca_Ax3(v0) = v2 & ( ~ (v2 =
% 6.47/1.71            0) | (v3 = 0 & v1 = 0)))) &  ! [v0: $i] :  ! [v1: any] : ( ~ (cc(v0) =
% 6.47/1.71        v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (cd(v0) = v3 & ca_Ax3(v0)
% 6.47/1.71        = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) &  ! [v0: $i] : ( ~ (cd(v0) =
% 6.47/1.71        0) |  ~ $i(v0) |  ? [v1: any] :  ? [v2: any] : (cc(v0) = v1 & ca_Ax3(v0) =
% 6.47/1.71        v2 & ( ~ (v1 = 0) | v2 = 0))) &  ! [v0: $i] : ( ~ (cc(v0) = 0) |  ~ $i(v0)
% 6.47/1.71      |  ? [v1: any] :  ? [v2: any] : (cd(v0) = v1 & ca_Ax3(v0) = v2 & ( ~ (v1 =
% 6.47/1.71            0) | v2 = 0))) &  ! [v0: $i] : ( ~ (ca_Ax3(v0) = 0) |  ~ $i(v0) |
% 6.47/1.71      (cd(v0) = 0 & cc(v0) = 0))
% 6.47/1.71  
% 6.47/1.71    (axiom_13)
% 6.47/1.72    cUnsatisfiable(i2003_11_14_17_22_10903) = 0 & $i(i2003_11_14_17_22_10903)
% 6.47/1.72  
% 6.47/1.72    (axiom_2)
% 6.47/1.72     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (cUnsatisfiable(v0) =
% 6.47/1.72        0) |  ~ (ca_Ax3(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3
% 6.47/1.72          = 0) & rr(v0, v1) = v3)) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] :
% 6.47/1.72    (v1 = 0 |  ~ (cUnsatisfiable(v0) = v1) |  ~ (rr(v0, v2) = 0) |  ~ $i(v2) |  ~
% 6.47/1.72      $i(v0) |  ? [v3: $i] :  ? [v4: int] :  ? [v5: int] :  ? [v6: int] : ($i(v3)
% 6.47/1.72        & ((v4 = 0 &  ~ (v5 = 0) & ca_Ax3(v3) = v5 & rr(v0, v3) = 0) | ( ~ (v6 =
% 6.47/1.72              0) & cowlThing(v2) = v6)))) &  ! [v0: $i] :  ! [v1: int] :  ! [v2:
% 6.47/1.72      $i] : (v1 = 0 |  ~ (cUnsatisfiable(v0) = v1) |  ~ (cowlThing(v2) = 0) |  ~
% 6.47/1.72      $i(v2) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] :  ? [v5: int] :  ? [v6:
% 6.47/1.72        int] : ($i(v3) & ((v4 = 0 &  ~ (v5 = 0) & ca_Ax3(v3) = v5 & rr(v0, v3) =
% 6.47/1.72            0) | ( ~ (v6 = 0) & rr(v0, v2) = v6)))) &  ! [v0: $i] :  ! [v1: $i] :
% 6.47/1.72    ( ~ (cUnsatisfiable(v0) = 0) |  ~ (rr(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 6.47/1.72      ca_Ax3(v1) = 0) &  ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) | 
% 6.47/1.72      ? [v1: $i] : (rr(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1)))
% 6.47/1.72  
% 6.47/1.72    (axiom_3)
% 6.47/1.72     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cdxcomp(v0) = v1) |  ~ $i(v0) |  ?
% 6.47/1.72      [v2: int] : ( ~ (v2 = 0) & cc(v0) = v2)) &  ! [v0: $i] : ( ~ (cc(v0) = 0) | 
% 6.47/1.72      ~ $i(v0) | cdxcomp(v0) = 0)
% 6.47/1.72  
% 6.47/1.72    (axiom_6)
% 6.47/1.73     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cd(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 6.47/1.73        $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 6.47/1.73      (cd(v0) = 0) |  ~ (ra_Px1(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0))
% 6.47/1.73  
% 6.47/1.73    (axiom_7)
% 6.97/1.73     ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] : (v1 = 0 |  ~ (ra_Px1(v0, v2) = 0) |
% 6.97/1.73       ~ (cdxcomp(v0) = v1) |  ~ $i(v2) |  ~ $i(v0)) &  ! [v0: $i] : ( ~
% 6.97/1.73      (cdxcomp(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1)))
% 6.97/1.73  
% 6.97/1.73  Further assumptions not needed in the proof:
% 6.97/1.73  --------------------------------------------
% 6.97/1.73  axiom_0, axiom_1, axiom_10, axiom_11, axiom_4, axiom_5, axiom_8, axiom_9
% 6.97/1.73  
% 6.97/1.73  Those formulas are unsatisfiable:
% 6.97/1.73  ---------------------------------
% 6.97/1.73  
% 6.97/1.73  Begin of proof
% 6.97/1.73  | 
% 6.97/1.73  | ALPHA: (axiom_2) implies:
% 6.97/1.73  |   (1)   ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 6.97/1.73  |          (rr(v0, v1) = 0 & cowlThing(v1) = 0 & $i(v1)))
% 6.97/1.73  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ (rr(v0,
% 6.97/1.73  |              v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | ca_Ax3(v1) = 0)
% 6.97/1.73  | 
% 6.97/1.73  | ALPHA: (axiom_3) implies:
% 6.97/1.73  |   (3)   ! [v0: $i] : ( ~ (cc(v0) = 0) |  ~ $i(v0) | cdxcomp(v0) = 0)
% 6.97/1.73  | 
% 6.97/1.73  | ALPHA: (axiom_6) implies:
% 6.97/1.73  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ (cd(v0) = 0) |  ~ (ra_Px1(v0, v1) = 0)
% 6.97/1.73  |          |  ~ $i(v1) |  ~ $i(v0))
% 6.97/1.73  | 
% 6.97/1.73  | ALPHA: (axiom_7) implies:
% 6.97/1.74  |   (5)   ! [v0: $i] : ( ~ (cdxcomp(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 6.97/1.74  |          (ra_Px1(v0, v1) = 0 & $i(v1)))
% 6.97/1.74  | 
% 6.97/1.74  | ALPHA: (axiom_12) implies:
% 6.97/1.74  |   (6)   ! [v0: $i] : ( ~ (ca_Ax3(v0) = 0) |  ~ $i(v0) | (cd(v0) = 0 & cc(v0) =
% 6.97/1.74  |            0))
% 6.97/1.74  | 
% 6.97/1.74  | ALPHA: (axiom_13) implies:
% 6.97/1.74  |   (7)  $i(i2003_11_14_17_22_10903)
% 6.97/1.74  |   (8)  cUnsatisfiable(i2003_11_14_17_22_10903) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (1) with i2003_11_14_17_22_10903, simplifying with
% 6.97/1.74  |              (7), (8) gives:
% 6.97/1.74  |   (9)   ? [v0: $i] : (rr(i2003_11_14_17_22_10903, v0) = 0 & cowlThing(v0) = 0
% 6.97/1.74  |          & $i(v0))
% 6.97/1.74  | 
% 6.97/1.74  | DELTA: instantiating (9) with fresh symbol all_22_0 gives:
% 6.97/1.74  |   (10)  rr(i2003_11_14_17_22_10903, all_22_0) = 0 & cowlThing(all_22_0) = 0 &
% 6.97/1.74  |         $i(all_22_0)
% 6.97/1.74  | 
% 6.97/1.74  | ALPHA: (10) implies:
% 6.97/1.74  |   (11)  $i(all_22_0)
% 6.97/1.74  |   (12)  rr(i2003_11_14_17_22_10903, all_22_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (2) with i2003_11_14_17_22_10903, all_22_0,
% 6.97/1.74  |              simplifying with (7), (8), (11), (12) gives:
% 6.97/1.74  |   (13)  ca_Ax3(all_22_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (6) with all_22_0, simplifying with (11), (13)
% 6.97/1.74  |              gives:
% 6.97/1.74  |   (14)  cd(all_22_0) = 0 & cc(all_22_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | ALPHA: (14) implies:
% 6.97/1.74  |   (15)  cc(all_22_0) = 0
% 6.97/1.74  |   (16)  cd(all_22_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (3) with all_22_0, simplifying with (11), (15)
% 6.97/1.74  |              gives:
% 6.97/1.74  |   (17)  cdxcomp(all_22_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (5) with all_22_0, simplifying with (11), (17)
% 6.97/1.74  |              gives:
% 6.97/1.74  |   (18)   ? [v0: $i] : (ra_Px1(all_22_0, v0) = 0 & $i(v0))
% 6.97/1.74  | 
% 6.97/1.74  | DELTA: instantiating (18) with fresh symbol all_47_0 gives:
% 6.97/1.74  |   (19)  ra_Px1(all_22_0, all_47_0) = 0 & $i(all_47_0)
% 6.97/1.74  | 
% 6.97/1.74  | ALPHA: (19) implies:
% 6.97/1.74  |   (20)  $i(all_47_0)
% 6.97/1.74  |   (21)  ra_Px1(all_22_0, all_47_0) = 0
% 6.97/1.74  | 
% 6.97/1.74  | GROUND_INST: instantiating (4) with all_22_0, all_47_0, simplifying with (11),
% 6.97/1.74  |              (16), (20), (21) gives:
% 6.97/1.74  |   (22)  $false
% 6.97/1.75  | 
% 6.97/1.75  | CLOSE: (22) is inconsistent.
% 6.97/1.75  | 
% 6.97/1.75  End of proof
% 6.97/1.75  % SZS output end Proof for theBenchmark
% 6.97/1.75  
% 6.97/1.75  1156ms
%------------------------------------------------------------------------------