%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM613+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 : n014.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 11:48:58 EDT 2023 % Result : Theorem 23.60s 4.03s % Output : Proof 48.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM613+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n014.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 16:38:02 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.83/1.57 Prover 4: Preprocessing ... % 4.83/1.58 Prover 1: Preprocessing ... % 6.73/1.70 Prover 6: Preprocessing ... % 6.73/1.70 Prover 5: Preprocessing ... % 6.73/1.70 Prover 3: Preprocessing ... % 6.73/1.70 Prover 0: Preprocessing ... % 6.73/1.73 Prover 2: Preprocessing ... % 19.06/3.37 Prover 6: Proving ... % 19.06/3.37 Prover 3: Constructing countermodel ... % 19.06/3.37 Prover 1: Constructing countermodel ... % 21.92/3.75 Prover 5: Proving ... % 23.60/4.02 Prover 3: proved (3371ms) % 23.60/4.02 % 23.60/4.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 23.60/4.03 % 24.24/4.04 Prover 6: stopped % 24.24/4.04 Prover 5: stopped % 24.24/4.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.24/4.06 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.24/4.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.91/4.34 Prover 8: Preprocessing ... % 25.91/4.35 Prover 10: Preprocessing ... % 26.84/4.41 Prover 7: Preprocessing ... % 30.50/4.94 Prover 8: Warning: ignoring some quantifiers % 30.50/4.98 Prover 8: Constructing countermodel ... % 34.69/5.43 Prover 10: Constructing countermodel ... % 36.15/5.62 Prover 7: Constructing countermodel ... % 40.53/6.19 Prover 10: Found proof (size 22) % 40.53/6.20 Prover 10: proved (2121ms) % 40.53/6.20 Prover 7: stopped % 40.53/6.20 Prover 1: stopped % 40.53/6.20 Prover 8: stopped % 44.15/6.76 Prover 4: Constructing countermodel ... % 44.15/6.79 Prover 4: stopped % 44.91/6.94 Prover 2: Proving ... % 45.41/6.97 Prover 2: stopped % 47.58/7.55 Prover 0: Proving ... % 47.89/7.57 Prover 0: stopped % 47.89/7.57 % 47.89/7.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 47.89/7.57 % 47.95/7.58 % SZS output start Proof for theBenchmark % 47.95/7.59 Assumptions after simplification: % 47.95/7.59 --------------------------------- % 47.95/7.59 % 47.95/7.59 (mSuccEquSucc) % 48.13/7.65 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.13/7.65 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 48.13/7.65 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 48.13/7.65 % 48.13/7.65 (m__) % 48.13/7.65 $i(xP) & $i(xk) & ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0)) % 48.13/7.65 % 48.13/7.65 (m__3533) % 48.13/7.65 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk, % 48.13/7.65 szNzAzT0) % 48.13/7.65 % 48.13/7.65 (m__5078) % 48.13/7.65 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & % 48.13/7.66 sbrdtbr0(xQ) = xK & $i(v0) & aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & % 48.13/7.66 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | % 48.13/7.66 aElementOf0(v1, xO))) % 48.13/7.66 % 48.13/7.66 (m__5255) % 48.13/7.66 $i(xP) & $i(xQ) & $i(xk) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 48.13/7.66 (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 & szszuzczcdt0(v1) = v0 & % 48.13/7.66 szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0)) % 48.13/7.66 % 48.13/7.66 (function-axioms) % 48.13/7.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.13/7.67 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 48.13/7.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 48.13/7.67 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 48.13/7.67 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 48.13/7.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 48.13/7.67 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 48.13/7.67 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 48.13/7.67 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 48.13/7.67 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 48.13/7.67 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 48.13/7.67 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 48.13/7.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 48.13/7.67 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 48.13/7.67 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 48.13/7.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 48.13/7.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.13/7.67 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 48.13/7.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 48.13/7.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.13/7.67 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 48.13/7.67 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 48.13/7.67 v0)) % 48.13/7.67 % 48.13/7.67 Further assumptions not needed in the proof: % 48.13/7.67 -------------------------------------------- % 48.13/7.67 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 48.13/7.67 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 48.13/7.67 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 48.13/7.67 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 48.13/7.67 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 48.13/7.67 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 48.13/7.67 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 48.13/7.67 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 48.13/7.67 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 48.13/7.67 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, % 48.13/7.67 m__3453, m__3462, m__3520, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, % 48.13/7.67 m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, % 48.13/7.67 m__4908, m__4982, m__4998, m__5093, m__5106, m__5116, m__5147, m__5164, m__5173, % 48.13/7.67 m__5182, m__5195, m__5208 % 48.13/7.67 % 48.13/7.67 Those formulas are unsatisfiable: % 48.13/7.67 --------------------------------- % 48.13/7.67 % 48.13/7.67 Begin of proof % 48.13/7.68 | % 48.13/7.68 | ALPHA: (mSuccEquSucc) implies: % 48.13/7.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 48.13/7.68 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ % 48.13/7.68 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 48.13/7.68 | % 48.13/7.68 | ALPHA: (m__3533) implies: % 48.13/7.68 | (2) aElementOf0(xk, szNzAzT0) % 48.13/7.68 | % 48.13/7.68 | ALPHA: (m__5078) implies: % 48.13/7.68 | (3) ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & sbrdtbr0(xQ) = xK & $i(v0) & % 48.13/7.68 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] : % 48.13/7.68 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xO))) % 48.13/7.68 | % 48.13/7.68 | ALPHA: (m__5255) implies: % 48.13/7.68 | (4) ? [v0: $i] : ? [v1: $i] : (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 & % 48.13/7.68 | szszuzczcdt0(v1) = v0 & szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) & % 48.13/7.68 | aElementOf0(v1, szNzAzT0)) % 48.13/7.68 | % 48.13/7.68 | ALPHA: (m__) implies: % 48.13/7.68 | (5) $i(xk) % 48.13/7.68 | (6) ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0)) % 48.13/7.68 | % 48.13/7.68 | ALPHA: (function-axioms) implies: % 48.13/7.68 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = % 48.13/7.68 | v1) | ~ (sbrdtbr0(v2) = v0)) % 48.13/7.68 | % 48.13/7.69 | DELTA: instantiating (6) with fresh symbol all_82_0 gives: % 48.13/7.69 | (8) ~ (all_82_0 = xk) & sbrdtbr0(xP) = all_82_0 & $i(all_82_0) % 48.13/7.69 | % 48.13/7.69 | ALPHA: (8) implies: % 48.13/7.69 | (9) ~ (all_82_0 = xk) % 48.13/7.69 | (10) sbrdtbr0(xP) = all_82_0 % 48.13/7.69 | % 48.13/7.69 | DELTA: instantiating (4) with fresh symbols all_92_0, all_92_1 gives: % 48.13/7.69 | (11) sbrdtbr0(xP) = all_92_0 & sbrdtbr0(xQ) = all_92_1 & % 48.13/7.69 | szszuzczcdt0(all_92_0) = all_92_1 & szszuzczcdt0(xk) = all_92_1 & % 48.13/7.69 | $i(all_92_0) & $i(all_92_1) & aElementOf0(all_92_0, szNzAzT0) % 48.13/7.69 | % 48.13/7.69 | ALPHA: (11) implies: % 48.13/7.69 | (12) aElementOf0(all_92_0, szNzAzT0) % 48.13/7.69 | (13) $i(all_92_0) % 48.13/7.69 | (14) szszuzczcdt0(xk) = all_92_1 % 48.13/7.69 | (15) szszuzczcdt0(all_92_0) = all_92_1 % 48.13/7.69 | (16) sbrdtbr0(xQ) = all_92_1 % 48.13/7.69 | (17) sbrdtbr0(xP) = all_92_0 % 48.13/7.69 | % 48.13/7.69 | DELTA: instantiating (3) with fresh symbol all_94_0 gives: % 48.13/7.69 | (18) slbdtsldtrb0(xO, xK) = all_94_0 & sbrdtbr0(xQ) = xK & $i(all_94_0) & % 48.13/7.69 | aSubsetOf0(xQ, xO) & aElementOf0(xQ, all_94_0) & aSet0(xQ) & ! [v0: % 48.13/7.69 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO)) % 48.13/7.69 | % 48.13/7.69 | ALPHA: (18) implies: % 48.13/7.69 | (19) sbrdtbr0(xQ) = xK % 48.13/7.69 | % 48.13/7.69 | GROUND_INST: instantiating (7) with xK, all_92_1, xQ, simplifying with (16), % 48.13/7.69 | (19) gives: % 48.13/7.69 | (20) all_92_1 = xK % 48.13/7.69 | % 48.13/7.69 | GROUND_INST: instantiating (7) with all_82_0, all_92_0, xP, simplifying with % 48.13/7.69 | (10), (17) gives: % 48.13/7.69 | (21) all_92_0 = all_82_0 % 48.13/7.69 | % 48.13/7.69 | REDUCE: (15), (20), (21) imply: % 48.13/7.69 | (22) szszuzczcdt0(all_82_0) = xK % 48.13/7.69 | % 48.13/7.69 | REDUCE: (14), (20) imply: % 48.13/7.69 | (23) szszuzczcdt0(xk) = xK % 48.13/7.69 | % 48.13/7.69 | REDUCE: (13), (21) imply: % 48.13/7.69 | (24) $i(all_82_0) % 48.13/7.69 | % 48.13/7.69 | REDUCE: (12), (21) imply: % 48.13/7.69 | (25) aElementOf0(all_82_0, szNzAzT0) % 48.13/7.69 | % 48.13/7.69 | GROUND_INST: instantiating (1) with xk, all_82_0, xK, simplifying with (2), % 48.13/7.69 | (5), (22), (23), (24), (25) gives: % 48.13/7.69 | (26) all_82_0 = xk % 48.13/7.69 | % 48.13/7.69 | REDUCE: (9), (26) imply: % 48.13/7.69 | (27) $false % 48.13/7.69 | % 48.13/7.69 | CLOSE: (27) is inconsistent. % 48.13/7.69 | % 48.13/7.69 End of proof % 48.13/7.69 % SZS output end Proof for theBenchmark % 48.13/7.69 % 48.13/7.69 7073ms %------------------------------------------------------------------------------