%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM557+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 : n023.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 19.09s 3.19s % Output : Proof 24.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM557+1 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n023.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 13:27:56 EDT 2023 % 0.13/0.34 % CPUTime : % 0.52/0.61 ________ _____ % 0.52/0.61 ___ __ \_________(_)________________________________ % 0.52/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.61 % 0.52/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.61 (2023-06-19) % 0.52/0.61 % 0.52/0.61 (c) Philipp Rümmer, 2009-2023 % 0.52/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.61 Amanda Stjerna. % 0.52/0.61 Free software under BSD-3-Clause. % 0.52/0.61 % 0.52/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.61 % 0.52/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.62 Running up to 7 provers in parallel. % 0.52/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.52/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 3.69/1.20 Prover 1: Preprocessing ... % 3.69/1.20 Prover 4: Preprocessing ... % 4.14/1.24 Prover 3: Preprocessing ... % 4.14/1.24 Prover 5: Preprocessing ... % 4.14/1.24 Prover 0: Preprocessing ... % 4.14/1.24 Prover 2: Preprocessing ... % 4.14/1.24 Prover 6: Preprocessing ... % 10.27/2.04 Prover 1: Constructing countermodel ... % 10.46/2.12 Prover 3: Constructing countermodel ... % 10.91/2.15 Prover 6: Proving ... % 11.19/2.19 Prover 5: Constructing countermodel ... % 12.10/2.33 Prover 2: Proving ... % 15.54/2.73 Prover 4: Constructing countermodel ... % 16.52/2.86 Prover 0: Proving ... % 19.09/3.18 Prover 2: proved (2557ms) % 19.09/3.18 % 19.09/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.09/3.19 % 19.09/3.19 Prover 3: stopped % 19.09/3.19 Prover 0: stopped % 19.09/3.19 Prover 6: stopped % 19.09/3.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.09/3.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.09/3.19 Prover 5: stopped % 19.09/3.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.09/3.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.09/3.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.64/3.31 Prover 8: Preprocessing ... % 19.64/3.32 Prover 13: Preprocessing ... % 20.18/3.33 Prover 7: Preprocessing ... % 20.18/3.35 Prover 11: Preprocessing ... % 20.18/3.35 Prover 10: Preprocessing ... % 21.65/3.53 Prover 8: Warning: ignoring some quantifiers % 21.65/3.53 Prover 8: Constructing countermodel ... % 21.65/3.54 Prover 10: Constructing countermodel ... % 21.65/3.54 Prover 7: Constructing countermodel ... % 22.85/3.69 Prover 13: Constructing countermodel ... % 23.56/3.83 Prover 10: Found proof (size 23) % 23.56/3.83 Prover 10: proved (641ms) % 23.56/3.83 Prover 7: stopped % 23.56/3.83 Prover 8: stopped % 24.05/3.83 Prover 1: stopped % 24.05/3.83 Prover 4: stopped % 24.05/3.83 Prover 13: stopped % 24.19/3.89 Prover 11: Constructing countermodel ... % 24.19/3.91 Prover 11: stopped % 24.19/3.91 % 24.19/3.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 24.19/3.91 % 24.19/3.92 % SZS output start Proof for theBenchmark % 24.19/3.92 Assumptions after simplification: % 24.19/3.92 --------------------------------- % 24.19/3.92 % 24.19/3.92 (mDefSel) % 24.54/3.95 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 24.54/3.95 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | % 24.54/3.95 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 24.54/3.95 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 24.54/3.95 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ % 24.54/3.95 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 24.54/3.95 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 24.54/3.95 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 24.54/3.95 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 24.54/3.95 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ? % 24.54/3.95 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~ % 24.54/3.95 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) & % 24.54/3.95 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4, % 24.54/3.95 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 24.54/3.95 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~ % 24.54/3.95 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1, % 24.54/3.95 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 24.54/3.95 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) % 24.54/3.95 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2)) % 24.54/3.95 % 24.54/3.95 (m__) % 24.54/3.95 $i(xP) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & % 24.54/3.95 ~ aElementOf0(xP, v0)) % 24.54/3.95 % 24.54/3.95 (m__2202) % 24.54/3.95 $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0) % 24.54/3.95 % 24.54/3.95 (m__2202_02) % 24.54/3.95 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS) % 24.54/3.95 % 24.54/3.95 (m__2227) % 24.54/3.96 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = % 24.54/3.96 slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & % 24.54/3.96 $i(v0) & aSubsetOf0(v0, v1)) % 24.54/3.96 % 24.54/3.96 (m__2270) % 24.54/3.96 $i(xQ) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & % 24.54/3.96 aElementOf0(xQ, v0)) % 24.54/3.96 % 24.54/3.96 (m__2431) % 24.54/3.96 sbrdtbr0(xP) = xk & $i(xP) & $i(xS) & $i(xk) & aSubsetOf0(xP, xS) % 24.54/3.96 % 24.54/3.96 (function-axioms) % 24.54/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 24.54/3.96 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] % 24.54/3.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = % 24.54/3.96 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.54/3.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 24.54/3.96 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 24.54/3.96 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 24.54/3.96 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & % 24.54/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) % 24.54/3.96 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 24.54/3.96 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 24.54/3.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 24.54/3.96 (szszuzczcdt0(v2) = v0)) % 24.54/3.96 % 24.54/3.96 Further assumptions not needed in the proof: % 24.54/3.96 -------------------------------------------- % 24.54/3.96 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 24.54/3.96 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 24.54/3.96 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSub, mDiffCons, % 24.54/3.96 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, % 24.54/3.96 mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 24.54/3.96 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, % 24.54/3.96 mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, % 24.54/3.96 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, % 24.54/3.96 m__2256, m__2291, m__2304, m__2323, m__2338, m__2357, m__2411 % 24.54/3.96 % 24.54/3.96 Those formulas are unsatisfiable: % 24.54/3.96 --------------------------------- % 24.54/3.96 % 24.54/3.96 Begin of proof % 24.54/3.96 | % 24.54/3.96 | ALPHA: (mDefSel) implies: % 24.54/3.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 24.54/3.97 | (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~ % 24.54/3.97 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ % 24.54/3.97 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__2202) implies: % 24.54/3.97 | (2) aElementOf0(xk, szNzAzT0) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__2202_02) implies: % 24.54/3.97 | (3) aSet0(xS) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__2227) implies: % 24.54/3.97 | (4) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) = % 24.54/3.97 | v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, % 24.54/3.97 | v1)) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__2270) implies: % 24.54/3.97 | (5) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & aElementOf0(xQ, % 24.54/3.97 | v0)) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__2431) implies: % 24.54/3.97 | (6) aSubsetOf0(xP, xS) % 24.54/3.97 | (7) sbrdtbr0(xP) = xk % 24.54/3.97 | % 24.54/3.97 | ALPHA: (m__) implies: % 24.54/3.97 | (8) $i(xk) % 24.54/3.97 | (9) $i(xS) % 24.54/3.97 | (10) $i(xP) % 24.54/3.97 | (11) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & ~ aElementOf0(xP, % 24.54/3.97 | v0)) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (function-axioms) implies: % 24.54/3.97 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 24.54/3.97 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) % 24.54/3.97 | % 24.54/3.97 | DELTA: instantiating (11) with fresh symbol all_55_0 gives: % 24.54/3.97 | (13) slbdtsldtrb0(xS, xk) = all_55_0 & $i(all_55_0) & ~ aElementOf0(xP, % 24.54/3.97 | all_55_0) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (13) implies: % 24.54/3.97 | (14) ~ aElementOf0(xP, all_55_0) % 24.54/3.97 | (15) slbdtsldtrb0(xS, xk) = all_55_0 % 24.54/3.97 | % 24.54/3.97 | DELTA: instantiating (5) with fresh symbol all_57_0 gives: % 24.54/3.97 | (16) slbdtsldtrb0(xS, xk) = all_57_0 & $i(all_57_0) & aElementOf0(xQ, % 24.54/3.97 | all_57_0) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (16) implies: % 24.54/3.97 | (17) $i(all_57_0) % 24.54/3.97 | (18) slbdtsldtrb0(xS, xk) = all_57_0 % 24.54/3.97 | % 24.54/3.97 | DELTA: instantiating (4) with fresh symbols all_61_0, all_61_1 gives: % 24.54/3.97 | (19) ~ (all_61_1 = slcrc0) & slbdtsldtrb0(xT, xk) = all_61_0 & % 24.54/3.97 | slbdtsldtrb0(xS, xk) = all_61_1 & $i(all_61_0) & $i(all_61_1) & % 24.54/3.97 | aSubsetOf0(all_61_1, all_61_0) % 24.54/3.97 | % 24.54/3.97 | ALPHA: (19) implies: % 24.54/3.97 | (20) slbdtsldtrb0(xS, xk) = all_61_1 % 24.54/3.97 | % 24.54/3.98 | GROUND_INST: instantiating (12) with all_57_0, all_61_1, xk, xS, simplifying % 24.54/3.98 | with (18), (20) gives: % 24.54/3.98 | (21) all_61_1 = all_57_0 % 24.54/3.98 | % 24.54/3.98 | GROUND_INST: instantiating (12) with all_55_0, all_61_1, xk, xS, simplifying % 24.54/3.98 | with (15), (20) gives: % 24.54/3.98 | (22) all_61_1 = all_55_0 % 24.54/3.98 | % 24.54/3.98 | COMBINE_EQS: (21), (22) imply: % 24.54/3.98 | (23) all_57_0 = all_55_0 % 24.54/3.98 | % 24.54/3.98 | SIMP: (23) implies: % 24.54/3.98 | (24) all_57_0 = all_55_0 % 24.54/3.98 | % 24.72/3.98 | REDUCE: (17), (24) imply: % 24.72/3.98 | (25) $i(all_55_0) % 24.72/3.98 | % 24.72/3.98 | GROUND_INST: instantiating (1) with xS, xk, all_55_0, xP, simplifying with % 24.72/3.98 | (2), (3), (6), (7), (8), (9), (10), (14), (15), (25) gives: % 24.72/3.98 | (26) $false % 24.72/3.98 | % 24.72/3.98 | CLOSE: (26) is inconsistent. % 24.72/3.98 | % 24.72/3.98 End of proof % 24.72/3.98 % SZS output end Proof for theBenchmark % 24.72/3.98 % 24.72/3.98 3372ms %------------------------------------------------------------------------------