TSTP Solution File: NUM602+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM602+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 11:48:53 EDT 2023
% Result : Theorem 24.58s 4.05s
% Output : Proof 45.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM602+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 07:49:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.48/1.63 Prover 4: Preprocessing ...
% 6.48/1.63 Prover 1: Preprocessing ...
% 6.82/1.66 Prover 2: Preprocessing ...
% 6.82/1.66 Prover 0: Preprocessing ...
% 6.82/1.66 Prover 3: Preprocessing ...
% 6.82/1.66 Prover 6: Preprocessing ...
% 6.82/1.66 Prover 5: Preprocessing ...
% 19.11/3.37 Prover 1: Constructing countermodel ...
% 19.11/3.37 Prover 3: Constructing countermodel ...
% 19.91/3.41 Prover 6: Proving ...
% 21.86/3.70 Prover 5: Proving ...
% 24.58/4.05 Prover 3: proved (3431ms)
% 24.58/4.05
% 24.58/4.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.58/4.05
% 24.58/4.06 Prover 5: stopped
% 24.58/4.06 Prover 6: stopped
% 24.58/4.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.58/4.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.58/4.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.63/4.41 Prover 10: Preprocessing ...
% 27.63/4.41 Prover 8: Preprocessing ...
% 27.63/4.42 Prover 7: Preprocessing ...
% 31.75/4.97 Prover 8: Warning: ignoring some quantifiers
% 31.75/5.00 Prover 8: Constructing countermodel ...
% 34.09/5.30 Prover 10: Constructing countermodel ...
% 35.19/5.44 Prover 7: Constructing countermodel ...
% 38.90/5.92 Prover 10: Found proof (size 18)
% 38.90/5.92 Prover 10: proved (1852ms)
% 38.90/5.93 Prover 7: stopped
% 39.44/5.93 Prover 8: stopped
% 39.44/5.93 Prover 1: stopped
% 42.91/6.58 Prover 4: Constructing countermodel ...
% 42.91/6.61 Prover 4: stopped
% 45.04/6.92 Prover 2: Proving ...
% 45.04/6.94 Prover 2: stopped
% 45.04/6.95 Prover 0: Proving ...
% 45.35/6.97 Prover 0: stopped
% 45.35/6.97
% 45.35/6.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.35/6.97
% 45.35/6.98 % SZS output start Proof for theBenchmark
% 45.35/6.99 Assumptions after simplification:
% 45.35/6.99 ---------------------------------
% 45.35/6.99
% 45.35/6.99 (mCountNFin_01)
% 45.35/7.00 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 45.35/7.00
% 45.35/7.00 (mDefEmp)
% 45.35/7.00 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 45.35/7.00 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 45.35/7.00 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 45.35/7.00
% 45.35/7.00 (m__)
% 45.35/7.04 $i(xx) & $i(xe) & $i(szNzAzT0) & ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) |
% 45.35/7.04 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0))
% 45.35/7.04
% 45.35/7.04 (m__4982)
% 45.35/7.05 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 45.35/7.05 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 45.35/7.05 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 45.35/7.05 aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 45.35/7.05 sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) & aElementOf0(v4,
% 45.35/7.05 szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ?
% 45.35/7.05 [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 & sdtlpdtrp0(xe, v3) = v2 & $i(v3) &
% 45.35/7.05 aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 45.35/7.05
% 45.35/7.05 (m__5009)
% 45.35/7.05 $i(xx) & $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 45.35/7.05 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xx &
% 45.35/7.05 $i(v2) & $i(v1) & $i(v0) & aElementOf0(v2, v1) & aElementOf0(xx, xO))
% 45.35/7.05
% 45.35/7.05 Further assumptions not needed in the proof:
% 45.35/7.05 --------------------------------------------
% 45.35/7.05 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 45.35/7.05 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 45.35/7.05 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 45.35/7.05 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 45.35/7.05 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 45.35/7.05 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 45.35/7.05 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 45.35/7.05 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 45.35/7.05 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 45.35/7.05 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 45.35/7.05 m__3520, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182,
% 45.35/7.05 m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, m__4908
% 45.35/7.05
% 45.35/7.05 Those formulas are unsatisfiable:
% 45.35/7.05 ---------------------------------
% 45.35/7.05
% 45.35/7.05 Begin of proof
% 45.35/7.05 |
% 45.35/7.05 | ALPHA: (mDefEmp) implies:
% 45.35/7.06 | (1) aSet0(slcrc0)
% 45.35/7.06 |
% 45.35/7.06 | ALPHA: (mCountNFin_01) implies:
% 45.35/7.06 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 45.35/7.06 |
% 45.35/7.06 | ALPHA: (m__4982) implies:
% 45.35/7.06 | (3) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) =
% 45.35/7.06 | v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 45.35/7.06 | (sdtlpdtrp0(xe, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 45.35/7.06 | aElementOf0(v3, v1) | ? [v4: $i] : (sdtlpdtrp0(xd, v4) = v0 &
% 45.35/7.06 | sdtlpdtrp0(xe, v4) = v2 & $i(v4) & aElementOf0(v4, v1) &
% 45.35/7.06 | aElementOf0(v4, szNzAzT0))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 45.35/7.06 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v0 &
% 45.35/7.06 | sdtlpdtrp0(xe, v3) = v2 & $i(v3) & aElementOf0(v3, v1) &
% 45.35/7.06 | aElementOf0(v3, szNzAzT0))))
% 45.35/7.06 |
% 45.35/7.06 | ALPHA: (m__5009) implies:
% 45.35/7.06 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 45.35/7.06 | sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, v2) = xx & $i(v2) & $i(v1) &
% 45.35/7.06 | $i(v0) & aElementOf0(v2, v1) & aElementOf0(xx, xO))
% 45.77/7.06 |
% 45.77/7.06 | ALPHA: (m__) implies:
% 45.77/7.07 | (5) $i(xx)
% 45.77/7.07 | (6) ! [v0: $i] : ( ~ (sdtlpdtrp0(xe, v0) = xx) | ~ $i(v0) | ~
% 45.77/7.07 | aElementOf0(v0, szNzAzT0))
% 45.77/7.07 |
% 45.77/7.07 | DELTA: instantiating (4) with fresh symbols all_78_0, all_78_1, all_78_2
% 45.77/7.07 | gives:
% 45.77/7.07 | (7) szDzizrdt0(xd) = all_78_2 & sdtlbdtrb0(xd, all_78_2) = all_78_1 &
% 45.77/7.07 | sdtlpdtrp0(xe, all_78_0) = xx & $i(all_78_0) & $i(all_78_1) &
% 45.77/7.07 | $i(all_78_2) & aElementOf0(all_78_0, all_78_1) & aElementOf0(xx, xO)
% 45.77/7.07 |
% 45.77/7.07 | ALPHA: (7) implies:
% 45.77/7.07 | (8) aElementOf0(xx, xO)
% 45.77/7.07 |
% 45.77/7.07 | DELTA: instantiating (3) with fresh symbols all_86_0, all_86_1 gives:
% 45.77/7.07 | (9) szDzizrdt0(xd) = all_86_1 & sdtlbdtrb0(xd, all_86_1) = all_86_0 &
% 45.77/7.07 | $i(all_86_0) & $i(all_86_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 45.77/7.07 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 45.77/7.07 | aElementOf0(v1, all_86_0) | ? [v2: $i] : (sdtlpdtrp0(xd, v2) =
% 45.77/7.07 | all_86_1 & sdtlpdtrp0(xe, v2) = v0 & $i(v2) & aElementOf0(v2,
% 45.77/7.07 | all_86_0) & aElementOf0(v2, szNzAzT0))) & ! [v0: $i] : ( ~
% 45.77/7.07 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xd, v1) =
% 45.77/7.07 | all_86_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) & aElementOf0(v1,
% 45.77/7.07 | all_86_0) & aElementOf0(v1, szNzAzT0)))
% 45.77/7.07 |
% 45.77/7.07 | ALPHA: (9) implies:
% 45.77/7.07 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] :
% 45.77/7.07 | (sdtlpdtrp0(xd, v1) = all_86_1 & sdtlpdtrp0(xe, v1) = v0 & $i(v1) &
% 45.77/7.07 | aElementOf0(v1, all_86_0) & aElementOf0(v1, szNzAzT0)))
% 45.77/7.07 |
% 45.77/7.07 | BETA: splitting (2) gives:
% 45.77/7.07 |
% 45.77/7.07 | Case 1:
% 45.77/7.07 | |
% 45.77/7.07 | | (11) ~ aSet0(slcrc0)
% 45.77/7.07 | |
% 45.77/7.08 | | PRED_UNIFY: (1), (11) imply:
% 45.77/7.08 | | (12) $false
% 45.77/7.08 | |
% 45.77/7.08 | | CLOSE: (12) is inconsistent.
% 45.77/7.08 | |
% 45.77/7.08 | Case 2:
% 45.77/7.08 | |
% 45.77/7.08 | |
% 45.77/7.08 | | GROUND_INST: instantiating (10) with xx, simplifying with (5), (8) gives:
% 45.77/7.08 | | (13) ? [v0: $i] : (sdtlpdtrp0(xd, v0) = all_86_1 & sdtlpdtrp0(xe, v0) =
% 45.77/7.08 | | xx & $i(v0) & aElementOf0(v0, all_86_0) & aElementOf0(v0,
% 45.77/7.08 | | szNzAzT0))
% 45.77/7.08 | |
% 45.77/7.08 | | DELTA: instantiating (13) with fresh symbol all_120_0 gives:
% 45.77/7.08 | | (14) sdtlpdtrp0(xd, all_120_0) = all_86_1 & sdtlpdtrp0(xe, all_120_0) =
% 45.77/7.08 | | xx & $i(all_120_0) & aElementOf0(all_120_0, all_86_0) &
% 45.77/7.08 | | aElementOf0(all_120_0, szNzAzT0)
% 45.77/7.08 | |
% 45.77/7.08 | | ALPHA: (14) implies:
% 45.77/7.08 | | (15) aElementOf0(all_120_0, szNzAzT0)
% 45.77/7.08 | | (16) $i(all_120_0)
% 45.77/7.08 | | (17) sdtlpdtrp0(xe, all_120_0) = xx
% 45.77/7.08 | |
% 45.77/7.08 | | GROUND_INST: instantiating (6) with all_120_0, simplifying with (15), (16),
% 45.77/7.08 | | (17) gives:
% 45.77/7.08 | | (18) $false
% 45.77/7.08 | |
% 45.77/7.08 | | CLOSE: (18) is inconsistent.
% 45.77/7.08 | |
% 45.77/7.08 | End of split
% 45.77/7.08 |
% 45.77/7.08 End of proof
% 45.77/7.08 % SZS output end Proof for theBenchmark
% 45.77/7.08
% 45.77/7.08 6482ms
%------------------------------------------------------------------------------