TSTP Solution File: SYN950+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN950+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n003.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 : Fri Sep  1 03:29:20 EDT 2023

% Result   : Theorem 3.19s 1.17s
% Output   : Proof 4.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SYN950+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sat Aug 26 21:41:24 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.59  ________       _____
% 0.19/0.59  ___  __ \_________(_)________________________________
% 0.19/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59  (2023-06-19)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2023
% 0.19/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59                Amanda Stjerna.
% 0.19/0.59  Free software under BSD-3-Clause.
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60  Running up to 7 provers in parallel.
% 0.19/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.69/0.95  Prover 1: Preprocessing ...
% 1.69/0.95  Prover 4: Preprocessing ...
% 2.06/0.99  Prover 0: Preprocessing ...
% 2.06/1.00  Prover 2: Preprocessing ...
% 2.06/1.00  Prover 5: Preprocessing ...
% 2.06/1.00  Prover 6: Preprocessing ...
% 2.06/1.00  Prover 3: Preprocessing ...
% 2.59/1.07  Prover 1: Constructing countermodel ...
% 2.59/1.07  Prover 3: Constructing countermodel ...
% 2.59/1.07  Prover 2: Proving ...
% 2.59/1.07  Prover 6: Proving ...
% 2.59/1.07  Prover 5: Proving ...
% 2.78/1.09  Prover 4: Constructing countermodel ...
% 2.78/1.10  Prover 0: Proving ...
% 3.19/1.14  Prover 3: gave up
% 3.19/1.14  Prover 1: gave up
% 3.19/1.16  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.19/1.16  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.19/1.17  Prover 7: Preprocessing ...
% 3.19/1.17  Prover 8: Preprocessing ...
% 3.19/1.17  Prover 0: proved (559ms)
% 3.19/1.17  
% 3.19/1.17  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.19/1.17  
% 3.19/1.18  Prover 6: stopped
% 3.19/1.19  Prover 2: stopped
% 3.19/1.19  Prover 7: Warning: ignoring some quantifiers
% 3.19/1.19  Prover 7: Constructing countermodel ...
% 3.19/1.19  Prover 5: stopped
% 3.19/1.19  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.19/1.19  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.19/1.19  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.19/1.19  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.19/1.20  Prover 8: Warning: ignoring some quantifiers
% 3.19/1.20  Prover 8: Constructing countermodel ...
% 3.19/1.20  Prover 13: Preprocessing ...
% 3.19/1.21  Prover 16: Preprocessing ...
% 3.19/1.21  Prover 10: Preprocessing ...
% 3.19/1.21  Prover 11: Preprocessing ...
% 3.70/1.22  Prover 10: Warning: ignoring some quantifiers
% 3.70/1.22  Prover 10: Constructing countermodel ...
% 3.70/1.23  Prover 16: Warning: ignoring some quantifiers
% 3.70/1.23  Prover 16: Constructing countermodel ...
% 3.70/1.23  Prover 13: Warning: ignoring some quantifiers
% 3.70/1.24  Prover 13: Constructing countermodel ...
% 3.70/1.24  Prover 10: gave up
% 3.70/1.25  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 3.70/1.25  Prover 8: gave up
% 3.70/1.25  Prover 19: Preprocessing ...
% 3.70/1.26  Prover 7: gave up
% 4.12/1.28  Prover 11: Constructing countermodel ...
% 4.12/1.28  Prover 16: gave up
% 4.12/1.29  Prover 13: gave up
% 4.12/1.29  Prover 19: Warning: ignoring some quantifiers
% 4.12/1.30  Prover 19: Constructing countermodel ...
% 4.12/1.33  Prover 4: Found proof (size 52)
% 4.12/1.33  Prover 4: proved (708ms)
% 4.12/1.33  Prover 19: stopped
% 4.12/1.33  Prover 11: stopped
% 4.12/1.33  
% 4.12/1.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.12/1.33  
% 4.12/1.34  % SZS output start Proof for theBenchmark
% 4.12/1.34  Assumptions after simplification:
% 4.12/1.34  ---------------------------------
% 4.12/1.34  
% 4.12/1.34    (prove_this)
% 4.12/1.40     ? [v0: $i] :  ? [v1: $i] :  ? [v2: any] :  ? [v3: any] : (p(v1) = v3 & p(v0)
% 4.12/1.40      = v2 & $i(v1) & $i(v0) &  ! [v4: $i] :  ! [v5: MultipleValueBool] : ( ~ (v3
% 4.12/1.40          = 0) |  ~ (v2 = 0) |  ~ (p(v4) = v5) |  ~ $i(v4)) &  ! [v4: $i] :  !
% 4.12/1.40      [v5: MultipleValueBool] : ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (q(v4) = v5) |  ~
% 4.12/1.40        $i(v4)) &  ! [v4: $i] :  ! [v5: int] : ( ~ (v3 = 0) | v5 = 0 |  ~ (p(v4) =
% 4.12/1.40          v5) |  ~ $i(v4)) &  ! [v4: $i] :  ! [v5: MultipleValueBool] : ( ~ (v3 =
% 4.12/1.40          0) |  ~ (q(v4) = v5) |  ~ $i(v4) | p(v4) = 0) &  ! [v4: $i] :  ! [v5:
% 4.12/1.40        int] : ( ~ (v2 = 0) | v5 = 0 |  ~ (q(v4) = v5) |  ~ $i(v4)) &  ! [v4: $i]
% 4.12/1.40      :  ! [v5: MultipleValueBool] : ( ~ (v2 = 0) |  ~ (p(v4) = v5) |  ~ $i(v4) |
% 4.12/1.40        q(v4) = 0) &  ! [v4: $i] :  ! [v5: int] : (v5 = 0 |  ~ (p(v4) = v5) |  ~
% 4.12/1.40        $i(v4) | q(v4) = 0) &  ! [v4: $i] :  ! [v5: int] : (v5 = 0 |  ~ (p(v4) =
% 4.12/1.40          v5) |  ~ $i(v4) |  ? [v6: int] : ( ~ (v6 = 0) & q(v4) = v6)) &  ! [v4:
% 4.12/1.40        $i] :  ! [v5: int] : (v5 = 0 |  ~ (q(v4) = v5) |  ~ $i(v4) | p(v4) = 0) & 
% 4.12/1.40      ! [v4: $i] : ( ~ (q(v4) = 0) |  ~ $i(v4) | p(v4) = 0))
% 4.12/1.40  
% 4.12/1.40    (function-axioms)
% 4.12/1.40     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 =
% 4.12/1.40      v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 4.12/1.40    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2)
% 4.12/1.40        = v0))
% 4.12/1.40  
% 4.12/1.40  Those formulas are unsatisfiable:
% 4.12/1.40  ---------------------------------
% 4.12/1.40  
% 4.12/1.40  Begin of proof
% 4.12/1.40  | 
% 4.12/1.40  | ALPHA: (function-axioms) implies:
% 4.12/1.40  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.12/1.40  |        (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0))
% 4.12/1.40  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.12/1.40  |        (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 4.12/1.40  | 
% 4.12/1.41  | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.12/1.41  |        all_3_2, all_3_3 gives:
% 4.12/1.41  |   (3)  p(all_3_2) = all_3_0 & p(all_3_3) = all_3_1 & $i(all_3_2) & $i(all_3_3)
% 4.12/1.41  |        &  ! [v0: $i] :  ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) |  ~
% 4.12/1.41  |          (all_3_1 = 0) |  ~ (p(v0) = v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1:
% 4.12/1.41  |          MultipleValueBool] : ( ~ (all_3_0 = 0) |  ~ (all_3_1 = 0) |  ~ (q(v0)
% 4.12/1.41  |            = v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1: int] : ( ~ (all_3_0 = 0)
% 4.12/1.41  |          | v1 = 0 |  ~ (p(v0) = v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1:
% 4.12/1.41  |          MultipleValueBool] : ( ~ (all_3_0 = 0) |  ~ (q(v0) = v1) |  ~ $i(v0)
% 4.12/1.41  |          | p(v0) = 0) &  ! [v0: $i] :  ! [v1: int] : ( ~ (all_3_1 = 0) | v1 =
% 4.12/1.41  |          0 |  ~ (q(v0) = v1) |  ~ $i(v0)) &  ! [v0: $i] :  ! [v1:
% 4.12/1.41  |          MultipleValueBool] : ( ~ (all_3_1 = 0) |  ~ (p(v0) = v1) |  ~ $i(v0)
% 4.12/1.41  |          | q(v0) = 0) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (p(v0) = v1)
% 4.12/1.41  |          |  ~ $i(v0) | q(v0) = 0) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 4.12/1.41  |          (p(v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & q(v0) = v2))
% 4.12/1.41  |        &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (q(v0) = v1) |  ~ $i(v0) |
% 4.12/1.41  |          p(v0) = 0) &  ! [v0: $i] : ( ~ (q(v0) = 0) |  ~ $i(v0) | p(v0) = 0)
% 4.12/1.41  | 
% 4.12/1.41  | ALPHA: (3) implies:
% 4.12/1.41  |   (4)  $i(all_3_3)
% 4.12/1.42  |   (5)  $i(all_3_2)
% 4.12/1.42  |   (6)  p(all_3_3) = all_3_1
% 4.12/1.42  |   (7)  p(all_3_2) = all_3_0
% 4.12/1.42  |   (8)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (p(v0) = v1) |  ~ $i(v0) |  ?
% 4.12/1.42  |          [v2: int] : ( ~ (v2 = 0) & q(v0) = v2))
% 4.12/1.42  |   (9)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (p(v0) = v1) |  ~ $i(v0) |
% 4.12/1.42  |          q(v0) = 0)
% 4.12/1.42  |   (10)   ! [v0: $i] :  ! [v1: MultipleValueBool] : ( ~ (all_3_1 = 0) |  ~
% 4.12/1.42  |           (p(v0) = v1) |  ~ $i(v0) | q(v0) = 0)
% 4.12/1.42  |   (11)   ! [v0: $i] :  ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 |  ~ (p(v0) =
% 4.12/1.42  |             v1) |  ~ $i(v0))
% 4.12/1.42  |   (12)   ! [v0: $i] :  ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) |  ~
% 4.12/1.42  |           (all_3_1 = 0) |  ~ (p(v0) = v1) |  ~ $i(v0))
% 4.12/1.42  | 
% 4.12/1.42  | GROUND_INST: instantiating (11) with all_3_3, all_3_1, simplifying with (4),
% 4.12/1.42  |              (6) gives:
% 4.12/1.42  |   (13)   ~ (all_3_0 = 0) | all_3_1 = 0
% 4.12/1.42  | 
% 4.12/1.42  | GROUND_INST: instantiating (12) with all_3_2, 0, simplifying with (5) gives:
% 4.12/1.42  |   (14)   ~ (all_3_0 = 0) |  ~ (all_3_1 = 0) |  ~ (p(all_3_2) = 0)
% 4.12/1.42  | 
% 4.12/1.42  | GROUND_INST: instantiating (10) with all_3_2, all_3_0, simplifying with (5),
% 4.12/1.42  |              (7) gives:
% 4.12/1.42  |   (15)   ~ (all_3_1 = 0) | q(all_3_2) = 0
% 4.12/1.42  | 
% 4.12/1.42  | GROUND_INST: instantiating (9) with all_3_2, all_3_0, simplifying with (5),
% 4.12/1.42  |              (7) gives:
% 4.12/1.42  |   (16)  all_3_0 = 0 | q(all_3_2) = 0
% 4.12/1.42  | 
% 4.12/1.42  | GROUND_INST: instantiating (8) with all_3_2, all_3_0, simplifying with (5),
% 4.12/1.42  |              (7) gives:
% 4.12/1.42  |   (17)  all_3_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.12/1.42  | 
% 4.12/1.42  | BETA: splitting (16) gives:
% 4.12/1.42  | 
% 4.12/1.42  | Case 1:
% 4.12/1.42  | | 
% 4.12/1.42  | |   (18)  q(all_3_2) = 0
% 4.12/1.42  | | 
% 4.12/1.42  | | BETA: splitting (17) gives:
% 4.12/1.42  | | 
% 4.12/1.42  | | Case 1:
% 4.12/1.42  | | | 
% 4.12/1.42  | | |   (19)  all_3_0 = 0
% 4.12/1.42  | | | 
% 4.12/1.42  | | | REDUCE: (7), (19) imply:
% 4.12/1.42  | | |   (20)  p(all_3_2) = 0
% 4.12/1.42  | | | 
% 4.12/1.42  | | | BETA: splitting (13) gives:
% 4.12/1.42  | | | 
% 4.12/1.42  | | | Case 1:
% 4.12/1.42  | | | | 
% 4.12/1.43  | | | |   (21)   ~ (all_3_0 = 0)
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | REF_CLOSE: (2), (7), (20), (21) are inconsistent by sub-proof #2.
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | Case 2:
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | |   (22)  all_3_1 = 0
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | BETA: splitting (14) gives:
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | Case 1:
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | |   (23)   ~ (p(all_3_2) = 0)
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | | BETA: splitting (17) gives:
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | | Case 1:
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | PRED_UNIFY: (20), (23) imply:
% 4.12/1.43  | | | | | |   (24)  $false
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | CLOSE: (24) is inconsistent.
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | Case 2:
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | |   (25)   ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | DELTA: instantiating (25) with fresh symbol all_37_0 gives:
% 4.12/1.43  | | | | | |   (26)   ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | REF_CLOSE: (1), (18), (26) are inconsistent by sub-proof #1.
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | End of split
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | Case 2:
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | |   (27)   ~ (all_3_0 = 0) |  ~ (all_3_1 = 0)
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | | BETA: splitting (27) gives:
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | | Case 1:
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | |   (28)   ~ (all_3_0 = 0)
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | REF_CLOSE: (2), (7), (20), (28) are inconsistent by sub-proof #2.
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | Case 2:
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | |   (29)   ~ (all_3_1 = 0)
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | REDUCE: (22), (29) imply:
% 4.12/1.43  | | | | | |   (30)  $false
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | | CLOSE: (30) is inconsistent.
% 4.12/1.43  | | | | | | 
% 4.12/1.43  | | | | | End of split
% 4.12/1.43  | | | | | 
% 4.12/1.43  | | | | End of split
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | End of split
% 4.12/1.43  | | | 
% 4.12/1.43  | | Case 2:
% 4.12/1.43  | | | 
% 4.12/1.43  | | |   (31)   ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0)
% 4.12/1.43  | | | 
% 4.12/1.43  | | | DELTA: instantiating (31) with fresh symbol all_37_0 gives:
% 4.12/1.43  | | |   (32)   ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.12/1.43  | | | 
% 4.12/1.43  | | | REF_CLOSE: (1), (18), (32) are inconsistent by sub-proof #1.
% 4.12/1.43  | | | 
% 4.12/1.43  | | End of split
% 4.12/1.43  | | 
% 4.12/1.43  | Case 2:
% 4.12/1.43  | | 
% 4.12/1.43  | |   (33)  all_3_0 = 0
% 4.12/1.43  | |   (34)   ~ (q(all_3_2) = 0)
% 4.12/1.43  | | 
% 4.12/1.43  | | REDUCE: (7), (33) imply:
% 4.12/1.43  | |   (35)  p(all_3_2) = 0
% 4.12/1.43  | | 
% 4.12/1.43  | | BETA: splitting (15) gives:
% 4.12/1.43  | | 
% 4.12/1.43  | | Case 1:
% 4.12/1.43  | | | 
% 4.12/1.43  | | |   (36)  q(all_3_2) = 0
% 4.12/1.43  | | | 
% 4.12/1.43  | | | PRED_UNIFY: (34), (36) imply:
% 4.12/1.43  | | |   (37)  $false
% 4.12/1.43  | | | 
% 4.12/1.43  | | | CLOSE: (37) is inconsistent.
% 4.12/1.43  | | | 
% 4.12/1.43  | | Case 2:
% 4.12/1.43  | | | 
% 4.12/1.43  | | |   (38)   ~ (all_3_1 = 0)
% 4.12/1.43  | | | 
% 4.12/1.43  | | | BETA: splitting (13) gives:
% 4.12/1.43  | | | 
% 4.12/1.43  | | | Case 1:
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | |   (39)   ~ (all_3_0 = 0)
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | REF_CLOSE: (2), (7), (35), (39) are inconsistent by sub-proof #2.
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | Case 2:
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | |   (40)  all_3_1 = 0
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | REDUCE: (38), (40) imply:
% 4.12/1.43  | | | |   (41)  $false
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | | CLOSE: (41) is inconsistent.
% 4.12/1.43  | | | | 
% 4.12/1.43  | | | End of split
% 4.12/1.43  | | | 
% 4.12/1.43  | | End of split
% 4.12/1.43  | | 
% 4.12/1.43  | End of split
% 4.12/1.43  | 
% 4.12/1.43  End of proof
% 4.12/1.43  
% 4.12/1.43  Sub-proof #1 shows that the following formulas are inconsistent:
% 4.12/1.43  ----------------------------------------------------------------
% 4.12/1.44    (1)   ~ (all_37_0 = 0) & q(all_3_2) = all_37_0
% 4.12/1.44    (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.12/1.44         (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0))
% 4.12/1.44    (3)  q(all_3_2) = 0
% 4.12/1.44  
% 4.12/1.44  Begin of proof
% 4.12/1.44  | 
% 4.12/1.44  | ALPHA: (1) implies:
% 4.12/1.44  |   (4)   ~ (all_37_0 = 0)
% 4.12/1.44  |   (5)  q(all_3_2) = all_37_0
% 4.12/1.44  | 
% 4.12/1.44  | GROUND_INST: instantiating (2) with 0, all_37_0, all_3_2, simplifying with
% 4.12/1.44  |              (3), (5) gives:
% 4.12/1.44  |   (6)  all_37_0 = 0
% 4.12/1.44  | 
% 4.12/1.44  | REDUCE: (4), (6) imply:
% 4.12/1.44  |   (7)  $false
% 4.12/1.44  | 
% 4.12/1.44  | CLOSE: (7) is inconsistent.
% 4.12/1.44  | 
% 4.12/1.44  End of proof
% 4.12/1.44  
% 4.12/1.44  Sub-proof #2 shows that the following formulas are inconsistent:
% 4.12/1.44  ----------------------------------------------------------------
% 4.12/1.44    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.12/1.44         (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 4.12/1.44    (2)  p(all_3_2) = all_3_0
% 4.12/1.44    (3)  p(all_3_2) = 0
% 4.12/1.44    (4)   ~ (all_3_0 = 0)
% 4.12/1.44  
% 4.12/1.44  Begin of proof
% 4.12/1.44  | 
% 4.12/1.44  | GROUND_INST: instantiating (1) with all_3_0, 0, all_3_2, simplifying with (2),
% 4.12/1.44  |              (3) gives:
% 4.12/1.44  |   (5)  all_3_0 = 0
% 4.12/1.44  | 
% 4.12/1.44  | REDUCE: (4), (5) imply:
% 4.12/1.44  |   (6)  $false
% 4.12/1.44  | 
% 4.12/1.44  | CLOSE: (6) is inconsistent.
% 4.12/1.44  | 
% 4.12/1.44  End of proof
% 4.12/1.44  % SZS output end Proof for theBenchmark
% 4.12/1.44  
% 4.12/1.44  847ms
%------------------------------------------------------------------------------