%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM605+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 : n004.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 11:48:55 EDT 2023 % Result : Theorem 32.91s 5.11s % Output : Proof 41.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM605+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.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 08:36:38 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.16/1.35 Prover 4: Preprocessing ... % 4.16/1.36 Prover 1: Preprocessing ... % 5.05/1.41 Prover 5: Preprocessing ... % 5.05/1.41 Prover 6: Preprocessing ... % 5.05/1.41 Prover 2: Preprocessing ... % 5.05/1.41 Prover 3: Preprocessing ... % 5.05/1.41 Prover 0: Preprocessing ... % 13.80/2.66 Prover 1: Constructing countermodel ... % 14.95/2.77 Prover 6: Proving ... % 14.95/2.78 Prover 3: Constructing countermodel ... % 16.68/2.97 Prover 5: Proving ... % 18.14/3.17 Prover 2: Proving ... % 23.34/3.88 Prover 4: Constructing countermodel ... % 26.91/4.32 Prover 0: Proving ... % 32.91/5.10 Prover 2: proved (4494ms) % 32.91/5.11 % 32.91/5.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 32.91/5.11 % 32.91/5.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 32.91/5.12 Prover 3: stopped % 32.91/5.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.91/5.12 Prover 5: stopped % 32.91/5.12 Prover 6: stopped % 32.91/5.12 Prover 0: stopped % 32.91/5.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.91/5.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 32.91/5.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 34.13/5.33 Prover 11: Preprocessing ... % 34.13/5.34 Prover 8: Preprocessing ... % 34.13/5.35 Prover 7: Preprocessing ... % 34.13/5.35 Prover 13: Preprocessing ... % 34.13/5.38 Prover 10: Preprocessing ... % 36.79/5.61 Prover 7: Constructing countermodel ... % 37.50/5.71 Prover 10: Constructing countermodel ... % 37.50/5.73 Prover 8: Warning: ignoring some quantifiers % 37.50/5.74 Prover 8: Constructing countermodel ... % 38.16/5.86 Prover 13: Warning: ignoring some quantifiers % 38.96/5.89 Prover 13: Constructing countermodel ... % 40.48/6.12 Prover 10: Found proof (size 21) % 40.48/6.12 Prover 10: proved (984ms) % 40.48/6.12 Prover 8: stopped % 40.48/6.12 Prover 7: stopped % 40.48/6.12 Prover 1: stopped % 40.48/6.12 Prover 13: stopped % 40.48/6.12 Prover 4: stopped % 41.43/6.35 Prover 11: Constructing countermodel ... % 41.43/6.38 Prover 11: stopped % 41.43/6.38 % 41.43/6.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 41.43/6.38 % 41.43/6.39 % SZS output start Proof for theBenchmark % 41.80/6.40 Assumptions after simplification: % 41.80/6.40 --------------------------------- % 41.80/6.40 % 41.80/6.40 (mCardSeg) % 41.80/6.44 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) % 41.80/6.44 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 41.80/6.44 % 41.80/6.44 (mDefSel) % 41.80/6.45 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 41.80/6.45 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | % 41.80/6.45 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 41.80/6.45 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 41.80/6.45 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ % 41.80/6.45 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 41.80/6.45 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 41.80/6.45 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 41.80/6.45 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 41.80/6.45 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ? % 41.80/6.45 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~ % 41.80/6.45 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) & % 41.80/6.45 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4, % 41.80/6.45 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 41.80/6.45 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~ % 41.80/6.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1, % 41.80/6.45 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 41.80/6.45 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) % 41.80/6.45 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2)) % 41.80/6.45 % 41.80/6.45 (mSegZero) % 41.80/6.45 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 41.80/6.45 % 41.80/6.45 (mZeroNum) % 41.80/6.45 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 41.80/6.45 % 41.80/6.45 (m__) % 41.80/6.45 xQ = slcrc0 & $i(slcrc0) % 41.80/6.45 % 41.80/6.45 (m__3418) % 41.80/6.45 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 41.80/6.45 % 41.80/6.45 (m__3462) % 41.80/6.45 ~ (xK = sz00) & $i(xK) & $i(sz00) % 41.80/6.45 % 41.80/6.45 (m__3520) % 41.80/6.46 ~ (xK = sz00) & $i(xK) & $i(sz00) % 41.80/6.46 % 41.80/6.46 (m__3623) % 41.80/6.46 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 41.80/6.46 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 41.80/6.46 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 41.80/6.46 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 41.80/6.46 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i] % 41.80/6.46 : (sdtlpdtrp0(xN, v4) = v5 & szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & % 41.80/6.46 aSubsetOf0(v5, v3) & isCountable0(v5))) % 41.80/6.46 % 41.80/6.46 (m__4891) % 41.80/6.46 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 41.80/6.46 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 41.80/6.46 aSet0(xO)) % 41.80/6.46 % 41.80/6.46 (m__5078) % 41.80/6.46 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) & % 41.80/6.46 aElementOf0(xQ, v0)) % 41.80/6.46 % 41.80/6.46 Further assumptions not needed in the proof: % 41.80/6.46 -------------------------------------------- % 41.80/6.46 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 41.80/6.46 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, % 41.80/6.46 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, % 41.80/6.46 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 41.80/6.46 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 41.80/6.46 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 41.80/6.46 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 41.80/6.46 mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 41.80/6.46 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 41.80/6.46 m__3291, m__3398, m__3435, m__3453, m__3533, m__3671, m__3754, m__3821, m__3965, % 41.80/6.46 m__4151, m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, % 41.80/6.46 m__4908, m__4982, m__4998 % 41.80/6.46 % 41.80/6.46 Those formulas are unsatisfiable: % 41.80/6.46 --------------------------------- % 41.80/6.46 % 41.80/6.46 Begin of proof % 41.80/6.46 | % 41.80/6.46 | ALPHA: (mZeroNum) implies: % 41.80/6.46 | (1) aElementOf0(sz00, szNzAzT0) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (mSegZero) implies: % 41.80/6.46 | (2) slbdtrb0(sz00) = slcrc0 % 41.80/6.46 | % 41.80/6.46 | ALPHA: (mCardSeg) implies: % 41.80/6.46 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~ % 41.80/6.46 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (mDefSel) implies: % 41.80/6.46 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 41.80/6.46 | (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | ~ % 41.80/6.46 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | % 41.80/6.46 | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (m__3418) implies: % 41.80/6.46 | (5) aElementOf0(xK, szNzAzT0) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (m__3520) implies: % 41.80/6.46 | (6) ~ (xK = sz00) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (m__3623) implies: % 41.80/6.46 | (7) $i(sz00) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (m__4891) implies: % 41.80/6.46 | (8) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = % 41.80/6.46 | xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 41.80/6.46 | % 41.80/6.46 | ALPHA: (m__5078) implies: % 41.80/6.47 | (9) $i(xK) % 41.80/6.47 | (10) $i(xO) % 41.80/6.47 | (11) $i(xQ) % 41.80/6.47 | (12) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) & aElementOf0(xQ, % 41.80/6.47 | v0)) % 41.80/6.47 | % 41.80/6.47 | ALPHA: (m__) implies: % 41.80/6.47 | (13) xQ = slcrc0 % 41.80/6.47 | % 41.80/6.47 | DELTA: instantiating (12) with fresh symbol all_76_0 gives: % 41.80/6.47 | (14) slbdtsldtrb0(xO, xK) = all_76_0 & $i(all_76_0) & aElementOf0(xQ, % 41.80/6.47 | all_76_0) % 41.80/6.47 | % 41.80/6.47 | ALPHA: (14) implies: % 41.80/6.47 | (15) aElementOf0(xQ, all_76_0) % 41.80/6.47 | (16) $i(all_76_0) % 41.80/6.47 | (17) slbdtsldtrb0(xO, xK) = all_76_0 % 41.80/6.47 | % 41.80/6.47 | DELTA: instantiating (8) with fresh symbols all_82_0, all_82_1 gives: % 41.80/6.47 | (18) szDzizrdt0(xd) = all_82_1 & sdtlcdtrc0(xe, all_82_0) = xO & % 41.80/6.47 | sdtlbdtrb0(xd, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1) & % 41.80/6.47 | aSet0(xO) % 41.80/6.47 | % 41.80/6.47 | ALPHA: (18) implies: % 41.80/6.47 | (19) aSet0(xO) % 41.80/6.47 | % 41.80/6.47 | REDUCE: (11), (13) imply: % 41.80/6.47 | (20) $i(slcrc0) % 41.80/6.47 | % 41.80/6.47 | REDUCE: (13), (15) imply: % 41.80/6.47 | (21) aElementOf0(slcrc0, all_76_0) % 41.80/6.47 | % 41.80/6.47 | GROUND_INST: instantiating (3) with sz00, slcrc0, simplifying with (1), (2), % 41.80/6.47 | (7) gives: % 41.80/6.47 | (22) sbrdtbr0(slcrc0) = sz00 % 41.80/6.47 | % 41.80/6.47 | GROUND_INST: instantiating (4) with xO, xK, all_76_0, slcrc0, sz00, % 41.80/6.47 | simplifying with (5), (9), (10), (16), (17), (19), (20), (21), % 41.80/6.47 | (22) gives: % 41.80/6.47 | (23) xK = sz00 % 41.80/6.47 | % 41.80/6.47 | REDUCE: (6), (23) imply: % 41.80/6.47 | (24) $false % 41.80/6.47 | % 41.80/6.47 | CLOSE: (24) is inconsistent. % 41.80/6.47 | % 41.80/6.47 End of proof % 41.80/6.47 % SZS output end Proof for theBenchmark % 41.80/6.47 % 41.80/6.47 5882ms %------------------------------------------------------------------------------