%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM555+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 : n021.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 11:48:35 EDT 2023 % Result : Theorem 18.20s 3.23s % Output : Proof 21.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 11:03:11 EDT 2023 % 0.13/0.34 % 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. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.67/1.20 Prover 1: Preprocessing ... % 3.67/1.20 Prover 4: Preprocessing ... % 4.05/1.24 Prover 6: Preprocessing ... % 4.05/1.24 Prover 2: Preprocessing ... % 4.05/1.24 Prover 5: Preprocessing ... % 4.05/1.24 Prover 0: Preprocessing ... % 4.05/1.24 Prover 3: Preprocessing ... % 10.83/2.20 Prover 3: Constructing countermodel ... % 10.83/2.21 Prover 1: Constructing countermodel ... % 10.83/2.25 Prover 6: Proving ... % 11.34/2.25 Prover 5: Constructing countermodel ... % 11.45/2.30 Prover 2: Proving ... % 13.55/2.63 Prover 4: Constructing countermodel ... % 13.55/2.64 Prover 0: Proving ... % 18.20/3.21 Prover 2: proved (2595ms) % 18.20/3.22 % 18.20/3.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.20/3.23 % 18.20/3.23 Prover 5: stopped % 18.20/3.24 Prover 3: stopped % 18.20/3.24 Prover 6: stopped % 18.20/3.24 Prover 0: stopped % 18.20/3.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.20/3.24 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.20/3.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.20/3.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.20/3.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.76/3.34 Prover 10: Preprocessing ... % 18.76/3.34 Prover 7: Preprocessing ... % 18.76/3.38 Prover 11: Preprocessing ... % 19.54/3.40 Prover 8: Preprocessing ... % 19.54/3.40 Prover 13: Preprocessing ... % 19.54/3.46 Prover 10: Constructing countermodel ... % 19.54/3.57 Prover 7: Constructing countermodel ... % 19.54/3.58 Prover 10: Found proof (size 18) % 19.54/3.58 Prover 10: proved (341ms) % 19.54/3.59 Prover 11: stopped % 19.54/3.59 Prover 1: stopped % 19.54/3.60 Prover 4: stopped % 19.54/3.60 Prover 7: stopped % 21.22/3.63 Prover 8: Warning: ignoring some quantifiers % 21.22/3.64 Prover 8: Constructing countermodel ... % 21.22/3.64 Prover 13: Constructing countermodel ... % 21.22/3.65 Prover 8: stopped % 21.22/3.66 Prover 13: stopped % 21.22/3.66 % 21.22/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.22/3.66 % 21.22/3.66 % SZS output start Proof for theBenchmark % 21.22/3.66 Assumptions after simplification: % 21.22/3.66 --------------------------------- % 21.22/3.66 % 21.22/3.67 (mDefDiff) % 21.22/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 21.22/3.69 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 21.22/3.69 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 21.22/3.69 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 21.22/3.69 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 21.22/3.69 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 21.22/3.69 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 21.22/3.69 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 21.22/3.69 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 21.22/3.69 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 21.22/3.69 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 21.22/3.69 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.22/3.69 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 21.22/3.69 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 21.22/3.69 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.22/3.69 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 21.22/3.69 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 21.22/3.69 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 21.22/3.69 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 21.22/3.69 % 21.22/3.69 (m__) % 21.22/3.69 $i(xy) & $i(xQ) & $i(xx) & ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & $i(v0) & % 21.22/3.69 aElementOf0(xx, v0)) % 21.22/3.69 % 21.22/3.69 (m__2291) % 21.22/3.69 sbrdtbr0(xQ) = xk & $i(xQ) & $i(xk) & isFinite0(xQ) & aSet0(xQ) % 21.22/3.69 % 21.22/3.69 (m__2304) % 21.22/3.69 $i(xy) & $i(xQ) & aElementOf0(xy, xQ) & aElement0(xy) % 21.22/3.69 % 21.22/3.69 (m__2323) % 21.22/3.70 $i(xQ) & $i(xx) & ~ aElementOf0(xx, xQ) % 21.22/3.70 % 21.22/3.70 (m__2338) % 21.22/3.70 $i(xQ) & $i(xx) & ~ aElementOf0(xx, xQ) % 21.22/3.70 % 21.22/3.70 (m__2357) % 21.22/3.70 $i(xP) & $i(xy) & $i(xQ) & $i(xx) & ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & % 21.22/3.70 sdtpldt0(v0, xx) = xP & $i(v0)) % 21.22/3.70 % 21.22/3.70 (function-axioms) % 21.22/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.22/3.70 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] % 21.22/3.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = % 21.22/3.70 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.22/3.70 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 21.22/3.70 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.22/3.70 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 21.22/3.70 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & % 21.22/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) % 21.22/3.70 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 21.22/3.70 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 21.22/3.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 21.22/3.70 (szszuzczcdt0(v2) = v0)) % 21.22/3.70 % 21.22/3.70 Further assumptions not needed in the proof: % 21.22/3.70 -------------------------------------------- % 21.22/3.70 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 21.22/3.70 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 21.22/3.70 mDefCons, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub, mDiffCons, % 21.22/3.70 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, % 21.22/3.70 mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 21.22/3.70 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, % 21.22/3.70 mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, % 21.22/3.70 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, % 21.22/3.70 m__2202, m__2202_02, m__2227, m__2256, m__2270 % 21.22/3.70 % 21.22/3.70 Those formulas are unsatisfiable: % 21.22/3.70 --------------------------------- % 21.22/3.70 % 21.22/3.70 Begin of proof % 21.22/3.70 | % 21.22/3.70 | ALPHA: (mDefDiff) implies: % 21.22/3.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 21.22/3.70 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.22/3.70 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) | % 21.22/3.70 | aElementOf0(v3, v0)) % 21.22/3.70 | % 21.22/3.70 | ALPHA: (m__2291) implies: % 21.22/3.70 | (2) aSet0(xQ) % 21.22/3.70 | % 21.22/3.70 | ALPHA: (m__2304) implies: % 21.22/3.70 | (3) aElement0(xy) % 21.22/3.70 | % 21.22/3.70 | ALPHA: (m__2338) implies: % 21.22/3.70 | (4) ~ aElementOf0(xx, xQ) % 21.22/3.70 | % 21.22/3.70 | ALPHA: (m__2357) implies: % 21.22/3.70 | (5) ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & sdtpldt0(v0, xx) = xP & $i(v0)) % 21.22/3.70 | % 21.22/3.70 | ALPHA: (m__) implies: % 21.22/3.70 | (6) $i(xx) % 21.22/3.70 | (7) $i(xQ) % 21.22/3.70 | (8) $i(xy) % 21.22/3.71 | (9) ? [v0: $i] : (sdtmndt0(xQ, xy) = v0 & $i(v0) & aElementOf0(xx, v0)) % 21.22/3.71 | % 21.22/3.71 | ALPHA: (function-axioms) implies: % 21.22/3.71 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.22/3.71 | (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 21.22/3.71 | % 21.22/3.71 | DELTA: instantiating (5) with fresh symbol all_53_0 gives: % 21.22/3.71 | (11) sdtmndt0(xQ, xy) = all_53_0 & sdtpldt0(all_53_0, xx) = xP & % 21.22/3.71 | $i(all_53_0) % 21.22/3.71 | % 21.22/3.71 | ALPHA: (11) implies: % 21.22/3.71 | (12) sdtmndt0(xQ, xy) = all_53_0 % 21.22/3.71 | % 21.22/3.71 | DELTA: instantiating (9) with fresh symbol all_57_0 gives: % 21.22/3.71 | (13) sdtmndt0(xQ, xy) = all_57_0 & $i(all_57_0) & aElementOf0(xx, all_57_0) % 21.22/3.71 | % 21.22/3.71 | ALPHA: (13) implies: % 21.22/3.71 | (14) aElementOf0(xx, all_57_0) % 21.22/3.71 | (15) $i(all_57_0) % 21.22/3.71 | (16) sdtmndt0(xQ, xy) = all_57_0 % 21.22/3.71 | % 21.22/3.71 | GROUND_INST: instantiating (10) with all_53_0, all_57_0, xy, xQ, simplifying % 21.22/3.71 | with (12), (16) gives: % 21.22/3.71 | (17) all_57_0 = all_53_0 % 21.22/3.71 | % 21.22/3.71 | REDUCE: (15), (17) imply: % 21.22/3.71 | (18) $i(all_53_0) % 21.22/3.71 | % 21.22/3.71 | REDUCE: (14), (17) imply: % 21.22/3.71 | (19) aElementOf0(xx, all_53_0) % 21.22/3.71 | % 21.22/3.71 | GROUND_INST: instantiating (1) with xQ, xy, all_53_0, xx, simplifying with % 21.22/3.71 | (2), (3), (4), (6), (7), (8), (12), (18), (19) gives: % 21.22/3.71 | (20) $false % 21.22/3.71 | % 21.22/3.71 | CLOSE: (20) is inconsistent. % 21.22/3.71 | % 21.22/3.71 End of proof % 21.22/3.71 % SZS output end Proof for theBenchmark % 21.22/3.71 % 21.22/3.71 3112ms %------------------------------------------------------------------------------