TSTP Solution File: SEU161+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU161+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n028.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 17:42:55 EDT 2023

% Result   : Theorem 3.97s 1.27s
% Output   : Proof 4.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU161+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 17:59:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  ________       _____
% 0.20/0.58  ___  __ \_________(_)________________________________
% 0.20/0.58  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.58  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.58  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58  
% 0.20/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58  (2023-06-19)
% 0.20/0.58  
% 0.20/0.58  (c) Philipp Rümmer, 2009-2023
% 0.20/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58                Amanda Stjerna.
% 0.20/0.58  Free software under BSD-3-Clause.
% 0.20/0.58  
% 0.20/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58  
% 0.20/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.59  Running up to 7 provers in parallel.
% 0.20/0.60  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.60  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.60  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.60  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.60  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.60  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.60  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.90/0.96  Prover 1: Preprocessing ...
% 1.90/0.96  Prover 4: Preprocessing ...
% 1.90/1.01  Prover 0: Preprocessing ...
% 2.42/1.01  Prover 5: Preprocessing ...
% 2.42/1.01  Prover 3: Preprocessing ...
% 2.42/1.01  Prover 2: Preprocessing ...
% 2.42/1.01  Prover 6: Preprocessing ...
% 2.98/1.13  Prover 1: Warning: ignoring some quantifiers
% 2.98/1.14  Prover 6: Proving ...
% 2.98/1.15  Prover 1: Constructing countermodel ...
% 2.98/1.15  Prover 5: Proving ...
% 2.98/1.16  Prover 3: Warning: ignoring some quantifiers
% 2.98/1.16  Prover 4: Constructing countermodel ...
% 2.98/1.17  Prover 3: Constructing countermodel ...
% 3.58/1.18  Prover 2: Proving ...
% 3.71/1.21  Prover 0: Proving ...
% 3.97/1.26  Prover 3: proved (662ms)
% 3.97/1.26  
% 3.97/1.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.97/1.27  
% 3.97/1.27  Prover 5: stopped
% 3.97/1.27  Prover 2: stopped
% 3.97/1.27  Prover 6: stopped
% 3.97/1.27  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.97/1.27  Prover 0: stopped
% 3.97/1.27  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.97/1.27  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.97/1.27  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.97/1.28  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.97/1.31  Prover 11: Preprocessing ...
% 3.97/1.31  Prover 10: Preprocessing ...
% 4.50/1.31  Prover 13: Preprocessing ...
% 4.50/1.31  Prover 7: Preprocessing ...
% 4.50/1.31  Prover 8: Preprocessing ...
% 4.50/1.34  Prover 7: Constructing countermodel ...
% 4.50/1.35  Prover 1: Found proof (size 12)
% 4.50/1.35  Prover 1: proved (749ms)
% 4.50/1.35  Prover 11: stopped
% 4.50/1.35  Prover 4: stopped
% 4.50/1.35  Prover 7: stopped
% 4.50/1.35  Prover 10: Constructing countermodel ...
% 4.50/1.36  Prover 10: stopped
% 4.50/1.36  Prover 13: stopped
% 4.50/1.37  Prover 8: Warning: ignoring some quantifiers
% 4.50/1.37  Prover 8: Constructing countermodel ...
% 4.50/1.38  Prover 8: stopped
% 4.50/1.38  
% 4.50/1.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.50/1.38  
% 4.50/1.38  % SZS output start Proof for theBenchmark
% 4.50/1.38  Assumptions after simplification:
% 4.50/1.38  ---------------------------------
% 4.50/1.38  
% 4.50/1.38    (l23_zfmisc_1)
% 4.50/1.42     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v1 |  ~
% 4.50/1.42      (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ~ $i(v1) |  ~ $i(v0)
% 4.50/1.42      |  ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.50/1.42  
% 4.50/1.42    (t46_zfmisc_1)
% 4.50/1.42     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v1) &
% 4.50/1.42      singleton(v0) = v2 & in(v0, v1) = 0 & set_union2(v2, v1) = v3 & $i(v3) &
% 4.50/1.42      $i(v2) & $i(v1) & $i(v0))
% 4.50/1.42  
% 4.50/1.42    (function-axioms)
% 4.50/1.42     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.50/1.42    [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 4.50/1.42      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 4.50/1.42      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0: $i] :  !
% 4.50/1.42    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~
% 4.50/1.42      (singleton(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 4.50/1.42      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~
% 4.50/1.42      (empty(v2) = v0))
% 4.50/1.42  
% 4.50/1.42  Further assumptions not needed in the proof:
% 4.50/1.42  --------------------------------------------
% 4.50/1.43  antisymmetry_r2_hidden, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 4.50/1.43  idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0
% 4.50/1.43  
% 4.50/1.43  Those formulas are unsatisfiable:
% 4.50/1.43  ---------------------------------
% 4.50/1.43  
% 4.50/1.43  Begin of proof
% 4.50/1.43  | 
% 4.50/1.43  | ALPHA: (function-axioms) implies:
% 4.50/1.43  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.50/1.43  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 4.50/1.43  | 
% 4.50/1.43  | DELTA: instantiating (t46_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 4.50/1.43  |        all_14_2, all_14_3 gives:
% 4.50/1.43  |   (2)   ~ (all_14_0 = all_14_2) & singleton(all_14_3) = all_14_1 &
% 4.50/1.43  |        in(all_14_3, all_14_2) = 0 & set_union2(all_14_1, all_14_2) = all_14_0
% 4.50/1.43  |        & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3)
% 4.50/1.43  | 
% 4.50/1.43  | ALPHA: (2) implies:
% 4.50/1.43  |   (3)   ~ (all_14_0 = all_14_2)
% 4.50/1.43  |   (4)  $i(all_14_3)
% 4.50/1.43  |   (5)  $i(all_14_2)
% 4.50/1.43  |   (6)  set_union2(all_14_1, all_14_2) = all_14_0
% 4.50/1.43  |   (7)  in(all_14_3, all_14_2) = 0
% 4.50/1.43  |   (8)  singleton(all_14_3) = all_14_1
% 4.50/1.43  | 
% 4.50/1.44  | GROUND_INST: instantiating (l23_zfmisc_1) with all_14_3, all_14_2, all_14_1,
% 4.50/1.44  |              all_14_0, simplifying with (4), (5), (6), (8) gives:
% 4.50/1.44  |   (9)  all_14_0 = all_14_2 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_14_3,
% 4.50/1.44  |            all_14_2) = v0)
% 4.50/1.44  | 
% 4.50/1.44  | BETA: splitting (9) gives:
% 4.50/1.44  | 
% 4.50/1.44  | Case 1:
% 4.50/1.44  | | 
% 4.50/1.44  | |   (10)  all_14_0 = all_14_2
% 4.50/1.44  | | 
% 4.50/1.44  | | REDUCE: (3), (10) imply:
% 4.50/1.44  | |   (11)  $false
% 4.50/1.44  | | 
% 4.50/1.44  | | CLOSE: (11) is inconsistent.
% 4.50/1.44  | | 
% 4.50/1.44  | Case 2:
% 4.50/1.44  | | 
% 4.50/1.44  | |   (12)   ? [v0: int] : ( ~ (v0 = 0) & in(all_14_3, all_14_2) = v0)
% 4.50/1.44  | | 
% 4.50/1.44  | | DELTA: instantiating (12) with fresh symbol all_32_0 gives:
% 4.50/1.44  | |   (13)   ~ (all_32_0 = 0) & in(all_14_3, all_14_2) = all_32_0
% 4.50/1.44  | | 
% 4.50/1.44  | | ALPHA: (13) implies:
% 4.50/1.44  | |   (14)   ~ (all_32_0 = 0)
% 4.50/1.44  | |   (15)  in(all_14_3, all_14_2) = all_32_0
% 4.50/1.44  | | 
% 4.50/1.44  | | GROUND_INST: instantiating (1) with 0, all_32_0, all_14_2, all_14_3,
% 4.50/1.44  | |              simplifying with (7), (15) gives:
% 4.50/1.44  | |   (16)  all_32_0 = 0
% 4.50/1.44  | | 
% 4.50/1.44  | | REDUCE: (14), (16) imply:
% 4.50/1.44  | |   (17)  $false
% 4.50/1.44  | | 
% 4.50/1.44  | | CLOSE: (17) is inconsistent.
% 4.50/1.44  | | 
% 4.50/1.44  | End of split
% 4.50/1.44  | 
% 4.50/1.44  End of proof
% 4.50/1.44  % SZS output end Proof for theBenchmark
% 4.50/1.44  
% 4.50/1.44  863ms
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