%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG125+4 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.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 13:58:02 EDT 2023 % Result : Theorem 9.37s 2.10s % Output : Proof 16.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : RNG125+4 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.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 : Sun Aug 27 01:54:26 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. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 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 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 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 % 3.33/1.25 Prover 1: Preprocessing ... % 3.33/1.26 Prover 4: Preprocessing ... % 4.01/1.30 Prover 3: Preprocessing ... % 4.01/1.30 Prover 0: Preprocessing ... % 4.01/1.30 Prover 6: Preprocessing ... % 4.01/1.30 Prover 5: Preprocessing ... % 4.01/1.30 Prover 2: Preprocessing ... % 9.37/2.07 Prover 3: Constructing countermodel ... % 9.37/2.08 Prover 5: Constructing countermodel ... % 9.37/2.08 Prover 6: Constructing countermodel ... % 9.37/2.09 Prover 3: proved (1467ms) % 9.37/2.09 Prover 6: proved (1463ms) % 9.37/2.10 % 9.37/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.37/2.10 % 9.37/2.10 % 9.37/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.37/2.10 % 9.37/2.10 Prover 5: stopped % 9.37/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.37/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.06/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.06/2.17 Prover 2: Constructing countermodel ... % 10.06/2.17 Prover 2: stopped % 10.06/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.71/2.23 Prover 1: Constructing countermodel ... % 11.47/2.29 Prover 7: Preprocessing ... % 11.60/2.31 Prover 8: Preprocessing ... % 11.60/2.35 Prover 10: Preprocessing ... % 11.60/2.37 Prover 11: Preprocessing ... % 11.60/2.41 Prover 0: Constructing countermodel ... % 11.60/2.41 Prover 0: stopped % 12.31/2.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.05/2.57 Prover 13: Preprocessing ... % 13.71/2.67 Prover 1: Found proof (size 15) % 13.71/2.67 Prover 1: proved (2044ms) % 14.44/2.69 Prover 13: stopped % 14.65/2.74 Prover 7: Constructing countermodel ... % 14.65/2.75 Prover 10: Constructing countermodel ... % 14.65/2.76 Prover 7: stopped % 14.65/2.77 Prover 10: stopped % 14.65/2.78 Prover 8: Warning: ignoring some quantifiers % 14.65/2.79 Prover 4: Constructing countermodel ... % 14.65/2.79 Prover 8: Constructing countermodel ... % 14.65/2.81 Prover 8: stopped % 15.35/2.82 Prover 4: stopped % 15.75/2.96 Prover 11: Constructing countermodel ... % 15.75/2.97 Prover 11: stopped % 15.75/2.97 % 15.75/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.75/2.97 % 15.75/2.98 % SZS output start Proof for theBenchmark % 16.15/2.98 Assumptions after simplification: % 16.15/2.98 --------------------------------- % 16.15/2.98 % 16.15/2.98 (m__2383) % 16.17/3.01 $i(xu) & $i(xb) & $i(xa) & ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 16.17/3.01 [v3: any] : (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v1 & % 16.17/3.01 doDivides0(xu, xb) = v2 & doDivides0(xu, xa) = v0 & (( ~ (v3 = 0) & ~ (v2 = % 16.17/3.01 0) & ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xb) | ~ $i(v4) | ? [v5: % 16.17/3.01 int] : ( ~ (v5 = 0) & aElement0(v4) = v5))) | ( ~ (v1 = 0) & ~ (v0 % 16.17/3.01 = 0) & ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xa) | ~ $i(v4) | ? [v5: % 16.17/3.01 int] : ( ~ (v5 = 0) & aElement0(v4) = v5))))) % 16.17/3.01 % 16.17/3.01 (m__2479) % 16.17/3.01 doDivides0(xu, xa) = 0 & $i(xu) & $i(xa) & ? [v0: $i] : (sdtasdt0(xu, v0) = % 16.17/3.01 xa & aElement0(v0) = 0 & $i(v0)) % 16.17/3.01 % 16.17/3.01 (m__2612) % 16.17/3.02 doDivides0(xu, xb) = 0 & $i(xu) & $i(xb) & ? [v0: $i] : (sdtasdt0(xu, v0) = % 16.17/3.02 xb & aElement0(v0) = 0 & $i(v0)) % 16.17/3.02 % 16.17/3.02 (function-axioms) % 16.17/3.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.17/3.03 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~ % 16.17/3.03 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.17/3.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.17/3.03 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3, % 16.17/3.03 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.17/3.03 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) | % 16.17/3.03 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.17/3.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.17/3.03 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: % 16.17/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.17/3.03 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 16.17/3.03 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.17/3.03 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 16.17/3.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.17/3.03 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.17/3.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 16.17/3.03 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.17/3.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.17/3.03 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 16.17/3.03 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 16.17/3.03 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.17/3.03 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.17/3.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) % 16.17/3.03 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 16.17/3.03 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: % 16.17/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 16.17/3.03 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0: % 16.17/3.03 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 16.17/3.03 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] : % 16.17/3.03 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ % 16.17/3.03 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.17/3.03 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.17/3.03 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | % 16.17/3.03 ~ (aElement0(v2) = v0)) % 16.17/3.03 % 16.17/3.03 Further assumptions not needed in the proof: % 16.17/3.03 -------------------------------------------- % 16.17/3.03 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 16.17/3.03 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, % 16.17/3.03 mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, % 16.17/3.03 mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, % 16.17/3.03 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__, % 16.17/3.03 m__2091, m__2110, m__2129, m__2174, m__2203, m__2228, m__2273, m__2416 % 16.17/3.03 % 16.17/3.03 Those formulas are unsatisfiable: % 16.17/3.03 --------------------------------- % 16.17/3.03 % 16.17/3.03 Begin of proof % 16.17/3.03 | % 16.17/3.03 | ALPHA: (m__2383) implies: % 16.17/3.03 | (1) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 16.17/3.03 | (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v1 & doDivides0(xu, % 16.17/3.03 | xb) = v2 & doDivides0(xu, xa) = v0 & (( ~ (v3 = 0) & ~ (v2 = 0) & % 16.17/3.03 | ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xb) | ~ $i(v4) | ? [v5: % 16.17/3.03 | int] : ( ~ (v5 = 0) & aElement0(v4) = v5))) | ( ~ (v1 = 0) & % 16.17/3.03 | ~ (v0 = 0) & ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xa) | ~ % 16.17/3.03 | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = v5))))) % 16.17/3.03 | % 16.17/3.03 | ALPHA: (m__2479) implies: % 16.17/3.04 | (2) doDivides0(xu, xa) = 0 % 16.17/3.04 | % 16.17/3.04 | ALPHA: (m__2612) implies: % 16.17/3.04 | (3) doDivides0(xu, xb) = 0 % 16.17/3.04 | % 16.17/3.04 | ALPHA: (function-axioms) implies: % 16.17/3.04 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.17/3.04 | ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 16.17/3.04 | (doDivides0(v3, v2) = v0)) % 16.17/3.04 | % 16.17/3.04 | DELTA: instantiating (1) with fresh symbols all_48_0, all_48_1, all_48_2, % 16.17/3.04 | all_48_3 gives: % 16.17/3.04 | (5) aDivisorOf0(xu, xb) = all_48_0 & aDivisorOf0(xu, xa) = all_48_2 & % 16.17/3.04 | doDivides0(xu, xb) = all_48_1 & doDivides0(xu, xa) = all_48_3 & (( ~ % 16.17/3.04 | (all_48_0 = 0) & ~ (all_48_1 = 0) & ! [v0: $i] : ( ~ % 16.17/3.04 | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 16.17/3.04 | & aElement0(v0) = v1))) | ( ~ (all_48_2 = 0) & ~ (all_48_3 = % 16.17/3.04 | 0) & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ? % 16.17/3.04 | [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)))) % 16.17/3.04 | % 16.17/3.04 | ALPHA: (5) implies: % 16.17/3.04 | (6) doDivides0(xu, xa) = all_48_3 % 16.17/3.04 | (7) doDivides0(xu, xb) = all_48_1 % 16.17/3.04 | (8) ( ~ (all_48_0 = 0) & ~ (all_48_1 = 0) & ! [v0: $i] : ( ~ % 16.17/3.04 | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 16.17/3.04 | aElement0(v0) = v1))) | ( ~ (all_48_2 = 0) & ~ (all_48_3 = 0) & % 16.17/3.04 | ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ? [v1: int] : % 16.17/3.04 | ( ~ (v1 = 0) & aElement0(v0) = v1))) % 16.17/3.04 | % 16.17/3.04 | GROUND_INST: instantiating (4) with 0, all_48_3, xa, xu, simplifying with (2), % 16.17/3.04 | (6) gives: % 16.17/3.04 | (9) all_48_3 = 0 % 16.17/3.04 | % 16.17/3.04 | GROUND_INST: instantiating (4) with 0, all_48_1, xb, xu, simplifying with (3), % 16.17/3.04 | (7) gives: % 16.17/3.04 | (10) all_48_1 = 0 % 16.17/3.04 | % 16.17/3.04 | BETA: splitting (8) gives: % 16.17/3.04 | % 16.17/3.04 | Case 1: % 16.17/3.04 | | % 16.17/3.04 | | (11) ~ (all_48_0 = 0) & ~ (all_48_1 = 0) & ! [v0: $i] : ( ~ % 16.17/3.04 | | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 16.17/3.04 | | & aElement0(v0) = v1)) % 16.17/3.04 | | % 16.17/3.04 | | ALPHA: (11) implies: % 16.17/3.04 | | (12) ~ (all_48_1 = 0) % 16.17/3.04 | | % 16.17/3.04 | | REDUCE: (10), (12) imply: % 16.17/3.04 | | (13) $false % 16.17/3.05 | | % 16.17/3.05 | | CLOSE: (13) is inconsistent. % 16.17/3.05 | | % 16.17/3.05 | Case 2: % 16.17/3.05 | | % 16.17/3.05 | | (14) ~ (all_48_2 = 0) & ~ (all_48_3 = 0) & ! [v0: $i] : ( ~ % 16.17/3.05 | | (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 16.17/3.05 | | & aElement0(v0) = v1)) % 16.17/3.05 | | % 16.17/3.05 | | ALPHA: (14) implies: % 16.17/3.05 | | (15) ~ (all_48_3 = 0) % 16.17/3.05 | | % 16.17/3.05 | | REDUCE: (9), (15) imply: % 16.17/3.05 | | (16) $false % 16.17/3.05 | | % 16.17/3.05 | | CLOSE: (16) is inconsistent. % 16.17/3.05 | | % 16.17/3.05 | End of split % 16.17/3.05 | % 16.17/3.05 End of proof % 16.17/3.05 % SZS output end Proof for theBenchmark % 16.17/3.05 % 16.17/3.05 2441ms %------------------------------------------------------------------------------