TSTP Solution File: RNG101+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG101+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 : n015.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 13:57:52 EDT 2023
% Result : Theorem 19.21s 3.30s
% Output : Proof 19.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG101+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n015.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 : Sun Aug 27 01:59:23 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 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 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 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 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 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
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.85/1.21 Prover 1: Preprocessing ...
% 3.85/1.21 Prover 4: Preprocessing ...
% 3.85/1.25 Prover 6: Preprocessing ...
% 3.85/1.25 Prover 3: Preprocessing ...
% 3.85/1.25 Prover 5: Preprocessing ...
% 3.85/1.25 Prover 0: Preprocessing ...
% 3.85/1.25 Prover 2: Preprocessing ...
% 9.24/1.96 Prover 5: Proving ...
% 9.24/1.99 Prover 3: Constructing countermodel ...
% 9.24/2.00 Prover 1: Constructing countermodel ...
% 9.24/2.00 Prover 6: Proving ...
% 9.24/2.10 Prover 2: Proving ...
% 11.25/2.27 Prover 4: Constructing countermodel ...
% 12.09/2.37 Prover 0: Proving ...
% 12.49/2.41 Prover 3: gave up
% 12.49/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.82/2.49 Prover 7: Preprocessing ...
% 13.54/2.58 Prover 1: gave up
% 13.87/2.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.35/2.68 Prover 8: Preprocessing ...
% 14.35/2.74 Prover 7: Constructing countermodel ...
% 16.19/2.93 Prover 8: Warning: ignoring some quantifiers
% 16.19/2.94 Prover 8: Constructing countermodel ...
% 18.51/3.29 Prover 7: Found proof (size 11)
% 18.51/3.29 Prover 7: proved (874ms)
% 18.51/3.29 Prover 4: stopped
% 18.51/3.29 Prover 6: stopped
% 18.51/3.29 Prover 0: stopped
% 18.51/3.29 Prover 2: stopped
% 19.21/3.29 Prover 5: stopped
% 19.21/3.30 Prover 8: stopped
% 19.21/3.30
% 19.21/3.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.21/3.30
% 19.21/3.30 % SZS output start Proof for theBenchmark
% 19.21/3.30 Assumptions after simplification:
% 19.21/3.30 ---------------------------------
% 19.21/3.30
% 19.21/3.30 (mDefPrIdeal)
% 19.21/3.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 19.21/3.33 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.21/3.33 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 19.21/3.33 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 19.21/3.33 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 19.21/3.33 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 19.21/3.33 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 19.21/3.33 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 19.21/3.33 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 19.21/3.33 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 19.21/3.33 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 19.21/3.33 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 19.21/3.33 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 19.21/3.33
% 19.21/3.33 (m__)
% 19.21/3.33 $i(xx) & $i(xc) & ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xx) | ~ $i(v0) | ~
% 19.21/3.33 aElement0(v0))
% 19.21/3.33
% 19.21/3.33 (m__1905)
% 19.21/3.33 $i(xc) & aElement0(xc)
% 19.21/3.33
% 19.21/3.33 (m__1933)
% 19.21/3.34 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0)
% 19.21/3.34 & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz))
% 19.21/3.34
% 19.21/3.34 Further assumptions not needed in the proof:
% 19.21/3.34 --------------------------------------------
% 19.21/3.34 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 19.21/3.34 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 19.21/3.34 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm,
% 19.21/3.34 mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort, mSortsB,
% 19.21/3.34 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr
% 19.21/3.34
% 19.21/3.34 Those formulas are unsatisfiable:
% 19.21/3.34 ---------------------------------
% 19.21/3.34
% 19.21/3.34 Begin of proof
% 19.21/3.34 |
% 19.21/3.34 | ALPHA: (mDefPrIdeal) implies:
% 19.21/3.34 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 19.21/3.34 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 19.21/3.34 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 19.21/3.34 | aElement0(v3)))
% 19.21/3.34 |
% 19.21/3.34 | ALPHA: (m__1905) implies:
% 19.21/3.34 | (2) aElement0(xc)
% 19.21/3.34 |
% 19.21/3.34 | ALPHA: (m__1933) implies:
% 19.21/3.34 | (3) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) &
% 19.21/3.34 | aElementOf0(xx, v0) & aElement0(xz))
% 19.21/3.34 |
% 19.21/3.34 | ALPHA: (m__) implies:
% 19.21/3.34 | (4) $i(xc)
% 19.21/3.34 | (5) $i(xx)
% 19.21/3.34 | (6) ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = xx) | ~ $i(v0) | ~
% 19.21/3.34 | aElement0(v0))
% 19.21/3.34 |
% 19.21/3.34 | DELTA: instantiating (3) with fresh symbol all_34_0 gives:
% 19.21/3.34 | (7) slsdtgt0(xc) = all_34_0 & $i(all_34_0) & aElementOf0(xy, all_34_0) &
% 19.21/3.34 | aElementOf0(xx, all_34_0) & aElement0(xz)
% 19.21/3.34 |
% 19.21/3.34 | ALPHA: (7) implies:
% 19.21/3.34 | (8) aElementOf0(xx, all_34_0)
% 19.21/3.34 | (9) $i(all_34_0)
% 19.21/3.34 | (10) slsdtgt0(xc) = all_34_0
% 19.21/3.34 |
% 19.21/3.34 | GROUND_INST: instantiating (1) with xc, all_34_0, xx, simplifying with (2),
% 19.21/3.34 | (4), (5), (8), (9), (10) gives:
% 19.21/3.34 | (11) ? [v0: $i] : (sdtasdt0(xc, v0) = xx & $i(v0) & aElement0(v0))
% 19.21/3.34 |
% 19.21/3.34 | DELTA: instantiating (11) with fresh symbol all_45_0 gives:
% 19.21/3.35 | (12) sdtasdt0(xc, all_45_0) = xx & $i(all_45_0) & aElement0(all_45_0)
% 19.21/3.35 |
% 19.21/3.35 | ALPHA: (12) implies:
% 19.21/3.35 | (13) aElement0(all_45_0)
% 19.21/3.35 | (14) $i(all_45_0)
% 19.21/3.35 | (15) sdtasdt0(xc, all_45_0) = xx
% 19.21/3.35 |
% 19.21/3.35 | GROUND_INST: instantiating (6) with all_45_0, simplifying with (13), (14),
% 19.21/3.35 | (15) gives:
% 19.21/3.35 | (16) $false
% 19.21/3.35 |
% 19.21/3.35 | CLOSE: (16) is inconsistent.
% 19.21/3.35 |
% 19.21/3.35 End of proof
% 19.21/3.35 % SZS output end Proof for theBenchmark
% 19.21/3.35
% 19.21/3.35 2726ms
%------------------------------------------------------------------------------