TSTP Solution File: DAT047_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : DAT047_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 : 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 : Wed Aug 30 22:19:00 EDT 2023

% Result   : Theorem 7.54s 1.78s
% Output   : Proof 10.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT047_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug 24 14:48:10 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.63  ________       _____
% 0.22/0.63  ___  __ \_________(_)________________________________
% 0.22/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63  
% 0.22/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63  (2023-06-19)
% 0.22/0.63  
% 0.22/0.63  (c) Philipp Rümmer, 2009-2023
% 0.22/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63                Amanda Stjerna.
% 0.22/0.63  Free software under BSD-3-Clause.
% 0.22/0.63  
% 0.22/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63  
% 0.22/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.64  Running up to 7 provers in parallel.
% 0.22/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.49/1.08  Prover 1: Preprocessing ...
% 2.49/1.09  Prover 4: Preprocessing ...
% 2.97/1.12  Prover 2: Preprocessing ...
% 2.97/1.12  Prover 0: Preprocessing ...
% 2.97/1.12  Prover 5: Preprocessing ...
% 2.97/1.12  Prover 3: Preprocessing ...
% 2.97/1.12  Prover 6: Preprocessing ...
% 4.64/1.40  Prover 5: Proving ...
% 4.64/1.42  Prover 1: Constructing countermodel ...
% 4.64/1.42  Prover 6: Constructing countermodel ...
% 4.64/1.43  Prover 3: Constructing countermodel ...
% 4.88/1.46  Prover 4: Constructing countermodel ...
% 4.88/1.46  Prover 0: Proving ...
% 5.78/1.51  Prover 2: Proving ...
% 7.54/1.77  Prover 3: proved (1111ms)
% 7.54/1.77  
% 7.54/1.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.54/1.78  
% 7.54/1.78  Prover 6: stopped
% 7.54/1.78  Prover 2: stopped
% 7.54/1.78  Prover 0: stopped
% 7.54/1.78  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.54/1.78  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.54/1.78  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.54/1.79  Prover 5: stopped
% 7.54/1.80  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.95/1.80  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.95/1.83  Prover 11: Preprocessing ...
% 7.95/1.83  Prover 7: Preprocessing ...
% 7.95/1.84  Prover 10: Preprocessing ...
% 7.95/1.84  Prover 8: Preprocessing ...
% 7.95/1.85  Prover 13: Preprocessing ...
% 8.33/1.93  Prover 7: Constructing countermodel ...
% 8.33/1.94  Prover 13: Warning: ignoring some quantifiers
% 8.33/1.94  Prover 8: Warning: ignoring some quantifiers
% 8.33/1.95  Prover 13: Constructing countermodel ...
% 9.01/1.96  Prover 8: Constructing countermodel ...
% 9.01/1.96  Prover 10: Constructing countermodel ...
% 9.01/1.99  Prover 11: Constructing countermodel ...
% 9.33/2.11  Prover 1: Found proof (size 169)
% 9.33/2.12  Prover 1: proved (1465ms)
% 9.33/2.12  Prover 7: stopped
% 9.33/2.12  Prover 11: stopped
% 9.33/2.12  Prover 13: stopped
% 9.33/2.12  Prover 8: stopped
% 9.33/2.12  Prover 4: stopped
% 9.33/2.12  Prover 10: stopped
% 9.33/2.12  
% 9.33/2.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.33/2.12  
% 10.26/2.17  % SZS output start Proof for theBenchmark
% 10.26/2.17  Assumptions after simplification:
% 10.26/2.17  ---------------------------------
% 10.26/2.17  
% 10.26/2.17    (ax1)
% 10.26/2.19    collection(empty) &  ! [v0: collection] :  ! [v1: int] : ( ~ ($lesseq(v1, -1))
% 10.26/2.19      |  ~ (count(v0) = v1) |  ~ collection(v0)) &  ! [v0: int] :  ~ (in(v0,
% 10.26/2.19        empty) = 0)
% 10.26/2.19  
% 10.26/2.19    (ax2)
% 10.26/2.20    collection(empty) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] :
% 10.26/2.20     ! [v3: int] : (v3 = 0 |  ~ (add(v0, v1) = v2) |  ~ (in(v0, v2) = v3) |  ~
% 10.26/2.20      collection(v1)) &  ! [v0: collection] : (v0 = empty |  ~ (count(v0) = 0) | 
% 10.26/2.20      ~ collection(v0)) &  ! [v0: int] : (v0 = 0 |  ~ (count(empty) = v0))
% 10.26/2.20  
% 10.26/2.20    (ax3)
% 10.53/2.20     ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 10.53/2.20        = v2) |  ~ (in(v0, v2) = 0) |  ~ collection(v1)) &  ! [v0: int] :  ! [v1:
% 10.53/2.20      collection] :  ! [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~
% 10.53/2.20      collection(v1) |  ? [v3: any] :  ? [v4: int] :  ? [v5: int] : (count(v2) =
% 10.53/2.20        v4 & count(v1) = v5 & in(v0, v1) = v3 & ($difference(v5, v4) = -1 | v3 =
% 10.53/2.20          0))) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 10.53/2.20      (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 10.53/2.20      [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 =
% 10.53/2.20            0) |  ~ ($difference(v4, v3) = -1))))
% 10.53/2.20  
% 10.53/2.20    (ax4)
% 10.53/2.21     ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] :  !
% 10.53/2.21    [v4: int] : (v4 = 0 |  ~ (add(v2, v1) = v3) |  ~ (in(v0, v3) = v4) |  ~
% 10.53/2.21      collection(v1) | ( ~ (v2 = v0) &  ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 10.53/2.21          v5))) &  ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3:
% 10.53/2.21      collection] : (v2 = v0 |  ~ (add(v2, v1) = v3) |  ~ (in(v0, v3) = 0) |  ~
% 10.53/2.21      collection(v1) | in(v0, v1) = 0) &  ! [v0: int] :  ! [v1: collection] :  !
% 10.53/2.21    [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :
% 10.53/2.21       ? [v4: int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 10.53/2.21        = v3 & ( ~ (v3 = 0) | v5 = v4))) &  ! [v0: int] :  ! [v1: collection] :  !
% 10.53/2.21    [v2: collection] : ( ~ (add(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :
% 10.53/2.21       ? [v4: int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 10.53/2.21        = v5 & ( ~ (v4 = v3) | v5 = 0)))
% 10.53/2.21  
% 10.53/2.21    (ax5)
% 10.53/2.22     ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] :  !
% 10.53/2.22    [v4: int] : (v4 = 0 | v2 = v0 |  ~ (remove(v2, v1) = v3) |  ~ (in(v0, v3) =
% 10.53/2.22        v4) |  ~ collection(v1) |  ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 10.53/2.22    &  ! [v0: int] :  ! [v1: collection] :  ! [v2: int] :  ! [v3: collection] : (
% 10.53/2.22      ~ (remove(v2, v1) = v3) |  ~ (in(v0, v3) = 0) |  ~ collection(v1) | ( ~ (v2
% 10.53/2.22          = v0) & in(v0, v1) = 0)) &  ! [v0: int] :  ! [v1: collection] :  ! [v2:
% 10.53/2.22      collection] : ( ~ (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :
% 10.53/2.22       ? [v4: int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 10.53/2.22        = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1))) &  ! [v0: int] :  ! [v1:
% 10.53/2.22      collection] :  ! [v2: collection] : ( ~ (remove(v0, v1) = v2) |  ~
% 10.53/2.22      collection(v1) |  ? [v3: int] :  ? [v4: int] :  ? [v5: any] : (count(v2) =
% 10.53/2.22        v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5
% 10.53/2.22          = 0)))
% 10.53/2.22  
% 10.53/2.22    (ax6)
% 10.53/2.22     ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 10.53/2.22        = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ? [v5: int] :
% 10.53/2.22      (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & (v5 = v4 | v3 = 0))) & 
% 10.53/2.22    ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (remove(v0, v1)
% 10.53/2.22        = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ? [v5: any] :
% 10.53/2.22      (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 =
% 10.53/2.22            v3))))
% 10.53/2.22  
% 10.53/2.22    (co1)
% 10.53/2.22    collection(empty) &  ? [v0: collection] :  ? [v1: collection] :  ? [v2:
% 10.53/2.22      collection] :  ? [v3: int] : ( ~ (v3 = 1) & remove(3, v0) = v1 & add(5, v1)
% 10.53/2.22      = v2 & add(3, empty) = v0 & count(v2) = v3 & collection(v2) & collection(v1)
% 10.53/2.22      & collection(v0))
% 10.53/2.22  
% 10.53/2.22    (function-axioms)
% 10.53/2.23     ! [v0: collection] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int]
% 10.53/2.23    : (v1 = v0 |  ~ (remove(v3, v2) = v1) |  ~ (remove(v3, v2) = v0)) &  ! [v0:
% 10.53/2.23      collection] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int] : (v1
% 10.53/2.23      = v0 |  ~ (add(v3, v2) = v1) |  ~ (add(v3, v2) = v0)) &  ! [v0:
% 10.53/2.23      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: collection] :  !
% 10.53/2.23    [v3: int] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 10.53/2.23      int] :  ! [v1: int] :  ! [v2: collection] : (v1 = v0 |  ~ (count(v2) = v1) |
% 10.53/2.23       ~ (count(v2) = v0))
% 10.53/2.23  
% 10.53/2.23  Further assumptions not needed in the proof:
% 10.53/2.23  --------------------------------------------
% 10.53/2.23  ax7
% 10.53/2.23  
% 10.53/2.23  Those formulas are unsatisfiable:
% 10.53/2.23  ---------------------------------
% 10.53/2.23  
% 10.53/2.23  Begin of proof
% 10.53/2.23  | 
% 10.53/2.23  | ALPHA: (ax1) implies:
% 10.53/2.23  |   (1)   ! [v0: int] :  ~ (in(v0, empty) = 0)
% 10.53/2.23  |   (2)   ! [v0: collection] :  ! [v1: int] : ( ~ ($lesseq(v1, -1)) |  ~
% 10.53/2.23  |          (count(v0) = v1) |  ~ collection(v0))
% 10.53/2.23  | 
% 10.53/2.23  | ALPHA: (ax2) implies:
% 10.53/2.23  |   (3)   ! [v0: int] : (v0 = 0 |  ~ (count(empty) = v0))
% 10.53/2.23  |   (4)   ! [v0: collection] : (v0 = empty |  ~ (count(v0) = 0) |  ~
% 10.53/2.23  |          collection(v0))
% 10.53/2.23  |   (5)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] :  ! [v3: int]
% 10.53/2.23  |        : (v3 = 0 |  ~ (add(v0, v1) = v2) |  ~ (in(v0, v2) = v3) |  ~
% 10.53/2.23  |          collection(v1))
% 10.53/2.23  | 
% 10.53/2.23  | ALPHA: (ax3) implies:
% 10.53/2.23  |   (6)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 10.53/2.23  |              v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 10.53/2.23  |          [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 10.53/2.23  |              (v5 = 0) |  ~ ($difference(v4, v3) = -1))))
% 10.53/2.24  |   (7)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 10.53/2.24  |              v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ?
% 10.53/2.24  |          [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 &
% 10.53/2.24  |            ($difference(v5, v4) = -1 | v3 = 0)))
% 10.53/2.24  | 
% 10.53/2.24  | ALPHA: (ax4) implies:
% 10.53/2.24  |   (8)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 10.53/2.24  |              v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4: int] :  ?
% 10.53/2.24  |          [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 10.53/2.24  |              (v4 = v3) | v5 = 0)))
% 10.53/2.24  |   (9)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~ (add(v0,
% 10.53/2.24  |              v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4: int] :  ?
% 10.53/2.24  |          [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~
% 10.53/2.24  |              (v3 = 0) | v5 = v4)))
% 10.53/2.24  | 
% 10.53/2.24  | ALPHA: (ax5) implies:
% 10.53/2.24  |   (10)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 10.53/2.24  |           (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4:
% 10.53/2.24  |             int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0,
% 10.53/2.24  |               v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5 = 0)))
% 10.53/2.24  |   (11)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 10.53/2.24  |           (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4:
% 10.53/2.24  |             int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0,
% 10.53/2.24  |               v1) = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1)))
% 10.53/2.24  | 
% 10.53/2.24  | ALPHA: (ax6) implies:
% 10.53/2.24  |   (12)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 10.53/2.24  |           (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: int] :  ? [v4:
% 10.53/2.24  |             int] :  ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0,
% 10.53/2.24  |               v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = v3))))
% 10.53/2.24  |   (13)   ! [v0: int] :  ! [v1: collection] :  ! [v2: collection] : ( ~
% 10.53/2.24  |           (remove(v0, v1) = v2) |  ~ collection(v1) |  ? [v3: any] :  ? [v4:
% 10.53/2.24  |             int] :  ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0,
% 10.53/2.24  |               v1) = v3 & (v5 = v4 | v3 = 0)))
% 10.53/2.24  | 
% 10.53/2.24  | ALPHA: (co1) implies:
% 10.53/2.24  |   (14)  collection(empty)
% 10.53/2.25  |   (15)   ? [v0: collection] :  ? [v1: collection] :  ? [v2: collection] :  ?
% 10.53/2.25  |         [v3: int] : ( ~ (v3 = 1) & remove(3, v0) = v1 & add(5, v1) = v2 &
% 10.53/2.25  |           add(3, empty) = v0 & count(v2) = v3 & collection(v2) &
% 10.53/2.25  |           collection(v1) & collection(v0))
% 10.53/2.25  | 
% 10.53/2.25  | ALPHA: (function-axioms) implies:
% 10.53/2.25  |   (16)   ! [v0: int] :  ! [v1: int] :  ! [v2: collection] : (v1 = v0 |  ~
% 10.53/2.25  |           (count(v2) = v1) |  ~ (count(v2) = v0))
% 10.53/2.25  |   (17)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.53/2.25  |           collection] :  ! [v3: int] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~
% 10.53/2.25  |           (in(v3, v2) = v0))
% 10.53/2.25  | 
% 10.53/2.25  | DELTA: instantiating (15) with fresh symbols all_13_0, all_13_1, all_13_2,
% 10.53/2.25  |        all_13_3 gives:
% 10.53/2.25  |   (18)   ~ (all_13_0 = 1) & remove(3, all_13_3) = all_13_2 & add(5, all_13_2)
% 10.53/2.25  |         = all_13_1 & add(3, empty) = all_13_3 & count(all_13_1) = all_13_0 &
% 10.53/2.25  |         collection(all_13_1) & collection(all_13_2) & collection(all_13_3)
% 10.53/2.25  | 
% 10.53/2.25  | ALPHA: (18) implies:
% 10.53/2.25  |   (19)   ~ (all_13_0 = 1)
% 10.53/2.25  |   (20)  collection(all_13_3)
% 10.53/2.25  |   (21)  collection(all_13_2)
% 10.53/2.25  |   (22)  count(all_13_1) = all_13_0
% 10.53/2.25  |   (23)  add(3, empty) = all_13_3
% 10.53/2.25  |   (24)  add(5, all_13_2) = all_13_1
% 10.53/2.25  |   (25)  remove(3, all_13_3) = all_13_2
% 10.53/2.25  | 
% 10.53/2.25  | GROUND_INST: instantiating (9) with 3, empty, all_13_3, simplifying with (14),
% 10.53/2.25  |              (23) gives:
% 10.53/2.25  |   (26)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_3) = v1 &
% 10.53/2.25  |           count(empty) = v2 & in(3, empty) = v0 & ( ~ (v0 = 0) | v2 = v1))
% 10.53/2.25  | 
% 10.53/2.25  | GROUND_INST: instantiating (7) with 3, empty, all_13_3, simplifying with (14),
% 10.53/2.25  |              (23) gives:
% 10.53/2.25  |   (27)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_3) = v1 &
% 10.53/2.25  |           count(empty) = v2 & in(3, empty) = v0 & ($difference(v2, v1) = -1 |
% 10.53/2.25  |             v0 = 0))
% 10.53/2.25  | 
% 10.53/2.25  | GROUND_INST: instantiating (6) with 3, empty, all_13_3, simplifying with (14),
% 10.53/2.25  |              (23) gives:
% 10.53/2.25  |   (28)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_3) = v0 &
% 10.53/2.25  |           count(empty) = v1 & in(3, empty) = v2 & ( ~ (v2 = 0) |  ~
% 10.53/2.25  |             ($difference(v1, v0) = -1)))
% 10.53/2.25  | 
% 10.53/2.25  | GROUND_INST: instantiating (8) with 3, empty, all_13_3, simplifying with (14),
% 10.53/2.25  |              (23) gives:
% 10.81/2.26  |   (29)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_3) = v0 &
% 10.81/2.26  |           count(empty) = v1 & in(3, empty) = v2 & ( ~ (v1 = v0) | v2 = 0))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (9) with 5, all_13_2, all_13_1, simplifying with
% 10.81/2.26  |              (21), (24) gives:
% 10.81/2.26  |   (30)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_1) = v1 &
% 10.81/2.26  |           count(all_13_2) = v2 & in(5, all_13_2) = v0 & ( ~ (v0 = 0) | v2 =
% 10.81/2.26  |             v1))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (7) with 5, all_13_2, all_13_1, simplifying with
% 10.81/2.26  |              (21), (24) gives:
% 10.81/2.26  |   (31)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_1) = v1 &
% 10.81/2.26  |           count(all_13_2) = v2 & in(5, all_13_2) = v0 & ($difference(v2, v1) =
% 10.81/2.26  |             -1 | v0 = 0))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (6) with 5, all_13_2, all_13_1, simplifying with
% 10.81/2.26  |              (21), (24) gives:
% 10.81/2.26  |   (32)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_1) = v0 &
% 10.81/2.26  |           count(all_13_2) = v1 & in(5, all_13_2) = v2 & ( ~ (v2 = 0) |  ~
% 10.81/2.26  |             ($difference(v1, v0) = -1)))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (8) with 5, all_13_2, all_13_1, simplifying with
% 10.81/2.26  |              (21), (24) gives:
% 10.81/2.26  |   (33)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_1) = v0 &
% 10.81/2.26  |           count(all_13_2) = v1 & in(5, all_13_2) = v2 & ( ~ (v1 = v0) | v2 =
% 10.81/2.26  |             0))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (11) with 3, all_13_3, all_13_2, simplifying with
% 10.81/2.26  |              (20), (25) gives:
% 10.81/2.26  |   (34)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_2) = v1 &
% 10.81/2.26  |           count(all_13_3) = v2 & in(3, all_13_3) = v0 & ( ~ (v0 = 0) |
% 10.81/2.26  |             $difference(v2, v1) = 1))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (13) with 3, all_13_3, all_13_2, simplifying with
% 10.81/2.26  |              (20), (25) gives:
% 10.81/2.26  |   (35)   ? [v0: any] :  ? [v1: int] :  ? [v2: int] : (count(all_13_2) = v1 &
% 10.81/2.26  |           count(all_13_3) = v2 & in(3, all_13_3) = v0 & (v2 = v1 | v0 = 0))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (12) with 3, all_13_3, all_13_2, simplifying with
% 10.81/2.26  |              (20), (25) gives:
% 10.81/2.26  |   (36)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_2) = v0 &
% 10.81/2.26  |           count(all_13_3) = v1 & in(3, all_13_3) = v2 & ( ~ (v2 = 0) |  ~ (v1
% 10.81/2.26  |               = v0)))
% 10.81/2.26  | 
% 10.81/2.26  | GROUND_INST: instantiating (10) with 3, all_13_3, all_13_2, simplifying with
% 10.81/2.26  |              (20), (25) gives:
% 10.81/2.27  |   (37)   ? [v0: int] :  ? [v1: int] :  ? [v2: any] : (count(all_13_2) = v0 &
% 10.81/2.27  |           count(all_13_3) = v1 & in(3, all_13_3) = v2 & ( ~ ($difference(v1,
% 10.81/2.27  |                 v0) = 1) | v2 = 0))
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (37) with fresh symbols all_22_0, all_22_1, all_22_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (38)  count(all_13_2) = all_22_2 & count(all_13_3) = all_22_1 & in(3,
% 10.81/2.27  |           all_13_3) = all_22_0 & ( ~ ($difference(all_22_1, all_22_2) = 1) |
% 10.81/2.27  |           all_22_0 = 0)
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (38) implies:
% 10.81/2.27  |   (39)  in(3, all_13_3) = all_22_0
% 10.81/2.27  |   (40)  count(all_13_3) = all_22_1
% 10.81/2.27  |   (41)  count(all_13_2) = all_22_2
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (36) with fresh symbols all_24_0, all_24_1, all_24_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (42)  count(all_13_2) = all_24_2 & count(all_13_3) = all_24_1 & in(3,
% 10.81/2.27  |           all_13_3) = all_24_0 & ( ~ (all_24_0 = 0) |  ~ (all_24_1 =
% 10.81/2.27  |             all_24_2))
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (42) implies:
% 10.81/2.27  |   (43)  in(3, all_13_3) = all_24_0
% 10.81/2.27  |   (44)  count(all_13_3) = all_24_1
% 10.81/2.27  |   (45)  count(all_13_2) = all_24_2
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (35) with fresh symbols all_26_0, all_26_1, all_26_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (46)  count(all_13_2) = all_26_1 & count(all_13_3) = all_26_0 & in(3,
% 10.81/2.27  |           all_13_3) = all_26_2 & (all_26_0 = all_26_1 | all_26_2 = 0)
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (46) implies:
% 10.81/2.27  |   (47)  in(3, all_13_3) = all_26_2
% 10.81/2.27  |   (48)  count(all_13_3) = all_26_0
% 10.81/2.27  |   (49)  count(all_13_2) = all_26_1
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1, all_28_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (50)  count(all_13_2) = all_28_1 & count(all_13_3) = all_28_0 & in(3,
% 10.81/2.27  |           all_13_3) = all_28_2 & ( ~ (all_28_2 = 0) | $difference(all_28_0,
% 10.81/2.27  |             all_28_1) = 1)
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (50) implies:
% 10.81/2.27  |   (51)  in(3, all_13_3) = all_28_2
% 10.81/2.27  |   (52)  count(all_13_3) = all_28_0
% 10.81/2.27  |   (53)  count(all_13_2) = all_28_1
% 10.81/2.27  |   (54)   ~ (all_28_2 = 0) | $difference(all_28_0, all_28_1) = 1
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (28) with fresh symbols all_30_0, all_30_1, all_30_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (55)  count(all_13_3) = all_30_2 & count(empty) = all_30_1 & in(3, empty) =
% 10.81/2.27  |         all_30_0 & ( ~ (all_30_0 = 0) |  ~ ($difference(all_30_1, all_30_2) =
% 10.81/2.27  |             -1))
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (55) implies:
% 10.81/2.27  |   (56)  in(3, empty) = all_30_0
% 10.81/2.27  |   (57)  count(all_13_3) = all_30_2
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (32) with fresh symbols all_32_0, all_32_1, all_32_2
% 10.81/2.27  |        gives:
% 10.81/2.27  |   (58)  count(all_13_1) = all_32_2 & count(all_13_2) = all_32_1 & in(5,
% 10.81/2.27  |           all_13_2) = all_32_0 & ( ~ (all_32_0 = 0) |  ~
% 10.81/2.27  |           ($difference(all_32_1, all_32_2) = -1))
% 10.81/2.27  | 
% 10.81/2.27  | ALPHA: (58) implies:
% 10.81/2.27  |   (59)  in(5, all_13_2) = all_32_0
% 10.81/2.27  |   (60)  count(all_13_2) = all_32_1
% 10.81/2.27  |   (61)  count(all_13_1) = all_32_2
% 10.81/2.27  | 
% 10.81/2.27  | DELTA: instantiating (30) with fresh symbols all_34_0, all_34_1, all_34_2
% 10.81/2.27  |        gives:
% 10.81/2.28  |   (62)  count(all_13_1) = all_34_1 & count(all_13_2) = all_34_0 & in(5,
% 10.81/2.28  |           all_13_2) = all_34_2 & ( ~ (all_34_2 = 0) | all_34_0 = all_34_1)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (62) implies:
% 10.81/2.28  |   (63)  in(5, all_13_2) = all_34_2
% 10.81/2.28  |   (64)  count(all_13_2) = all_34_0
% 10.81/2.28  |   (65)  count(all_13_1) = all_34_1
% 10.81/2.28  | 
% 10.81/2.28  | DELTA: instantiating (29) with fresh symbols all_36_0, all_36_1, all_36_2
% 10.81/2.28  |        gives:
% 10.81/2.28  |   (66)  count(all_13_3) = all_36_2 & count(empty) = all_36_1 & in(3, empty) =
% 10.81/2.28  |         all_36_0 & ( ~ (all_36_1 = all_36_2) | all_36_0 = 0)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (66) implies:
% 10.81/2.28  |   (67)  count(all_13_3) = all_36_2
% 10.81/2.28  | 
% 10.81/2.28  | DELTA: instantiating (31) with fresh symbols all_38_0, all_38_1, all_38_2
% 10.81/2.28  |        gives:
% 10.81/2.28  |   (68)  count(all_13_1) = all_38_1 & count(all_13_2) = all_38_0 & in(5,
% 10.81/2.28  |           all_13_2) = all_38_2 & ($difference(all_38_0, all_38_1) = -1 |
% 10.81/2.28  |           all_38_2 = 0)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (68) implies:
% 10.81/2.28  |   (69)  in(5, all_13_2) = all_38_2
% 10.81/2.28  |   (70)  count(all_13_2) = all_38_0
% 10.81/2.28  |   (71)  count(all_13_1) = all_38_1
% 10.81/2.28  |   (72)  $difference(all_38_0, all_38_1) = -1 | all_38_2 = 0
% 10.81/2.28  | 
% 10.81/2.28  | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 10.81/2.28  |        gives:
% 10.81/2.28  |   (73)  count(all_13_3) = all_40_1 & count(empty) = all_40_0 & in(3, empty) =
% 10.81/2.28  |         all_40_2 & ( ~ (all_40_2 = 0) | all_40_0 = all_40_1)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (73) implies:
% 10.81/2.28  |   (74)  in(3, empty) = all_40_2
% 10.81/2.28  |   (75)  count(empty) = all_40_0
% 10.81/2.28  |   (76)  count(all_13_3) = all_40_1
% 10.81/2.28  |   (77)   ~ (all_40_2 = 0) | all_40_0 = all_40_1
% 10.81/2.28  | 
% 10.81/2.28  | DELTA: instantiating (27) with fresh symbols all_42_0, all_42_1, all_42_2
% 10.81/2.28  |        gives:
% 10.81/2.28  |   (78)  count(all_13_3) = all_42_1 & count(empty) = all_42_0 & in(3, empty) =
% 10.81/2.28  |         all_42_2 & ($difference(all_42_0, all_42_1) = -1 | all_42_2 = 0)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (78) implies:
% 10.81/2.28  |   (79)  in(3, empty) = all_42_2
% 10.81/2.28  |   (80)  count(empty) = all_42_0
% 10.81/2.28  |   (81)  count(all_13_3) = all_42_1
% 10.81/2.28  |   (82)  $difference(all_42_0, all_42_1) = -1 | all_42_2 = 0
% 10.81/2.28  | 
% 10.81/2.28  | DELTA: instantiating (33) with fresh symbols all_44_0, all_44_1, all_44_2
% 10.81/2.28  |        gives:
% 10.81/2.28  |   (83)  count(all_13_1) = all_44_2 & count(all_13_2) = all_44_1 & in(5,
% 10.81/2.28  |           all_13_2) = all_44_0 & ( ~ (all_44_1 = all_44_2) | all_44_0 = 0)
% 10.81/2.28  | 
% 10.81/2.28  | ALPHA: (83) implies:
% 10.81/2.28  |   (84)  in(5, all_13_2) = all_44_0
% 10.81/2.28  |   (85)  count(all_13_2) = all_44_1
% 10.81/2.28  |   (86)  count(all_13_1) = all_44_2
% 10.81/2.28  | 
% 10.81/2.28  | GROUND_INST: instantiating (17) with all_40_2, all_42_2, empty, 3, simplifying
% 10.81/2.28  |              with (74), (79) gives:
% 10.81/2.29  |   (87)  all_42_2 = all_40_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_30_0, all_42_2, empty, 3, simplifying
% 10.81/2.29  |              with (56), (79) gives:
% 10.81/2.29  |   (88)  all_42_2 = all_30_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_26_2, all_28_2, all_13_3, 3,
% 10.81/2.29  |              simplifying with (47), (51) gives:
% 10.81/2.29  |   (89)  all_28_2 = all_26_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_24_0, all_28_2, all_13_3, 3,
% 10.81/2.29  |              simplifying with (43), (51) gives:
% 10.81/2.29  |   (90)  all_28_2 = all_24_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_22_0, all_28_2, all_13_3, 3,
% 10.81/2.29  |              simplifying with (39), (51) gives:
% 10.81/2.29  |   (91)  all_28_2 = all_22_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_38_2, all_44_0, all_13_2, 5,
% 10.81/2.29  |              simplifying with (69), (84) gives:
% 10.81/2.29  |   (92)  all_44_0 = all_38_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_34_2, all_44_0, all_13_2, 5,
% 10.81/2.29  |              simplifying with (63), (84) gives:
% 10.81/2.29  |   (93)  all_44_0 = all_34_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (17) with all_32_0, all_44_0, all_13_2, 5,
% 10.81/2.29  |              simplifying with (59), (84) gives:
% 10.81/2.29  |   (94)  all_44_0 = all_32_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_40_0, all_42_0, empty, simplifying
% 10.81/2.29  |              with (75), (80) gives:
% 10.81/2.29  |   (95)  all_42_0 = all_40_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (3) with all_42_0, simplifying with (80) gives:
% 10.81/2.29  |   (96)  all_42_0 = 0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_28_0, all_36_2, all_13_3, simplifying
% 10.81/2.29  |              with (52), (67) gives:
% 10.81/2.29  |   (97)  all_36_2 = all_28_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_26_0, all_40_1, all_13_3, simplifying
% 10.81/2.29  |              with (48), (76) gives:
% 10.81/2.29  |   (98)  all_40_1 = all_26_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_22_1, all_40_1, all_13_3, simplifying
% 10.81/2.29  |              with (40), (76) gives:
% 10.81/2.29  |   (99)  all_40_1 = all_22_1
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_36_2, all_42_1, all_13_3, simplifying
% 10.81/2.29  |              with (67), (81) gives:
% 10.81/2.29  |   (100)  all_42_1 = all_36_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_30_2, all_42_1, all_13_3, simplifying
% 10.81/2.29  |              with (57), (81) gives:
% 10.81/2.29  |   (101)  all_42_1 = all_30_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_26_0, all_42_1, all_13_3, simplifying
% 10.81/2.29  |              with (48), (81) gives:
% 10.81/2.29  |   (102)  all_42_1 = all_26_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_24_1, all_42_1, all_13_3, simplifying
% 10.81/2.29  |              with (44), (81) gives:
% 10.81/2.29  |   (103)  all_42_1 = all_24_1
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_28_1, all_32_1, all_13_2, simplifying
% 10.81/2.29  |              with (53), (60) gives:
% 10.81/2.29  |   (104)  all_32_1 = all_28_1
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_24_2, all_32_1, all_13_2, simplifying
% 10.81/2.29  |              with (45), (60) gives:
% 10.81/2.29  |   (105)  all_32_1 = all_24_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_34_0, all_38_0, all_13_2, simplifying
% 10.81/2.29  |              with (64), (70) gives:
% 10.81/2.29  |   (106)  all_38_0 = all_34_0
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_32_1, all_38_0, all_13_2, simplifying
% 10.81/2.29  |              with (60), (70) gives:
% 10.81/2.29  |   (107)  all_38_0 = all_32_1
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_22_2, all_38_0, all_13_2, simplifying
% 10.81/2.29  |              with (41), (70) gives:
% 10.81/2.29  |   (108)  all_38_0 = all_22_2
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_32_1, all_44_1, all_13_2, simplifying
% 10.81/2.29  |              with (60), (85) gives:
% 10.81/2.29  |   (109)  all_44_1 = all_32_1
% 10.81/2.29  | 
% 10.81/2.29  | GROUND_INST: instantiating (16) with all_26_1, all_44_1, all_13_2, simplifying
% 10.81/2.29  |              with (49), (85) gives:
% 10.81/2.29  |   (110)  all_44_1 = all_26_1
% 10.81/2.29  | 
% 10.81/2.30  | GROUND_INST: instantiating (16) with all_13_0, all_34_1, all_13_1, simplifying
% 10.81/2.30  |              with (22), (65) gives:
% 10.81/2.30  |   (111)  all_34_1 = all_13_0
% 10.81/2.30  | 
% 10.81/2.30  | GROUND_INST: instantiating (16) with all_34_1, all_38_1, all_13_1, simplifying
% 10.81/2.30  |              with (65), (71) gives:
% 10.81/2.30  |   (112)  all_38_1 = all_34_1
% 10.81/2.30  | 
% 10.81/2.30  | GROUND_INST: instantiating (16) with all_38_1, all_44_2, all_13_1, simplifying
% 10.81/2.30  |              with (71), (86) gives:
% 10.81/2.30  |   (113)  all_44_2 = all_38_1
% 10.81/2.30  | 
% 10.81/2.30  | GROUND_INST: instantiating (16) with all_32_2, all_44_2, all_13_1, simplifying
% 10.81/2.30  |              with (61), (86) gives:
% 10.81/2.30  |   (114)  all_44_2 = all_32_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (92), (94) imply:
% 10.81/2.30  |   (115)  all_38_2 = all_32_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (92), (93) imply:
% 10.81/2.30  |   (116)  all_38_2 = all_34_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (109), (110) imply:
% 10.81/2.30  |   (117)  all_32_1 = all_26_1
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (117) implies:
% 10.81/2.30  |   (118)  all_32_1 = all_26_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (113), (114) imply:
% 10.81/2.30  |   (119)  all_38_1 = all_32_2
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (119) implies:
% 10.81/2.30  |   (120)  all_38_1 = all_32_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (95), (96) imply:
% 10.81/2.30  |   (121)  all_40_0 = 0
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (121) implies:
% 10.81/2.30  |   (122)  all_40_0 = 0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (100), (101) imply:
% 10.81/2.30  |   (123)  all_36_2 = all_30_2
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (123) implies:
% 10.81/2.30  |   (124)  all_36_2 = all_30_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (101), (102) imply:
% 10.81/2.30  |   (125)  all_30_2 = all_26_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (101), (103) imply:
% 10.81/2.30  |   (126)  all_30_2 = all_24_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (87), (88) imply:
% 10.81/2.30  |   (127)  all_40_2 = all_30_0
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (127) implies:
% 10.81/2.30  |   (128)  all_40_2 = all_30_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (98), (99) imply:
% 10.81/2.30  |   (129)  all_26_0 = all_22_1
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (129) implies:
% 10.81/2.30  |   (130)  all_26_0 = all_22_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (106), (107) imply:
% 10.81/2.30  |   (131)  all_34_0 = all_32_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (106), (108) imply:
% 10.81/2.30  |   (132)  all_34_0 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (112), (120) imply:
% 10.81/2.30  |   (133)  all_34_1 = all_32_2
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (133) implies:
% 10.81/2.30  |   (134)  all_34_1 = all_32_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (115), (116) imply:
% 10.81/2.30  |   (135)  all_34_2 = all_32_0
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (135) implies:
% 10.81/2.30  |   (136)  all_34_2 = all_32_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (97), (124) imply:
% 10.81/2.30  |   (137)  all_30_2 = all_28_0
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (137) implies:
% 10.81/2.30  |   (138)  all_30_2 = all_28_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (131), (132) imply:
% 10.81/2.30  |   (139)  all_32_1 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (139) implies:
% 10.81/2.30  |   (140)  all_32_1 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (111), (134) imply:
% 10.81/2.30  |   (141)  all_32_2 = all_13_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (104), (118) imply:
% 10.81/2.30  |   (142)  all_28_1 = all_26_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (104), (140) imply:
% 10.81/2.30  |   (143)  all_28_1 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (104), (105) imply:
% 10.81/2.30  |   (144)  all_28_1 = all_24_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (126), (138) imply:
% 10.81/2.30  |   (145)  all_28_0 = all_24_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (125), (138) imply:
% 10.81/2.30  |   (146)  all_28_0 = all_26_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (145), (146) imply:
% 10.81/2.30  |   (147)  all_26_0 = all_24_1
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (147) implies:
% 10.81/2.30  |   (148)  all_26_0 = all_24_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (142), (143) imply:
% 10.81/2.30  |   (149)  all_26_1 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (142), (144) imply:
% 10.81/2.30  |   (150)  all_26_1 = all_24_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (89), (90) imply:
% 10.81/2.30  |   (151)  all_26_2 = all_24_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (89), (91) imply:
% 10.81/2.30  |   (152)  all_26_2 = all_22_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (130), (148) imply:
% 10.81/2.30  |   (153)  all_24_1 = all_22_1
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (153) implies:
% 10.81/2.30  |   (154)  all_24_1 = all_22_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (149), (150) imply:
% 10.81/2.30  |   (155)  all_24_2 = all_22_2
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (151), (152) imply:
% 10.81/2.30  |   (156)  all_24_0 = all_22_0
% 10.81/2.30  | 
% 10.81/2.30  | SIMP: (156) implies:
% 10.81/2.30  |   (157)  all_24_0 = all_22_0
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (145), (154) imply:
% 10.81/2.30  |   (158)  all_28_0 = all_22_1
% 10.81/2.30  | 
% 10.81/2.30  | COMBINE_EQS: (138), (158) imply:
% 10.81/2.30  |   (159)  all_30_2 = all_22_1
% 10.81/2.30  | 
% 10.81/2.31  | COMBINE_EQS: (120), (141) imply:
% 10.81/2.31  |   (160)  all_38_1 = all_13_0
% 10.81/2.31  | 
% 10.81/2.31  | COMBINE_EQS: (101), (159) imply:
% 10.81/2.31  |   (161)  all_42_1 = all_22_1
% 10.81/2.31  | 
% 10.81/2.31  | GROUND_INST: instantiating (5) with 3, empty, all_13_3, all_22_0, simplifying
% 10.81/2.31  |              with (14), (23), (39) gives:
% 10.81/2.31  |   (162)  all_22_0 = 0
% 10.81/2.31  | 
% 10.81/2.31  | GROUND_INST: instantiating (2) with all_13_2, all_22_2, simplifying with (21),
% 10.81/2.31  |              (41) gives:
% 10.81/2.31  |   (163)  $lesseq(0, all_22_2)
% 10.81/2.31  | 
% 10.81/2.31  | COMBINE_EQS: (91), (162) imply:
% 10.81/2.31  |   (164)  all_28_2 = 0
% 10.81/2.31  | 
% 10.81/2.31  | BETA: splitting (54) gives:
% 10.81/2.31  | 
% 10.81/2.31  | Case 1:
% 10.81/2.31  | | 
% 10.81/2.31  | |   (165)   ~ (all_28_2 = 0)
% 10.81/2.31  | | 
% 10.81/2.31  | | REDUCE: (164), (165) imply:
% 10.81/2.31  | |   (166)  $false
% 10.81/2.31  | | 
% 10.81/2.31  | | CLOSE: (166) is inconsistent.
% 10.81/2.31  | | 
% 10.81/2.31  | Case 2:
% 10.81/2.31  | | 
% 10.81/2.31  | |   (167)  $difference(all_28_0, all_28_1) = 1
% 10.81/2.31  | | 
% 10.81/2.31  | | COMBINE_EQS: (158), (167) imply:
% 10.81/2.31  | |   (168)  $difference(all_28_1, all_22_1) = -1
% 10.81/2.31  | | 
% 10.81/2.31  | | COMBINE_EQS: (143), (168) imply:
% 10.81/2.31  | |   (169)  $difference(all_22_1, all_22_2) = 1
% 10.81/2.31  | | 
% 10.81/2.31  | | SIMP: (169) implies:
% 10.81/2.31  | |   (170)  $difference(all_22_1, all_22_2) = 1
% 10.81/2.31  | | 
% 10.81/2.31  | | COMBINE_EQS: (99), (170) imply:
% 10.81/2.31  | |   (171)  $difference(all_40_1, all_22_2) = 1
% 10.81/2.31  | | 
% 10.81/2.31  | | COMBINE_EQS: (161), (170) imply:
% 10.81/2.31  | |   (172)  $difference(all_42_1, all_22_2) = 1
% 10.81/2.31  | | 
% 10.81/2.31  | | BETA: splitting (77) gives:
% 10.81/2.31  | | 
% 10.81/2.31  | | Case 1:
% 10.81/2.31  | | | 
% 10.81/2.31  | | |   (173)   ~ (all_40_2 = 0)
% 10.81/2.31  | | | 
% 10.81/2.31  | | | REDUCE: (128), (173) imply:
% 10.81/2.31  | | |   (174)   ~ (all_30_0 = 0)
% 10.81/2.31  | | | 
% 10.81/2.31  | | | BETA: splitting (82) gives:
% 10.81/2.31  | | | 
% 10.81/2.31  | | | Case 1:
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | |   (175)  all_42_2 = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | COMBINE_EQS: (88), (175) imply:
% 10.81/2.31  | | | |   (176)  all_30_0 = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | SIMP: (176) implies:
% 10.81/2.31  | | | |   (177)  all_30_0 = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | REDUCE: (174), (177) imply:
% 10.81/2.31  | | | |   (178)  $false
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | CLOSE: (178) is inconsistent.
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | Case 2:
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | |   (179)  $difference(all_42_0, all_42_1) = -1
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | COMBINE_EQS: (96), (179) imply:
% 10.81/2.31  | | | |   (180)  all_42_1 = 1
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | SIMP: (180) implies:
% 10.81/2.31  | | | |   (181)  all_42_1 = 1
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | COMBINE_EQS: (172), (181) imply:
% 10.81/2.31  | | | |   (182)  all_22_2 = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | COMBINE_EQS: (108), (182) imply:
% 10.81/2.31  | | | |   (183)  all_38_0 = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | REDUCE: (41), (182) imply:
% 10.81/2.31  | | | |   (184)  count(all_13_2) = 0
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | BETA: splitting (72) gives:
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | | Case 1:
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | |   (185)  all_38_2 = 0
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | COMBINE_EQS: (115), (185) imply:
% 10.81/2.31  | | | | |   (186)  all_32_0 = 0
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | SIMP: (186) implies:
% 10.81/2.31  | | | | |   (187)  all_32_0 = 0
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | REDUCE: (59), (187) imply:
% 10.81/2.31  | | | | |   (188)  in(5, all_13_2) = 0
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | GROUND_INST: instantiating (4) with all_13_2, simplifying with (21),
% 10.81/2.31  | | | | |              (184) gives:
% 10.81/2.31  | | | | |   (189)  all_13_2 = empty
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | REDUCE: (188), (189) imply:
% 10.81/2.31  | | | | |   (190)  in(5, empty) = 0
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | GROUND_INST: instantiating (1) with 5, simplifying with (190) gives:
% 10.81/2.31  | | | | |   (191)  $false
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | CLOSE: (191) is inconsistent.
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | Case 2:
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | |   (192)  $difference(all_38_0, all_38_1) = -1
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | COMBINE_EQS: (183), (192) imply:
% 10.81/2.31  | | | | |   (193)  all_38_1 = 1
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | COMBINE_EQS: (160), (193) imply:
% 10.81/2.31  | | | | |   (194)  all_13_0 = 1
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | REDUCE: (19), (194) imply:
% 10.81/2.31  | | | | |   (195)  $false
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | | CLOSE: (195) is inconsistent.
% 10.81/2.31  | | | | | 
% 10.81/2.31  | | | | End of split
% 10.81/2.31  | | | | 
% 10.81/2.31  | | | End of split
% 10.81/2.31  | | | 
% 10.81/2.31  | | Case 2:
% 10.81/2.31  | | | 
% 10.81/2.32  | | |   (196)  all_40_0 = all_40_1
% 10.81/2.32  | | | 
% 10.81/2.32  | | | COMBINE_EQS: (122), (196) imply:
% 10.81/2.32  | | |   (197)  all_40_1 = 0
% 10.81/2.32  | | | 
% 10.81/2.32  | | | COMBINE_EQS: (171), (197) imply:
% 10.81/2.32  | | |   (198)  all_22_2 = -1
% 10.81/2.32  | | | 
% 10.81/2.32  | | | REDUCE: (163), (198) imply:
% 10.81/2.32  | | |   (199)  $false
% 10.81/2.32  | | | 
% 10.81/2.32  | | | CLOSE: (199) is inconsistent.
% 10.81/2.32  | | | 
% 10.81/2.32  | | End of split
% 10.81/2.32  | | 
% 10.81/2.32  | End of split
% 10.81/2.32  | 
% 10.81/2.32  End of proof
% 10.81/2.32  % SZS output end Proof for theBenchmark
% 10.81/2.32  
% 10.81/2.32  1686ms
%------------------------------------------------------------------------------