TSTP Solution File: SET047+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 15:23:25 EDT 2023

% Result   : Theorem 4.21s 1.36s
% Output   : Proof 5.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.15  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36  % Computer : n014.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 : Sat Aug 26 13:17:17 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.21/0.64  ________       _____
% 0.21/0.64  ___  __ \_________(_)________________________________
% 0.21/0.64  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.64  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.64  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64  
% 0.21/0.64  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64  (2023-06-19)
% 0.21/0.64  
% 0.21/0.64  (c) Philipp Rümmer, 2009-2023
% 0.21/0.64  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64                Amanda Stjerna.
% 0.21/0.64  Free software under BSD-3-Clause.
% 0.21/0.64  
% 0.21/0.64  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64  
% 0.21/0.64  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65  Running up to 7 provers in parallel.
% 0.21/0.67  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.82/1.01  Prover 4: Preprocessing ...
% 1.82/1.01  Prover 1: Preprocessing ...
% 2.18/1.06  Prover 0: Preprocessing ...
% 2.18/1.06  Prover 2: Preprocessing ...
% 2.18/1.06  Prover 3: Preprocessing ...
% 2.27/1.06  Prover 6: Preprocessing ...
% 2.27/1.06  Prover 5: Preprocessing ...
% 2.70/1.15  Prover 5: Proving ...
% 2.70/1.15  Prover 2: Proving ...
% 2.97/1.16  Prover 6: Proving ...
% 2.97/1.16  Prover 3: Constructing countermodel ...
% 2.97/1.17  Prover 1: Constructing countermodel ...
% 2.97/1.19  Prover 0: Proving ...
% 2.97/1.20  Prover 4: Constructing countermodel ...
% 4.21/1.36  Prover 3: proved (695ms)
% 4.21/1.36  
% 4.21/1.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/1.36  
% 4.21/1.37  Prover 2: stopped
% 4.21/1.37  Prover 6: stopped
% 4.21/1.37  Prover 0: stopped
% 4.21/1.37  Prover 5: stopped
% 4.21/1.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.21/1.38  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.21/1.38  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.21/1.38  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.21/1.38  Prover 10: Preprocessing ...
% 4.21/1.38  Prover 7: Preprocessing ...
% 4.21/1.38  Prover 8: Preprocessing ...
% 4.21/1.38  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.21/1.38  Prover 11: Preprocessing ...
% 4.21/1.39  Prover 13: Preprocessing ...
% 4.21/1.41  Prover 10: Warning: ignoring some quantifiers
% 4.21/1.41  Prover 10: Constructing countermodel ...
% 4.21/1.41  Prover 13: Warning: ignoring some quantifiers
% 4.21/1.41  Prover 7: Warning: ignoring some quantifiers
% 4.21/1.41  Prover 13: Constructing countermodel ...
% 4.21/1.42  Prover 7: Constructing countermodel ...
% 4.21/1.43  Prover 13: gave up
% 4.21/1.43  Prover 10: gave up
% 4.21/1.45  Prover 8: Warning: ignoring some quantifiers
% 4.21/1.45  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.21/1.45  Prover 8: Constructing countermodel ...
% 4.21/1.45  Prover 16: Preprocessing ...
% 4.21/1.45  Prover 7: gave up
% 4.21/1.45  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.21/1.45  Prover 11: Constructing countermodel ...
% 4.21/1.45  Prover 19: Preprocessing ...
% 4.21/1.47  Prover 1: Found proof (size 63)
% 4.21/1.47  Prover 1: proved (811ms)
% 4.21/1.47  Prover 8: stopped
% 4.21/1.47  Prover 11: stopped
% 4.21/1.47  Prover 4: Found proof (size 69)
% 4.21/1.47  Prover 4: proved (806ms)
% 4.21/1.47  Prover 16: Warning: ignoring some quantifiers
% 4.21/1.47  Prover 16: Constructing countermodel ...
% 4.21/1.47  Prover 16: stopped
% 4.59/1.51  Prover 19: Warning: ignoring some quantifiers
% 4.59/1.51  Prover 19: Constructing countermodel ...
% 4.59/1.51  Prover 19: stopped
% 4.59/1.51  
% 4.59/1.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.59/1.51  
% 4.59/1.52  % SZS output start Proof for theBenchmark
% 4.59/1.52  Assumptions after simplification:
% 4.59/1.52  ---------------------------------
% 4.59/1.52  
% 4.59/1.52    (pel43)
% 5.41/1.55     ? [v0: $i] :  ? [v1: $i] :  ? [v2: any] :  ? [v3: any] : (set_equal(v1, v0) =
% 5.41/1.55      v3 & set_equal(v0, v1) = v2 & $i(v1) & $i(v0) & ((v3 = 0 &  ~ (v2 = 0)) |
% 5.41/1.55        (v2 = 0 &  ~ (v3 = 0))))
% 5.41/1.55  
% 5.41/1.55    (pel43_1)
% 5.41/1.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (set_equal(v0, v1) =
% 5.41/1.56        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] :  ? [v5: any] :
% 5.41/1.56      (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) |  ~
% 5.41/1.56          (v4 = 0)) & (v5 = 0 | v4 = 0))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 5.41/1.56      (set_equal(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v2: $i] :  ! [v3:
% 5.41/1.56          int] : (v3 = 0 |  ~ (element(v2, v0) = v3) |  ~ $i(v2) |  ? [v4: int] :
% 5.41/1.56          ( ~ (v4 = 0) & element(v2, v1) = v4)) &  ! [v2: $i] : ( ~ (element(v2,
% 5.41/1.56              v0) = 0) |  ~ $i(v2) | element(v2, v1) = 0)))
% 5.41/1.56  
% 5.41/1.56    (function-axioms)
% 5.41/1.56     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.41/1.56    [v3: $i] : (v1 = v0 |  ~ (set_equal(v3, v2) = v1) |  ~ (set_equal(v3, v2) =
% 5.41/1.56        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 5.41/1.56      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3,
% 5.41/1.56          v2) = v0))
% 5.41/1.56  
% 5.41/1.56  Those formulas are unsatisfiable:
% 5.41/1.56  ---------------------------------
% 5.41/1.56  
% 5.41/1.56  Begin of proof
% 5.41/1.56  | 
% 5.41/1.56  | ALPHA: (pel43_1) implies:
% 5.41/1.57  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (set_equal(v0, v1) = 0) |  ~ $i(v1) | 
% 5.41/1.57  |          ~ $i(v0) | ( ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (element(v2,
% 5.41/1.57  |                  v0) = v3) |  ~ $i(v2) |  ? [v4: int] : ( ~ (v4 = 0) &
% 5.41/1.57  |                element(v2, v1) = v4)) &  ! [v2: $i] : ( ~ (element(v2, v0) =
% 5.41/1.57  |                0) |  ~ $i(v2) | element(v2, v1) = 0)))
% 5.41/1.57  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (set_equal(v0,
% 5.41/1.57  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] : 
% 5.41/1.57  |          ? [v5: any] : (element(v3, v1) = v5 & element(v3, v0) = v4 & $i(v3) &
% 5.41/1.57  |            ( ~ (v5 = 0) |  ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 5.41/1.57  | 
% 5.41/1.57  | ALPHA: (function-axioms) implies:
% 5.41/1.57  |   (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.41/1.57  |         ! [v3: $i] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3,
% 5.41/1.57  |              v2) = v0))
% 5.41/1.57  | 
% 5.41/1.57  | DELTA: instantiating (pel43) with fresh symbols all_4_0, all_4_1, all_4_2,
% 5.41/1.57  |        all_4_3 gives:
% 5.41/1.57  |   (4)  set_equal(all_4_2, all_4_3) = all_4_0 & set_equal(all_4_3, all_4_2) =
% 5.41/1.57  |        all_4_1 & $i(all_4_2) & $i(all_4_3) & ((all_4_0 = 0 &  ~ (all_4_1 = 0))
% 5.41/1.57  |          | (all_4_1 = 0 &  ~ (all_4_0 = 0)))
% 5.41/1.57  | 
% 5.41/1.57  | ALPHA: (4) implies:
% 5.41/1.57  |   (5)  $i(all_4_3)
% 5.41/1.58  |   (6)  $i(all_4_2)
% 5.41/1.58  |   (7)  set_equal(all_4_3, all_4_2) = all_4_1
% 5.41/1.58  |   (8)  set_equal(all_4_2, all_4_3) = all_4_0
% 5.41/1.58  |   (9)  (all_4_0 = 0 &  ~ (all_4_1 = 0)) | (all_4_1 = 0 &  ~ (all_4_0 = 0))
% 5.41/1.58  | 
% 5.41/1.58  | GROUND_INST: instantiating (2) with all_4_3, all_4_2, all_4_1, simplifying
% 5.41/1.58  |              with (5), (6), (7) gives:
% 5.41/1.58  |   (10)  all_4_1 = 0 |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (element(v0,
% 5.41/1.58  |             all_4_2) = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0)
% 5.41/1.58  |             |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.41/1.58  | 
% 5.41/1.58  | GROUND_INST: instantiating (2) with all_4_2, all_4_3, all_4_0, simplifying
% 5.41/1.58  |              with (5), (6), (8) gives:
% 5.41/1.58  |   (11)  all_4_0 = 0 |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (element(v0,
% 5.41/1.58  |             all_4_2) = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0)
% 5.41/1.58  |             |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.41/1.58  | 
% 5.41/1.58  | BETA: splitting (9) gives:
% 5.41/1.58  | 
% 5.41/1.58  | Case 1:
% 5.41/1.58  | | 
% 5.41/1.58  | |   (12)  all_4_0 = 0 &  ~ (all_4_1 = 0)
% 5.41/1.58  | | 
% 5.41/1.58  | | ALPHA: (12) implies:
% 5.58/1.58  | |   (13)  all_4_0 = 0
% 5.58/1.58  | |   (14)   ~ (all_4_1 = 0)
% 5.58/1.58  | | 
% 5.58/1.58  | | REDUCE: (8), (13) imply:
% 5.58/1.58  | |   (15)  set_equal(all_4_2, all_4_3) = 0
% 5.58/1.58  | | 
% 5.58/1.58  | | BETA: splitting (10) gives:
% 5.58/1.58  | | 
% 5.58/1.58  | | Case 1:
% 5.58/1.58  | | | 
% 5.58/1.58  | | |   (16)  all_4_1 = 0
% 5.58/1.58  | | | 
% 5.58/1.58  | | | REDUCE: (14), (16) imply:
% 5.58/1.58  | | |   (17)  $false
% 5.58/1.59  | | | 
% 5.58/1.59  | | | CLOSE: (17) is inconsistent.
% 5.58/1.59  | | | 
% 5.58/1.59  | | Case 2:
% 5.58/1.59  | | | 
% 5.58/1.59  | | |   (18)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (element(v0, all_4_2)
% 5.58/1.59  | | |           = v2 & element(v0, all_4_3) = v1 & $i(v0) & ( ~ (v2 = 0) |  ~
% 5.58/1.59  | | |             (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.58/1.59  | | | 
% 5.58/1.59  | | | DELTA: instantiating (18) with fresh symbols all_17_0, all_17_1, all_17_2
% 5.58/1.59  | | |        gives:
% 5.58/1.59  | | |   (19)  element(all_17_2, all_4_2) = all_17_0 & element(all_17_2, all_4_3)
% 5.58/1.59  | | |         = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) |  ~ (all_17_1 =
% 5.58/1.59  | | |             0)) & (all_17_0 = 0 | all_17_1 = 0)
% 5.58/1.59  | | | 
% 5.58/1.59  | | | ALPHA: (19) implies:
% 5.58/1.59  | | |   (20)  $i(all_17_2)
% 5.58/1.59  | | |   (21)  element(all_17_2, all_4_3) = all_17_1
% 5.58/1.59  | | |   (22)  element(all_17_2, all_4_2) = all_17_0
% 5.58/1.59  | | |   (23)  all_17_0 = 0 | all_17_1 = 0
% 5.58/1.59  | | |   (24)   ~ (all_17_0 = 0) |  ~ (all_17_1 = 0)
% 5.58/1.59  | | | 
% 5.58/1.59  | | | GROUND_INST: instantiating (1) with all_4_2, all_4_3, simplifying with
% 5.58/1.59  | | |              (5), (6), (15) gives:
% 5.58/1.59  | | |   (25)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (element(v0, all_4_2) =
% 5.58/1.59  | | |             v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.59  | | |               all_4_3) = v2)) &  ! [v0: $i] : ( ~ (element(v0, all_4_2) =
% 5.58/1.59  | | |             0) |  ~ $i(v0) | element(v0, all_4_3) = 0)
% 5.58/1.59  | | | 
% 5.58/1.59  | | | ALPHA: (25) implies:
% 5.58/1.59  | | |   (26)   ! [v0: $i] : ( ~ (element(v0, all_4_2) = 0) |  ~ $i(v0) |
% 5.58/1.59  | | |           element(v0, all_4_3) = 0)
% 5.58/1.59  | | |   (27)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (element(v0, all_4_2) =
% 5.58/1.59  | | |             v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.59  | | |               all_4_3) = v2))
% 5.58/1.59  | | | 
% 5.58/1.59  | | | GROUND_INST: instantiating (27) with all_17_2, all_17_0, simplifying with
% 5.58/1.59  | | |              (20), (22) gives:
% 5.58/1.59  | | |   (28)  all_17_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2,
% 5.58/1.59  | | |             all_4_3) = v0)
% 5.58/1.59  | | | 
% 5.58/1.59  | | | BETA: splitting (23) gives:
% 5.58/1.59  | | | 
% 5.58/1.59  | | | Case 1:
% 5.58/1.59  | | | | 
% 5.58/1.59  | | | |   (29)  all_17_0 = 0
% 5.58/1.59  | | | | 
% 5.58/1.59  | | | | REDUCE: (22), (29) imply:
% 5.58/1.60  | | | |   (30)  element(all_17_2, all_4_2) = 0
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | | BETA: splitting (24) gives:
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | | Case 1:
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | |   (31)   ~ (all_17_0 = 0)
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | REDUCE: (29), (31) imply:
% 5.58/1.60  | | | | |   (32)  $false
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | CLOSE: (32) is inconsistent.
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | Case 2:
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | |   (33)   ~ (all_17_1 = 0)
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | GROUND_INST: instantiating (26) with all_17_2, simplifying with (20),
% 5.58/1.60  | | | | |              (30) gives:
% 5.58/1.60  | | | | |   (34)  element(all_17_2, all_4_3) = 0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_3, all_17_2,
% 5.58/1.60  | | | | |              simplifying with (21), (34) gives:
% 5.58/1.60  | | | | |   (35)  all_17_1 = 0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | REDUCE: (33), (35) imply:
% 5.58/1.60  | | | | |   (36)  $false
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | CLOSE: (36) is inconsistent.
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | End of split
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | Case 2:
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | |   (37)  all_17_1 = 0
% 5.58/1.60  | | | |   (38)   ~ (all_17_0 = 0)
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | | REDUCE: (21), (37) imply:
% 5.58/1.60  | | | |   (39)  element(all_17_2, all_4_3) = 0
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | | BETA: splitting (28) gives:
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | | Case 1:
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | |   (40)  all_17_0 = 0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | REDUCE: (38), (40) imply:
% 5.58/1.60  | | | | |   (41)  $false
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | CLOSE: (41) is inconsistent.
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | Case 2:
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | |   (42)   ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_3) = v0)
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | DELTA: instantiating (42) with fresh symbol all_33_0 gives:
% 5.58/1.60  | | | | |   (43)   ~ (all_33_0 = 0) & element(all_17_2, all_4_3) = all_33_0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | ALPHA: (43) implies:
% 5.58/1.60  | | | | |   (44)   ~ (all_33_0 = 0)
% 5.58/1.60  | | | | |   (45)  element(all_17_2, all_4_3) = all_33_0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_3, all_17_2,
% 5.58/1.60  | | | | |              simplifying with (39), (45) gives:
% 5.58/1.60  | | | | |   (46)  all_33_0 = 0
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | REDUCE: (44), (46) imply:
% 5.58/1.60  | | | | |   (47)  $false
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | | CLOSE: (47) is inconsistent.
% 5.58/1.60  | | | | | 
% 5.58/1.60  | | | | End of split
% 5.58/1.60  | | | | 
% 5.58/1.60  | | | End of split
% 5.58/1.60  | | | 
% 5.58/1.60  | | End of split
% 5.58/1.60  | | 
% 5.58/1.60  | Case 2:
% 5.58/1.60  | | 
% 5.58/1.60  | |   (48)  all_4_1 = 0 &  ~ (all_4_0 = 0)
% 5.58/1.60  | | 
% 5.58/1.60  | | ALPHA: (48) implies:
% 5.58/1.60  | |   (49)  all_4_1 = 0
% 5.58/1.60  | |   (50)   ~ (all_4_0 = 0)
% 5.58/1.60  | | 
% 5.58/1.60  | | REDUCE: (7), (49) imply:
% 5.58/1.60  | |   (51)  set_equal(all_4_3, all_4_2) = 0
% 5.58/1.60  | | 
% 5.58/1.60  | | BETA: splitting (11) gives:
% 5.58/1.60  | | 
% 5.58/1.60  | | Case 1:
% 5.58/1.60  | | | 
% 5.58/1.60  | | |   (52)  all_4_0 = 0
% 5.58/1.60  | | | 
% 5.58/1.60  | | | REDUCE: (50), (52) imply:
% 5.58/1.60  | | |   (53)  $false
% 5.58/1.60  | | | 
% 5.58/1.60  | | | CLOSE: (53) is inconsistent.
% 5.58/1.60  | | | 
% 5.58/1.60  | | Case 2:
% 5.58/1.60  | | | 
% 5.58/1.60  | | |   (54)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (element(v0, all_4_2)
% 5.58/1.60  | | |           = v1 & element(v0, all_4_3) = v2 & $i(v0) & ( ~ (v2 = 0) |  ~
% 5.58/1.60  | | |             (v1 = 0)) & (v2 = 0 | v1 = 0))
% 5.58/1.60  | | | 
% 5.58/1.60  | | | DELTA: instantiating (54) with fresh symbols all_17_0, all_17_1, all_17_2
% 5.58/1.60  | | |        gives:
% 5.58/1.61  | | |   (55)  element(all_17_2, all_4_2) = all_17_1 & element(all_17_2, all_4_3)
% 5.58/1.61  | | |         = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) |  ~ (all_17_1 =
% 5.58/1.61  | | |             0)) & (all_17_0 = 0 | all_17_1 = 0)
% 5.58/1.61  | | | 
% 5.58/1.61  | | | ALPHA: (55) implies:
% 5.58/1.61  | | |   (56)  $i(all_17_2)
% 5.58/1.61  | | |   (57)  element(all_17_2, all_4_3) = all_17_0
% 5.58/1.61  | | |   (58)  element(all_17_2, all_4_2) = all_17_1
% 5.58/1.61  | | |   (59)  all_17_0 = 0 | all_17_1 = 0
% 5.58/1.61  | | |   (60)   ~ (all_17_0 = 0) |  ~ (all_17_1 = 0)
% 5.58/1.61  | | | 
% 5.58/1.61  | | | GROUND_INST: instantiating (1) with all_4_3, all_4_2, simplifying with
% 5.58/1.61  | | |              (5), (6), (51) gives:
% 5.58/1.61  | | |   (61)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (element(v0, all_4_3) =
% 5.58/1.61  | | |             v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.61  | | |               all_4_2) = v2)) &  ! [v0: $i] : ( ~ (element(v0, all_4_3) =
% 5.58/1.61  | | |             0) |  ~ $i(v0) | element(v0, all_4_2) = 0)
% 5.58/1.61  | | | 
% 5.58/1.61  | | | ALPHA: (61) implies:
% 5.58/1.61  | | |   (62)   ! [v0: $i] : ( ~ (element(v0, all_4_3) = 0) |  ~ $i(v0) |
% 5.58/1.61  | | |           element(v0, all_4_2) = 0)
% 5.58/1.61  | | |   (63)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (element(v0, all_4_3) =
% 5.58/1.61  | | |             v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & element(v0,
% 5.58/1.61  | | |               all_4_2) = v2))
% 5.58/1.61  | | | 
% 5.58/1.61  | | | GROUND_INST: instantiating (63) with all_17_2, all_17_0, simplifying with
% 5.58/1.61  | | |              (56), (57) gives:
% 5.58/1.61  | | |   (64)  all_17_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2,
% 5.58/1.61  | | |             all_4_2) = v0)
% 5.58/1.61  | | | 
% 5.58/1.61  | | | BETA: splitting (59) gives:
% 5.58/1.61  | | | 
% 5.58/1.61  | | | Case 1:
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | |   (65)  all_17_0 = 0
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | REDUCE: (57), (65) imply:
% 5.58/1.61  | | | |   (66)  element(all_17_2, all_4_3) = 0
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | BETA: splitting (60) gives:
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | Case 1:
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | |   (67)   ~ (all_17_0 = 0)
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | REDUCE: (65), (67) imply:
% 5.58/1.61  | | | | |   (68)  $false
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | CLOSE: (68) is inconsistent.
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | Case 2:
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | |   (69)   ~ (all_17_1 = 0)
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | GROUND_INST: instantiating (62) with all_17_2, simplifying with (56),
% 5.58/1.61  | | | | |              (66) gives:
% 5.58/1.61  | | | | |   (70)  element(all_17_2, all_4_2) = 0
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | GROUND_INST: instantiating (3) with all_17_1, 0, all_4_2, all_17_2,
% 5.58/1.61  | | | | |              simplifying with (58), (70) gives:
% 5.58/1.61  | | | | |   (71)  all_17_1 = 0
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | REDUCE: (69), (71) imply:
% 5.58/1.61  | | | | |   (72)  $false
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | CLOSE: (72) is inconsistent.
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | End of split
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | Case 2:
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | |   (73)  all_17_1 = 0
% 5.58/1.61  | | | |   (74)   ~ (all_17_0 = 0)
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | REDUCE: (58), (73) imply:
% 5.58/1.61  | | | |   (75)  element(all_17_2, all_4_2) = 0
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | BETA: splitting (64) gives:
% 5.58/1.61  | | | | 
% 5.58/1.61  | | | | Case 1:
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | |   (76)  all_17_0 = 0
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | REDUCE: (74), (76) imply:
% 5.58/1.61  | | | | |   (77)  $false
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | CLOSE: (77) is inconsistent.
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | Case 2:
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | |   (78)   ? [v0: int] : ( ~ (v0 = 0) & element(all_17_2, all_4_2) = v0)
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | DELTA: instantiating (78) with fresh symbol all_33_0 gives:
% 5.58/1.61  | | | | |   (79)   ~ (all_33_0 = 0) & element(all_17_2, all_4_2) = all_33_0
% 5.58/1.61  | | | | | 
% 5.58/1.61  | | | | | ALPHA: (79) implies:
% 5.58/1.61  | | | | |   (80)   ~ (all_33_0 = 0)
% 5.58/1.62  | | | | |   (81)  element(all_17_2, all_4_2) = all_33_0
% 5.58/1.62  | | | | | 
% 5.58/1.62  | | | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_4_2, all_17_2,
% 5.58/1.62  | | | | |              simplifying with (75), (81) gives:
% 5.58/1.62  | | | | |   (82)  all_33_0 = 0
% 5.58/1.62  | | | | | 
% 5.58/1.62  | | | | | REDUCE: (80), (82) imply:
% 5.58/1.62  | | | | |   (83)  $false
% 5.58/1.62  | | | | | 
% 5.58/1.62  | | | | | CLOSE: (83) is inconsistent.
% 5.58/1.62  | | | | | 
% 5.58/1.62  | | | | End of split
% 5.58/1.62  | | | | 
% 5.58/1.62  | | | End of split
% 5.58/1.62  | | | 
% 5.58/1.62  | | End of split
% 5.58/1.62  | | 
% 5.58/1.62  | End of split
% 5.58/1.62  | 
% 5.58/1.62  End of proof
% 5.58/1.62  % SZS output end Proof for theBenchmark
% 5.58/1.62  
% 5.58/1.62  979ms
%------------------------------------------------------------------------------