TSTP Solution File: SEU152+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU152+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n017.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 17:42:49 EDT 2023

% Result   : Theorem 4.30s 1.34s
% Output   : Proof 5.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU152+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n017.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 : Wed Aug 23 19:45:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.17/1.03  Prover 4: Preprocessing ...
% 2.17/1.03  Prover 1: Preprocessing ...
% 2.17/1.07  Prover 0: Preprocessing ...
% 2.17/1.07  Prover 5: Preprocessing ...
% 2.17/1.07  Prover 2: Preprocessing ...
% 2.17/1.07  Prover 6: Preprocessing ...
% 2.17/1.07  Prover 3: Preprocessing ...
% 3.15/1.19  Prover 1: Warning: ignoring some quantifiers
% 3.15/1.20  Prover 3: Warning: ignoring some quantifiers
% 3.15/1.21  Prover 6: Proving ...
% 3.44/1.21  Prover 3: Constructing countermodel ...
% 3.44/1.21  Prover 1: Constructing countermodel ...
% 3.44/1.21  Prover 2: Proving ...
% 3.44/1.21  Prover 5: Proving ...
% 3.44/1.23  Prover 4: Constructing countermodel ...
% 3.64/1.24  Prover 0: Proving ...
% 3.64/1.32  Prover 3: gave up
% 4.30/1.33  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.30/1.33  Prover 1: gave up
% 4.30/1.33  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.30/1.33  Prover 6: gave up
% 4.30/1.33  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.30/1.33  Prover 5: proved (691ms)
% 4.30/1.33  
% 4.30/1.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.34  
% 4.30/1.35  Prover 2: proved (702ms)
% 4.30/1.35  
% 4.30/1.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.35  
% 4.30/1.35  Prover 7: Preprocessing ...
% 4.30/1.35  Prover 0: proved (704ms)
% 4.30/1.35  
% 4.30/1.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.35  
% 4.30/1.36  Prover 9: Preprocessing ...
% 4.30/1.36  Prover 8: Preprocessing ...
% 4.30/1.36  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.30/1.36  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.30/1.37  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.30/1.37  Prover 7: Warning: ignoring some quantifiers
% 4.30/1.37  Prover 11: Preprocessing ...
% 4.30/1.37  Prover 10: Preprocessing ...
% 4.30/1.38  Prover 13: Preprocessing ...
% 4.30/1.39  Prover 8: Warning: ignoring some quantifiers
% 4.30/1.39  Prover 7: Constructing countermodel ...
% 4.30/1.40  Prover 8: Constructing countermodel ...
% 4.30/1.41  Prover 4: Found proof (size 19)
% 4.30/1.41  Prover 4: proved (764ms)
% 4.30/1.41  Prover 8: stopped
% 4.30/1.42  Prover 13: stopped
% 4.30/1.42  Prover 7: stopped
% 4.30/1.42  Prover 10: Warning: ignoring some quantifiers
% 4.30/1.42  Prover 10: Constructing countermodel ...
% 4.30/1.43  Prover 9: Warning: ignoring some quantifiers
% 4.30/1.43  Prover 10: stopped
% 4.30/1.43  Prover 9: Constructing countermodel ...
% 4.30/1.43  Prover 11: Constructing countermodel ...
% 4.30/1.43  Prover 9: stopped
% 4.30/1.44  Prover 11: stopped
% 4.30/1.44  
% 4.30/1.44  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.30/1.44  
% 4.30/1.44  % SZS output start Proof for theBenchmark
% 4.30/1.44  Assumptions after simplification:
% 4.30/1.44  ---------------------------------
% 4.30/1.44  
% 4.30/1.44    (l23_zfmisc_1)
% 4.30/1.47     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v1) &
% 4.30/1.47      singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) = 0 & $i(v3) &
% 4.30/1.47      $i(v2) & $i(v1) & $i(v0))
% 4.30/1.47  
% 4.30/1.47    (l2_zfmisc_1)
% 4.30/1.48     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 4.30/1.48      (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 4.30/1.48      [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0: $i] :  ! [v1: $i] : 
% 4.30/1.48    ! [v2: int] : (v2 = 0 |  ~ (in(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 4.30/1.48        $i] :  ? [v4: int] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) =
% 4.30/1.48        v4 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 4.30/1.48      (singleton(v0) = v2) |  ~ (subset(v2, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 4.30/1.48      in(v0, v1) = 0) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (in(v0, v1) = 0) |  ~
% 4.30/1.48      $i(v1) |  ~ $i(v0) |  ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0
% 4.30/1.48        & $i(v2)))
% 4.30/1.48  
% 4.30/1.48    (t12_xboole_1)
% 4.30/1.48     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (set_union2(v0, v1) =
% 4.30/1.48        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1)
% 4.30/1.48        = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |  ~ $i(v1)
% 4.30/1.48      |  ~ $i(v0) | set_union2(v0, v1) = v1)
% 4.30/1.48  
% 4.30/1.49    (function-axioms)
% 4.30/1.49     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.30/1.49    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 4.30/1.49    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 4.30/1.49      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0:
% 4.30/1.49      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 4.30/1.49    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0: $i] :  !
% 4.30/1.49    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~
% 4.30/1.49      (singleton(v2) = v0))
% 4.30/1.49  
% 4.30/1.49  Further assumptions not needed in the proof:
% 4.30/1.49  --------------------------------------------
% 5.24/1.49  antisymmetry_r2_hidden, commutativity_k2_xboole_0, dt_k1_tarski, dt_k2_xboole_0,
% 5.24/1.49  idempotence_k2_xboole_0, reflexivity_r1_tarski
% 5.24/1.49  
% 5.24/1.49  Those formulas are unsatisfiable:
% 5.24/1.49  ---------------------------------
% 5.24/1.49  
% 5.24/1.49  Begin of proof
% 5.24/1.49  | 
% 5.24/1.49  | ALPHA: (l2_zfmisc_1) implies:
% 5.24/1.50  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (in(v0, v1) = 0) |  ~ $i(v1) |  ~
% 5.24/1.50  |          $i(v0) |  ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0 &
% 5.24/1.50  |            $i(v2)))
% 5.24/1.50  | 
% 5.24/1.50  | ALPHA: (t12_xboole_1) implies:
% 5.24/1.50  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (set_union2(v0,
% 5.24/1.50  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) &
% 5.24/1.50  |            subset(v0, v1) = v3))
% 5.24/1.50  | 
% 5.24/1.50  | ALPHA: (function-axioms) implies:
% 5.24/1.50  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2)
% 5.24/1.50  |            = v1) |  ~ (singleton(v2) = v0))
% 5.24/1.50  |   (4)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.24/1.50  |         ! [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2)
% 5.24/1.50  |            = v0))
% 5.24/1.50  | 
% 5.24/1.50  | DELTA: instantiating (l23_zfmisc_1) with fresh symbols all_9_0, all_9_1,
% 5.24/1.50  |        all_9_2, all_9_3 gives:
% 5.24/1.50  |   (5)   ~ (all_9_0 = all_9_2) & singleton(all_9_3) = all_9_1 &
% 5.24/1.50  |        set_union2(all_9_1, all_9_2) = all_9_0 & in(all_9_3, all_9_2) = 0 &
% 5.24/1.50  |        $i(all_9_0) & $i(all_9_1) & $i(all_9_2) & $i(all_9_3)
% 5.24/1.50  | 
% 5.24/1.50  | ALPHA: (5) implies:
% 5.24/1.50  |   (6)   ~ (all_9_0 = all_9_2)
% 5.24/1.50  |   (7)  $i(all_9_3)
% 5.24/1.50  |   (8)  $i(all_9_2)
% 5.24/1.51  |   (9)  $i(all_9_1)
% 5.24/1.51  |   (10)  in(all_9_3, all_9_2) = 0
% 5.24/1.51  |   (11)  set_union2(all_9_1, all_9_2) = all_9_0
% 5.24/1.51  |   (12)  singleton(all_9_3) = all_9_1
% 5.24/1.51  | 
% 5.24/1.51  | GROUND_INST: instantiating (1) with all_9_3, all_9_2, simplifying with (7),
% 5.24/1.51  |              (8), (10) gives:
% 5.24/1.51  |   (13)   ? [v0: $i] : (singleton(all_9_3) = v0 & subset(v0, all_9_2) = 0 &
% 5.24/1.51  |           $i(v0))
% 5.24/1.51  | 
% 5.24/1.51  | GROUND_INST: instantiating (2) with all_9_1, all_9_2, all_9_0, simplifying
% 5.24/1.51  |              with (8), (9), (11) gives:
% 5.24/1.51  |   (14)  all_9_0 = all_9_2 |  ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1,
% 5.24/1.51  |             all_9_2) = v0)
% 5.24/1.51  | 
% 5.24/1.51  | DELTA: instantiating (13) with fresh symbol all_19_0 gives:
% 5.24/1.51  |   (15)  singleton(all_9_3) = all_19_0 & subset(all_19_0, all_9_2) = 0 &
% 5.24/1.51  |         $i(all_19_0)
% 5.24/1.51  | 
% 5.24/1.51  | ALPHA: (15) implies:
% 5.24/1.51  |   (16)  subset(all_19_0, all_9_2) = 0
% 5.24/1.51  |   (17)  singleton(all_9_3) = all_19_0
% 5.24/1.51  | 
% 5.24/1.51  | BETA: splitting (14) gives:
% 5.24/1.51  | 
% 5.24/1.51  | Case 1:
% 5.24/1.51  | | 
% 5.24/1.51  | |   (18)  all_9_0 = all_9_2
% 5.24/1.51  | | 
% 5.24/1.51  | | REDUCE: (6), (18) imply:
% 5.24/1.51  | |   (19)  $false
% 5.24/1.51  | | 
% 5.24/1.51  | | CLOSE: (19) is inconsistent.
% 5.24/1.51  | | 
% 5.24/1.51  | Case 2:
% 5.24/1.51  | | 
% 5.24/1.51  | |   (20)   ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, all_9_2) = v0)
% 5.24/1.51  | | 
% 5.24/1.51  | | DELTA: instantiating (20) with fresh symbol all_25_0 gives:
% 5.24/1.51  | |   (21)   ~ (all_25_0 = 0) & subset(all_9_1, all_9_2) = all_25_0
% 5.24/1.51  | | 
% 5.24/1.51  | | ALPHA: (21) implies:
% 5.24/1.52  | |   (22)   ~ (all_25_0 = 0)
% 5.24/1.52  | |   (23)  subset(all_9_1, all_9_2) = all_25_0
% 5.24/1.52  | | 
% 5.24/1.52  | | GROUND_INST: instantiating (3) with all_9_1, all_19_0, all_9_3, simplifying
% 5.24/1.52  | |              with (12), (17) gives:
% 5.24/1.52  | |   (24)  all_19_0 = all_9_1
% 5.24/1.52  | | 
% 5.24/1.52  | | REDUCE: (16), (24) imply:
% 5.24/1.52  | |   (25)  subset(all_9_1, all_9_2) = 0
% 5.24/1.52  | | 
% 5.24/1.52  | | GROUND_INST: instantiating (4) with all_25_0, 0, all_9_2, all_9_1,
% 5.24/1.52  | |              simplifying with (23), (25) gives:
% 5.24/1.52  | |   (26)  all_25_0 = 0
% 5.24/1.52  | | 
% 5.24/1.52  | | REDUCE: (22), (26) imply:
% 5.24/1.52  | |   (27)  $false
% 5.24/1.52  | | 
% 5.24/1.52  | | CLOSE: (27) is inconsistent.
% 5.24/1.52  | | 
% 5.24/1.52  | End of split
% 5.24/1.52  | 
% 5.24/1.52  End of proof
% 5.24/1.52  % SZS output end Proof for theBenchmark
% 5.24/1.52  
% 5.24/1.52  896ms
%------------------------------------------------------------------------------