TSTP Solution File: RNG087+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 13:57:46 EDT 2023

% Result   : Theorem 20.90s 3.55s
% Output   : Proof 20.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n003.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 : Sun Aug 27 01:39:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.62  ________       _____
% 0.21/0.62  ___  __ \_________(_)________________________________
% 0.21/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62  
% 0.21/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62  (2023-06-19)
% 0.21/0.62  
% 0.21/0.62  (c) Philipp Rümmer, 2009-2023
% 0.21/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62                Amanda Stjerna.
% 0.21/0.62  Free software under BSD-3-Clause.
% 0.21/0.62  
% 0.21/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.66  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.84/1.13  Prover 4: Preprocessing ...
% 2.84/1.13  Prover 1: Preprocessing ...
% 3.26/1.17  Prover 2: Preprocessing ...
% 3.26/1.17  Prover 3: Preprocessing ...
% 3.26/1.17  Prover 5: Preprocessing ...
% 3.26/1.17  Prover 6: Preprocessing ...
% 3.26/1.17  Prover 0: Preprocessing ...
% 7.35/1.77  Prover 3: Constructing countermodel ...
% 7.35/1.77  Prover 1: Constructing countermodel ...
% 7.71/1.82  Prover 6: Proving ...
% 8.03/1.90  Prover 5: Proving ...
% 8.03/1.90  Prover 4: Constructing countermodel ...
% 8.81/1.95  Prover 2: Proving ...
% 9.23/2.04  Prover 0: Proving ...
% 13.28/2.56  Prover 3: gave up
% 13.28/2.56  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.56/2.61  Prover 7: Preprocessing ...
% 14.50/2.72  Prover 7: Constructing countermodel ...
% 20.19/3.55  Prover 7: Found proof (size 15)
% 20.19/3.55  Prover 7: proved (988ms)
% 20.19/3.55  Prover 0: stopped
% 20.19/3.55  Prover 5: stopped
% 20.19/3.55  Prover 2: stopped
% 20.19/3.55  Prover 6: stopped
% 20.19/3.55  Prover 4: stopped
% 20.90/3.55  Prover 1: stopped
% 20.90/3.55  
% 20.90/3.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.90/3.55  
% 20.90/3.56  % SZS output start Proof for theBenchmark
% 20.90/3.56  Assumptions after simplification:
% 20.90/3.56  ---------------------------------
% 20.90/3.56  
% 20.90/3.56    (mDefIdeal)
% 20.90/3.59     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (sdtasdt0(v2, v1)
% 20.90/3.59        = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aIdeal0(v0) |  ~
% 20.90/3.59      aElementOf0(v1, v0) |  ~ aElement0(v2) | aElementOf0(v3, v0)) &  ! [v0: $i]
% 20.90/3.59    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) |  ~
% 20.90/3.59      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aIdeal0(v0) |  ~ aElementOf0(v2, v0) | 
% 20.90/3.59      ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 20.90/3.59      aIdeal0(v0) | aSet0(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ aSet0(v0) |
% 20.90/3.59      aIdeal0(v0) |  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ?
% 20.90/3.59      [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2,
% 20.90/3.59              v1) = v3 & $i(v3) & aElement0(v2) &  ~ aElementOf0(v3, v0)) |
% 20.90/3.59          (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) &  ~
% 20.90/3.59            aElementOf0(v5, v0)))))
% 20.90/3.59  
% 20.90/3.59    (mDefSSum)
% 20.90/3.60     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 20.90/3.60      $i] : ( ~ (sdtpldt1(v0, v1) = v2) |  ~ (sdtpldt0(v4, v5) = v3) |  ~ $i(v5) |
% 20.90/3.60       ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 20.90/3.60      aElementOf0(v5, v1) |  ~ aElementOf0(v4, v0) |  ~ aSet0(v1) |  ~ aSet0(v0) |
% 20.90/3.60      aElementOf0(v3, v2)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 20.90/3.60    : (v3 = v2 |  ~ (sdtpldt1(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) | 
% 20.90/3.60      ~ aSet0(v3) |  ~ aSet0(v1) |  ~ aSet0(v0) |  ? [v4: $i] :  ? [v5: $i] :  ?
% 20.90/3.60      [v6: $i] :  ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3)
% 20.90/3.60          |  ! [v8: $i] :  ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) |  ~ $i(v9) | 
% 20.90/3.60            ~ $i(v8) |  ~ aElementOf0(v9, v1) |  ~ aElementOf0(v8, v0))) &
% 20.90/3.60        (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6,
% 20.90/3.60              v1) & aElementOf0(v5, v0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.90/3.60      $i] :  ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 20.90/3.60      $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aSet0(v1) |  ~ aSet0(v0) | 
% 20.90/3.60      ? [v4: $i] :  ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 20.90/3.60        aElementOf0(v5, v1) & aElementOf0(v4, v0))) &  ! [v0: $i] :  ! [v1: $i] : 
% 20.90/3.60    ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 20.90/3.60       ~ aSet0(v1) |  ~ aSet0(v0) | aSet0(v2))
% 20.90/3.60  
% 20.90/3.60    (m__)
% 20.90/3.60    $i(xy) & $i(xJ) & $i(xI) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) =
% 20.90/3.60        xy) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1, xJ) |  ~ aElementOf0(v0,
% 20.90/3.60        xI))
% 20.90/3.60  
% 20.90/3.60    (m__870)
% 20.90/3.60    $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI)
% 20.90/3.60  
% 20.90/3.60    (m__901)
% 20.90/3.60    $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) &  ? [v0: $i] : (sdtpldt1(xI, xJ) =
% 20.90/3.60      v0 & $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 20.90/3.60  
% 20.90/3.60  Further assumptions not needed in the proof:
% 20.90/3.60  --------------------------------------------
% 20.90/3.60  mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefSInt, mEOfElem,
% 20.90/3.60  mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort,
% 20.90/3.60  mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__934
% 20.90/3.60  
% 20.90/3.60  Those formulas are unsatisfiable:
% 20.90/3.60  ---------------------------------
% 20.90/3.60  
% 20.90/3.60  Begin of proof
% 20.90/3.60  | 
% 20.90/3.60  | ALPHA: (mDefSSum) implies:
% 20.90/3.60  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 20.90/3.60  |          (sdtpldt1(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 20.90/3.60  |          $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aSet0(v1) |  ~ aSet0(v0) |  ?
% 20.90/3.60  |          [v4: $i] :  ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 20.90/3.60  |            aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 20.90/3.60  | 
% 20.90/3.60  | ALPHA: (mDefIdeal) implies:
% 20.90/3.60  |   (2)   ! [v0: $i] : ( ~ $i(v0) |  ~ aIdeal0(v0) | aSet0(v0))
% 20.90/3.60  | 
% 20.90/3.60  | ALPHA: (m__870) implies:
% 20.90/3.60  |   (3)  aIdeal0(xI)
% 20.90/3.60  |   (4)  aIdeal0(xJ)
% 20.90/3.60  | 
% 20.90/3.60  | ALPHA: (m__901) implies:
% 20.90/3.60  |   (5)   ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 20.90/3.60  |          aElementOf0(xx, v0) & aElement0(xz))
% 20.90/3.60  | 
% 20.90/3.60  | ALPHA: (m__) implies:
% 20.90/3.60  |   (6)  $i(xI)
% 20.90/3.60  |   (7)  $i(xJ)
% 20.90/3.60  |   (8)  $i(xy)
% 20.90/3.61  |   (9)   ! [v0: $i] :  ! [v1: $i] : ( ~ (sdtpldt0(v0, v1) = xy) |  ~ $i(v1) | 
% 20.90/3.61  |          ~ $i(v0) |  ~ aElementOf0(v1, xJ) |  ~ aElementOf0(v0, xI))
% 20.90/3.61  | 
% 20.90/3.61  | DELTA: instantiating (5) with fresh symbol all_23_0 gives:
% 20.90/3.61  |   (10)  sdtpldt1(xI, xJ) = all_23_0 & $i(all_23_0) & aElementOf0(xy, all_23_0)
% 20.90/3.61  |         & aElementOf0(xx, all_23_0) & aElement0(xz)
% 20.90/3.61  | 
% 20.90/3.61  | ALPHA: (10) implies:
% 20.90/3.61  |   (11)  aElementOf0(xy, all_23_0)
% 20.90/3.61  |   (12)  $i(all_23_0)
% 20.90/3.61  |   (13)  sdtpldt1(xI, xJ) = all_23_0
% 20.90/3.61  | 
% 20.90/3.61  | GROUND_INST: instantiating (2) with xI, simplifying with (3), (6) gives:
% 20.90/3.61  |   (14)  aSet0(xI)
% 20.90/3.61  | 
% 20.90/3.61  | GROUND_INST: instantiating (2) with xJ, simplifying with (4), (7) gives:
% 20.90/3.61  |   (15)  aSet0(xJ)
% 20.90/3.61  | 
% 20.90/3.61  | GROUND_INST: instantiating (1) with xI, xJ, all_23_0, xy, simplifying with
% 20.90/3.61  |              (6), (7), (8), (11), (12), (13), (14), (15) gives:
% 20.90/3.61  |   (16)   ? [v0: $i] :  ? [v1: $i] : (sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0) &
% 20.90/3.61  |           aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 20.90/3.61  | 
% 20.90/3.61  | DELTA: instantiating (16) with fresh symbols all_50_0, all_50_1 gives:
% 20.90/3.61  |   (17)  sdtpldt0(all_50_1, all_50_0) = xy & $i(all_50_0) & $i(all_50_1) &
% 20.90/3.61  |         aElementOf0(all_50_0, xJ) & aElementOf0(all_50_1, xI)
% 20.90/3.61  | 
% 20.90/3.61  | ALPHA: (17) implies:
% 20.90/3.61  |   (18)  aElementOf0(all_50_1, xI)
% 20.90/3.61  |   (19)  aElementOf0(all_50_0, xJ)
% 20.90/3.61  |   (20)  $i(all_50_1)
% 20.90/3.61  |   (21)  $i(all_50_0)
% 20.90/3.61  |   (22)  sdtpldt0(all_50_1, all_50_0) = xy
% 20.90/3.61  | 
% 20.90/3.61  | GROUND_INST: instantiating (9) with all_50_1, all_50_0, simplifying with (18),
% 20.90/3.61  |              (19), (20), (21), (22) gives:
% 20.90/3.61  |   (23)  $false
% 20.90/3.61  | 
% 20.90/3.61  | CLOSE: (23) is inconsistent.
% 20.90/3.61  | 
% 20.90/3.61  End of proof
% 20.90/3.61  % SZS output end Proof for theBenchmark
% 20.90/3.61  
% 20.90/3.61  2991ms
%------------------------------------------------------------------------------