%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM551+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 : n002.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 11:48:34 EDT 2023 % Result : Theorem 27.14s 4.29s % Output : Proof 34.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM551+1 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n002.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Aug 25 12:18:02 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.85/1.20 Prover 4: Preprocessing ... % 3.85/1.20 Prover 1: Preprocessing ... % 3.85/1.24 Prover 3: Preprocessing ... % 3.85/1.24 Prover 0: Preprocessing ... % 3.85/1.24 Prover 2: Preprocessing ... % 3.85/1.24 Prover 5: Preprocessing ... % 3.85/1.24 Prover 6: Preprocessing ... % 10.00/2.07 Prover 1: Constructing countermodel ... % 10.20/2.09 Prover 3: Constructing countermodel ... % 10.64/2.15 Prover 6: Proving ... % 10.84/2.17 Prover 5: Constructing countermodel ... % 11.70/2.30 Prover 2: Proving ... % 13.29/2.58 Prover 4: Constructing countermodel ... % 14.53/2.67 Prover 0: Proving ... % 27.14/4.28 Prover 3: proved (3653ms) % 27.14/4.28 % 27.14/4.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.14/4.29 % 27.14/4.30 Prover 5: stopped % 27.14/4.30 Prover 6: stopped % 27.14/4.30 Prover 0: stopped % 27.14/4.30 Prover 2: stopped % 27.14/4.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.14/4.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.14/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.14/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 27.14/4.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.86/4.53 Prover 7: Preprocessing ... % 28.86/4.58 Prover 8: Preprocessing ... % 28.86/4.60 Prover 11: Preprocessing ... % 29.64/4.61 Prover 13: Preprocessing ... % 29.64/4.61 Prover 10: Preprocessing ... % 30.35/4.71 Prover 7: Constructing countermodel ... % 30.35/4.76 Prover 8: Warning: ignoring some quantifiers % 30.35/4.77 Prover 8: Constructing countermodel ... % 31.09/4.79 Prover 10: Constructing countermodel ... % 31.98/4.91 Prover 13: Constructing countermodel ... % 32.68/5.10 Prover 11: Constructing countermodel ... % 34.03/5.17 Prover 10: Found proof (size 23) % 34.03/5.17 Prover 10: proved (873ms) % 34.03/5.17 Prover 11: stopped % 34.03/5.17 Prover 13: stopped % 34.03/5.17 Prover 7: stopped % 34.03/5.17 Prover 8: stopped % 34.03/5.17 Prover 1: stopped % 34.03/5.18 Prover 4: stopped % 34.03/5.18 % 34.03/5.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 34.03/5.18 % 34.03/5.18 % SZS output start Proof for theBenchmark % 34.08/5.18 Assumptions after simplification: % 34.08/5.18 --------------------------------- % 34.08/5.18 % 34.08/5.18 (mDefEmp) % 34.08/5.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 34.08/5.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 34.08/5.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 34.08/5.19 % 34.08/5.19 (mDefSeg) % 34.20/5.22 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 34.20/5.22 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 34.20/5.22 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 34.20/5.22 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 34.20/5.22 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 34.20/5.22 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 34.20/5.22 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 34.20/5.22 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 34.20/5.22 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 34.20/5.22 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 34.20/5.22 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 34.20/5.22 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 34.20/5.22 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 34.20/5.22 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 34.20/5.22 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 34.20/5.22 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 34.20/5.22 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 34.20/5.22 | aSet0(v1)) % 34.20/5.22 % 34.20/5.22 (mEOfElem) % 34.20/5.22 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 34.20/5.22 ~ aSet0(v0) | aElement0(v1)) % 34.20/5.22 % 34.20/5.22 (mSegZero) % 34.20/5.22 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 34.20/5.22 % 34.20/5.22 (mZeroNum) % 34.20/5.22 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 34.20/5.22 % 34.20/5.22 (m__) % 34.20/5.22 $i(xQ) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0)) % 34.20/5.22 % 34.20/5.22 (m__2202_02) % 34.20/5.22 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS) % 34.20/5.22 % 34.20/5.22 (m__2291) % 34.20/5.22 sbrdtbr0(xQ) = xk & $i(xQ) & $i(xk) & isFinite0(xQ) & aSet0(xQ) % 34.20/5.22 % 34.20/5.22 (m__2313) % 34.27/5.22 ~ (xQ = slcrc0) & $i(xQ) & $i(slcrc0) % 34.27/5.22 % 34.27/5.22 Further assumptions not needed in the proof: % 34.27/5.22 -------------------------------------------- % 34.27/5.22 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 34.27/5.22 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 34.27/5.22 mDefCons, mDefDiff, mDefMax, mDefMin, mDefSel, mDefSub, mDiffCons, mElmSort, % 34.27/5.22 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm, % 34.27/5.22 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, % 34.27/5.22 mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSelCSet, % 34.27/5.22 mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 34.27/5.22 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, m__2202, m__2227, m__2256, m__2270 % 34.27/5.22 % 34.27/5.22 Those formulas are unsatisfiable: % 34.27/5.22 --------------------------------- % 34.27/5.22 % 34.27/5.22 Begin of proof % 34.27/5.22 | % 34.27/5.22 | ALPHA: (mDefEmp) implies: % 34.27/5.22 | (1) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] : % 34.27/5.22 | ($i(v1) & aElementOf0(v1, v0))) % 34.27/5.22 | % 34.27/5.22 | ALPHA: (mZeroNum) implies: % 34.27/5.22 | (2) aElementOf0(sz00, szNzAzT0) % 34.27/5.22 | % 34.27/5.22 | ALPHA: (mDefSeg) implies: % 34.27/5.23 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = % 34.27/5.23 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ % 34.27/5.23 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3, % 34.27/5.23 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 & % 34.27/5.23 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) | % 34.27/5.23 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) & % 34.27/5.23 | aElementOf0(v3, szNzAzT0))))) % 34.27/5.23 | % 34.27/5.23 | ALPHA: (mSegZero) implies: % 34.27/5.23 | (4) slbdtrb0(sz00) = slcrc0 % 34.27/5.23 | % 34.27/5.23 | ALPHA: (m__2202_02) implies: % 34.27/5.23 | (5) $i(sz00) % 34.27/5.23 | % 34.27/5.23 | ALPHA: (m__2291) implies: % 34.27/5.23 | (6) aSet0(xQ) % 34.27/5.23 | % 34.27/5.23 | ALPHA: (m__2313) implies: % 34.27/5.23 | (7) ~ (xQ = slcrc0) % 34.27/5.23 | % 34.27/5.23 | ALPHA: (m__) implies: % 34.27/5.23 | (8) $i(xQ) % 34.27/5.23 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0)) % 34.27/5.23 | % 34.27/5.23 | GROUND_INST: instantiating (1) with xQ, simplifying with (6), (8) gives: % 34.27/5.23 | (10) xQ = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ)) % 34.27/5.23 | % 34.27/5.23 | GROUND_INST: instantiating (3) with sz00, slcrc0, xQ, simplifying with (2), % 34.27/5.23 | (4), (5), (6), (8) gives: % 34.27/5.23 | (11) xQ = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ % 34.27/5.23 | aElementOf0(v0, xQ) | ~ aElementOf0(v0, szNzAzT0) | % 34.27/5.23 | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) & % 34.27/5.23 | (aElementOf0(v0, xQ) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 34.27/5.23 | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0)))) % 34.27/5.23 | % 34.27/5.23 | BETA: splitting (10) gives: % 34.27/5.23 | % 34.27/5.23 | Case 1: % 34.27/5.23 | | % 34.27/5.23 | | (12) xQ = slcrc0 % 34.27/5.23 | | % 34.27/5.23 | | REDUCE: (7), (12) imply: % 34.27/5.23 | | (13) $false % 34.27/5.23 | | % 34.27/5.23 | | CLOSE: (13) is inconsistent. % 34.27/5.23 | | % 34.27/5.23 | Case 2: % 34.27/5.23 | | % 34.27/5.23 | | (14) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ)) % 34.27/5.23 | | % 34.27/5.23 | | DELTA: instantiating (14) with fresh symbol all_87_0 gives: % 34.27/5.23 | | (15) $i(all_87_0) & aElementOf0(all_87_0, xQ) % 34.27/5.23 | | % 34.27/5.23 | | ALPHA: (15) implies: % 34.27/5.23 | | (16) aElementOf0(all_87_0, xQ) % 34.27/5.23 | | (17) $i(all_87_0) % 34.27/5.23 | | % 34.27/5.23 | | BETA: splitting (11) gives: % 34.27/5.23 | | % 34.27/5.23 | | Case 1: % 34.27/5.23 | | | % 34.27/5.23 | | | (18) xQ = slcrc0 % 34.27/5.23 | | | % 34.27/5.23 | | | REDUCE: (7), (18) imply: % 34.27/5.23 | | | (19) $false % 34.27/5.23 | | | % 34.27/5.23 | | | CLOSE: (19) is inconsistent. % 34.27/5.24 | | | % 34.27/5.24 | | Case 2: % 34.27/5.24 | | | % 34.27/5.24 | | | % 34.27/5.24 | | | GROUND_INST: instantiating (mEOfElem) with xQ, all_87_0, simplifying with % 34.27/5.24 | | | (6), (8), (16), (17) gives: % 34.27/5.24 | | | (20) aElement0(all_87_0) % 34.27/5.24 | | | % 34.27/5.24 | | | GROUND_INST: instantiating (9) with all_87_0, simplifying with (16), (17), % 34.27/5.24 | | | (20) gives: % 34.27/5.24 | | | (21) $false % 34.27/5.24 | | | % 34.27/5.24 | | | CLOSE: (21) is inconsistent. % 34.27/5.24 | | | % 34.27/5.24 | | End of split % 34.27/5.24 | | % 34.27/5.24 | End of split % 34.27/5.24 | % 34.27/5.24 End of proof % 34.27/5.24 % SZS output end Proof for theBenchmark % 34.27/5.24 % 34.27/5.24 4630ms %------------------------------------------------------------------------------