%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM576+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 : n024.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 11:48:43 EDT 2023 % Result : Theorem 21.85s 3.74s % Output : Proof 36.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM576+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n024.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 08:51:39 EDT 2023 % 0.13/0.33 % 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 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 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 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 % 4.65/1.42 Prover 4: Preprocessing ... % 4.65/1.44 Prover 1: Preprocessing ... % 5.31/1.46 Prover 6: Preprocessing ... % 5.31/1.46 Prover 0: Preprocessing ... % 5.31/1.46 Prover 3: Preprocessing ... % 5.31/1.46 Prover 5: Preprocessing ... % 5.31/1.46 Prover 2: Preprocessing ... % 13.96/2.61 Prover 6: Proving ... % 14.13/2.69 Prover 1: Constructing countermodel ... % 14.89/2.76 Prover 3: Constructing countermodel ... % 16.28/2.91 Prover 5: Proving ... % 21.85/3.64 Prover 2: Proving ... % 21.85/3.73 Prover 3: proved (3109ms) % 21.85/3.74 % 21.85/3.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.85/3.74 % 21.85/3.74 Prover 6: stopped % 21.85/3.74 Prover 5: stopped % 21.85/3.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.85/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.85/3.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.85/3.76 Prover 2: stopped % 21.85/3.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.96/3.94 Prover 11: Preprocessing ... % 24.38/3.98 Prover 8: Preprocessing ... % 24.38/3.98 Prover 10: Preprocessing ... % 24.38/4.00 Prover 7: Preprocessing ... % 28.29/4.49 Prover 7: Constructing countermodel ... % 28.29/4.49 Prover 8: Warning: ignoring some quantifiers % 28.56/4.53 Prover 8: Constructing countermodel ... % 29.21/4.61 Prover 10: Constructing countermodel ... % 29.79/4.72 Prover 4: Constructing countermodel ... % 33.52/5.19 Prover 10: Found proof (size 17) % 33.52/5.19 Prover 10: proved (1436ms) % 33.52/5.19 Prover 4: stopped % 33.52/5.19 Prover 8: stopped % 33.52/5.19 Prover 7: stopped % 33.52/5.19 Prover 1: stopped % 34.00/5.28 Prover 0: Proving ... % 34.00/5.29 Prover 0: stopped % 35.78/5.70 Prover 11: Constructing countermodel ... % 35.78/5.73 Prover 11: stopped % 35.78/5.73 % 35.78/5.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 35.78/5.73 % 35.78/5.73 % SZS output start Proof for theBenchmark % 35.78/5.74 Assumptions after simplification: % 35.78/5.74 --------------------------------- % 35.78/5.74 % 35.78/5.74 (mCountNFin_01) % 35.78/5.74 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 35.78/5.74 % 35.78/5.74 (mDefEmp) % 35.78/5.74 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 35.78/5.74 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 35.78/5.74 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 35.78/5.74 % 35.78/5.74 (mLessASymm) % 35.78/5.74 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | % 35.78/5.74 ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, szNzAzT0) % 35.78/5.74 | ~ aElementOf0(v0, szNzAzT0)) % 35.78/5.74 % 35.78/5.74 (mLessTotal) % 36.16/5.77 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) % 36.16/5.77 = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 36.16/5.77 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1)) % 36.16/5.77 % 36.16/5.77 (m__) % 36.16/5.77 $i(xj) & $i(xi) & ? [v0: $i] : ? [v1: $i] : ( ~ (xj = xi) & szszuzczcdt0(xj) % 36.16/5.77 = v0 & szszuzczcdt0(xi) = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, xj) & ~ % 36.16/5.77 sdtlseqdt0(v0, xi)) % 36.16/5.77 % 36.16/5.77 (m__3856) % 36.16/5.77 $i(xj) & $i(xi) & $i(szNzAzT0) & aElementOf0(xj, szNzAzT0) & aElementOf0(xi, % 36.16/5.77 szNzAzT0) % 36.16/5.77 % 36.16/5.77 Further assumptions not needed in the proof: % 36.16/5.77 -------------------------------------------- % 36.16/5.77 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 36.16/5.77 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 36.16/5.77 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 36.16/5.77 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 36.16/5.77 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 36.16/5.77 mImgRng, mLessRefl, mLessRel, mLessSucc, mLessTrans, mMinMin, mNATSet, % 36.16/5.77 mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc, % 36.16/5.77 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, % 36.16/5.77 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, % 36.16/5.77 mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520, % 36.16/5.77 m__3533, m__3623, m__3671, m__3754 % 36.16/5.77 % 36.16/5.77 Those formulas are unsatisfiable: % 36.16/5.77 --------------------------------- % 36.16/5.77 % 36.16/5.77 Begin of proof % 36.16/5.77 | % 36.16/5.77 | ALPHA: (mDefEmp) implies: % 36.16/5.77 | (1) aSet0(slcrc0) % 36.16/5.77 | % 36.16/5.77 | ALPHA: (mCountNFin_01) implies: % 36.16/5.77 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 36.16/5.77 | % 36.16/5.77 | ALPHA: (mLessASymm) implies: % 36.16/5.77 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 36.16/5.77 | sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, % 36.16/5.77 | szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 36.16/5.77 | % 36.16/5.77 | ALPHA: (mLessTotal) implies: % 36.16/5.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) = v2) | % 36.16/5.77 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 36.16/5.77 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1)) % 36.16/5.77 | % 36.16/5.77 | ALPHA: (m__3856) implies: % 36.16/5.78 | (5) aElementOf0(xi, szNzAzT0) % 36.16/5.78 | (6) aElementOf0(xj, szNzAzT0) % 36.16/5.78 | % 36.16/5.78 | ALPHA: (m__) implies: % 36.16/5.78 | (7) $i(xi) % 36.16/5.78 | (8) $i(xj) % 36.16/5.78 | (9) ? [v0: $i] : ? [v1: $i] : ( ~ (xj = xi) & szszuzczcdt0(xj) = v0 & % 36.16/5.78 | szszuzczcdt0(xi) = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, xj) & ~ % 36.16/5.78 | sdtlseqdt0(v0, xi)) % 36.16/5.78 | % 36.16/5.78 | DELTA: instantiating (9) with fresh symbols all_69_0, all_69_1 gives: % 36.16/5.78 | (10) ~ (xj = xi) & szszuzczcdt0(xj) = all_69_1 & szszuzczcdt0(xi) = % 36.16/5.78 | all_69_0 & $i(all_69_0) & $i(all_69_1) & ~ sdtlseqdt0(all_69_0, xj) & % 36.16/5.78 | ~ sdtlseqdt0(all_69_1, xi) % 36.16/5.78 | % 36.16/5.78 | ALPHA: (10) implies: % 36.16/5.78 | (11) ~ (xj = xi) % 36.16/5.78 | (12) ~ sdtlseqdt0(all_69_1, xi) % 36.16/5.78 | (13) ~ sdtlseqdt0(all_69_0, xj) % 36.16/5.78 | (14) szszuzczcdt0(xi) = all_69_0 % 36.16/5.78 | (15) szszuzczcdt0(xj) = all_69_1 % 36.16/5.78 | % 36.16/5.78 | BETA: splitting (2) gives: % 36.16/5.78 | % 36.16/5.78 | Case 1: % 36.16/5.78 | | % 36.16/5.78 | | (16) ~ aSet0(slcrc0) % 36.16/5.78 | | % 36.16/5.78 | | PRED_UNIFY: (1), (16) imply: % 36.16/5.78 | | (17) $false % 36.16/5.78 | | % 36.16/5.78 | | CLOSE: (17) is inconsistent. % 36.16/5.78 | | % 36.16/5.78 | Case 2: % 36.16/5.78 | | % 36.16/5.78 | | % 36.16/5.78 | | GROUND_INST: instantiating (4) with xj, xi, all_69_0, simplifying with (5), % 36.16/5.78 | | (6), (7), (8), (13), (14) gives: % 36.16/5.78 | | (18) sdtlseqdt0(xj, xi) % 36.16/5.78 | | % 36.16/5.78 | | GROUND_INST: instantiating (4) with xi, xj, all_69_1, simplifying with (5), % 36.16/5.78 | | (6), (7), (8), (12), (15) gives: % 36.16/5.78 | | (19) sdtlseqdt0(xi, xj) % 36.16/5.78 | | % 36.16/5.78 | | GROUND_INST: instantiating (3) with xi, xj, simplifying with (5), (6), (7), % 36.16/5.78 | | (8), (18), (19) gives: % 36.16/5.78 | | (20) xj = xi % 36.16/5.78 | | % 36.16/5.78 | | REDUCE: (11), (20) imply: % 36.16/5.78 | | (21) $false % 36.16/5.78 | | % 36.16/5.78 | | CLOSE: (21) is inconsistent. % 36.16/5.78 | | % 36.16/5.78 | End of split % 36.16/5.78 | % 36.16/5.78 End of proof % 36.16/5.78 % SZS output end Proof for theBenchmark % 36.16/5.79 % 36.16/5.79 5192ms %------------------------------------------------------------------------------