TSTP Solution File: KRS171+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS171+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 : n021.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 3.81s 1.32s
% Output   : Proof 5.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS171+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 02:07:58 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.59  ________       _____
% 0.18/0.59  ___  __ \_________(_)________________________________
% 0.18/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59  
% 0.18/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59  (2023-06-19)
% 0.18/0.59  
% 0.18/0.59  (c) Philipp Rümmer, 2009-2023
% 0.18/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59                Amanda Stjerna.
% 0.18/0.59  Free software under BSD-3-Clause.
% 0.18/0.59  
% 0.18/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59  
% 0.18/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60  Running up to 7 provers in parallel.
% 0.18/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.85/0.97  Prover 1: Preprocessing ...
% 1.85/0.98  Prover 4: Preprocessing ...
% 1.85/1.01  Prover 6: Preprocessing ...
% 1.85/1.01  Prover 3: Preprocessing ...
% 1.85/1.01  Prover 0: Preprocessing ...
% 1.85/1.01  Prover 2: Preprocessing ...
% 1.85/1.01  Prover 5: Preprocessing ...
% 2.91/1.11  Prover 5: Proving ...
% 2.91/1.12  Prover 2: Proving ...
% 2.91/1.16  Prover 6: Constructing countermodel ...
% 2.91/1.16  Prover 3: Constructing countermodel ...
% 2.91/1.16  Prover 1: Constructing countermodel ...
% 3.42/1.17  Prover 4: Constructing countermodel ...
% 3.63/1.22  Prover 0: Proving ...
% 3.81/1.31  Prover 6: proved (693ms)
% 3.81/1.32  
% 3.81/1.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.32  
% 3.81/1.32  Prover 3: proved (696ms)
% 3.81/1.32  
% 3.81/1.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.32  
% 4.51/1.32  Prover 0: stopped
% 4.51/1.32  Prover 5: stopped
% 4.51/1.32  Prover 2: stopped
% 4.51/1.33  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.51/1.33  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.51/1.33  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.51/1.33  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.51/1.33  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.51/1.34  Prover 7: Preprocessing ...
% 4.51/1.35  Prover 13: Preprocessing ...
% 4.51/1.35  Prover 8: Preprocessing ...
% 4.51/1.35  Prover 11: Preprocessing ...
% 4.51/1.36  Prover 10: Preprocessing ...
% 4.51/1.37  Prover 13: Warning: ignoring some quantifiers
% 4.51/1.37  Prover 10: Warning: ignoring some quantifiers
% 4.51/1.37  Prover 10: Constructing countermodel ...
% 4.51/1.37  Prover 7: Warning: ignoring some quantifiers
% 4.51/1.38  Prover 7: Constructing countermodel ...
% 4.51/1.38  Prover 13: Constructing countermodel ...
% 4.51/1.39  Prover 10: gave up
% 4.51/1.40  Prover 8: Warning: ignoring some quantifiers
% 4.51/1.40  Prover 13: gave up
% 4.51/1.41  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.51/1.41  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.51/1.41  Prover 8: Constructing countermodel ...
% 4.51/1.42  Prover 16: Preprocessing ...
% 4.51/1.42  Prover 4: Found proof (size 68)
% 4.51/1.42  Prover 4: proved (802ms)
% 4.51/1.42  Prover 19: Preprocessing ...
% 4.51/1.42  Prover 1: Found proof (size 54)
% 4.51/1.42  Prover 1: proved (811ms)
% 4.51/1.43  Prover 7: stopped
% 4.51/1.44  Prover 8: stopped
% 4.51/1.44  Prover 16: Warning: ignoring some quantifiers
% 4.51/1.44  Prover 16: Constructing countermodel ...
% 4.51/1.44  Prover 16: stopped
% 4.51/1.45  Prover 11: Constructing countermodel ...
% 4.51/1.45  Prover 11: stopped
% 4.51/1.46  Prover 19: Warning: ignoring some quantifiers
% 4.51/1.47  Prover 19: Constructing countermodel ...
% 4.51/1.48  Prover 19: stopped
% 4.51/1.48  
% 4.51/1.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.51/1.48  
% 4.51/1.49  % SZS output start Proof for theBenchmark
% 5.28/1.49  Assumptions after simplification:
% 5.28/1.49  ---------------------------------
% 5.28/1.49  
% 5.28/1.50    (axiom_0)
% 5.28/1.53     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~ $i(v0)) & 
% 5.28/1.53    ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 5.28/1.53  
% 5.28/1.53    (axiom_1)
% 5.28/1.53     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_integer(v0) = v1) |  ~ $i(v0) |
% 5.28/1.53      xsd_string(v0) = 0) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 5.28/1.53      (xsd_string(v0) = v1) |  ~ $i(v0) | xsd_integer(v0) = 0) &  ! [v0: $i] : ( ~
% 5.28/1.53      (xsd_integer(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) &
% 5.28/1.53        xsd_string(v0) = v1)) &  ! [v0: $i] : ( ~ (xsd_string(v0) = 0) |  ~ $i(v0)
% 5.28/1.53      |  ? [v1: int] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 5.28/1.53  
% 5.28/1.53    (axiom_2)
% 5.28/1.54     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasLeader(v0, v1) =
% 5.28/1.54        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rhasHead(v0,
% 5.28/1.54          v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasHead(v0, v1) = 0) |  ~
% 5.28/1.54      $i(v1) |  ~ $i(v0) | rhasLeader(v0, v1) = 0)
% 5.28/1.54  
% 5.28/1.54    (axiom_3)
% 5.28/1.54     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasHead(v0, v1) =
% 5.28/1.54        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & rhasLeader(v0,
% 5.28/1.54          v1) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rhasLeader(v0, v1) = 0) | 
% 5.28/1.54      ~ $i(v1) |  ~ $i(v0) | rhasHead(v0, v1) = 0)
% 5.28/1.54  
% 5.28/1.54    (the_axiom)
% 5.28/1.54     ? [v0: $i] :  ? [v1: $i] :  ? [v2: any] :  ? [v3: any] :  ? [v4: $i] :  ?
% 5.28/1.54    [v5: any] :  ? [v6: any] :  ? [v7: $i] :  ? [v8: any] :  ? [v9: any] : ($i(v7)
% 5.28/1.54      & $i(v4) & $i(v1) & $i(v0) & ((rhasLeader(v0, v1) = v2 & rhasHead(v0, v1) =
% 5.28/1.54          v3 & ((v3 = 0 &  ~ (v2 = 0)) | (v2 = 0 &  ~ (v3 = 0)))) |
% 5.28/1.54        (xsd_integer(v4) = v6 & xsd_string(v4) = v5 & ((v6 = 0 & v5 = 0) | ( ~ (v6
% 5.28/1.54                = 0) &  ~ (v5 = 0)))) | (cowlNothing(v7) = v9 & cowlThing(v7) = v8
% 5.28/1.54          & ( ~ (v8 = 0) | v9 = 0))))
% 5.28/1.54  
% 5.28/1.54    (function-axioms)
% 5.28/1.55     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.28/1.55    [v3: $i] : (v1 = v0 |  ~ (rhasLeader(v3, v2) = v1) |  ~ (rhasLeader(v3, v2) =
% 5.28/1.55        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 5.28/1.55      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~ (rhasHead(v3,
% 5.28/1.55          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 5.28/1.55    ! [v2: $i] : (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0))
% 5.28/1.55    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1
% 5.28/1.55      = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0)) &  ! [v0:
% 5.28/1.55      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 5.28/1.55      ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0)) &  ! [v0:
% 5.28/1.55      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 5.28/1.55      ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 5.28/1.55  
% 5.28/1.55  Those formulas are unsatisfiable:
% 5.28/1.55  ---------------------------------
% 5.28/1.55  
% 5.28/1.55  Begin of proof
% 5.28/1.55  | 
% 5.28/1.55  | ALPHA: (axiom_0) implies:
% 5.28/1.55  |   (1)   ! [v0: $i] : ( ~ (cowlNothing(v0) = 0) |  ~ $i(v0))
% 5.28/1.55  |   (2)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cowlThing(v0) = v1) |  ~
% 5.28/1.55  |          $i(v0))
% 5.28/1.55  | 
% 5.28/1.55  | ALPHA: (axiom_1) implies:
% 5.28/1.55  |   (3)   ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : (
% 5.28/1.55  |            ~ (v1 = 0) & xsd_string(v0) = v1))
% 5.28/1.55  |   (4)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_string(v0) = v1) |  ~
% 5.28/1.55  |          $i(v0) | xsd_integer(v0) = 0)
% 5.28/1.56  |   (5)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (xsd_integer(v0) = v1) |  ~
% 5.28/1.56  |          $i(v0) | xsd_string(v0) = 0)
% 5.28/1.56  | 
% 5.28/1.56  | ALPHA: (axiom_2) implies:
% 5.28/1.56  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasLeader(v0,
% 5.28/1.56  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) &
% 5.28/1.56  |            rhasHead(v0, v1) = v3))
% 5.28/1.56  | 
% 5.28/1.56  | ALPHA: (axiom_3) implies:
% 5.28/1.56  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (rhasHead(v0,
% 5.28/1.56  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) &
% 5.28/1.56  |            rhasLeader(v0, v1) = v3))
% 5.28/1.56  | 
% 5.28/1.56  | ALPHA: (function-axioms) implies:
% 5.28/1.56  |   (8)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.28/1.56  |        (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0))
% 5.28/1.56  |   (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.28/1.56  |         ! [v3: $i] : (v1 = v0 |  ~ (rhasHead(v3, v2) = v1) |  ~ (rhasHead(v3,
% 5.28/1.56  |              v2) = v0))
% 5.28/1.56  |   (10)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 5.28/1.56  |         :  ! [v3: $i] : (v1 = v0 |  ~ (rhasLeader(v3, v2) = v1) |  ~
% 5.28/1.56  |           (rhasLeader(v3, v2) = v0))
% 5.28/1.56  | 
% 5.28/1.56  | DELTA: instantiating (the_axiom) with fresh symbols all_7_0, all_7_1, all_7_2,
% 5.28/1.56  |        all_7_3, all_7_4, all_7_5, all_7_6, all_7_7, all_7_8, all_7_9 gives:
% 5.28/1.56  |   (11)  $i(all_7_2) & $i(all_7_5) & $i(all_7_8) & $i(all_7_9) &
% 5.28/1.56  |         ((rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8)
% 5.28/1.56  |             = all_7_6 & ((all_7_6 = 0 &  ~ (all_7_7 = 0)) | (all_7_7 = 0 &  ~
% 5.28/1.56  |                 (all_7_6 = 0)))) | (xsd_integer(all_7_5) = all_7_3 &
% 5.28/1.56  |             xsd_string(all_7_5) = all_7_4 & ((all_7_3 = 0 & all_7_4 = 0) | ( ~
% 5.28/1.56  |                 (all_7_3 = 0) &  ~ (all_7_4 = 0)))) | (cowlNothing(all_7_2) =
% 5.28/1.56  |             all_7_0 & cowlThing(all_7_2) = all_7_1 & ( ~ (all_7_1 = 0) |
% 5.28/1.56  |               all_7_0 = 0)))
% 5.28/1.56  | 
% 5.28/1.56  | ALPHA: (11) implies:
% 5.28/1.56  |   (12)  $i(all_7_9)
% 5.28/1.56  |   (13)  $i(all_7_8)
% 5.28/1.56  |   (14)  $i(all_7_5)
% 5.28/1.57  |   (15)  $i(all_7_2)
% 5.28/1.57  |   (16)  (rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8) =
% 5.28/1.57  |           all_7_6 & ((all_7_6 = 0 &  ~ (all_7_7 = 0)) | (all_7_7 = 0 &  ~
% 5.28/1.57  |               (all_7_6 = 0)))) | (xsd_integer(all_7_5) = all_7_3 &
% 5.28/1.57  |           xsd_string(all_7_5) = all_7_4 & ((all_7_3 = 0 & all_7_4 = 0) | ( ~
% 5.28/1.57  |               (all_7_3 = 0) &  ~ (all_7_4 = 0)))) | (cowlNothing(all_7_2) =
% 5.28/1.57  |           all_7_0 & cowlThing(all_7_2) = all_7_1 & ( ~ (all_7_1 = 0) | all_7_0
% 5.28/1.57  |             = 0))
% 5.28/1.57  | 
% 5.28/1.57  | BETA: splitting (16) gives:
% 5.93/1.57  | 
% 5.93/1.57  | Case 1:
% 5.93/1.57  | | 
% 5.93/1.57  | |   (17)  rhasLeader(all_7_9, all_7_8) = all_7_7 & rhasHead(all_7_9, all_7_8)
% 5.93/1.57  | |         = all_7_6 & ((all_7_6 = 0 &  ~ (all_7_7 = 0)) | (all_7_7 = 0 &  ~
% 5.93/1.57  | |             (all_7_6 = 0)))
% 5.93/1.57  | | 
% 5.93/1.57  | | ALPHA: (17) implies:
% 5.93/1.57  | |   (18)  rhasHead(all_7_9, all_7_8) = all_7_6
% 5.93/1.57  | |   (19)  rhasLeader(all_7_9, all_7_8) = all_7_7
% 5.93/1.57  | |   (20)  (all_7_6 = 0 &  ~ (all_7_7 = 0)) | (all_7_7 = 0 &  ~ (all_7_6 = 0))
% 5.93/1.57  | | 
% 5.93/1.57  | | GROUND_INST: instantiating (7) with all_7_9, all_7_8, all_7_6, simplifying
% 5.93/1.57  | |              with (12), (13), (18) gives:
% 5.93/1.57  | |   (21)  all_7_6 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & rhasLeader(all_7_9,
% 5.93/1.57  | |             all_7_8) = v0)
% 5.93/1.57  | | 
% 5.93/1.57  | | GROUND_INST: instantiating (6) with all_7_9, all_7_8, all_7_7, simplifying
% 5.93/1.57  | |              with (12), (13), (19) gives:
% 5.93/1.57  | |   (22)  all_7_7 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_7_9,
% 5.93/1.57  | |             all_7_8) = v0)
% 5.93/1.57  | | 
% 5.93/1.57  | | BETA: splitting (20) gives:
% 5.93/1.57  | | 
% 5.93/1.57  | | Case 1:
% 5.93/1.57  | | | 
% 5.93/1.57  | | |   (23)  all_7_6 = 0 &  ~ (all_7_7 = 0)
% 5.93/1.57  | | | 
% 5.93/1.57  | | | ALPHA: (23) implies:
% 5.93/1.57  | | |   (24)  all_7_6 = 0
% 5.93/1.57  | | |   (25)   ~ (all_7_7 = 0)
% 5.93/1.57  | | | 
% 5.93/1.57  | | | REDUCE: (18), (24) imply:
% 5.93/1.57  | | |   (26)  rhasHead(all_7_9, all_7_8) = 0
% 5.93/1.57  | | | 
% 5.93/1.57  | | | BETA: splitting (22) gives:
% 5.93/1.57  | | | 
% 5.93/1.57  | | | Case 1:
% 5.93/1.57  | | | | 
% 5.93/1.57  | | | |   (27)  all_7_7 = 0
% 5.93/1.57  | | | | 
% 5.93/1.57  | | | | REDUCE: (25), (27) imply:
% 5.93/1.57  | | | |   (28)  $false
% 5.96/1.57  | | | | 
% 5.96/1.57  | | | | CLOSE: (28) is inconsistent.
% 5.96/1.57  | | | | 
% 5.96/1.57  | | | Case 2:
% 5.96/1.57  | | | | 
% 5.96/1.57  | | | |   (29)   ? [v0: int] : ( ~ (v0 = 0) & rhasHead(all_7_9, all_7_8) = v0)
% 5.96/1.57  | | | | 
% 5.96/1.57  | | | | DELTA: instantiating (29) with fresh symbol all_27_0 gives:
% 5.96/1.58  | | | |   (30)   ~ (all_27_0 = 0) & rhasHead(all_7_9, all_7_8) = all_27_0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | ALPHA: (30) implies:
% 5.96/1.58  | | | |   (31)   ~ (all_27_0 = 0)
% 5.96/1.58  | | | |   (32)  rhasHead(all_7_9, all_7_8) = all_27_0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | GROUND_INST: instantiating (9) with 0, all_27_0, all_7_8, all_7_9,
% 5.96/1.58  | | | |              simplifying with (26), (32) gives:
% 5.96/1.58  | | | |   (33)  all_27_0 = 0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | REDUCE: (31), (33) imply:
% 5.96/1.58  | | | |   (34)  $false
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | CLOSE: (34) is inconsistent.
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | End of split
% 5.96/1.58  | | | 
% 5.96/1.58  | | Case 2:
% 5.96/1.58  | | | 
% 5.96/1.58  | | |   (35)  all_7_7 = 0 &  ~ (all_7_6 = 0)
% 5.96/1.58  | | | 
% 5.96/1.58  | | | ALPHA: (35) implies:
% 5.96/1.58  | | |   (36)  all_7_7 = 0
% 5.96/1.58  | | |   (37)   ~ (all_7_6 = 0)
% 5.96/1.58  | | | 
% 5.96/1.58  | | | REDUCE: (19), (36) imply:
% 5.96/1.58  | | |   (38)  rhasLeader(all_7_9, all_7_8) = 0
% 5.96/1.58  | | | 
% 5.96/1.58  | | | BETA: splitting (21) gives:
% 5.96/1.58  | | | 
% 5.96/1.58  | | | Case 1:
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | |   (39)  all_7_6 = 0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | REDUCE: (37), (39) imply:
% 5.96/1.58  | | | |   (40)  $false
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | CLOSE: (40) is inconsistent.
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | Case 2:
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | |   (41)   ? [v0: int] : ( ~ (v0 = 0) & rhasLeader(all_7_9, all_7_8) = v0)
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | DELTA: instantiating (41) with fresh symbol all_27_0 gives:
% 5.96/1.58  | | | |   (42)   ~ (all_27_0 = 0) & rhasLeader(all_7_9, all_7_8) = all_27_0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | ALPHA: (42) implies:
% 5.96/1.58  | | | |   (43)   ~ (all_27_0 = 0)
% 5.96/1.58  | | | |   (44)  rhasLeader(all_7_9, all_7_8) = all_27_0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | GROUND_INST: instantiating (10) with 0, all_27_0, all_7_8, all_7_9,
% 5.96/1.58  | | | |              simplifying with (38), (44) gives:
% 5.96/1.58  | | | |   (45)  all_27_0 = 0
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | REDUCE: (43), (45) imply:
% 5.96/1.58  | | | |   (46)  $false
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | | CLOSE: (46) is inconsistent.
% 5.96/1.58  | | | | 
% 5.96/1.58  | | | End of split
% 5.96/1.58  | | | 
% 5.96/1.58  | | End of split
% 5.96/1.58  | | 
% 5.96/1.58  | Case 2:
% 5.96/1.58  | | 
% 5.96/1.58  | |   (47)  (xsd_integer(all_7_5) = all_7_3 & xsd_string(all_7_5) = all_7_4 &
% 5.96/1.58  | |           ((all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) &  ~ (all_7_4 =
% 5.96/1.58  | |                 0)))) | (cowlNothing(all_7_2) = all_7_0 & cowlThing(all_7_2)
% 5.96/1.58  | |           = all_7_1 & ( ~ (all_7_1 = 0) | all_7_0 = 0))
% 5.96/1.58  | | 
% 5.96/1.58  | | BETA: splitting (47) gives:
% 5.96/1.58  | | 
% 5.96/1.58  | | Case 1:
% 5.96/1.58  | | | 
% 5.96/1.58  | | |   (48)  xsd_integer(all_7_5) = all_7_3 & xsd_string(all_7_5) = all_7_4 &
% 5.96/1.58  | | |         ((all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) &  ~ (all_7_4 =
% 5.96/1.58  | | |               0)))
% 5.96/1.58  | | | 
% 5.96/1.58  | | | ALPHA: (48) implies:
% 5.96/1.58  | | |   (49)  xsd_string(all_7_5) = all_7_4
% 5.96/1.58  | | |   (50)  xsd_integer(all_7_5) = all_7_3
% 5.96/1.58  | | |   (51)  (all_7_3 = 0 & all_7_4 = 0) | ( ~ (all_7_3 = 0) &  ~ (all_7_4 =
% 5.96/1.58  | | |             0))
% 5.96/1.58  | | | 
% 5.96/1.58  | | | GROUND_INST: instantiating (4) with all_7_5, all_7_4, simplifying with
% 5.96/1.58  | | |              (14), (49) gives:
% 5.96/1.58  | | |   (52)  all_7_4 = 0 | xsd_integer(all_7_5) = 0
% 5.96/1.58  | | | 
% 5.96/1.58  | | | GROUND_INST: instantiating (5) with all_7_5, all_7_3, simplifying with
% 5.96/1.58  | | |              (14), (50) gives:
% 5.96/1.58  | | |   (53)  all_7_3 = 0 | xsd_string(all_7_5) = 0
% 5.96/1.58  | | | 
% 5.96/1.59  | | | BETA: splitting (51) gives:
% 5.96/1.59  | | | 
% 5.96/1.59  | | | Case 1:
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | |   (54)  all_7_3 = 0 & all_7_4 = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | ALPHA: (54) implies:
% 5.96/1.59  | | | |   (55)  all_7_4 = 0
% 5.96/1.59  | | | |   (56)  all_7_3 = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | REDUCE: (50), (56) imply:
% 5.96/1.59  | | | |   (57)  xsd_integer(all_7_5) = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | REDUCE: (49), (55) imply:
% 5.96/1.59  | | | |   (58)  xsd_string(all_7_5) = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | REF_CLOSE: (3), (8), (14), (57), (58) are inconsistent by sub-proof #1.
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | Case 2:
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | |   (59)   ~ (all_7_3 = 0) &  ~ (all_7_4 = 0)
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | ALPHA: (59) implies:
% 5.96/1.59  | | | |   (60)   ~ (all_7_4 = 0)
% 5.96/1.59  | | | |   (61)   ~ (all_7_3 = 0)
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | BETA: splitting (53) gives:
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | Case 1:
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | |   (62)  xsd_string(all_7_5) = 0
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | | BETA: splitting (52) gives:
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | | Case 1:
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | |   (63)  xsd_integer(all_7_5) = 0
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | | REF_CLOSE: (3), (8), (14), (62), (63) are inconsistent by sub-proof
% 5.96/1.59  | | | | | |            #1.
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | Case 2:
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | |   (64)  all_7_4 = 0
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | | REDUCE: (60), (64) imply:
% 5.96/1.59  | | | | | |   (65)  $false
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | | CLOSE: (65) is inconsistent.
% 5.96/1.59  | | | | | | 
% 5.96/1.59  | | | | | End of split
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | Case 2:
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | |   (66)  all_7_3 = 0
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | | REDUCE: (61), (66) imply:
% 5.96/1.59  | | | | |   (67)  $false
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | | CLOSE: (67) is inconsistent.
% 5.96/1.59  | | | | | 
% 5.96/1.59  | | | | End of split
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | End of split
% 5.96/1.59  | | | 
% 5.96/1.59  | | Case 2:
% 5.96/1.59  | | | 
% 5.96/1.59  | | |   (68)  cowlNothing(all_7_2) = all_7_0 & cowlThing(all_7_2) = all_7_1 & (
% 5.96/1.59  | | |           ~ (all_7_1 = 0) | all_7_0 = 0)
% 5.96/1.59  | | | 
% 5.96/1.59  | | | ALPHA: (68) implies:
% 5.96/1.59  | | |   (69)  cowlThing(all_7_2) = all_7_1
% 5.96/1.59  | | |   (70)  cowlNothing(all_7_2) = all_7_0
% 5.96/1.59  | | |   (71)   ~ (all_7_1 = 0) | all_7_0 = 0
% 5.96/1.59  | | | 
% 5.96/1.59  | | | GROUND_INST: instantiating (2) with all_7_2, all_7_1, simplifying with
% 5.96/1.59  | | |              (15), (69) gives:
% 5.96/1.59  | | |   (72)  all_7_1 = 0
% 5.96/1.59  | | | 
% 5.96/1.59  | | | BETA: splitting (71) gives:
% 5.96/1.59  | | | 
% 5.96/1.59  | | | Case 1:
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | |   (73)   ~ (all_7_1 = 0)
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | REDUCE: (72), (73) imply:
% 5.96/1.59  | | | |   (74)  $false
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | CLOSE: (74) is inconsistent.
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | Case 2:
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | |   (75)  all_7_0 = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | REDUCE: (70), (75) imply:
% 5.96/1.59  | | | |   (76)  cowlNothing(all_7_2) = 0
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | GROUND_INST: instantiating (1) with all_7_2, simplifying with (15), (76)
% 5.96/1.59  | | | |              gives:
% 5.96/1.59  | | | |   (77)  $false
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | | CLOSE: (77) is inconsistent.
% 5.96/1.59  | | | | 
% 5.96/1.59  | | | End of split
% 5.96/1.59  | | | 
% 5.96/1.59  | | End of split
% 5.96/1.59  | | 
% 5.96/1.59  | End of split
% 5.96/1.59  | 
% 5.96/1.59  End of proof
% 5.96/1.59  
% 5.96/1.59  Sub-proof #1 shows that the following formulas are inconsistent:
% 5.96/1.59  ----------------------------------------------------------------
% 5.96/1.59    (1)  xsd_integer(all_7_5) = 0
% 5.96/1.59    (2)  $i(all_7_5)
% 5.96/1.59    (3)   ! [v0: $i] : ( ~ (xsd_integer(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~
% 5.96/1.59             (v1 = 0) & xsd_string(v0) = v1))
% 5.96/1.60    (4)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.96/1.60         (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0))
% 5.96/1.60    (5)  xsd_string(all_7_5) = 0
% 5.96/1.60  
% 5.96/1.60  Begin of proof
% 5.96/1.60  | 
% 5.96/1.60  | GROUND_INST: instantiating (3) with all_7_5, simplifying with (1), (2) gives:
% 5.96/1.60  |   (6)   ? [v0: int] : ( ~ (v0 = 0) & xsd_string(all_7_5) = v0)
% 5.96/1.60  | 
% 5.96/1.60  | DELTA: instantiating (6) with fresh symbol all_28_0 gives:
% 5.96/1.60  |   (7)   ~ (all_28_0 = 0) & xsd_string(all_7_5) = all_28_0
% 5.96/1.60  | 
% 5.96/1.60  | ALPHA: (7) implies:
% 5.96/1.60  |   (8)   ~ (all_28_0 = 0)
% 5.96/1.60  |   (9)  xsd_string(all_7_5) = all_28_0
% 5.96/1.60  | 
% 5.96/1.60  | GROUND_INST: instantiating (4) with 0, all_28_0, all_7_5, simplifying with
% 5.96/1.60  |              (5), (9) gives:
% 5.96/1.60  |   (10)  all_28_0 = 0
% 5.96/1.60  | 
% 5.96/1.60  | REDUCE: (8), (10) imply:
% 5.96/1.60  |   (11)  $false
% 5.96/1.60  | 
% 5.96/1.60  | CLOSE: (11) is inconsistent.
% 5.96/1.60  | 
% 5.96/1.60  End of proof
% 5.96/1.60  % SZS output end Proof for theBenchmark
% 5.96/1.60  
% 5.96/1.60  1005ms
%------------------------------------------------------------------------------