%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM613+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 : n015.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 19.26s 3.42s % Output : Proof 28.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : NUM613+1 : TPTP v8.1.2. Released v4.0.0. % 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n015.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 13:53:07 EDT 2023 % 0.13/0.33 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.39/1.48 Prover 1: Preprocessing ... % 5.56/1.50 Prover 4: Preprocessing ... % 5.82/1.53 Prover 2: Preprocessing ... % 5.82/1.53 Prover 0: Preprocessing ... % 5.82/1.53 Prover 6: Preprocessing ... % 5.82/1.54 Prover 3: Preprocessing ... % 5.82/1.54 Prover 5: Preprocessing ... % 14.62/2.76 Prover 1: Constructing countermodel ... % 14.62/2.79 Prover 3: Constructing countermodel ... % 14.62/2.79 Prover 6: Proving ... % 16.37/2.93 Prover 5: Proving ... % 16.37/3.00 Prover 2: Proving ... % 19.26/3.41 Prover 3: proved (2783ms) % 19.26/3.41 % 19.26/3.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.26/3.42 % 19.26/3.43 Prover 5: stopped % 19.26/3.43 Prover 6: stopped % 19.26/3.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.26/3.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.26/3.44 Prover 2: stopped % 19.26/3.45 Prover 4: Constructing countermodel ... % 19.26/3.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.26/3.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.55/3.63 Prover 8: Preprocessing ... % 21.55/3.65 Prover 0: Proving ... % 21.55/3.69 Prover 0: stopped % 21.55/3.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.55/3.72 Prover 7: Preprocessing ... % 22.29/3.74 Prover 11: Preprocessing ... % 22.29/3.74 Prover 10: Preprocessing ... % 23.48/3.89 Prover 13: Preprocessing ... % 23.89/3.97 Prover 8: Warning: ignoring some quantifiers % 23.89/3.99 Prover 8: Constructing countermodel ... % 23.89/3.99 Prover 10: Constructing countermodel ... % 24.65/4.04 Prover 7: Constructing countermodel ... % 25.20/4.23 Prover 13: Warning: ignoring some quantifiers % 25.20/4.25 Prover 13: Constructing countermodel ... % 26.75/4.32 Prover 10: Found proof (size 19) % 26.75/4.32 Prover 10: proved (875ms) % 26.75/4.32 Prover 4: stopped % 26.75/4.32 Prover 7: stopped % 26.75/4.33 Prover 8: stopped % 26.75/4.33 Prover 1: stopped % 26.75/4.33 Prover 13: stopped % 28.02/4.63 Prover 11: Constructing countermodel ... % 28.19/4.67 Prover 11: stopped % 28.19/4.67 % 28.19/4.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 28.19/4.67 % 28.19/4.68 % SZS output start Proof for theBenchmark % 28.19/4.69 Assumptions after simplification: % 28.19/4.69 --------------------------------- % 28.19/4.69 % 28.19/4.69 (mSuccEquSucc) % 28.56/4.73 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.56/4.74 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 28.56/4.74 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 28.56/4.74 % 28.56/4.74 (m__) % 28.56/4.74 $i(xP) & $i(xk) & ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0)) % 28.56/4.74 % 28.56/4.74 (m__3533) % 28.56/4.74 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk, % 28.56/4.74 szNzAzT0) % 28.56/4.74 % 28.56/4.74 (m__5255) % 28.56/4.74 $i(xP) & $i(xQ) & $i(xk) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 28.56/4.74 (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 & szszuzczcdt0(v1) = v0 & % 28.56/4.74 szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, szNzAzT0)) % 28.56/4.74 % 28.56/4.74 (function-axioms) % 28.56/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.56/4.76 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 28.56/4.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 28.56/4.76 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 28.56/4.76 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 28.56/4.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 28.56/4.76 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 28.56/4.76 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 28.56/4.76 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 28.56/4.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 28.56/4.76 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 28.56/4.76 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 28.56/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 28.56/4.76 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 28.56/4.76 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 28.56/4.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 28.56/4.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.56/4.76 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 28.56/4.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 28.56/4.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.56/4.76 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 28.56/4.76 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 28.56/4.76 v0)) % 28.56/4.76 % 28.56/4.76 Further assumptions not needed in the proof: % 28.56/4.76 -------------------------------------------- % 28.56/4.76 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 28.56/4.76 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 28.56/4.76 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 28.56/4.76 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 28.56/4.76 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 28.56/4.76 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 28.56/4.76 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 28.56/4.76 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 28.56/4.76 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 28.56/4.76 mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, % 28.56/4.76 m__3453, m__3462, m__3520, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, % 28.56/4.76 m__4182, m__4331, m__4411, m__4618, m__4660, m__4730, m__4758, m__4854, m__4891, % 28.56/4.76 m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147, m__5164, % 28.56/4.76 m__5173, m__5182, m__5195, m__5208 % 28.56/4.76 % 28.56/4.76 Those formulas are unsatisfiable: % 28.56/4.76 --------------------------------- % 28.56/4.76 % 28.56/4.76 Begin of proof % 28.56/4.76 | % 28.56/4.76 | ALPHA: (mSuccEquSucc) implies: % 28.56/4.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.56/4.76 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ % 28.56/4.76 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 28.56/4.76 | % 28.56/4.76 | ALPHA: (m__3533) implies: % 28.56/4.77 | (2) aElementOf0(xk, szNzAzT0) % 28.56/4.77 | (3) szszuzczcdt0(xk) = xK % 28.56/4.77 | % 28.56/4.77 | ALPHA: (m__5255) implies: % 28.56/4.77 | (4) ? [v0: $i] : ? [v1: $i] : (sbrdtbr0(xP) = v1 & sbrdtbr0(xQ) = v0 & % 28.56/4.77 | szszuzczcdt0(v1) = v0 & szszuzczcdt0(xk) = v0 & $i(v1) & $i(v0) & % 28.56/4.77 | aElementOf0(v1, szNzAzT0)) % 28.56/4.77 | % 28.56/4.77 | ALPHA: (m__) implies: % 28.56/4.77 | (5) $i(xk) % 28.56/4.77 | (6) ? [v0: $i] : ( ~ (v0 = xk) & sbrdtbr0(xP) = v0 & $i(v0)) % 28.56/4.77 | % 28.56/4.77 | ALPHA: (function-axioms) implies: % 28.56/4.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.56/4.77 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 28.56/4.77 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) = % 28.56/4.77 | v1) | ~ (sbrdtbr0(v2) = v0)) % 28.56/4.77 | % 28.56/4.77 | DELTA: instantiating (6) with fresh symbol all_76_0 gives: % 28.56/4.77 | (9) ~ (all_76_0 = xk) & sbrdtbr0(xP) = all_76_0 & $i(all_76_0) % 28.56/4.77 | % 28.56/4.77 | ALPHA: (9) implies: % 28.56/4.77 | (10) ~ (all_76_0 = xk) % 28.56/4.77 | (11) sbrdtbr0(xP) = all_76_0 % 28.56/4.77 | % 28.56/4.77 | DELTA: instantiating (4) with fresh symbols all_90_0, all_90_1 gives: % 28.56/4.77 | (12) sbrdtbr0(xP) = all_90_0 & sbrdtbr0(xQ) = all_90_1 & % 28.56/4.77 | szszuzczcdt0(all_90_0) = all_90_1 & szszuzczcdt0(xk) = all_90_1 & % 28.56/4.77 | $i(all_90_0) & $i(all_90_1) & aElementOf0(all_90_0, szNzAzT0) % 28.56/4.77 | % 28.56/4.77 | ALPHA: (12) implies: % 28.56/4.77 | (13) aElementOf0(all_90_0, szNzAzT0) % 28.56/4.77 | (14) $i(all_90_0) % 28.56/4.77 | (15) szszuzczcdt0(xk) = all_90_1 % 28.56/4.77 | (16) szszuzczcdt0(all_90_0) = all_90_1 % 28.56/4.77 | (17) sbrdtbr0(xP) = all_90_0 % 28.56/4.77 | % 28.56/4.77 | GROUND_INST: instantiating (7) with xK, all_90_1, xk, simplifying with (3), % 28.56/4.77 | (15) gives: % 28.56/4.78 | (18) all_90_1 = xK % 28.56/4.78 | % 28.56/4.78 | GROUND_INST: instantiating (8) with all_76_0, all_90_0, xP, simplifying with % 28.56/4.78 | (11), (17) gives: % 28.56/4.78 | (19) all_90_0 = all_76_0 % 28.56/4.78 | % 28.56/4.78 | REDUCE: (16), (18), (19) imply: % 28.56/4.78 | (20) szszuzczcdt0(all_76_0) = xK % 28.56/4.78 | % 28.56/4.78 | REDUCE: (14), (19) imply: % 28.56/4.78 | (21) $i(all_76_0) % 28.56/4.78 | % 28.56/4.78 | REDUCE: (13), (19) imply: % 28.56/4.78 | (22) aElementOf0(all_76_0, szNzAzT0) % 28.56/4.78 | % 28.56/4.78 | GROUND_INST: instantiating (1) with xk, all_76_0, xK, simplifying with (2), % 28.56/4.78 | (3), (5), (20), (21), (22) gives: % 28.56/4.78 | (23) all_76_0 = xk % 28.56/4.78 | % 28.56/4.78 | REDUCE: (10), (23) imply: % 28.56/4.78 | (24) $false % 28.56/4.78 | % 28.56/4.78 | CLOSE: (24) is inconsistent. % 28.56/4.78 | % 28.56/4.78 End of proof % 28.56/4.78 % SZS output end Proof for theBenchmark % 28.56/4.78 % 28.56/4.78 4189ms %------------------------------------------------------------------------------