TSTP Solution File: SET788+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET788+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 : n001.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 15:26:27 EDT 2023

% Result   : Theorem 4.08s 1.23s
% Output   : Proof 5.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n001.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 16:23:16 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.60  ________       _____
% 0.21/0.60  ___  __ \_________(_)________________________________
% 0.21/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60  
% 0.21/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60  (2023-06-19)
% 0.21/0.60  
% 0.21/0.60  (c) Philipp Rümmer, 2009-2023
% 0.21/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60                Amanda Stjerna.
% 0.21/0.60  Free software under BSD-3-Clause.
% 0.21/0.60  
% 0.21/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60  
% 0.21/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61  Running up to 7 provers in parallel.
% 0.21/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.50/0.91  Prover 4: Preprocessing ...
% 1.50/0.91  Prover 1: Preprocessing ...
% 2.06/0.95  Prover 3: Preprocessing ...
% 2.06/0.95  Prover 5: Preprocessing ...
% 2.06/0.95  Prover 0: Preprocessing ...
% 2.06/0.95  Prover 2: Preprocessing ...
% 2.06/0.95  Prover 6: Preprocessing ...
% 2.36/1.02  Prover 5: Proving ...
% 2.36/1.02  Prover 2: Proving ...
% 2.36/1.04  Prover 6: Proving ...
% 2.36/1.04  Prover 1: Constructing countermodel ...
% 2.36/1.04  Prover 3: Constructing countermodel ...
% 2.82/1.06  Prover 0: Proving ...
% 2.82/1.06  Prover 4: Constructing countermodel ...
% 4.08/1.23  Prover 3: proved (592ms)
% 4.08/1.23  
% 4.08/1.23  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/1.23  
% 4.08/1.24  Prover 5: stopped
% 4.08/1.24  Prover 2: stopped
% 4.08/1.24  Prover 6: stopped
% 4.08/1.24  Prover 0: stopped
% 4.08/1.25  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.08/1.25  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.08/1.25  Prover 7: Preprocessing ...
% 4.08/1.25  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.08/1.25  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.08/1.25  Prover 8: Preprocessing ...
% 4.08/1.25  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.08/1.26  Prover 10: Preprocessing ...
% 4.08/1.26  Prover 13: Preprocessing ...
% 4.08/1.26  Prover 11: Preprocessing ...
% 4.08/1.27  Prover 10: Warning: ignoring some quantifiers
% 4.08/1.27  Prover 10: Constructing countermodel ...
% 4.08/1.27  Prover 13: Warning: ignoring some quantifiers
% 4.08/1.27  Prover 13: Constructing countermodel ...
% 4.08/1.27  Prover 7: Warning: ignoring some quantifiers
% 4.08/1.27  Prover 7: Constructing countermodel ...
% 4.45/1.28  Prover 8: Warning: ignoring some quantifiers
% 4.45/1.28  Prover 8: Constructing countermodel ...
% 4.45/1.29  Prover 10: gave up
% 4.45/1.29  Prover 13: gave up
% 4.45/1.30  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.45/1.30  Prover 7: gave up
% 4.45/1.30  Prover 16: Preprocessing ...
% 4.45/1.31  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 4.45/1.31  Prover 16: Warning: ignoring some quantifiers
% 4.45/1.31  Prover 16: Constructing countermodel ...
% 4.45/1.32  Prover 19: Preprocessing ...
% 4.45/1.33  Prover 4: Found proof (size 68)
% 4.45/1.33  Prover 4: proved (704ms)
% 4.45/1.33  Prover 1: stopped
% 4.45/1.33  Prover 8: stopped
% 4.45/1.33  Prover 16: stopped
% 4.45/1.34  Prover 11: Constructing countermodel ...
% 4.45/1.34  Prover 11: stopped
% 4.94/1.36  Prover 19: Warning: ignoring some quantifiers
% 4.94/1.36  Prover 19: Constructing countermodel ...
% 4.94/1.36  Prover 19: stopped
% 4.94/1.36  
% 4.94/1.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/1.36  
% 4.94/1.37  % SZS output start Proof for theBenchmark
% 4.94/1.37  Assumptions after simplification:
% 4.94/1.37  ---------------------------------
% 4.94/1.37  
% 4.94/1.37    (prove_this)
% 4.94/1.41     ? [v0: $i] :  ? [v1: $i] :  ? [v2: any] :  ? [v3: any] : (equalish(v1, v0) =
% 4.94/1.41      v3 & equalish(v0, v1) = v2 & $i(v1) & $i(v0) &  ! [v4: $i] :  ! [v5: $i] : 
% 4.94/1.41      ! [v6: $i] :  ! [v7: int] : (v7 = 0 |  ~ (equalish(v4, v5) = 0) |  ~
% 4.94/1.41        (a_member_of(v6, v5) = v7) |  ~ $i(v6) |  ~ $i(v5) |  ~ $i(v4) |  ? [v8:
% 4.94/1.41          int] : ( ~ (v8 = 0) & a_member_of(v6, v4) = v8)) &  ! [v4: $i] :  ! [v5:
% 4.94/1.41        $i] :  ! [v6: $i] :  ! [v7: int] : (v7 = 0 |  ~ (equalish(v4, v5) = 0) | 
% 4.94/1.41        ~ (a_member_of(v6, v4) = v7) |  ~ $i(v6) |  ~ $i(v5) |  ~ $i(v4) |  ? [v8:
% 4.94/1.41          int] : ( ~ (v8 = 0) & a_member_of(v6, v5) = v8)) &  ! [v4: $i] :  ! [v5:
% 4.94/1.41        $i] :  ! [v6: int] : (v6 = 0 |  ~ (equalish(v4, v5) = v6) |  ~ $i(v5) |  ~
% 4.94/1.41        $i(v4) |  ? [v7: $i] :  ? [v8: any] :  ? [v9: any] : (a_member_of(v7, v5)
% 4.94/1.41          = v9 & a_member_of(v7, v4) = v8 & $i(v7) & ( ~ (v9 = 0) |  ~ (v8 = 0)) &
% 4.94/1.41          (v9 = 0 | v8 = 0))) &  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : ( ~
% 4.94/1.41        (equalish(v4, v5) = 0) |  ~ (a_member_of(v6, v5) = 0) |  ~ $i(v6) |  ~
% 4.94/1.41        $i(v5) |  ~ $i(v4) | a_member_of(v6, v4) = 0) &  ! [v4: $i] :  ! [v5: $i]
% 4.94/1.41      :  ! [v6: $i] : ( ~ (equalish(v4, v5) = 0) |  ~ (a_member_of(v6, v4) = 0) | 
% 4.94/1.41        ~ $i(v6) |  ~ $i(v5) |  ~ $i(v4) | a_member_of(v6, v5) = 0) & ((v3 = 0 & 
% 4.94/1.41          ~ (v2 = 0)) | (v2 = 0 &  ~ (v3 = 0))))
% 4.94/1.41  
% 4.94/1.41    (function-axioms)
% 4.94/1.41     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.94/1.41    [v3: $i] : (v1 = v0 |  ~ (equalish(v3, v2) = v1) |  ~ (equalish(v3, v2) = v0))
% 4.94/1.41    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.94/1.41    [v3: $i] : (v1 = v0 |  ~ (a_member_of(v3, v2) = v1) |  ~ (a_member_of(v3, v2)
% 4.94/1.41        = v0))
% 4.94/1.41  
% 4.94/1.41  Those formulas are unsatisfiable:
% 4.94/1.41  ---------------------------------
% 4.94/1.41  
% 4.94/1.41  Begin of proof
% 4.94/1.42  | 
% 4.94/1.42  | ALPHA: (function-axioms) implies:
% 4.94/1.42  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.94/1.42  |         ! [v3: $i] : (v1 = v0 |  ~ (a_member_of(v3, v2) = v1) |  ~
% 4.94/1.42  |          (a_member_of(v3, v2) = v0))
% 4.94/1.42  | 
% 4.94/1.42  | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.94/1.42  |        all_3_2, all_3_3 gives:
% 4.94/1.43  |   (2)  equalish(all_3_2, all_3_3) = all_3_0 & equalish(all_3_3, all_3_2) =
% 4.94/1.43  |        all_3_1 & $i(all_3_2) & $i(all_3_3) &  ! [v0: $i] :  ! [v1: $i] :  !
% 4.94/1.43  |        [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (equalish(v0, v1) = 0) |  ~
% 4.94/1.43  |          (a_member_of(v2, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 4.94/1.43  |          [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v0) = v4)) &  ! [v0: $i] :
% 4.94/1.43  |         ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~ (equalish(v0,
% 4.94/1.43  |              v1) = 0) |  ~ (a_member_of(v2, v0) = v3) |  ~ $i(v2) |  ~ $i(v1)
% 4.94/1.43  |          |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2, v1) =
% 4.94/1.43  |            v4)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 4.94/1.43  |          (equalish(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ?
% 4.94/1.43  |          [v4: any] :  ? [v5: any] : (a_member_of(v3, v1) = v5 &
% 4.94/1.43  |            a_member_of(v3, v0) = v4 & $i(v3) & ( ~ (v5 = 0) |  ~ (v4 = 0)) &
% 4.94/1.43  |            (v5 = 0 | v4 = 0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 4.94/1.43  |          (equalish(v0, v1) = 0) |  ~ (a_member_of(v2, v1) = 0) |  ~ $i(v2) | 
% 4.94/1.43  |          ~ $i(v1) |  ~ $i(v0) | a_member_of(v2, v0) = 0) &  ! [v0: $i] :  !
% 4.94/1.43  |        [v1: $i] :  ! [v2: $i] : ( ~ (equalish(v0, v1) = 0) |  ~
% 4.94/1.43  |          (a_member_of(v2, v0) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 4.94/1.43  |          a_member_of(v2, v1) = 0) & ((all_3_0 = 0 &  ~ (all_3_1 = 0)) |
% 4.94/1.43  |          (all_3_1 = 0 &  ~ (all_3_0 = 0)))
% 4.94/1.43  | 
% 4.94/1.43  | ALPHA: (2) implies:
% 4.94/1.43  |   (3)  $i(all_3_3)
% 4.94/1.43  |   (4)  $i(all_3_2)
% 4.94/1.43  |   (5)  equalish(all_3_3, all_3_2) = all_3_1
% 4.94/1.43  |   (6)  equalish(all_3_2, all_3_3) = all_3_0
% 4.94/1.43  |   (7)  (all_3_0 = 0 &  ~ (all_3_1 = 0)) | (all_3_1 = 0 &  ~ (all_3_0 = 0))
% 4.94/1.43  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (equalish(v0,
% 4.94/1.43  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: any] : 
% 4.94/1.43  |          ? [v5: any] : (a_member_of(v3, v1) = v5 & a_member_of(v3, v0) = v4 &
% 4.94/1.43  |            $i(v3) & ( ~ (v5 = 0) |  ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 4.94/1.43  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 4.94/1.43  |          (equalish(v0, v1) = 0) |  ~ (a_member_of(v2, v0) = v3) |  ~ $i(v2) | 
% 4.94/1.43  |          ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & a_member_of(v2,
% 4.94/1.43  |              v1) = v4))
% 4.94/1.43  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 4.94/1.43  |           (equalish(v0, v1) = 0) |  ~ (a_member_of(v2, v1) = v3) |  ~ $i(v2) |
% 4.94/1.44  |            ~ $i(v1) |  ~ $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) &
% 4.94/1.44  |             a_member_of(v2, v0) = v4))
% 4.94/1.44  | 
% 4.94/1.44  | GROUND_INST: instantiating (8) with all_3_3, all_3_2, all_3_1, simplifying
% 4.94/1.44  |              with (3), (4), (5) gives:
% 4.94/1.44  |   (11)  all_3_1 = 0 |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 4.94/1.44  |         (a_member_of(v0, all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 &
% 4.94/1.44  |           $i(v0) & ( ~ (v2 = 0) |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44  | 
% 4.94/1.44  | GROUND_INST: instantiating (8) with all_3_2, all_3_3, all_3_0, simplifying
% 4.94/1.44  |              with (3), (4), (6) gives:
% 4.94/1.44  |   (12)  all_3_0 = 0 |  ? [v0: $i] :  ? [v1: any] :  ? [v2: any] :
% 4.94/1.44  |         (a_member_of(v0, all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 &
% 4.94/1.44  |           $i(v0) & ( ~ (v2 = 0) |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44  | 
% 4.94/1.44  | BETA: splitting (7) gives:
% 4.94/1.44  | 
% 4.94/1.44  | Case 1:
% 4.94/1.44  | | 
% 4.94/1.44  | |   (13)  all_3_0 = 0 &  ~ (all_3_1 = 0)
% 4.94/1.44  | | 
% 4.94/1.44  | | ALPHA: (13) implies:
% 4.94/1.44  | |   (14)  all_3_0 = 0
% 4.94/1.44  | |   (15)   ~ (all_3_1 = 0)
% 4.94/1.44  | | 
% 4.94/1.44  | | REDUCE: (6), (14) imply:
% 4.94/1.44  | |   (16)  equalish(all_3_2, all_3_3) = 0
% 4.94/1.44  | | 
% 4.94/1.44  | | BETA: splitting (11) gives:
% 4.94/1.44  | | 
% 4.94/1.44  | | Case 1:
% 4.94/1.44  | | | 
% 4.94/1.44  | | |   (17)  all_3_1 = 0
% 4.94/1.44  | | | 
% 4.94/1.44  | | | REDUCE: (15), (17) imply:
% 4.94/1.44  | | |   (18)  $false
% 4.94/1.44  | | | 
% 4.94/1.44  | | | CLOSE: (18) is inconsistent.
% 4.94/1.44  | | | 
% 4.94/1.44  | | Case 2:
% 4.94/1.44  | | | 
% 4.94/1.44  | | |   (19)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (a_member_of(v0,
% 4.94/1.44  | | |             all_3_2) = v2 & a_member_of(v0, all_3_3) = v1 & $i(v0) & ( ~
% 4.94/1.44  | | |             (v2 = 0) |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.44  | | | 
% 4.94/1.44  | | | DELTA: instantiating (19) with fresh symbols all_17_0, all_17_1, all_17_2
% 4.94/1.44  | | |        gives:
% 4.94/1.44  | | |   (20)  a_member_of(all_17_2, all_3_2) = all_17_0 & a_member_of(all_17_2,
% 4.94/1.44  | | |           all_3_3) = all_17_1 & $i(all_17_2) & ( ~ (all_17_0 = 0) |  ~
% 4.94/1.44  | | |           (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 4.94/1.44  | | | 
% 4.94/1.44  | | | ALPHA: (20) implies:
% 4.94/1.44  | | |   (21)  $i(all_17_2)
% 4.94/1.44  | | |   (22)  a_member_of(all_17_2, all_3_3) = all_17_1
% 4.94/1.44  | | |   (23)  a_member_of(all_17_2, all_3_2) = all_17_0
% 4.94/1.45  | | |   (24)  all_17_0 = 0 | all_17_1 = 0
% 4.94/1.45  | | |   (25)   ~ (all_17_0 = 0) |  ~ (all_17_1 = 0)
% 4.94/1.45  | | | 
% 4.94/1.45  | | | GROUND_INST: instantiating (9) with all_3_2, all_3_3, all_17_2, all_17_0,
% 4.94/1.45  | | |              simplifying with (3), (4), (16), (21), (23) gives:
% 4.94/1.45  | | |   (26)  all_17_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.45  | | |             all_3_3) = v0)
% 4.94/1.45  | | | 
% 4.94/1.45  | | | GROUND_INST: instantiating (10) with all_3_2, all_3_3, all_17_2, all_17_1,
% 4.94/1.45  | | |              simplifying with (3), (4), (16), (21), (22) gives:
% 4.94/1.45  | | |   (27)  all_17_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.45  | | |             all_3_2) = v0)
% 4.94/1.45  | | | 
% 4.94/1.45  | | | BETA: splitting (24) gives:
% 4.94/1.45  | | | 
% 4.94/1.45  | | | Case 1:
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | |   (28)  all_17_0 = 0
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | REDUCE: (23), (28) imply:
% 4.94/1.45  | | | |   (29)  a_member_of(all_17_2, all_3_2) = 0
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | BETA: splitting (25) gives:
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | Case 1:
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | |   (30)   ~ (all_17_0 = 0)
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | REDUCE: (28), (30) imply:
% 4.94/1.45  | | | | |   (31)  $false
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | CLOSE: (31) is inconsistent.
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | Case 2:
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | |   (32)   ~ (all_17_1 = 0)
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | BETA: splitting (27) gives:
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | Case 1:
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | |   (33)  all_17_1 = 0
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | REDUCE: (32), (33) imply:
% 4.94/1.45  | | | | | |   (34)  $false
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | CLOSE: (34) is inconsistent.
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | Case 2:
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | |   (35)   ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2)
% 4.94/1.45  | | | | | |           = v0)
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | DELTA: instantiating (35) with fresh symbol all_34_0 gives:
% 4.94/1.45  | | | | | |   (36)   ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_2) =
% 4.94/1.45  | | | | | |         all_34_0
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | ALPHA: (36) implies:
% 4.94/1.45  | | | | | |   (37)   ~ (all_34_0 = 0)
% 4.94/1.45  | | | | | |   (38)  a_member_of(all_17_2, all_3_2) = all_34_0
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_2, all_17_2,
% 4.94/1.45  | | | | | |              simplifying with (29), (38) gives:
% 4.94/1.45  | | | | | |   (39)  all_34_0 = 0
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | REDUCE: (37), (39) imply:
% 4.94/1.45  | | | | | |   (40)  $false
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | | CLOSE: (40) is inconsistent.
% 4.94/1.45  | | | | | | 
% 4.94/1.45  | | | | | End of split
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | End of split
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | Case 2:
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | |   (41)  all_17_1 = 0
% 4.94/1.45  | | | |   (42)   ~ (all_17_0 = 0)
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | REDUCE: (22), (41) imply:
% 4.94/1.45  | | | |   (43)  a_member_of(all_17_2, all_3_3) = 0
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | BETA: splitting (26) gives:
% 4.94/1.45  | | | | 
% 4.94/1.45  | | | | Case 1:
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | |   (44)  all_17_0 = 0
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | REDUCE: (42), (44) imply:
% 4.94/1.45  | | | | |   (45)  $false
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | CLOSE: (45) is inconsistent.
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | Case 2:
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | |   (46)   ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3) =
% 4.94/1.45  | | | | |           v0)
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | DELTA: instantiating (46) with fresh symbol all_30_0 gives:
% 4.94/1.45  | | | | |   (47)   ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_3) = all_30_0
% 4.94/1.45  | | | | | 
% 4.94/1.45  | | | | | ALPHA: (47) implies:
% 4.94/1.46  | | | | |   (48)   ~ (all_30_0 = 0)
% 4.94/1.46  | | | | |   (49)  a_member_of(all_17_2, all_3_3) = all_30_0
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_3, all_17_2,
% 4.94/1.46  | | | | |              simplifying with (43), (49) gives:
% 4.94/1.46  | | | | |   (50)  all_30_0 = 0
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | REDUCE: (48), (50) imply:
% 4.94/1.46  | | | | |   (51)  $false
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | CLOSE: (51) is inconsistent.
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | End of split
% 4.94/1.46  | | | | 
% 4.94/1.46  | | | End of split
% 4.94/1.46  | | | 
% 4.94/1.46  | | End of split
% 4.94/1.46  | | 
% 4.94/1.46  | Case 2:
% 4.94/1.46  | | 
% 4.94/1.46  | |   (52)  all_3_1 = 0 &  ~ (all_3_0 = 0)
% 4.94/1.46  | | 
% 4.94/1.46  | | ALPHA: (52) implies:
% 4.94/1.46  | |   (53)  all_3_1 = 0
% 4.94/1.46  | |   (54)   ~ (all_3_0 = 0)
% 4.94/1.46  | | 
% 4.94/1.46  | | REDUCE: (5), (53) imply:
% 4.94/1.46  | |   (55)  equalish(all_3_3, all_3_2) = 0
% 4.94/1.46  | | 
% 4.94/1.46  | | BETA: splitting (12) gives:
% 4.94/1.46  | | 
% 4.94/1.46  | | Case 1:
% 4.94/1.46  | | | 
% 4.94/1.46  | | |   (56)  all_3_0 = 0
% 4.94/1.46  | | | 
% 4.94/1.46  | | | REDUCE: (54), (56) imply:
% 4.94/1.46  | | |   (57)  $false
% 4.94/1.46  | | | 
% 4.94/1.46  | | | CLOSE: (57) is inconsistent.
% 4.94/1.46  | | | 
% 4.94/1.46  | | Case 2:
% 4.94/1.46  | | | 
% 4.94/1.46  | | |   (58)   ? [v0: $i] :  ? [v1: any] :  ? [v2: any] : (a_member_of(v0,
% 4.94/1.46  | | |             all_3_2) = v1 & a_member_of(v0, all_3_3) = v2 & $i(v0) & ( ~
% 4.94/1.46  | | |             (v2 = 0) |  ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 4.94/1.46  | | | 
% 4.94/1.46  | | | DELTA: instantiating (58) with fresh symbols all_17_0, all_17_1, all_17_2
% 4.94/1.46  | | |        gives:
% 4.94/1.46  | | |   (59)  a_member_of(all_17_2, all_3_2) = all_17_1 & a_member_of(all_17_2,
% 4.94/1.46  | | |           all_3_3) = all_17_0 & $i(all_17_2) & ( ~ (all_17_0 = 0) |  ~
% 4.94/1.46  | | |           (all_17_1 = 0)) & (all_17_0 = 0 | all_17_1 = 0)
% 4.94/1.46  | | | 
% 4.94/1.46  | | | ALPHA: (59) implies:
% 4.94/1.46  | | |   (60)  $i(all_17_2)
% 4.94/1.46  | | |   (61)  a_member_of(all_17_2, all_3_3) = all_17_0
% 4.94/1.46  | | |   (62)  a_member_of(all_17_2, all_3_2) = all_17_1
% 4.94/1.46  | | |   (63)  all_17_0 = 0 | all_17_1 = 0
% 4.94/1.46  | | |   (64)   ~ (all_17_0 = 0) |  ~ (all_17_1 = 0)
% 4.94/1.46  | | | 
% 4.94/1.46  | | | GROUND_INST: instantiating (10) with all_3_3, all_3_2, all_17_2, all_17_1,
% 4.94/1.46  | | |              simplifying with (3), (4), (55), (60), (62) gives:
% 4.94/1.46  | | |   (65)  all_17_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.46  | | |             all_3_3) = v0)
% 4.94/1.46  | | | 
% 4.94/1.46  | | | GROUND_INST: instantiating (9) with all_3_3, all_3_2, all_17_2, all_17_0,
% 4.94/1.46  | | |              simplifying with (3), (4), (55), (60), (61) gives:
% 4.94/1.46  | | |   (66)  all_17_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2,
% 4.94/1.46  | | |             all_3_2) = v0)
% 4.94/1.46  | | | 
% 4.94/1.46  | | | BETA: splitting (63) gives:
% 4.94/1.46  | | | 
% 4.94/1.46  | | | Case 1:
% 4.94/1.46  | | | | 
% 4.94/1.46  | | | |   (67)  all_17_0 = 0
% 4.94/1.46  | | | | 
% 4.94/1.46  | | | | REDUCE: (61), (67) imply:
% 4.94/1.46  | | | |   (68)  a_member_of(all_17_2, all_3_3) = 0
% 4.94/1.46  | | | | 
% 4.94/1.46  | | | | BETA: splitting (64) gives:
% 4.94/1.46  | | | | 
% 4.94/1.46  | | | | Case 1:
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | |   (69)   ~ (all_17_0 = 0)
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | REDUCE: (67), (69) imply:
% 4.94/1.46  | | | | |   (70)  $false
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | CLOSE: (70) is inconsistent.
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | Case 2:
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | |   (71)   ~ (all_17_1 = 0)
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | BETA: splitting (65) gives:
% 4.94/1.46  | | | | | 
% 4.94/1.46  | | | | | Case 1:
% 4.94/1.46  | | | | | | 
% 4.94/1.46  | | | | | |   (72)  all_17_1 = 0
% 4.94/1.46  | | | | | | 
% 4.94/1.46  | | | | | | REDUCE: (71), (72) imply:
% 4.94/1.46  | | | | | |   (73)  $false
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | CLOSE: (73) is inconsistent.
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | Case 2:
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | |   (74)   ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_3)
% 4.94/1.47  | | | | | |           = v0)
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | DELTA: instantiating (74) with fresh symbol all_34_0 gives:
% 4.94/1.47  | | | | | |   (75)   ~ (all_34_0 = 0) & a_member_of(all_17_2, all_3_3) =
% 4.94/1.47  | | | | | |         all_34_0
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | ALPHA: (75) implies:
% 4.94/1.47  | | | | | |   (76)   ~ (all_34_0 = 0)
% 4.94/1.47  | | | | | |   (77)  a_member_of(all_17_2, all_3_3) = all_34_0
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | GROUND_INST: instantiating (1) with 0, all_34_0, all_3_3, all_17_2,
% 4.94/1.47  | | | | | |              simplifying with (68), (77) gives:
% 4.94/1.47  | | | | | |   (78)  all_34_0 = 0
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | REDUCE: (76), (78) imply:
% 4.94/1.47  | | | | | |   (79)  $false
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | | CLOSE: (79) is inconsistent.
% 4.94/1.47  | | | | | | 
% 4.94/1.47  | | | | | End of split
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | End of split
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | Case 2:
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | |   (80)  all_17_1 = 0
% 4.94/1.47  | | | |   (81)   ~ (all_17_0 = 0)
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | | REDUCE: (62), (80) imply:
% 4.94/1.47  | | | |   (82)  a_member_of(all_17_2, all_3_2) = 0
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | | BETA: splitting (66) gives:
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | | Case 1:
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | |   (83)  all_17_0 = 0
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | REDUCE: (81), (83) imply:
% 4.94/1.47  | | | | |   (84)  $false
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | CLOSE: (84) is inconsistent.
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | Case 2:
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | |   (85)   ? [v0: int] : ( ~ (v0 = 0) & a_member_of(all_17_2, all_3_2) =
% 4.94/1.47  | | | | |           v0)
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | DELTA: instantiating (85) with fresh symbol all_30_0 gives:
% 4.94/1.47  | | | | |   (86)   ~ (all_30_0 = 0) & a_member_of(all_17_2, all_3_2) = all_30_0
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | ALPHA: (86) implies:
% 4.94/1.47  | | | | |   (87)   ~ (all_30_0 = 0)
% 4.94/1.47  | | | | |   (88)  a_member_of(all_17_2, all_3_2) = all_30_0
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | GROUND_INST: instantiating (1) with 0, all_30_0, all_3_2, all_17_2,
% 4.94/1.47  | | | | |              simplifying with (82), (88) gives:
% 4.94/1.47  | | | | |   (89)  all_30_0 = 0
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | REDUCE: (87), (89) imply:
% 4.94/1.47  | | | | |   (90)  $false
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | | CLOSE: (90) is inconsistent.
% 4.94/1.47  | | | | | 
% 4.94/1.47  | | | | End of split
% 4.94/1.47  | | | | 
% 4.94/1.47  | | | End of split
% 4.94/1.47  | | | 
% 4.94/1.47  | | End of split
% 4.94/1.47  | | 
% 4.94/1.47  | End of split
% 4.94/1.47  | 
% 4.94/1.47  End of proof
% 5.24/1.47  % SZS output end Proof for theBenchmark
% 5.24/1.47  
% 5.24/1.47  869ms
%------------------------------------------------------------------------------