TSTP Solution File: KRS169+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS169+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 : n031.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 05:51:31 EDT 2023

% Result   : Theorem 3.82s 1.27s
% Output   : Proof 6.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS169+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n031.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 02:11:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.07/0.94  Prover 4: Preprocessing ...
% 2.07/0.94  Prover 1: Preprocessing ...
% 2.07/0.99  Prover 3: Preprocessing ...
% 2.07/0.99  Prover 2: Preprocessing ...
% 2.07/0.99  Prover 6: Preprocessing ...
% 2.07/0.99  Prover 0: Preprocessing ...
% 2.07/0.99  Prover 5: Preprocessing ...
% 2.97/1.09  Prover 5: Proving ...
% 2.97/1.10  Prover 2: Proving ...
% 2.97/1.14  Prover 4: Constructing countermodel ...
% 2.97/1.14  Prover 6: Constructing countermodel ...
% 2.97/1.14  Prover 1: Constructing countermodel ...
% 2.97/1.14  Prover 3: Constructing countermodel ...
% 3.53/1.17  Prover 0: Proving ...
% 3.82/1.26  Prover 3: proved (635ms)
% 3.82/1.27  
% 3.82/1.27  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.82/1.27  
% 3.82/1.27  Prover 6: stopped
% 3.82/1.27  Prover 2: stopped
% 3.82/1.29  Prover 5: stopped
% 3.82/1.29  Prover 0: stopped
% 3.82/1.29  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.82/1.29  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.82/1.29  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.82/1.29  Prover 8: Preprocessing ...
% 3.82/1.29  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.82/1.29  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.82/1.31  Prover 7: Preprocessing ...
% 3.82/1.31  Prover 13: Preprocessing ...
% 3.82/1.32  Prover 11: Preprocessing ...
% 3.82/1.33  Prover 7: Warning: ignoring some quantifiers
% 3.82/1.34  Prover 10: Preprocessing ...
% 3.82/1.34  Prover 7: Constructing countermodel ...
% 4.50/1.35  Prover 13: Warning: ignoring some quantifiers
% 4.50/1.35  Prover 13: Constructing countermodel ...
% 4.50/1.35  Prover 10: Warning: ignoring some quantifiers
% 4.50/1.36  Prover 10: Constructing countermodel ...
% 4.50/1.39  Prover 8: Warning: ignoring some quantifiers
% 4.50/1.39  Prover 8: Constructing countermodel ...
% 4.50/1.40  Prover 10: gave up
% 4.50/1.40  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.50/1.41  Prover 16: Preprocessing ...
% 4.50/1.41  Prover 11: Constructing countermodel ...
% 4.50/1.42  Prover 13: gave up
% 4.50/1.43  Prover 16: Warning: ignoring some quantifiers
% 4.50/1.43  Prover 1: Found proof (size 53)
% 4.50/1.43  Prover 1: proved (806ms)
% 4.50/1.43  Prover 16: Constructing countermodel ...
% 4.50/1.43  Prover 7: stopped
% 5.28/1.44  Prover 4: stopped
% 5.28/1.44  Prover 8: stopped
% 5.28/1.44  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.28/1.44  Prover 16: stopped
% 5.28/1.44  Prover 11: stopped
% 5.28/1.45  Prover 19: Preprocessing ...
% 5.28/1.49  Prover 19: Warning: ignoring some quantifiers
% 5.57/1.49  Prover 19: Constructing countermodel ...
% 5.57/1.50  Prover 19: stopped
% 5.57/1.50  
% 5.57/1.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.57/1.50  
% 5.57/1.51  % SZS output start Proof for theBenchmark
% 5.57/1.51  Assumptions after simplification:
% 5.57/1.51  ---------------------------------
% 5.57/1.51  
% 5.57/1.51    (axiom_0)
% 5.57/1.54     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~ $i(v0)) & 
% 5.57/1.54    ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 5.57/1.54  
% 5.57/1.54    (axiom_1)
% 5.57/1.54     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_string(v0) = v1) |  ~ $i(v0) |
% 5.57/1.54      xsd_integer(v0) = 0) &  ! [v0: $i] : ( ~ (xsd_string(v0) = 0) |  ~ $i(v0) | 
% 5.57/1.54      ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.57/1.54  
% 5.57/1.54    (axiom_2)
% 5.57/1.54    cowlThing(iX) = 0 & $i(iX)
% 5.57/1.54  
% 5.57/1.54    (axiom_3)
% 5.57/1.55    rhasLeader(iX, iY) = 0 & $i(iY) & $i(iX)
% 5.57/1.55  
% 5.57/1.55    (axiom_4)
% 5.57/1.55    cowlThing(iY) = 0 & $i(iY)
% 5.57/1.55  
% 5.57/1.55    (axiom_5)
% 5.57/1.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasLeader(v0, v1) =
% 5.57/1.55        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rhasHead(v0,
% 5.57/1.55          v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) | 
% 5.57/1.55      ~ $i(v1) |  ~ $i(v0) | rhasHead(v0, v1) = 0)
% 5.57/1.55  
% 5.57/1.55    (the_axiom)
% 5.57/1.55    $i(iY) & $i(iX) &  ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (rhasHead(iX,
% 5.57/1.55        iY) = v1 & cowlThing(iY) = v2 & cowlThing(iX) = v0 & ( ~ (v2 = 0) |  ~ (v1
% 5.57/1.55          = 0) |  ~ (v0 = 0) |  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] :
% 5.57/1.55        (xsd_string(v3) = v4 & xsd_integer(v3) = v5 & $i(v3) & ((v5 = 0 & v4 = 0)
% 5.57/1.55            | ( ~ (v5 = 0) &  ~ (v4 = 0)))) |  ? [v3: $i] :  ? [v4: any] :  ? [v5:
% 5.57/1.55          any] : (cowlNothing(v3) = v5 & cowlThing(v3) = v4 & $i(v3) & ( ~ (v4 =
% 5.57/1.55              0) | v5 = 0))))
% 5.57/1.55  
% 5.57/1.55    (function-axioms)
% 5.87/1.56     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.87/1.56    [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~ (rhasHead(v3, v2) = v0))
% 5.87/1.56    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.87/1.56    [v3: $i] : (v1 = v0 |  ~ (rhasLeader(v3, v2) = v1) |  ~ (rhasLeader(v3, v2) =
% 5.87/1.56        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 5.87/1.56      $i] : (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0)) &  !
% 5.87/1.56    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0
% 5.89/1.56      |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0)) &  ! [v0:
% 5.89/1.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 5.89/1.56      ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0)) &  ! [v0:
% 5.89/1.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 5.89/1.56      ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 5.89/1.56  
% 5.89/1.56  Those formulas are unsatisfiable:
% 5.89/1.56  ---------------------------------
% 5.89/1.56  
% 5.89/1.56  Begin of proof
% 5.89/1.56  | 
% 5.89/1.56  | ALPHA: (axiom_0) implies:
% 5.89/1.56  |   (1)   ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 5.89/1.56  |   (2)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~
% 5.89/1.56  |          $i(v0))
% 5.89/1.56  | 
% 5.89/1.56  | ALPHA: (axiom_1) implies:
% 5.89/1.56  |   (3)   ! [v0: $i] : ( ~ (xsd_string(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~
% 5.89/1.56  |            (v1 = 0) & xsd_integer(v0) = v1))
% 5.89/1.57  |   (4)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_string(v0) = v1) |  ~
% 5.89/1.57  |          $i(v0) | xsd_integer(v0) = 0)
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (axiom_2) implies:
% 5.89/1.57  |   (5)  cowlThing(iX) = 0
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (axiom_3) implies:
% 5.89/1.57  |   (6)  rhasLeader(iX, iY) = 0
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (axiom_4) implies:
% 5.89/1.57  |   (7)  cowlThing(iY) = 0
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (axiom_5) implies:
% 5.89/1.57  |   (8)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) |  ~ $i(v1) | 
% 5.89/1.57  |          ~ $i(v0) | rhasHead(v0, v1) = 0)
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (the_axiom) implies:
% 5.89/1.57  |   (9)  $i(iX)
% 5.89/1.57  |   (10)  $i(iY)
% 5.89/1.57  |   (11)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (rhasHead(iX, iY) = v1 &
% 5.89/1.57  |           cowlThing(iY) = v2 & cowlThing(iX) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0)
% 5.89/1.57  |             |  ~ (v0 = 0) |  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] :
% 5.89/1.57  |             (xsd_string(v3) = v4 & xsd_integer(v3) = v5 & $i(v3) & ((v5 = 0 &
% 5.89/1.57  |                   v4 = 0) | ( ~ (v5 = 0) &  ~ (v4 = 0)))) |  ? [v3: $i] :  ?
% 5.89/1.57  |             [v4: any] :  ? [v5: any] : (cowlNothing(v3) = v5 & cowlThing(v3) =
% 5.89/1.57  |               v4 & $i(v3) & ( ~ (v4 = 0) | v5 = 0))))
% 5.89/1.57  | 
% 5.89/1.57  | ALPHA: (function-axioms) implies:
% 5.89/1.58  |   (12)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 5.89/1.58  |         : (v1 = v0 |  ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 5.89/1.58  |   (13)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 5.89/1.58  |         : (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0))
% 5.89/1.58  |   (14)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 5.89/1.58  |         :  ! [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~
% 5.89/1.58  |           (rhasHead(v3, v2) = v0))
% 5.89/1.58  | 
% 5.89/1.58  | DELTA: instantiating (11) with fresh symbols all_7_0, all_7_1, all_7_2 gives:
% 5.89/1.58  |   (15)  rhasHead(iX, iY) = all_7_1 & cowlThing(iY) = all_7_0 & cowlThing(iX) =
% 5.89/1.58  |         all_7_2 & ( ~ (all_7_0 = 0) |  ~ (all_7_1 = 0) |  ~ (all_7_2 = 0) |  ?
% 5.89/1.58  |           [v0: $i] :  ? [v1: any] :  ? [v2: any] : (xsd_string(v0) = v1 &
% 5.89/1.58  |             xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0)
% 5.89/1.58  |                 &  ~ (v1 = 0)))) |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 5.89/1.58  |           (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) |
% 5.89/1.58  |               v2 = 0)))
% 5.89/1.58  | 
% 5.89/1.58  | ALPHA: (15) implies:
% 5.89/1.58  |   (16)  cowlThing(iX) = all_7_2
% 5.89/1.58  |   (17)  cowlThing(iY) = all_7_0
% 5.89/1.58  |   (18)  rhasHead(iX, iY) = all_7_1
% 5.89/1.58  |   (19)   ~ (all_7_0 = 0) |  ~ (all_7_1 = 0) |  ~ (all_7_2 = 0) |  ? [v0: $i] :
% 5.89/1.58  |          ? [v1: any] :  ? [v2: any] : (xsd_string(v0) = v1 & xsd_integer(v0) =
% 5.89/1.58  |           v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0)))) | 
% 5.89/1.58  |         ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (cowlNothing(v0) = v2 &
% 5.89/1.58  |           cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 5.89/1.58  | 
% 5.89/1.59  | GROUND_INST: instantiating (12) with 0, all_7_2, iX, simplifying with (5),
% 5.89/1.59  |              (16) gives:
% 5.89/1.59  |   (20)  all_7_2 = 0
% 5.89/1.59  | 
% 5.89/1.59  | GROUND_INST: instantiating (12) with 0, all_7_0, iY, simplifying with (7),
% 5.89/1.59  |              (17) gives:
% 5.89/1.59  |   (21)  all_7_0 = 0
% 5.89/1.59  | 
% 5.89/1.59  | GROUND_INST: instantiating (8) with iX, iY, simplifying with (6), (9), (10)
% 5.89/1.59  |              gives:
% 5.89/1.59  |   (22)  rhasHead(iX, iY) = 0
% 5.89/1.59  | 
% 5.89/1.59  | GROUND_INST: instantiating (14) with all_7_1, 0, iY, iX, simplifying with
% 5.89/1.59  |              (18), (22) gives:
% 5.89/1.59  |   (23)  all_7_1 = 0
% 5.89/1.59  | 
% 5.89/1.59  | BETA: splitting (19) gives:
% 5.89/1.59  | 
% 5.89/1.59  | Case 1:
% 5.89/1.59  | | 
% 5.89/1.59  | |   (24)   ~ (all_7_0 = 0)
% 5.89/1.59  | | 
% 5.89/1.59  | | REDUCE: (21), (24) imply:
% 5.89/1.59  | |   (25)  $false
% 5.89/1.59  | | 
% 5.89/1.59  | | CLOSE: (25) is inconsistent.
% 5.89/1.59  | | 
% 5.89/1.59  | Case 2:
% 5.89/1.59  | | 
% 5.89/1.59  | |   (26)   ~ (all_7_1 = 0) |  ~ (all_7_2 = 0) |  ? [v0: $i] :  ? [v1: any] : 
% 5.89/1.59  | |         ? [v2: any] : (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & $i(v0) &
% 5.89/1.59  | |           ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0)))) |  ? [v0: $i] :
% 5.89/1.59  | |          ? [v1: any] :  ? [v2: any] : (cowlNothing(v0) = v2 & cowlThing(v0)
% 5.89/1.59  | |           = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 5.89/1.59  | | 
% 5.89/1.59  | | BETA: splitting (26) gives:
% 5.89/1.59  | | 
% 5.89/1.59  | | Case 1:
% 5.89/1.59  | | | 
% 5.89/1.59  | | |   (27)   ~ (all_7_1 = 0)
% 5.89/1.59  | | | 
% 5.89/1.59  | | | REDUCE: (23), (27) imply:
% 5.89/1.59  | | |   (28)  $false
% 5.89/1.59  | | | 
% 5.89/1.59  | | | CLOSE: (28) is inconsistent.
% 5.89/1.59  | | | 
% 5.89/1.59  | | Case 2:
% 5.89/1.59  | | | 
% 5.89/1.59  | | |   (29)   ~ (all_7_2 = 0) |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 5.89/1.59  | | |         (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 &
% 5.89/1.59  | | |               v1 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0)))) |  ? [v0: $i] :  ?
% 5.89/1.59  | | |         [v1: any] :  ? [v2: any] : (cowlNothing(v0) = v2 & cowlThing(v0) =
% 5.89/1.59  | | |           v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 5.89/1.59  | | | 
% 5.89/1.59  | | | BETA: splitting (29) gives:
% 5.89/1.59  | | | 
% 5.89/1.59  | | | Case 1:
% 5.89/1.59  | | | | 
% 5.89/1.59  | | | |   (30)   ~ (all_7_2 = 0)
% 5.89/1.59  | | | | 
% 5.89/1.59  | | | | REDUCE: (20), (30) imply:
% 5.89/1.59  | | | |   (31)  $false
% 5.89/1.59  | | | | 
% 5.89/1.59  | | | | CLOSE: (31) is inconsistent.
% 5.89/1.59  | | | | 
% 5.89/1.59  | | | Case 2:
% 5.89/1.59  | | | | 
% 5.89/1.59  | | | |   (32)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (xsd_string(v0) = v1
% 5.89/1.59  | | | |           & xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | ( ~ (v2
% 5.89/1.59  | | | |                 = 0) &  ~ (v1 = 0)))) |  ? [v0: $i] :  ? [v1: any] :  ?
% 5.89/1.59  | | | |         [v2: any] : (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & $i(v0)
% 5.89/1.59  | | | |           & ( ~ (v1 = 0) | v2 = 0))
% 5.89/1.59  | | | | 
% 5.89/1.60  | | | | BETA: splitting (32) gives:
% 5.89/1.60  | | | | 
% 5.89/1.60  | | | | Case 1:
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | |   (33)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (xsd_string(v0) =
% 5.89/1.60  | | | | |           v1 & xsd_integer(v0) = v2 & $i(v0) & ((v2 = 0 & v1 = 0) | (
% 5.89/1.60  | | | | |               ~ (v2 = 0) &  ~ (v1 = 0))))
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | | DELTA: instantiating (33) with fresh symbols all_50_0, all_50_1,
% 5.89/1.60  | | | | |        all_50_2 gives:
% 5.89/1.60  | | | | |   (34)  xsd_string(all_50_2) = all_50_1 & xsd_integer(all_50_2) =
% 5.89/1.60  | | | | |         all_50_0 & $i(all_50_2) & ((all_50_0 = 0 & all_50_1 = 0) | ( ~
% 5.89/1.60  | | | | |             (all_50_0 = 0) &  ~ (all_50_1 = 0)))
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | | ALPHA: (34) implies:
% 5.89/1.60  | | | | |   (35)  $i(all_50_2)
% 5.89/1.60  | | | | |   (36)  xsd_integer(all_50_2) = all_50_0
% 5.89/1.60  | | | | |   (37)  xsd_string(all_50_2) = all_50_1
% 5.89/1.60  | | | | |   (38)  (all_50_0 = 0 & all_50_1 = 0) | ( ~ (all_50_0 = 0) &  ~
% 5.89/1.60  | | | | |           (all_50_1 = 0))
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | | GROUND_INST: instantiating (4) with all_50_2, all_50_1, simplifying
% 5.89/1.60  | | | | |              with (35), (37) gives:
% 5.89/1.60  | | | | |   (39)  all_50_1 = 0 | xsd_integer(all_50_2) = 0
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | | BETA: splitting (38) gives:
% 5.89/1.60  | | | | | 
% 5.89/1.60  | | | | | Case 1:
% 5.89/1.60  | | | | | | 
% 5.89/1.60  | | | | | |   (40)  all_50_0 = 0 & all_50_1 = 0
% 5.89/1.60  | | | | | | 
% 5.89/1.60  | | | | | | ALPHA: (40) implies:
% 5.89/1.60  | | | | | |   (41)  all_50_1 = 0
% 5.89/1.60  | | | | | |   (42)  all_50_0 = 0
% 5.89/1.60  | | | | | | 
% 5.89/1.60  | | | | | | REDUCE: (37), (41) imply:
% 5.89/1.60  | | | | | |   (43)  xsd_string(all_50_2) = 0
% 5.89/1.60  | | | | | | 
% 5.89/1.60  | | | | | | REDUCE: (36), (42) imply:
% 5.89/1.60  | | | | | |   (44)  xsd_integer(all_50_2) = 0
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | GROUND_INST: instantiating (3) with all_50_2, simplifying with (35),
% 6.10/1.60  | | | | | |              (43) gives:
% 6.10/1.60  | | | | | |   (45)   ? [v0: int] : ( ~ (v0 = 0) & xsd_integer(all_50_2) = v0)
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | DELTA: instantiating (45) with fresh symbol all_64_0 gives:
% 6.10/1.60  | | | | | |   (46)   ~ (all_64_0 = 0) & xsd_integer(all_50_2) = all_64_0
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | ALPHA: (46) implies:
% 6.10/1.60  | | | | | |   (47)   ~ (all_64_0 = 0)
% 6.10/1.60  | | | | | |   (48)  xsd_integer(all_50_2) = all_64_0
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | GROUND_INST: instantiating (13) with 0, all_64_0, all_50_2,
% 6.10/1.60  | | | | | |              simplifying with (44), (48) gives:
% 6.10/1.60  | | | | | |   (49)  all_64_0 = 0
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | REDUCE: (47), (49) imply:
% 6.10/1.60  | | | | | |   (50)  $false
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | CLOSE: (50) is inconsistent.
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | Case 2:
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | |   (51)   ~ (all_50_0 = 0) &  ~ (all_50_1 = 0)
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | ALPHA: (51) implies:
% 6.10/1.60  | | | | | |   (52)   ~ (all_50_1 = 0)
% 6.10/1.60  | | | | | |   (53)   ~ (all_50_0 = 0)
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | BETA: splitting (39) gives:
% 6.10/1.60  | | | | | | 
% 6.10/1.60  | | | | | | Case 1:
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | |   (54)  xsd_integer(all_50_2) = 0
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | | GROUND_INST: instantiating (13) with all_50_0, 0, all_50_2,
% 6.10/1.60  | | | | | | |              simplifying with (36), (54) gives:
% 6.10/1.60  | | | | | | |   (55)  all_50_0 = 0
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | | REDUCE: (53), (55) imply:
% 6.10/1.60  | | | | | | |   (56)  $false
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | | CLOSE: (56) is inconsistent.
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | Case 2:
% 6.10/1.60  | | | | | | | 
% 6.10/1.60  | | | | | | |   (57)  all_50_1 = 0
% 6.10/1.60  | | | | | | | 
% 6.10/1.61  | | | | | | | REDUCE: (52), (57) imply:
% 6.10/1.61  | | | | | | |   (58)  $false
% 6.10/1.61  | | | | | | | 
% 6.10/1.61  | | | | | | | CLOSE: (58) is inconsistent.
% 6.10/1.61  | | | | | | | 
% 6.10/1.61  | | | | | | End of split
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | End of split
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | Case 2:
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | |   (59)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (cowlNothing(v0) =
% 6.10/1.61  | | | | |           v2 & cowlThing(v0) = v1 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | | DELTA: instantiating (59) with fresh symbols all_50_0, all_50_1,
% 6.10/1.61  | | | | |        all_50_2 gives:
% 6.10/1.61  | | | | |   (60)  cowlNothing(all_50_2) = all_50_0 & cowlThing(all_50_2) =
% 6.10/1.61  | | | | |         all_50_1 & $i(all_50_2) & ( ~ (all_50_1 = 0) | all_50_0 = 0)
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | | ALPHA: (60) implies:
% 6.10/1.61  | | | | |   (61)  $i(all_50_2)
% 6.10/1.61  | | | | |   (62)  cowlThing(all_50_2) = all_50_1
% 6.10/1.61  | | | | |   (63)  cowlNothing(all_50_2) = all_50_0
% 6.10/1.61  | | | | |   (64)   ~ (all_50_1 = 0) | all_50_0 = 0
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | | GROUND_INST: instantiating (2) with all_50_2, all_50_1, simplifying
% 6.10/1.61  | | | | |              with (61), (62) gives:
% 6.10/1.61  | | | | |   (65)  all_50_1 = 0
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | | BETA: splitting (64) gives:
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | | Case 1:
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | |   (66)   ~ (all_50_1 = 0)
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | | REDUCE: (65), (66) imply:
% 6.10/1.61  | | | | | |   (67)  $false
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | | CLOSE: (67) is inconsistent.
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | Case 2:
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | |   (68)  all_50_0 = 0
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | | REDUCE: (63), (68) imply:
% 6.10/1.61  | | | | | |   (69)  cowlNothing(all_50_2) = 0
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | | GROUND_INST: instantiating (1) with all_50_2, simplifying with (61),
% 6.10/1.61  | | | | | |              (69) gives:
% 6.10/1.61  | | | | | |   (70)  $false
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | | CLOSE: (70) is inconsistent.
% 6.10/1.61  | | | | | | 
% 6.10/1.61  | | | | | End of split
% 6.10/1.61  | | | | | 
% 6.10/1.61  | | | | End of split
% 6.10/1.61  | | | | 
% 6.10/1.61  | | | End of split
% 6.10/1.61  | | | 
% 6.10/1.61  | | End of split
% 6.10/1.61  | | 
% 6.10/1.61  | End of split
% 6.10/1.61  | 
% 6.10/1.61  End of proof
% 6.10/1.61  % SZS output end Proof for theBenchmark
% 6.10/1.61  
% 6.10/1.61  1005ms
%------------------------------------------------------------------------------