TSTP Solution File: RNG124+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG124+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 : n029.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 13:58:01 EDT 2023

% Result   : Theorem 14.01s 2.72s
% Output   : Proof 18.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG124+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 : n029.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 03:16:10 EDT 2023
% 0.13/0.34  % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.31/1.19  Prover 4: Preprocessing ...
% 3.31/1.19  Prover 1: Preprocessing ...
% 3.87/1.23  Prover 0: Preprocessing ...
% 3.87/1.23  Prover 5: Preprocessing ...
% 3.87/1.23  Prover 3: Preprocessing ...
% 3.87/1.23  Prover 6: Preprocessing ...
% 3.87/1.23  Prover 2: Preprocessing ...
% 9.23/2.08  Prover 1: Constructing countermodel ...
% 9.23/2.13  Prover 6: Proving ...
% 9.23/2.15  Prover 5: Proving ...
% 9.23/2.15  Prover 3: Constructing countermodel ...
% 11.70/2.32  Prover 2: Proving ...
% 11.99/2.38  Prover 4: Constructing countermodel ...
% 13.18/2.49  Prover 0: Proving ...
% 14.01/2.71  Prover 3: proved (2070ms)
% 14.01/2.72  
% 14.01/2.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.01/2.72  
% 14.01/2.72  Prover 5: stopped
% 14.01/2.72  Prover 2: stopped
% 14.01/2.72  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.01/2.72  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.01/2.72  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.01/2.72  Prover 6: stopped
% 14.01/2.72  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.01/2.72  Prover 0: stopped
% 14.01/2.73  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.83/2.82  Prover 10: Preprocessing ...
% 14.83/2.82  Prover 7: Preprocessing ...
% 15.73/2.85  Prover 8: Preprocessing ...
% 15.73/2.86  Prover 13: Preprocessing ...
% 15.73/2.87  Prover 11: Preprocessing ...
% 17.23/3.05  Prover 10: Constructing countermodel ...
% 17.23/3.07  Prover 7: Constructing countermodel ...
% 17.53/3.12  Prover 8: Warning: ignoring some quantifiers
% 17.88/3.14  Prover 8: Constructing countermodel ...
% 18.38/3.23  Prover 13: Warning: ignoring some quantifiers
% 18.38/3.24  Prover 10: Found proof (size 18)
% 18.38/3.24  Prover 10: proved (524ms)
% 18.38/3.24  Prover 4: stopped
% 18.38/3.24  Prover 8: stopped
% 18.38/3.24  Prover 7: stopped
% 18.38/3.24  Prover 1: stopped
% 18.38/3.24  Prover 13: Constructing countermodel ...
% 18.75/3.26  Prover 13: stopped
% 18.75/3.26  Prover 11: Constructing countermodel ...
% 18.75/3.27  Prover 11: stopped
% 18.75/3.27  
% 18.75/3.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.75/3.28  
% 18.75/3.28  % SZS output start Proof for theBenchmark
% 18.75/3.28  Assumptions after simplification:
% 18.75/3.28  ---------------------------------
% 18.75/3.28  
% 18.75/3.28    (m__2273)
% 18.75/3.30    $i(xu) & $i(xI) & $i(sz00) &  ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0
% 18.75/3.30      & $i(v0) & aElementOf0(xu, xI) &  ! [v1: $i] :  ! [v2: $i] : (v1 = sz00 |  ~
% 18.75/3.30        (sbrdtbr0(v1) = v2) |  ~ $i(v1) |  ~ iLess0(v2, v0) |  ~ aElementOf0(v1,
% 18.75/3.30          xI)))
% 18.75/3.30  
% 18.75/3.30    (m__2666)
% 18.75/3.31    $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 18.75/3.31    [v2: $i] : (sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb & $i(v0) &
% 18.75/3.31      aElement0(xr) & aElement0(xq) & (xr = sz00 | (sbrdtbr0(xr) = v1 &
% 18.75/3.31          sbrdtbr0(xu) = v2 & $i(v2) & $i(v1) & iLess0(v1, v2))))
% 18.75/3.31  
% 18.75/3.31    (m__2673)
% 18.75/3.31     ~ (xr = sz00) & $i(xr) & $i(sz00)
% 18.75/3.31  
% 18.75/3.31    (m__2729)
% 18.75/3.31    $i(xr) & $i(xI) & aElementOf0(xr, xI)
% 18.75/3.31  
% 18.75/3.31    (function-axioms)
% 18.75/3.31     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.75/3.31      (sdtasasdt0(v3, v2) = v1) |  ~ (sdtasasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.75/3.31    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt1(v3, v2) = v1) |
% 18.75/3.31       ~ (sdtpldt1(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 18.75/3.31    [v3: $i] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0))
% 18.75/3.31    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.75/3.31      (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.75/3.31    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (slsdtgt0(v2) = v1) |  ~ (slsdtgt0(v2)
% 18.75/3.31        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 18.75/3.31      (sbrdtbr0(v2) = v1) |  ~ (sbrdtbr0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 18.75/3.31    ! [v2: $i] : (v1 = v0 |  ~ (smndt0(v2) = v1) |  ~ (smndt0(v2) = v0))
% 18.75/3.31  
% 18.75/3.31  Further assumptions not needed in the proof:
% 18.75/3.31  --------------------------------------------
% 18.75/3.31  mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 18.75/3.31  mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt,
% 18.75/3.31  mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso,
% 18.75/3.31  mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq,
% 18.75/3.31  mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__,
% 18.75/3.31  m__2091, m__2110, m__2129, m__2174, m__2203, m__2228, m__2383, m__2416, m__2479,
% 18.75/3.31  m__2612, m__2690, m__2699, m__2718
% 18.75/3.31  
% 18.75/3.31  Those formulas are unsatisfiable:
% 18.75/3.31  ---------------------------------
% 18.75/3.31  
% 18.75/3.31  Begin of proof
% 18.75/3.31  | 
% 18.75/3.31  | ALPHA: (m__2273) implies:
% 18.75/3.31  |   (1)   ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & $i(v0) &
% 18.75/3.31  |          aElementOf0(xu, xI) &  ! [v1: $i] :  ! [v2: $i] : (v1 = sz00 |  ~
% 18.75/3.31  |            (sbrdtbr0(v1) = v2) |  ~ $i(v1) |  ~ iLess0(v2, v0) |  ~
% 18.75/3.31  |            aElementOf0(v1, xI)))
% 18.75/3.31  | 
% 18.75/3.31  | ALPHA: (m__2666) implies:
% 18.75/3.31  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (sdtasdt0(xq, xu) = v0 &
% 18.75/3.31  |          sdtpldt0(v0, xr) = xb & $i(v0) & aElement0(xr) & aElement0(xq) & (xr
% 18.75/3.31  |            = sz00 | (sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & $i(v2) & $i(v1) &
% 18.75/3.31  |              iLess0(v1, v2))))
% 18.75/3.31  | 
% 18.75/3.31  | ALPHA: (m__2673) implies:
% 18.75/3.31  |   (3)   ~ (xr = sz00)
% 18.75/3.31  | 
% 18.75/3.31  | ALPHA: (m__2729) implies:
% 18.75/3.31  |   (4)  aElementOf0(xr, xI)
% 18.75/3.32  |   (5)  $i(xr)
% 18.75/3.32  | 
% 18.75/3.32  | ALPHA: (function-axioms) implies:
% 18.75/3.32  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (sbrdtbr0(v2) =
% 18.75/3.32  |            v1) |  ~ (sbrdtbr0(v2) = v0))
% 18.75/3.32  | 
% 18.75/3.32  | DELTA: instantiating (1) with fresh symbol all_45_0 gives:
% 18.75/3.32  |   (7)   ~ (xu = sz00) & sbrdtbr0(xu) = all_45_0 & $i(all_45_0) &
% 18.75/3.32  |        aElementOf0(xu, xI) &  ! [v0: $i] :  ! [v1: $i] : (v0 = sz00 |  ~
% 18.75/3.32  |          (sbrdtbr0(v0) = v1) |  ~ $i(v0) |  ~ iLess0(v1, all_45_0) |  ~
% 18.75/3.32  |          aElementOf0(v0, xI))
% 18.75/3.32  | 
% 18.75/3.32  | ALPHA: (7) implies:
% 18.75/3.32  |   (8)  sbrdtbr0(xu) = all_45_0
% 18.75/3.32  |   (9)   ! [v0: $i] :  ! [v1: $i] : (v0 = sz00 |  ~ (sbrdtbr0(v0) = v1) |  ~
% 18.75/3.32  |          $i(v0) |  ~ iLess0(v1, all_45_0) |  ~ aElementOf0(v0, xI))
% 18.75/3.32  | 
% 18.75/3.32  | DELTA: instantiating (2) with fresh symbols all_52_0, all_52_1, all_52_2
% 18.75/3.32  |        gives:
% 18.75/3.32  |   (10)  sdtasdt0(xq, xu) = all_52_2 & sdtpldt0(all_52_2, xr) = xb &
% 18.75/3.32  |         $i(all_52_2) & aElement0(xr) & aElement0(xq) & (xr = sz00 |
% 18.75/3.32  |           (sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 & $i(all_52_0) &
% 18.75/3.32  |             $i(all_52_1) & iLess0(all_52_1, all_52_0)))
% 18.75/3.32  | 
% 18.75/3.32  | ALPHA: (10) implies:
% 18.75/3.32  |   (11)  xr = sz00 | (sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 &
% 18.75/3.32  |           $i(all_52_0) & $i(all_52_1) & iLess0(all_52_1, all_52_0))
% 18.75/3.32  | 
% 18.75/3.32  | BETA: splitting (11) gives:
% 18.75/3.32  | 
% 18.75/3.32  | Case 1:
% 18.75/3.32  | | 
% 18.75/3.32  | |   (12)  xr = sz00
% 18.75/3.32  | | 
% 18.75/3.32  | | REDUCE: (3), (12) imply:
% 18.75/3.32  | |   (13)  $false
% 18.75/3.32  | | 
% 18.75/3.32  | | CLOSE: (13) is inconsistent.
% 18.75/3.32  | | 
% 18.75/3.32  | Case 2:
% 18.75/3.32  | | 
% 18.75/3.32  | |   (14)  sbrdtbr0(xr) = all_52_1 & sbrdtbr0(xu) = all_52_0 & $i(all_52_0) &
% 18.75/3.32  | |         $i(all_52_1) & iLess0(all_52_1, all_52_0)
% 18.75/3.32  | | 
% 18.75/3.32  | | ALPHA: (14) implies:
% 18.75/3.32  | |   (15)  iLess0(all_52_1, all_52_0)
% 18.75/3.32  | |   (16)  sbrdtbr0(xu) = all_52_0
% 18.75/3.32  | |   (17)  sbrdtbr0(xr) = all_52_1
% 18.75/3.32  | | 
% 18.75/3.32  | | GROUND_INST: instantiating (6) with all_45_0, all_52_0, xu, simplifying with
% 18.75/3.32  | |              (8), (16) gives:
% 18.75/3.32  | |   (18)  all_52_0 = all_45_0
% 18.75/3.32  | | 
% 18.75/3.32  | | REDUCE: (15), (18) imply:
% 18.75/3.32  | |   (19)  iLess0(all_52_1, all_45_0)
% 18.75/3.32  | | 
% 18.75/3.32  | | GROUND_INST: instantiating (9) with xr, all_52_1, simplifying with (4), (5),
% 18.75/3.32  | |              (17), (19) gives:
% 18.75/3.32  | |   (20)  xr = sz00
% 18.75/3.32  | | 
% 18.75/3.32  | | REDUCE: (3), (20) imply:
% 18.75/3.32  | |   (21)  $false
% 18.75/3.32  | | 
% 18.75/3.32  | | CLOSE: (21) is inconsistent.
% 18.75/3.32  | | 
% 18.75/3.32  | End of split
% 18.75/3.32  | 
% 18.75/3.32  End of proof
% 18.75/3.32  % SZS output end Proof for theBenchmark
% 18.75/3.32  
% 18.75/3.32  2703ms
%------------------------------------------------------------------------------