%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------