TSTP Solution File: DAT049_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : DAT049_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n018.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 : Wed Aug 30 22:19:01 EDT 2023

% Result   : Theorem 8.75s 1.93s
% Output   : Proof 14.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : DAT049_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30  % Computer : n018.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Thu Aug 24 15:00:58 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.13/0.51  ________       _____
% 0.13/0.51  ___  __ \_________(_)________________________________
% 0.13/0.51  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.13/0.51  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.13/0.51  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.13/0.51  
% 0.13/0.51  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.51  (2023-06-19)
% 0.13/0.51  
% 0.13/0.51  (c) Philipp Rümmer, 2009-2023
% 0.13/0.51  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.51                Amanda Stjerna.
% 0.13/0.51  Free software under BSD-3-Clause.
% 0.13/0.51  
% 0.13/0.51  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.51  
% 0.13/0.51  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.13/0.52  Running up to 7 provers in parallel.
% 0.13/0.55  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.55  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.55  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.55  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.55  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.55  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/0.99  Prover 1: Preprocessing ...
% 2.12/1.00  Prover 4: Preprocessing ...
% 2.57/1.06  Prover 2: Preprocessing ...
% 2.57/1.06  Prover 0: Preprocessing ...
% 2.57/1.06  Prover 3: Preprocessing ...
% 2.57/1.06  Prover 5: Preprocessing ...
% 2.57/1.06  Prover 6: Preprocessing ...
% 4.66/1.46  Prover 5: Proving ...
% 4.66/1.47  Prover 6: Constructing countermodel ...
% 4.66/1.47  Prover 1: Constructing countermodel ...
% 4.66/1.47  Prover 3: Constructing countermodel ...
% 4.66/1.53  Prover 0: Proving ...
% 5.94/1.54  Prover 4: Constructing countermodel ...
% 5.94/1.56  Prover 2: Proving ...
% 8.75/1.93  Prover 3: proved (1386ms)
% 8.75/1.93  
% 8.75/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.75/1.93  
% 8.75/1.93  Prover 6: stopped
% 8.75/1.93  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.75/1.94  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.75/1.96  Prover 0: stopped
% 8.75/1.96  Prover 5: stopped
% 8.75/1.96  Prover 2: stopped
% 8.75/1.97  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.75/1.97  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.75/1.98  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.75/2.00  Prover 8: Preprocessing ...
% 9.41/2.01  Prover 7: Preprocessing ...
% 9.41/2.01  Prover 11: Preprocessing ...
% 9.41/2.02  Prover 10: Preprocessing ...
% 9.41/2.03  Prover 13: Preprocessing ...
% 10.05/2.10  Prover 7: Constructing countermodel ...
% 10.05/2.11  Prover 10: Constructing countermodel ...
% 10.05/2.11  Prover 13: Warning: ignoring some quantifiers
% 10.05/2.12  Prover 13: Constructing countermodel ...
% 10.05/2.15  Prover 8: Warning: ignoring some quantifiers
% 10.05/2.15  Prover 8: Constructing countermodel ...
% 10.05/2.24  Prover 11: Constructing countermodel ...
% 12.47/2.48  Prover 1: Found proof (size 188)
% 12.47/2.48  Prover 1: proved (1944ms)
% 12.47/2.48  Prover 7: stopped
% 12.47/2.48  Prover 8: stopped
% 12.47/2.48  Prover 13: stopped
% 12.47/2.48  Prover 4: stopped
% 12.47/2.48  Prover 11: stopped
% 12.47/2.49  Prover 10: Found proof (size 180)
% 12.47/2.49  Prover 10: proved (518ms)
% 12.47/2.49  
% 12.47/2.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.47/2.49  
% 13.30/2.59  % SZS output start Proof for theBenchmark
% 13.30/2.59  Assumptions after simplification:
% 13.30/2.59  ---------------------------------
% 13.30/2.59  
% 13.30/2.59    (ax2)
% 13.30/2.62    collection(empty) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] :
% 13.30/2.62     ! [v3: int] : (v3 = 0 |  ~ (add(v0, v1) = v2) |  ~ (in(v0, v2) = v3) |  ~
% 13.30/2.62      collection(v1)) &  ! [v0: collection] : (v0 = empty |  ~ (count(v0) = 0) | 
% 13.30/2.62      ~ collection(v0)) &  ! [v0: int] : (v0 = 0 |  ~ (count(empty) = v0))
% 13.30/2.62  
% 13.30/2.62    (ax3)
% 13.30/2.62     ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 13.30/2.62        = v2) |  ~ (in(v0, v2) = 0) |  ~ collection(v1)) &  ! [v0: int] :  ! [v1:
% 13.30/2.62      collection] :  ! [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~
% 13.30/2.62      collection(v1) |  ? [v3: any] :  ? [v4: int] :  ? [v5: int] : (count(v2) =
% 13.30/2.62        v4 & count(v1) = v5 & in(v0, v1) = v3 & ($difference(v5, v4) = -1 | v3 =
% 13.30/2.62          0))) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 13.30/2.62      (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 13.30/2.62      [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 =
% 13.30/2.62            0) |  ~ ($difference(v4, v3) = -1))))
% 13.30/2.62  
% 13.30/2.62    (ax4)
% 13.30/2.63     ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] :  !
% 13.30/2.63    [v4: int] : (v4 = 0 |  ~ (add(v2, v1) = v3) |  ~ (in(v0, v3) = v4) |  ~
% 13.30/2.63      collection(v1) | ( ~ (v2 = v0) &  ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 13.30/2.63          v5))) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3:
% 13.30/2.63      collection] : (v2 = v0 |  ~ (add(v2, v1) = v3) |  ~ (in(v0, v3) = 0) |  ~
% 13.30/2.63      collection(v1) | in(v0, v1) = 0) &  ! [v0: int] :  ! [v1: collection] :  !
% 13.30/2.63    [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :
% 13.30/2.63       ? [v4: int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 13.30/2.63        = v3 & ( ~ (v3 = 0) | v5 = v4))) &  ! [v0: int] :  ! [v1: collection] :  !
% 13.30/2.63    [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :
% 13.30/2.63       ? [v4: int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 13.30/2.63        = v5 & ( ~ (v4 = v3) | v5 = 0)))
% 13.30/2.63  
% 13.30/2.63    (ax5)
% 13.30/2.64     ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] :  !
% 13.30/2.64    [v4: int] : (v4 = 0 | v2 = v0 |  ~ (remove(v2, v1) = v3) |  ~ (in(v0, v3) =
% 13.30/2.64        v4) |  ~ collection(v1) |  ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 13.30/2.64    &  ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] : (
% 13.30/2.64      ~ (remove(v2, v1) = v3) |  ~ (in(v0, v3) = 0) |  ~ collection(v1) | ( ~ (v2
% 13.30/2.64          = v0) & in(v0, v1) = 0)) &  ! [v0: int] :  ! [v1: collection] :  ! [v2:
% 13.30/2.64      collection] : ( ~ (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :
% 13.30/2.64       ? [v4: int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 13.30/2.64        = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1))) &  ! [v0: int] :  ! [v1:
% 13.30/2.64      collection] :  ! [v2: collection] : ( ~ (remove(v0, v1) = v2) |  ~
% 13.30/2.64      collection(v1) |  ? [v3: int] :  ? [v4: int] :  ? [v5: any] : (count(v2) =
% 13.30/2.64        v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5
% 13.30/2.64          = 0)))
% 13.30/2.64  
% 13.30/2.64    (ax6)
% 13.30/2.64     ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 13.30/2.64        = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ? [v5: int] :
% 13.30/2.64      (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & (v5 = v4 | v3 = 0))) & 
% 13.30/2.64    ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 13.30/2.64        = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ? [v5: any] :
% 13.30/2.64      (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 =
% 13.30/2.64            v3))))
% 13.30/2.64  
% 13.30/2.64    (co1)
% 13.30/2.64     ? [v0: collection] :  ? [v1: int] :  ? [v2: collection] :  ? [v3: collection]
% 13.30/2.64    :  ? [v4: int] :  ? [v5: collection] :  ? [v6: int] : ( ~ (v6 = v4) &
% 13.30/2.64      remove(v1, v2) = v3 & remove(v1, v0) = v5 & add(v1, v0) = v2 & count(v5) =
% 13.30/2.64      v6 & count(v3) = v4 & collection(v5) & collection(v3) & collection(v2) &
% 13.30/2.64      collection(v0))
% 13.30/2.64  
% 13.30/2.64    (function-axioms)
% 13.30/2.65     ! [v0: collection] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int]
% 13.30/2.65    : (v1 = v0 |  ~ (remove(v3, v2) = v1) |  ~ (remove(v3, v2) = v0)) &  ! [v0:
% 13.30/2.65      collection] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int] : (v1
% 13.30/2.65      = v0 |  ~ (add(v3, v2) = v1) |  ~ (add(v3, v2) = v0)) &  ! [v0:
% 13.30/2.65      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: collection] :  !
% 13.30/2.65    [v3: int] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 13.30/2.65      int] :  ! [v1: int] :  ! [v2: collection] : (v1 = v0 |  ~ (count(v2) = v1) |
% 13.30/2.65       ~ (count(v2) = v0))
% 13.30/2.65  
% 13.30/2.65  Further assumptions not needed in the proof:
% 13.30/2.65  --------------------------------------------
% 13.30/2.65  ax1, ax7
% 13.30/2.65  
% 13.30/2.65  Those formulas are unsatisfiable:
% 13.30/2.65  ---------------------------------
% 13.30/2.65  
% 13.30/2.65  Begin of proof
% 13.30/2.65  | 
% 13.30/2.65  | ALPHA: (ax2) implies:
% 13.30/2.65  |   (1)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int]
% 13.30/2.65  |        : (v3 = 0 |  ~ (add(v0, v1) = v2) |  ~ (in(v0, v2) = v3) |  ~
% 13.30/2.65  |          collection(v1))
% 13.30/2.65  | 
% 13.30/2.65  | ALPHA: (ax3) implies:
% 13.30/2.65  |   (2)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 13.30/2.65  |              v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 13.30/2.65  |          [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 13.30/2.65  |              (v5 = 0) |  ~ ($difference(v4, v3) = -1))))
% 13.30/2.66  |   (3)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 13.30/2.66  |              v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ?
% 13.30/2.66  |          [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 &
% 13.30/2.66  |            ($difference(v5, v4) = -1 | v3 = 0)))
% 13.30/2.66  | 
% 13.30/2.66  | ALPHA: (ax4) implies:
% 13.30/2.66  |   (4)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 13.30/2.66  |              v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 13.30/2.66  |          [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 13.30/2.66  |              (v4 = v3) | v5 = 0)))
% 13.30/2.66  |   (5)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 13.30/2.66  |              v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ?
% 13.30/2.66  |          [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~
% 13.30/2.66  |              (v3 = 0) | v5 = v4)))
% 13.30/2.66  | 
% 13.30/2.66  | ALPHA: (ax5) implies:
% 13.30/2.66  |   (6)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 13.30/2.66  |          (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4:
% 13.30/2.66  |            int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 13.30/2.66  |            = v5 & ( ~ ($difference(v4, v3) = 1) | v5 = 0)))
% 13.30/2.66  |   (7)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 13.30/2.66  |          (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4:
% 13.30/2.66  |            int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 13.30/2.66  |            = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1)))
% 13.30/2.66  | 
% 13.30/2.66  | ALPHA: (ax6) implies:
% 13.73/2.66  |   (8)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 13.73/2.66  |          (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4:
% 13.73/2.66  |            int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 13.73/2.67  |            = v5 & ( ~ (v5 = 0) |  ~ (v4 = v3))))
% 13.73/2.67  |   (9)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 13.73/2.67  |          (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4:
% 13.73/2.67  |            int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 13.73/2.67  |            = v3 & (v5 = v4 | v3 = 0)))
% 13.73/2.67  | 
% 13.73/2.67  | ALPHA: (function-axioms) implies:
% 13.73/2.67  |   (10)   ! [v0: int] :  ! [v1: int] :  ! [v2: collection] : (v1 = v0 |  ~
% 13.73/2.67  |           (count(v2) = v1) |  ~ (count(v2) = v0))
% 13.73/2.67  |   (11)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 13.73/2.67  |           collection] :  ! [v3: int] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~
% 13.73/2.67  |           (in(v3, v2) = v0))
% 13.73/2.67  | 
% 13.73/2.67  | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2,
% 13.73/2.67  |        all_13_3, all_13_4, all_13_5, all_13_6 gives:
% 13.73/2.67  |   (12)   ~ (all_13_0 = all_13_2) & remove(all_13_5, all_13_4) = all_13_3 &
% 13.73/2.67  |         remove(all_13_5, all_13_6) = all_13_1 & add(all_13_5, all_13_6) =
% 13.73/2.67  |         all_13_4 & count(all_13_1) = all_13_0 & count(all_13_3) = all_13_2 &
% 13.73/2.67  |         collection(all_13_1) & collection(all_13_3) & collection(all_13_4) &
% 13.73/2.67  |         collection(all_13_6)
% 13.73/2.67  | 
% 13.73/2.67  | ALPHA: (12) implies:
% 13.73/2.67  |   (13)   ~ (all_13_0 = all_13_2)
% 13.73/2.67  |   (14)  collection(all_13_6)
% 13.73/2.67  |   (15)  collection(all_13_4)
% 13.73/2.67  |   (16)  count(all_13_3) = all_13_2
% 13.73/2.67  |   (17)  count(all_13_1) = all_13_0
% 13.73/2.67  |   (18)  add(all_13_5, all_13_6) = all_13_4
% 13.73/2.68  |   (19)  remove(all_13_5, all_13_6) = all_13_1
% 13.73/2.68  |   (20)  remove(all_13_5, all_13_4) = all_13_3
% 13.73/2.68  | 
% 13.73/2.68  | GROUND_INST: instantiating (5) with all_13_5, all_13_6, all_13_4, simplifying
% 13.73/2.68  |              with (14), (18) gives:
% 13.73/2.68  |   (21)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_4) = v1 &
% 13.73/2.68  |           count(all_13_6) = v2 & in(all_13_5, all_13_6) = v0 & ( ~ (v0 = 0) |
% 13.73/2.68  |             v2 = v1))
% 13.73/2.68  | 
% 13.73/2.68  | GROUND_INST: instantiating (3) with all_13_5, all_13_6, all_13_4, simplifying
% 13.73/2.68  |              with (14), (18) gives:
% 13.73/2.68  |   (22)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_4) = v1 &
% 13.73/2.68  |           count(all_13_6) = v2 & in(all_13_5, all_13_6) = v0 &
% 13.73/2.68  |           ($difference(v2, v1) = -1 | v0 = 0))
% 13.73/2.68  | 
% 13.73/2.68  | GROUND_INST: instantiating (2) with all_13_5, all_13_6, all_13_4, simplifying
% 13.73/2.68  |              with (14), (18) gives:
% 13.82/2.68  |   (23)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_4) = v0 &
% 13.82/2.68  |           count(all_13_6) = v1 & in(all_13_5, all_13_6) = v2 & ( ~ (v2 = 0) | 
% 13.82/2.68  |             ~ ($difference(v1, v0) = -1)))
% 13.82/2.68  | 
% 13.82/2.68  | GROUND_INST: instantiating (4) with all_13_5, all_13_6, all_13_4, simplifying
% 13.82/2.68  |              with (14), (18) gives:
% 13.82/2.69  |   (24)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_4) = v0 &
% 13.82/2.69  |           count(all_13_6) = v1 & in(all_13_5, all_13_6) = v2 & ( ~ (v1 = v0) |
% 13.82/2.69  |             v2 = 0))
% 13.82/2.69  | 
% 13.82/2.69  | GROUND_INST: instantiating (7) with all_13_5, all_13_6, all_13_1, simplifying
% 13.82/2.69  |              with (14), (19) gives:
% 13.82/2.69  |   (25)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_1) = v1 &
% 13.82/2.69  |           count(all_13_6) = v2 & in(all_13_5, all_13_6) = v0 & ( ~ (v0 = 0) |
% 13.82/2.69  |             $difference(v2, v1) = 1))
% 13.82/2.69  | 
% 13.82/2.69  | GROUND_INST: instantiating (9) with all_13_5, all_13_6, all_13_1, simplifying
% 13.82/2.69  |              with (14), (19) gives:
% 13.82/2.69  |   (26)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_1) = v1 &
% 13.82/2.69  |           count(all_13_6) = v2 & in(all_13_5, all_13_6) = v0 & (v2 = v1 | v0 =
% 13.82/2.69  |             0))
% 13.82/2.69  | 
% 13.82/2.69  | GROUND_INST: instantiating (8) with all_13_5, all_13_6, all_13_1, simplifying
% 13.82/2.69  |              with (14), (19) gives:
% 13.82/2.69  |   (27)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_1) = v0 &
% 13.82/2.69  |           count(all_13_6) = v1 & in(all_13_5, all_13_6) = v2 & ( ~ (v2 = 0) | 
% 13.82/2.69  |             ~ (v1 = v0)))
% 13.82/2.69  | 
% 13.82/2.69  | GROUND_INST: instantiating (6) with all_13_5, all_13_6, all_13_1, simplifying
% 13.82/2.69  |              with (14), (19) gives:
% 13.82/2.69  |   (28)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_1) = v0 &
% 13.82/2.69  |           count(all_13_6) = v1 & in(all_13_5, all_13_6) = v2 & ( ~
% 13.82/2.69  |             ($difference(v1, v0) = 1) | v2 = 0))
% 13.82/2.69  | 
% 13.82/2.69  | GROUND_INST: instantiating (7) with all_13_5, all_13_4, all_13_3, simplifying
% 13.82/2.69  |              with (15), (20) gives:
% 13.82/2.70  |   (29)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_3) = v1 &
% 13.82/2.70  |           count(all_13_4) = v2 & in(all_13_5, all_13_4) = v0 & ( ~ (v0 = 0) |
% 13.82/2.70  |             $difference(v2, v1) = 1))
% 13.82/2.70  | 
% 13.82/2.70  | GROUND_INST: instantiating (9) with all_13_5, all_13_4, all_13_3, simplifying
% 13.82/2.70  |              with (15), (20) gives:
% 13.82/2.70  |   (30)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_3) = v1 &
% 13.82/2.70  |           count(all_13_4) = v2 & in(all_13_5, all_13_4) = v0 & (v2 = v1 | v0 =
% 13.82/2.70  |             0))
% 13.82/2.70  | 
% 13.82/2.70  | GROUND_INST: instantiating (8) with all_13_5, all_13_4, all_13_3, simplifying
% 13.82/2.70  |              with (15), (20) gives:
% 13.82/2.70  |   (31)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_3) = v0 &
% 13.82/2.70  |           count(all_13_4) = v1 & in(all_13_5, all_13_4) = v2 & ( ~ (v2 = 0) | 
% 13.82/2.70  |             ~ (v1 = v0)))
% 13.82/2.70  | 
% 13.82/2.70  | GROUND_INST: instantiating (6) with all_13_5, all_13_4, all_13_3, simplifying
% 13.82/2.70  |              with (15), (20) gives:
% 13.82/2.70  |   (32)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_3) = v0 &
% 13.82/2.70  |           count(all_13_4) = v1 & in(all_13_5, all_13_4) = v2 & ( ~
% 13.82/2.70  |             ($difference(v1, v0) = 1) | v2 = 0))
% 13.82/2.70  | 
% 13.82/2.70  | DELTA: instantiating (32) with fresh symbols all_22_0, all_22_1, all_22_2
% 13.82/2.70  |        gives:
% 13.82/2.70  |   (33)  count(all_13_3) = all_22_2 & count(all_13_4) = all_22_1 & in(all_13_5,
% 13.82/2.70  |           all_13_4) = all_22_0 & ( ~ ($difference(all_22_1, all_22_2) = 1) |
% 13.82/2.70  |           all_22_0 = 0)
% 13.82/2.70  | 
% 13.82/2.70  | ALPHA: (33) implies:
% 13.82/2.70  |   (34)  in(all_13_5, all_13_4) = all_22_0
% 13.82/2.71  |   (35)  count(all_13_4) = all_22_1
% 13.82/2.71  |   (36)  count(all_13_3) = all_22_2
% 13.82/2.71  | 
% 13.82/2.71  | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2
% 13.82/2.71  |        gives:
% 13.82/2.71  |   (37)  count(all_13_3) = all_24_1 & count(all_13_4) = all_24_0 & in(all_13_5,
% 13.82/2.71  |           all_13_4) = all_24_2 & (all_24_0 = all_24_1 | all_24_2 = 0)
% 13.82/2.71  | 
% 13.82/2.71  | ALPHA: (37) implies:
% 13.82/2.71  |   (38)  in(all_13_5, all_13_4) = all_24_2
% 13.82/2.71  |   (39)  count(all_13_4) = all_24_0
% 13.82/2.71  |   (40)  count(all_13_3) = all_24_1
% 13.82/2.71  | 
% 13.82/2.71  | DELTA: instantiating (29) with fresh symbols all_26_0, all_26_1, all_26_2
% 13.82/2.71  |        gives:
% 13.82/2.71  |   (41)  count(all_13_3) = all_26_1 & count(all_13_4) = all_26_0 & in(all_13_5,
% 13.82/2.71  |           all_13_4) = all_26_2 & ( ~ (all_26_2 = 0) | $difference(all_26_0,
% 13.82/2.71  |             all_26_1) = 1)
% 13.82/2.71  | 
% 13.82/2.71  | ALPHA: (41) implies:
% 13.82/2.71  |   (42)  in(all_13_5, all_13_4) = all_26_2
% 13.82/2.71  |   (43)  count(all_13_4) = all_26_0
% 13.82/2.71  |   (44)  count(all_13_3) = all_26_1
% 13.82/2.71  |   (45)   ~ (all_26_2 = 0) | $difference(all_26_0, all_26_1) = 1
% 13.82/2.71  | 
% 13.82/2.71  | DELTA: instantiating (28) with fresh symbols all_28_0, all_28_1, all_28_2
% 13.82/2.71  |        gives:
% 13.82/2.71  |   (46)  count(all_13_1) = all_28_2 & count(all_13_6) = all_28_1 & in(all_13_5,
% 13.82/2.71  |           all_13_6) = all_28_0 & ( ~ ($difference(all_28_1, all_28_2) = 1) |
% 13.82/2.71  |           all_28_0 = 0)
% 13.82/2.71  | 
% 13.82/2.71  | ALPHA: (46) implies:
% 13.82/2.71  |   (47)  in(all_13_5, all_13_6) = all_28_0
% 13.82/2.71  |   (48)  count(all_13_6) = all_28_1
% 13.82/2.71  |   (49)  count(all_13_1) = all_28_2
% 13.82/2.71  |   (50)   ~ ($difference(all_28_1, all_28_2) = 1) | all_28_0 = 0
% 13.82/2.71  | 
% 13.82/2.71  | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1, all_30_2
% 13.82/2.71  |        gives:
% 13.99/2.72  |   (51)  count(all_13_3) = all_30_2 & count(all_13_4) = all_30_1 & in(all_13_5,
% 13.99/2.72  |           all_13_4) = all_30_0 & ( ~ (all_30_0 = 0) |  ~ (all_30_1 =
% 13.99/2.72  |             all_30_2))
% 13.99/2.72  | 
% 13.99/2.72  | ALPHA: (51) implies:
% 13.99/2.72  |   (52)  in(all_13_5, all_13_4) = all_30_0
% 13.99/2.72  |   (53)  count(all_13_4) = all_30_1
% 13.99/2.72  |   (54)  count(all_13_3) = all_30_2
% 13.99/2.72  | 
% 13.99/2.72  | DELTA: instantiating (22) with fresh symbols all_32_0, all_32_1, all_32_2
% 13.99/2.72  |        gives:
% 13.99/2.72  |   (55)  count(all_13_4) = all_32_1 & count(all_13_6) = all_32_0 & in(all_13_5,
% 13.99/2.72  |           all_13_6) = all_32_2 & ($difference(all_32_0, all_32_1) = -1 |
% 13.99/2.72  |           all_32_2 = 0)
% 13.99/2.72  | 
% 13.99/2.72  | ALPHA: (55) implies:
% 13.99/2.72  |   (56)  in(all_13_5, all_13_6) = all_32_2
% 13.99/2.72  |   (57)  count(all_13_6) = all_32_0
% 13.99/2.72  |   (58)  count(all_13_4) = all_32_1
% 13.99/2.72  |   (59)  $difference(all_32_0, all_32_1) = -1 | all_32_2 = 0
% 13.99/2.72  | 
% 13.99/2.72  | DELTA: instantiating (21) with fresh symbols all_34_0, all_34_1, all_34_2
% 13.99/2.72  |        gives:
% 13.99/2.72  |   (60)  count(all_13_4) = all_34_1 & count(all_13_6) = all_34_0 & in(all_13_5,
% 13.99/2.72  |           all_13_6) = all_34_2 & ( ~ (all_34_2 = 0) | all_34_0 = all_34_1)
% 13.99/2.72  | 
% 13.99/2.72  | ALPHA: (60) implies:
% 13.99/2.72  |   (61)  in(all_13_5, all_13_6) = all_34_2
% 13.99/2.72  |   (62)  count(all_13_6) = all_34_0
% 13.99/2.72  |   (63)  count(all_13_4) = all_34_1
% 13.99/2.72  |   (64)   ~ (all_34_2 = 0) | all_34_0 = all_34_1
% 13.99/2.72  | 
% 13.99/2.72  | DELTA: instantiating (26) with fresh symbols all_36_0, all_36_1, all_36_2
% 13.99/2.72  |        gives:
% 13.99/2.73  |   (65)  count(all_13_1) = all_36_1 & count(all_13_6) = all_36_0 & in(all_13_5,
% 13.99/2.73  |           all_13_6) = all_36_2 & (all_36_0 = all_36_1 | all_36_2 = 0)
% 13.99/2.73  | 
% 13.99/2.73  | ALPHA: (65) implies:
% 13.99/2.73  |   (66)  in(all_13_5, all_13_6) = all_36_2
% 13.99/2.73  |   (67)  count(all_13_6) = all_36_0
% 13.99/2.73  |   (68)  count(all_13_1) = all_36_1
% 13.99/2.73  |   (69)  all_36_0 = all_36_1 | all_36_2 = 0
% 13.99/2.73  | 
% 14.05/2.73  | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 14.05/2.73  |        gives:
% 14.05/2.73  |   (70)  count(all_13_1) = all_38_1 & count(all_13_6) = all_38_0 & in(all_13_5,
% 14.05/2.73  |           all_13_6) = all_38_2 & ( ~ (all_38_2 = 0) | $difference(all_38_0,
% 14.05/2.73  |             all_38_1) = 1)
% 14.05/2.73  | 
% 14.05/2.73  | ALPHA: (70) implies:
% 14.05/2.73  |   (71)  in(all_13_5, all_13_6) = all_38_2
% 14.05/2.73  |   (72)  count(all_13_6) = all_38_0
% 14.05/2.73  |   (73)  count(all_13_1) = all_38_1
% 14.05/2.73  |   (74)   ~ (all_38_2 = 0) | $difference(all_38_0, all_38_1) = 1
% 14.05/2.73  | 
% 14.05/2.73  | DELTA: instantiating (27) with fresh symbols all_40_0, all_40_1, all_40_2
% 14.05/2.73  |        gives:
% 14.05/2.73  |   (75)  count(all_13_1) = all_40_2 & count(all_13_6) = all_40_1 & in(all_13_5,
% 14.05/2.73  |           all_13_6) = all_40_0 & ( ~ (all_40_0 = 0) |  ~ (all_40_1 =
% 14.05/2.73  |             all_40_2))
% 14.05/2.73  | 
% 14.05/2.73  | ALPHA: (75) implies:
% 14.05/2.73  |   (76)  in(all_13_5, all_13_6) = all_40_0
% 14.05/2.74  |   (77)  count(all_13_6) = all_40_1
% 14.05/2.74  |   (78)  count(all_13_1) = all_40_2
% 14.05/2.74  | 
% 14.05/2.74  | DELTA: instantiating (24) with fresh symbols all_42_0, all_42_1, all_42_2
% 14.05/2.74  |        gives:
% 14.05/2.74  |   (79)  count(all_13_4) = all_42_2 & count(all_13_6) = all_42_1 & in(all_13_5,
% 14.05/2.74  |           all_13_6) = all_42_0 & ( ~ (all_42_1 = all_42_2) | all_42_0 = 0)
% 14.05/2.74  | 
% 14.05/2.74  | ALPHA: (79) implies:
% 14.05/2.74  |   (80)  in(all_13_5, all_13_6) = all_42_0
% 14.05/2.74  |   (81)  count(all_13_6) = all_42_1
% 14.05/2.74  |   (82)  count(all_13_4) = all_42_2
% 14.05/2.74  | 
% 14.05/2.74  | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1, all_44_2
% 14.05/2.74  |        gives:
% 14.05/2.74  |   (83)  count(all_13_4) = all_44_2 & count(all_13_6) = all_44_1 & in(all_13_5,
% 14.05/2.74  |           all_13_6) = all_44_0 & ( ~ (all_44_0 = 0) |  ~
% 14.05/2.74  |           ($difference(all_44_1, all_44_2) = -1))
% 14.05/2.74  | 
% 14.05/2.74  | ALPHA: (83) implies:
% 14.05/2.74  |   (84)  in(all_13_5, all_13_6) = all_44_0
% 14.05/2.74  |   (85)  count(all_13_6) = all_44_1
% 14.05/2.74  |   (86)  count(all_13_4) = all_44_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_32_2, all_34_2, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (56), (61) gives:
% 14.05/2.74  |   (87)  all_34_2 = all_32_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_34_2, all_36_2, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (61), (66) gives:
% 14.05/2.74  |   (88)  all_36_2 = all_34_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_36_2, all_38_2, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (66), (71) gives:
% 14.05/2.74  |   (89)  all_38_2 = all_36_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_40_0, all_42_0, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (76), (80) gives:
% 14.05/2.74  |   (90)  all_42_0 = all_40_0
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_38_2, all_42_0, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (71), (80) gives:
% 14.05/2.74  |   (91)  all_42_0 = all_38_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_42_0, all_44_0, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (80), (84) gives:
% 14.05/2.74  |   (92)  all_44_0 = all_42_0
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_28_0, all_44_0, all_13_6, all_13_5,
% 14.05/2.74  |              simplifying with (47), (84) gives:
% 14.05/2.74  |   (93)  all_44_0 = all_28_0
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_26_2, all_30_0, all_13_4, all_13_5,
% 14.05/2.74  |              simplifying with (42), (52) gives:
% 14.05/2.74  |   (94)  all_30_0 = all_26_2
% 14.05/2.74  | 
% 14.05/2.74  | GROUND_INST: instantiating (11) with all_24_2, all_30_0, all_13_4, all_13_5,
% 14.05/2.75  |              simplifying with (38), (52) gives:
% 14.05/2.75  |   (95)  all_30_0 = all_24_2
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (11) with all_22_0, all_30_0, all_13_4, all_13_5,
% 14.05/2.75  |              simplifying with (34), (52) gives:
% 14.05/2.75  |   (96)  all_30_0 = all_22_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_34_0, all_36_0, all_13_6, simplifying
% 14.05/2.75  |              with (62), (67) gives:
% 14.05/2.75  |   (97)  all_36_0 = all_34_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_36_0, all_38_0, all_13_6, simplifying
% 14.05/2.75  |              with (67), (72) gives:
% 14.05/2.75  |   (98)  all_38_0 = all_36_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_38_0, all_42_1, all_13_6, simplifying
% 14.05/2.75  |              with (72), (81) gives:
% 14.05/2.75  |   (99)  all_42_1 = all_38_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_28_1, all_42_1, all_13_6, simplifying
% 14.05/2.75  |              with (48), (81) gives:
% 14.05/2.75  |   (100)  all_42_1 = all_28_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_40_1, all_44_1, all_13_6, simplifying
% 14.05/2.75  |              with (77), (85) gives:
% 14.05/2.75  |   (101)  all_44_1 = all_40_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_36_0, all_44_1, all_13_6, simplifying
% 14.05/2.75  |              with (67), (85) gives:
% 14.05/2.75  |   (102)  all_44_1 = all_36_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_32_0, all_44_1, all_13_6, simplifying
% 14.05/2.75  |              with (57), (85) gives:
% 14.05/2.75  |   (103)  all_44_1 = all_32_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_34_1, all_42_2, all_13_4, simplifying
% 14.05/2.75  |              with (63), (82) gives:
% 14.05/2.75  |   (104)  all_42_2 = all_34_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_26_0, all_42_2, all_13_4, simplifying
% 14.05/2.75  |              with (43), (82) gives:
% 14.05/2.75  |   (105)  all_42_2 = all_26_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_34_1, all_44_2, all_13_4, simplifying
% 14.05/2.75  |              with (63), (86) gives:
% 14.05/2.75  |   (106)  all_44_2 = all_34_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_32_1, all_44_2, all_13_4, simplifying
% 14.05/2.75  |              with (58), (86) gives:
% 14.05/2.75  |   (107)  all_44_2 = all_32_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_30_1, all_44_2, all_13_4, simplifying
% 14.05/2.75  |              with (53), (86) gives:
% 14.05/2.75  |   (108)  all_44_2 = all_30_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_24_0, all_44_2, all_13_4, simplifying
% 14.05/2.75  |              with (39), (86) gives:
% 14.05/2.75  |   (109)  all_44_2 = all_24_0
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_22_1, all_44_2, all_13_4, simplifying
% 14.05/2.75  |              with (35), (86) gives:
% 14.05/2.75  |   (110)  all_44_2 = all_22_1
% 14.05/2.75  | 
% 14.05/2.75  | GROUND_INST: instantiating (10) with all_13_2, all_24_1, all_13_3, simplifying
% 14.05/2.75  |              with (16), (40) gives:
% 14.05/2.75  |   (111)  all_24_1 = all_13_2
% 14.05/2.75  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_24_1, all_26_1, all_13_3, simplifying
% 14.05/2.76  |              with (40), (44) gives:
% 14.05/2.76  |   (112)  all_26_1 = all_24_1
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_26_1, all_30_2, all_13_3, simplifying
% 14.05/2.76  |              with (44), (54) gives:
% 14.05/2.76  |   (113)  all_30_2 = all_26_1
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_22_2, all_30_2, all_13_3, simplifying
% 14.05/2.76  |              with (36), (54) gives:
% 14.05/2.76  |   (114)  all_30_2 = all_22_2
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_28_2, all_36_1, all_13_1, simplifying
% 14.05/2.76  |              with (49), (68) gives:
% 14.05/2.76  |   (115)  all_36_1 = all_28_2
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_38_1, all_40_2, all_13_1, simplifying
% 14.05/2.76  |              with (73), (78) gives:
% 14.05/2.76  |   (116)  all_40_2 = all_38_1
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_36_1, all_40_2, all_13_1, simplifying
% 14.05/2.76  |              with (68), (78) gives:
% 14.05/2.76  |   (117)  all_40_2 = all_36_1
% 14.05/2.76  | 
% 14.05/2.76  | GROUND_INST: instantiating (10) with all_13_0, all_40_2, all_13_1, simplifying
% 14.05/2.76  |              with (17), (78) gives:
% 14.05/2.76  |   (118)  all_40_2 = all_13_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (92), (93) imply:
% 14.05/2.76  |   (119)  all_42_0 = all_28_0
% 14.05/2.76  | 
% 14.05/2.76  | SIMP: (119) implies:
% 14.05/2.76  |   (120)  all_42_0 = all_28_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (101), (102) imply:
% 14.05/2.76  |   (121)  all_40_1 = all_36_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (101), (103) imply:
% 14.05/2.76  |   (122)  all_40_1 = all_32_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (107), (110) imply:
% 14.05/2.76  |   (123)  all_32_1 = all_22_1
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (107), (109) imply:
% 14.05/2.76  |   (124)  all_32_1 = all_24_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (107), (108) imply:
% 14.05/2.76  |   (125)  all_32_1 = all_30_1
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (106), (107) imply:
% 14.05/2.76  |   (126)  all_34_1 = all_32_1
% 14.05/2.76  | 
% 14.05/2.76  | SIMP: (126) implies:
% 14.05/2.76  |   (127)  all_34_1 = all_32_1
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (90), (91) imply:
% 14.05/2.76  |   (128)  all_40_0 = all_38_2
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (90), (120) imply:
% 14.05/2.76  |   (129)  all_40_0 = all_28_0
% 14.05/2.76  | 
% 14.05/2.76  | COMBINE_EQS: (99), (100) imply:
% 14.05/2.76  |   (130)  all_38_0 = all_28_1
% 14.05/2.76  | 
% 14.05/2.77  | SIMP: (130) implies:
% 14.05/2.77  |   (131)  all_38_0 = all_28_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (104), (105) imply:
% 14.05/2.77  |   (132)  all_34_1 = all_26_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (132) implies:
% 14.05/2.77  |   (133)  all_34_1 = all_26_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (128), (129) imply:
% 14.05/2.77  |   (134)  all_38_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (134) implies:
% 14.05/2.77  |   (135)  all_38_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (121), (122) imply:
% 14.05/2.77  |   (136)  all_36_0 = all_32_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (136) implies:
% 14.05/2.77  |   (137)  all_36_0 = all_32_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (116), (118) imply:
% 14.05/2.77  |   (138)  all_38_1 = all_13_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (116), (117) imply:
% 14.05/2.77  |   (139)  all_38_1 = all_36_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (98), (131) imply:
% 14.05/2.77  |   (140)  all_36_0 = all_28_1
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (140) implies:
% 14.05/2.77  |   (141)  all_36_0 = all_28_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (138), (139) imply:
% 14.05/2.77  |   (142)  all_36_1 = all_13_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (142) implies:
% 14.05/2.77  |   (143)  all_36_1 = all_13_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (89), (135) imply:
% 14.05/2.77  |   (144)  all_36_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (144) implies:
% 14.05/2.77  |   (145)  all_36_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (97), (137) imply:
% 14.05/2.77  |   (146)  all_34_0 = all_32_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (97), (141) imply:
% 14.05/2.77  |   (147)  all_34_0 = all_28_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (115), (143) imply:
% 14.05/2.77  |   (148)  all_28_2 = all_13_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (148) implies:
% 14.05/2.77  |   (149)  all_28_2 = all_13_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (88), (145) imply:
% 14.05/2.77  |   (150)  all_34_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (150) implies:
% 14.05/2.77  |   (151)  all_34_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (146), (147) imply:
% 14.05/2.77  |   (152)  all_32_0 = all_28_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (127), (133) imply:
% 14.05/2.77  |   (153)  all_32_1 = all_26_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (153) implies:
% 14.05/2.77  |   (154)  all_32_1 = all_26_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (87), (151) imply:
% 14.05/2.77  |   (155)  all_32_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | SIMP: (155) implies:
% 14.05/2.77  |   (156)  all_32_2 = all_28_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (124), (125) imply:
% 14.05/2.77  |   (157)  all_30_1 = all_24_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (123), (125) imply:
% 14.05/2.77  |   (158)  all_30_1 = all_22_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (125), (154) imply:
% 14.05/2.77  |   (159)  all_30_1 = all_26_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (94), (95) imply:
% 14.05/2.77  |   (160)  all_26_2 = all_24_2
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (94), (96) imply:
% 14.05/2.77  |   (161)  all_26_2 = all_22_0
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (158), (159) imply:
% 14.05/2.77  |   (162)  all_26_0 = all_22_1
% 14.05/2.77  | 
% 14.05/2.77  | COMBINE_EQS: (157), (159) imply:
% 14.05/2.78  |   (163)  all_26_0 = all_24_0
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (113), (114) imply:
% 14.05/2.78  |   (164)  all_26_1 = all_22_2
% 14.05/2.78  | 
% 14.05/2.78  | SIMP: (164) implies:
% 14.05/2.78  |   (165)  all_26_1 = all_22_2
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (162), (163) imply:
% 14.05/2.78  |   (166)  all_24_0 = all_22_1
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (112), (165) imply:
% 14.05/2.78  |   (167)  all_24_1 = all_22_2
% 14.05/2.78  | 
% 14.05/2.78  | SIMP: (167) implies:
% 14.05/2.78  |   (168)  all_24_1 = all_22_2
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (160), (161) imply:
% 14.05/2.78  |   (169)  all_24_2 = all_22_0
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (111), (168) imply:
% 14.05/2.78  |   (170)  all_22_2 = all_13_2
% 14.05/2.78  | 
% 14.05/2.78  | SIMP: (170) implies:
% 14.05/2.78  |   (171)  all_22_2 = all_13_2
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (165), (171) imply:
% 14.05/2.78  |   (172)  all_26_1 = all_13_2
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (133), (162) imply:
% 14.05/2.78  |   (173)  all_34_1 = all_22_1
% 14.05/2.78  | 
% 14.05/2.78  | GROUND_INST: instantiating (1) with all_13_5, all_13_6, all_13_4, all_22_0,
% 14.05/2.78  |              simplifying with (14), (18), (34) gives:
% 14.05/2.78  |   (174)  all_22_0 = 0
% 14.05/2.78  | 
% 14.05/2.78  | COMBINE_EQS: (161), (174) imply:
% 14.05/2.78  |   (175)  all_26_2 = 0
% 14.05/2.78  | 
% 14.05/2.78  | BETA: splitting (45) gives:
% 14.05/2.78  | 
% 14.05/2.78  | Case 1:
% 14.05/2.78  | | 
% 14.05/2.78  | |   (176)   ~ (all_26_2 = 0)
% 14.05/2.78  | | 
% 14.05/2.78  | | REDUCE: (175), (176) imply:
% 14.05/2.78  | |   (177)  $false
% 14.05/2.78  | | 
% 14.05/2.78  | | CLOSE: (177) is inconsistent.
% 14.05/2.78  | | 
% 14.05/2.78  | Case 2:
% 14.05/2.78  | | 
% 14.05/2.78  | |   (178)  $difference(all_26_0, all_26_1) = 1
% 14.05/2.78  | | 
% 14.05/2.78  | | COMBINE_EQS: (162), (178) imply:
% 14.05/2.78  | |   (179)  $difference(all_26_1, all_22_1) = -1
% 14.05/2.78  | | 
% 14.05/2.78  | | COMBINE_EQS: (172), (179) imply:
% 14.05/2.78  | |   (180)  $difference(all_22_1, all_13_2) = 1
% 14.05/2.78  | | 
% 14.05/2.78  | | SIMP: (180) implies:
% 14.05/2.78  | |   (181)  $difference(all_22_1, all_13_2) = 1
% 14.05/2.78  | | 
% 14.05/2.78  | | COMBINE_EQS: (123), (181) imply:
% 14.05/2.78  | |   (182)  $difference(all_32_1, all_13_2) = 1
% 14.05/2.78  | | 
% 14.05/2.78  | | COMBINE_EQS: (173), (181) imply:
% 14.05/2.78  | |   (183)  $difference(all_34_1, all_13_2) = 1
% 14.05/2.78  | | 
% 14.05/2.78  | | BETA: splitting (50) gives:
% 14.05/2.78  | | 
% 14.05/2.78  | | Case 1:
% 14.05/2.78  | | | 
% 14.05/2.78  | | |   (184)   ~ ($difference(all_28_1, all_28_2) = 1)
% 14.05/2.78  | | | 
% 14.05/2.78  | | | REDUCE: (149), (184) imply:
% 14.05/2.79  | | |   (185)   ~ ($difference(all_28_1, all_13_0) = 1)
% 14.05/2.79  | | | 
% 14.05/2.79  | | | BETA: splitting (74) gives:
% 14.05/2.79  | | | 
% 14.05/2.79  | | | Case 1:
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | |   (186)   ~ (all_38_2 = 0)
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | REDUCE: (135), (186) imply:
% 14.05/2.79  | | | |   (187)   ~ (all_28_0 = 0)
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | BETA: splitting (69) gives:
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | Case 1:
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | |   (188)  all_36_2 = 0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | COMBINE_EQS: (145), (188) imply:
% 14.05/2.79  | | | | |   (189)  all_28_0 = 0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | SIMP: (189) implies:
% 14.05/2.79  | | | | |   (190)  all_28_0 = 0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | REDUCE: (187), (190) imply:
% 14.05/2.79  | | | | |   (191)  $false
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | CLOSE: (191) is inconsistent.
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | Case 2:
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | |   (192)  all_36_0 = all_36_1
% 14.05/2.79  | | | | |   (193)   ~ (all_36_2 = 0)
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | COMBINE_EQS: (141), (192) imply:
% 14.05/2.79  | | | | |   (194)  all_36_1 = all_28_1
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | COMBINE_EQS: (143), (194) imply:
% 14.05/2.79  | | | | |   (195)  all_28_1 = all_13_0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | SIMP: (195) implies:
% 14.05/2.79  | | | | |   (196)  all_28_1 = all_13_0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | COMBINE_EQS: (152), (196) imply:
% 14.05/2.79  | | | | |   (197)  all_32_0 = all_13_0
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | BETA: splitting (59) gives:
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | | Case 1:
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | |   (198)  all_32_2 = 0
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | COMBINE_EQS: (156), (198) imply:
% 14.05/2.79  | | | | | |   (199)  all_28_0 = 0
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | REDUCE: (187), (199) imply:
% 14.05/2.79  | | | | | |   (200)  $false
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | CLOSE: (200) is inconsistent.
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | Case 2:
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | |   (201)  $difference(all_32_0, all_32_1) = -1
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | COMBINE_EQS: (197), (201) imply:
% 14.05/2.79  | | | | | |   (202)  $difference(all_32_1, all_13_0) = 1
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | COMBINE_EQS: (182), (202) imply:
% 14.05/2.79  | | | | | |   (203)  all_13_0 = all_13_2
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | SIMP: (203) implies:
% 14.05/2.79  | | | | | |   (204)  all_13_0 = all_13_2
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | REDUCE: (13), (204) imply:
% 14.05/2.79  | | | | | |   (205)  $false
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | | CLOSE: (205) is inconsistent.
% 14.05/2.79  | | | | | | 
% 14.05/2.79  | | | | | End of split
% 14.05/2.79  | | | | | 
% 14.05/2.79  | | | | End of split
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | Case 2:
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | |   (206)  $difference(all_38_0, all_38_1) = 1
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | COMBINE_EQS: (131), (206) imply:
% 14.05/2.79  | | | |   (207)  $difference(all_38_1, all_28_1) = -1
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | SIMP: (207) implies:
% 14.05/2.79  | | | |   (208)  $difference(all_38_1, all_28_1) = -1
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | COMBINE_EQS: (138), (208) imply:
% 14.05/2.79  | | | |   (209)  $difference(all_28_1, all_13_0) = 1
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | SIMP: (209) implies:
% 14.05/2.79  | | | |   (210)  $difference(all_28_1, all_13_0) = 1
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | REDUCE: (185), (210) imply:
% 14.05/2.79  | | | |   (211)  $false
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | | CLOSE: (211) is inconsistent.
% 14.05/2.79  | | | | 
% 14.05/2.79  | | | End of split
% 14.05/2.79  | | | 
% 14.05/2.79  | | Case 2:
% 14.05/2.79  | | | 
% 14.05/2.79  | | |   (212)  $difference(all_28_1, all_28_2) = 1
% 14.05/2.79  | | |   (213)  all_28_0 = 0
% 14.05/2.79  | | | 
% 14.05/2.79  | | | COMBINE_EQS: (149), (212) imply:
% 14.05/2.80  | | |   (214)  $difference(all_28_1, all_13_0) = 1
% 14.05/2.80  | | | 
% 14.05/2.80  | | | COMBINE_EQS: (151), (213) imply:
% 14.05/2.80  | | |   (215)  all_34_2 = 0
% 14.05/2.80  | | | 
% 14.05/2.80  | | | COMBINE_EQS: (147), (214) imply:
% 14.05/2.80  | | |   (216)  $difference(all_34_0, all_13_0) = 1
% 14.05/2.80  | | | 
% 14.05/2.80  | | | BETA: splitting (64) gives:
% 14.05/2.80  | | | 
% 14.05/2.80  | | | Case 1:
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | |   (217)   ~ (all_34_2 = 0)
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | REDUCE: (215), (217) imply:
% 14.05/2.80  | | | |   (218)  $false
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | CLOSE: (218) is inconsistent.
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | Case 2:
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | |   (219)  all_34_0 = all_34_1
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | COMBINE_EQS: (216), (219) imply:
% 14.05/2.80  | | | |   (220)  $difference(all_34_1, all_13_0) = 1
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | COMBINE_EQS: (183), (220) imply:
% 14.05/2.80  | | | |   (221)  all_13_0 = all_13_2
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | SIMP: (221) implies:
% 14.05/2.80  | | | |   (222)  all_13_0 = all_13_2
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | REDUCE: (13), (222) imply:
% 14.05/2.80  | | | |   (223)  $false
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | | CLOSE: (223) is inconsistent.
% 14.05/2.80  | | | | 
% 14.05/2.80  | | | End of split
% 14.05/2.80  | | | 
% 14.05/2.80  | | End of split
% 14.05/2.80  | | 
% 14.05/2.80  | End of split
% 14.05/2.80  | 
% 14.05/2.80  End of proof
% 14.05/2.80  % SZS output end Proof for theBenchmark
% 14.05/2.80  
% 14.05/2.80  2290ms
%------------------------------------------------------------------------------