TSTP Solution File: SET583+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% 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 15:25:24 EDT 2023

% Result   : Theorem 3.62s 1.33s
% Output   : Proof 5.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET583+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32  % Computer : n001.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Sat Aug 26 08:54:30 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.16/0.60  ________       _____
% 0.16/0.60  ___  __ \_________(_)________________________________
% 0.16/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.16/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.16/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.16/0.60  
% 0.16/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.60  (2023-06-19)
% 0.16/0.60  
% 0.16/0.60  (c) Philipp Rümmer, 2009-2023
% 0.16/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.60                Amanda Stjerna.
% 0.16/0.60  Free software under BSD-3-Clause.
% 0.16/0.60  
% 0.16/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.60  
% 0.16/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.62  Running up to 7 provers in parallel.
% 0.16/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.73/1.02  Prover 4: Preprocessing ...
% 1.73/1.02  Prover 1: Preprocessing ...
% 2.29/1.08  Prover 5: Preprocessing ...
% 2.29/1.08  Prover 0: Preprocessing ...
% 2.29/1.08  Prover 6: Preprocessing ...
% 2.29/1.08  Prover 2: Preprocessing ...
% 2.29/1.08  Prover 3: Preprocessing ...
% 3.21/1.21  Prover 2: Proving ...
% 3.21/1.21  Prover 6: Proving ...
% 3.21/1.21  Prover 5: Proving ...
% 3.21/1.22  Prover 1: Constructing countermodel ...
% 3.21/1.24  Prover 3: Constructing countermodel ...
% 3.21/1.25  Prover 0: Proving ...
% 3.62/1.27  Prover 4: Constructing countermodel ...
% 3.62/1.33  Prover 2: proved (698ms)
% 3.62/1.33  
% 3.62/1.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.33  
% 3.62/1.33  Prover 3: stopped
% 3.62/1.33  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.62/1.33  Prover 6: stopped
% 3.62/1.35  Prover 0: stopped
% 3.62/1.35  Prover 5: stopped
% 3.62/1.35  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.62/1.35  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.62/1.35  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.62/1.35  Prover 7: Preprocessing ...
% 3.62/1.35  Prover 8: Preprocessing ...
% 3.62/1.36  Prover 10: Preprocessing ...
% 3.62/1.37  Prover 11: Preprocessing ...
% 4.33/1.37  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.33/1.38  Prover 7: Warning: ignoring some quantifiers
% 4.33/1.38  Prover 7: Constructing countermodel ...
% 4.33/1.40  Prover 10: Warning: ignoring some quantifiers
% 4.33/1.40  Prover 10: Constructing countermodel ...
% 4.33/1.41  Prover 13: Preprocessing ...
% 4.33/1.44  Prover 4: Found proof (size 14)
% 4.33/1.44  Prover 4: proved (800ms)
% 4.33/1.44  Prover 7: Found proof (size 6)
% 4.33/1.44  Prover 7: proved (109ms)
% 4.33/1.44  Prover 1: stopped
% 4.33/1.44  Prover 10: stopped
% 4.33/1.47  Prover 13: Warning: ignoring some quantifiers
% 4.33/1.47  Prover 13: Constructing countermodel ...
% 4.33/1.47  Prover 8: Warning: ignoring some quantifiers
% 4.33/1.47  Prover 13: stopped
% 4.33/1.48  Prover 8: Constructing countermodel ...
% 4.33/1.48  Prover 8: stopped
% 4.33/1.50  Prover 11: Constructing countermodel ...
% 4.33/1.51  Prover 11: stopped
% 4.33/1.51  
% 4.33/1.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.33/1.51  
% 4.33/1.51  % SZS output start Proof for theBenchmark
% 4.33/1.51  Assumptions after simplification:
% 4.33/1.51  ---------------------------------
% 4.33/1.51  
% 4.33/1.51    (equal_defn)
% 4.33/1.56     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ~ $i(v1) | 
% 4.33/1.56      ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [v0: $i]
% 4.33/1.56    :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 4.33/1.56      ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0: $i] :  ! [v1:
% 4.33/1.56      int] : (v1 = 0 |  ~ (subset(v0, v0) = v1) |  ~ $i(v0))
% 4.33/1.56  
% 4.33/1.56    (prove_extensionality)
% 4.33/1.56     ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) & subset(v1, v0) = 0 & subset(v0,
% 4.33/1.56        v1) = 0 & $i(v1) & $i(v0))
% 4.60/1.56  
% 4.60/1.56    (function-axioms)
% 4.60/1.57     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.60/1.57    [v3: $i] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) & 
% 4.60/1.57    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 4.60/1.57      $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 4.60/1.57  
% 4.60/1.57  Further assumptions not needed in the proof:
% 4.60/1.57  --------------------------------------------
% 4.60/1.57  reflexivity_of_subset, subset_defn
% 4.60/1.57  
% 4.60/1.57  Those formulas are unsatisfiable:
% 4.60/1.57  ---------------------------------
% 4.60/1.57  
% 4.60/1.57  Begin of proof
% 4.60/1.57  | 
% 4.60/1.57  | ALPHA: (equal_defn) implies:
% 4.60/1.57  |   (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ~
% 4.60/1.57  |          $i(v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) =
% 4.60/1.57  |            v2))
% 4.60/1.57  | 
% 4.60/1.57  | ALPHA: (function-axioms) implies:
% 4.60/1.58  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.60/1.58  |         ! [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2)
% 4.60/1.58  |            = v0))
% 4.60/1.58  | 
% 4.60/1.58  | DELTA: instantiating (prove_extensionality) with fresh symbols all_6_0,
% 4.60/1.58  |        all_6_1 gives:
% 4.60/1.58  |   (3)   ~ (all_6_0 = all_6_1) & subset(all_6_0, all_6_1) = 0 & subset(all_6_1,
% 4.60/1.58  |          all_6_0) = 0 & $i(all_6_0) & $i(all_6_1)
% 4.60/1.58  | 
% 4.60/1.58  | ALPHA: (3) implies:
% 4.60/1.58  |   (4)   ~ (all_6_0 = all_6_1)
% 4.60/1.58  |   (5)  $i(all_6_1)
% 4.60/1.58  |   (6)  $i(all_6_0)
% 4.60/1.58  |   (7)  subset(all_6_1, all_6_0) = 0
% 4.60/1.58  |   (8)  subset(all_6_0, all_6_1) = 0
% 4.60/1.58  | 
% 4.60/1.59  | GROUND_INST: instantiating (1) with all_6_1, all_6_0, simplifying with (5),
% 4.60/1.59  |              (6), (8) gives:
% 4.60/1.59  |   (9)  all_6_0 = all_6_1 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_6_1,
% 4.60/1.59  |            all_6_0) = v0)
% 4.60/1.59  | 
% 4.60/1.59  | BETA: splitting (9) gives:
% 4.60/1.59  | 
% 4.60/1.59  | Case 1:
% 4.60/1.59  | | 
% 4.60/1.59  | |   (10)  all_6_0 = all_6_1
% 4.60/1.59  | | 
% 4.60/1.59  | | REDUCE: (4), (10) imply:
% 4.60/1.59  | |   (11)  $false
% 4.60/1.59  | | 
% 4.60/1.59  | | CLOSE: (11) is inconsistent.
% 4.60/1.59  | | 
% 4.60/1.59  | Case 2:
% 4.60/1.59  | | 
% 5.48/1.59  | |   (12)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_6_1, all_6_0) = v0)
% 5.48/1.59  | | 
% 5.48/1.59  | | DELTA: instantiating (12) with fresh symbol all_15_0 gives:
% 5.48/1.59  | |   (13)   ~ (all_15_0 = 0) & subset(all_6_1, all_6_0) = all_15_0
% 5.48/1.59  | | 
% 5.48/1.59  | | ALPHA: (13) implies:
% 5.48/1.59  | |   (14)   ~ (all_15_0 = 0)
% 5.48/1.59  | |   (15)  subset(all_6_1, all_6_0) = all_15_0
% 5.48/1.59  | | 
% 5.49/1.59  | | GROUND_INST: instantiating (2) with 0, all_15_0, all_6_0, all_6_1,
% 5.49/1.59  | |              simplifying with (7), (15) gives:
% 5.49/1.60  | |   (16)  all_15_0 = 0
% 5.49/1.60  | | 
% 5.49/1.60  | | REDUCE: (14), (16) imply:
% 5.49/1.60  | |   (17)  $false
% 5.49/1.60  | | 
% 5.49/1.60  | | CLOSE: (17) is inconsistent.
% 5.49/1.60  | | 
% 5.49/1.60  | End of split
% 5.49/1.60  | 
% 5.49/1.60  End of proof
% 5.49/1.60  % SZS output end Proof for theBenchmark
% 5.49/1.60  
% 5.49/1.60  993ms
%------------------------------------------------------------------------------