%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM472+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 11:47:59 EDT 2023 % Result : Theorem 9.34s 2.16s % Output : Proof 16.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM472+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n025.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Fri Aug 25 16:43:52 EDT 2023 % 0.15/0.34 % 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. % 0.19/0.63 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 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 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 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 % 3.34/1.16 Prover 4: Preprocessing ... % 3.34/1.16 Prover 1: Preprocessing ... % 3.34/1.20 Prover 6: Preprocessing ... % 3.34/1.20 Prover 0: Preprocessing ... % 3.34/1.21 Prover 5: Preprocessing ... % 3.34/1.21 Prover 2: Preprocessing ... % 3.34/1.21 Prover 3: Preprocessing ... % 8.32/1.88 Prover 3: Constructing countermodel ... % 8.32/1.88 Prover 1: Constructing countermodel ... % 8.51/1.92 Prover 6: Proving ... % 8.70/2.01 Prover 5: Constructing countermodel ... % 9.34/2.09 Prover 2: Proving ... % 9.34/2.15 Prover 4: Constructing countermodel ... % 9.34/2.16 Prover 3: proved (1533ms) % 9.34/2.16 % 9.34/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.34/2.16 % 9.34/2.16 Prover 5: stopped % 9.34/2.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.34/2.18 Prover 6: stopped % 9.34/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.34/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.74/2.26 Prover 7: Preprocessing ... % 10.74/2.26 Prover 10: Preprocessing ... % 10.74/2.28 Prover 8: Preprocessing ... % 10.74/2.28 Prover 2: stopped % 10.74/2.30 Prover 0: Proving ... % 10.74/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.74/2.30 Prover 0: stopped % 11.33/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.38/2.38 Prover 11: Preprocessing ... % 11.38/2.39 Prover 13: Preprocessing ... % 12.11/2.48 Prover 10: Constructing countermodel ... % 12.80/2.55 Prover 8: Warning: ignoring some quantifiers % 12.80/2.56 Prover 8: Constructing countermodel ... % 13.68/2.64 Prover 7: Constructing countermodel ... % 14.43/2.73 Prover 13: Constructing countermodel ... % 15.14/2.97 Prover 10: Found proof (size 27) % 15.14/2.97 Prover 10: proved (777ms) % 15.14/2.97 Prover 7: stopped % 15.14/2.97 Prover 13: stopped % 15.14/2.97 Prover 1: stopped % 15.14/2.97 Prover 4: stopped % 15.14/2.97 Prover 8: stopped % 15.14/2.98 Prover 11: Constructing countermodel ... % 15.14/2.99 Prover 11: stopped % 15.14/2.99 % 15.14/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.14/2.99 % 15.14/3.00 % SZS output start Proof for theBenchmark % 15.14/3.00 Assumptions after simplification: % 15.14/3.00 --------------------------------- % 15.14/3.00 % 15.14/3.00 (mDefLE) % 16.65/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 16.65/3.03 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 16.65/3.03 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 16.65/3.03 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 16.65/3.03 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 16.65/3.03 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 16.65/3.03 % 16.65/3.03 (mMulComm) % 16.65/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 16.65/3.03 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.65/3.03 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 16.65/3.03 % 16.65/3.03 (mSortsB_02) % 16.65/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 16.65/3.03 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 16.65/3.03 aNaturalNumber0(v2)) % 16.65/3.03 % 16.65/3.03 (m__) % 16.69/3.03 $i(xn) & $i(xm) & ? [v0: $i] : (sdtpldt0(xm, xn) = v0 & $i(v0) & ~ % 16.69/3.03 sdtlseqdt0(xm, v0) & ! [v1: $i] : ( ~ (sdtpldt0(xm, v1) = v0) | ~ $i(v1) | % 16.69/3.03 ~ aNaturalNumber0(v1))) % 16.69/3.03 % 16.69/3.03 (m__1324) % 16.69/3.03 $i(xn) & $i(xm) & $i(xl) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & % 16.69/3.03 aNaturalNumber0(xl) % 16.69/3.03 % 16.69/3.04 (m__1324_04) % 16.69/3.04 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 16.69/3.04 (sdtasdt0(xl, v2) = xm & sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & % 16.69/3.04 $i(v2) & $i(v1) & $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 16.69/3.04 aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 16.69/3.04 % 16.69/3.04 (m__1379) % 16.69/3.04 $i(xq) & $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (sdtsldt0(v0, xl) = xq & % 16.69/3.04 sdtasdt0(xl, xq) = v0 & sdtpldt0(xm, xn) = v0 & $i(v0) & % 16.69/3.04 aNaturalNumber0(xq)) % 16.69/3.04 % 16.69/3.04 (function-axioms) % 16.69/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.04 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 16.69/3.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 16.69/3.04 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.69/3.04 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 16.69/3.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.04 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.69/3.04 % 16.69/3.04 Further assumptions not needed in the proof: % 16.69/3.04 -------------------------------------------- % 16.69/3.04 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefQuot, mDivSum, % 16.69/3.04 mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, % 16.69/3.04 mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort, mSortsB, mSortsC, mSortsC_01, % 16.69/3.04 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1347, m__1360 % 16.69/3.04 % 16.69/3.04 Those formulas are unsatisfiable: % 16.69/3.04 --------------------------------- % 16.69/3.04 % 16.69/3.04 Begin of proof % 16.69/3.04 | % 16.69/3.04 | ALPHA: (mDefLE) implies: % 16.69/3.04 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | % 16.69/3.04 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 16.69/3.04 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) % 16.69/3.04 | % 16.69/3.04 | ALPHA: (m__1324) implies: % 16.69/3.05 | (2) aNaturalNumber0(xl) % 16.69/3.05 | (3) aNaturalNumber0(xm) % 16.69/3.05 | (4) aNaturalNumber0(xn) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (m__1324_04) implies: % 16.69/3.05 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xl, v2) = xm & % 16.69/3.05 | sdtasdt0(xl, v1) = v0 & sdtpldt0(xm, xn) = v0 & $i(v2) & $i(v1) & % 16.69/3.05 | $i(v0) & doDivides0(xl, v0) & doDivides0(xl, xm) & % 16.69/3.05 | aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (m__1379) implies: % 16.69/3.05 | (6) $i(xl) % 16.69/3.05 | (7) ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtasdt0(xl, xq) = v0 & % 16.69/3.05 | sdtpldt0(xm, xn) = v0 & $i(v0) & aNaturalNumber0(xq)) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (m__) implies: % 16.69/3.05 | (8) $i(xn) % 16.69/3.05 | (9) ? [v0: $i] : (sdtpldt0(xm, xn) = v0 & $i(v0) & ~ sdtlseqdt0(xm, v0) & % 16.69/3.05 | ! [v1: $i] : ( ~ (sdtpldt0(xm, v1) = v0) | ~ $i(v1) | ~ % 16.69/3.05 | aNaturalNumber0(v1))) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (function-axioms) implies: % 16.69/3.05 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.69/3.05 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 16.69/3.05 | % 16.69/3.05 | DELTA: instantiating (7) with fresh symbol all_33_0 gives: % 16.69/3.05 | (11) sdtsldt0(all_33_0, xl) = xq & sdtasdt0(xl, xq) = all_33_0 & % 16.69/3.05 | sdtpldt0(xm, xn) = all_33_0 & $i(all_33_0) & aNaturalNumber0(xq) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (11) implies: % 16.69/3.05 | (12) sdtpldt0(xm, xn) = all_33_0 % 16.69/3.05 | % 16.69/3.05 | DELTA: instantiating (9) with fresh symbol all_35_0 gives: % 16.69/3.05 | (13) sdtpldt0(xm, xn) = all_35_0 & $i(all_35_0) & ~ sdtlseqdt0(xm, % 16.69/3.05 | all_35_0) & ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = all_35_0) | ~ % 16.69/3.05 | $i(v0) | ~ aNaturalNumber0(v0)) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (13) implies: % 16.69/3.05 | (14) ~ sdtlseqdt0(xm, all_35_0) % 16.69/3.05 | (15) sdtpldt0(xm, xn) = all_35_0 % 16.69/3.05 | % 16.69/3.05 | DELTA: instantiating (5) with fresh symbols all_38_0, all_38_1, all_38_2 % 16.69/3.05 | gives: % 16.69/3.05 | (16) sdtasdt0(xl, all_38_0) = xm & sdtasdt0(xl, all_38_1) = all_38_2 & % 16.69/3.05 | sdtpldt0(xm, xn) = all_38_2 & $i(all_38_0) & $i(all_38_1) & % 16.69/3.05 | $i(all_38_2) & doDivides0(xl, all_38_2) & doDivides0(xl, xm) & % 16.69/3.05 | aNaturalNumber0(all_38_0) & aNaturalNumber0(all_38_1) % 16.69/3.05 | % 16.69/3.05 | ALPHA: (16) implies: % 16.69/3.05 | (17) aNaturalNumber0(all_38_1) % 16.69/3.05 | (18) aNaturalNumber0(all_38_0) % 16.69/3.05 | (19) $i(all_38_1) % 16.69/3.05 | (20) $i(all_38_0) % 16.69/3.05 | (21) sdtpldt0(xm, xn) = all_38_2 % 16.69/3.05 | (22) sdtasdt0(xl, all_38_1) = all_38_2 % 16.69/3.05 | (23) sdtasdt0(xl, all_38_0) = xm % 16.69/3.05 | % 16.69/3.06 | GROUND_INST: instantiating (10) with all_35_0, all_38_2, xn, xm, simplifying % 16.69/3.06 | with (15), (21) gives: % 16.69/3.06 | (24) all_38_2 = all_35_0 % 16.69/3.06 | % 16.69/3.06 | GROUND_INST: instantiating (10) with all_33_0, all_38_2, xn, xm, simplifying % 16.69/3.06 | with (12), (21) gives: % 16.69/3.06 | (25) all_38_2 = all_33_0 % 16.69/3.06 | % 16.69/3.06 | COMBINE_EQS: (24), (25) imply: % 16.69/3.06 | (26) all_35_0 = all_33_0 % 16.69/3.06 | % 16.69/3.06 | SIMP: (26) implies: % 16.69/3.06 | (27) all_35_0 = all_33_0 % 16.69/3.06 | % 16.69/3.06 | REDUCE: (22), (25) imply: % 16.69/3.06 | (28) sdtasdt0(xl, all_38_1) = all_33_0 % 16.69/3.06 | % 16.69/3.06 | REDUCE: (14), (27) imply: % 16.69/3.06 | (29) ~ sdtlseqdt0(xm, all_33_0) % 16.69/3.06 | % 16.69/3.06 | GROUND_INST: instantiating (mSortsB_02) with xl, all_38_1, all_33_0, % 16.69/3.06 | simplifying with (2), (6), (17), (19), (28) gives: % 16.69/3.06 | (30) aNaturalNumber0(all_33_0) % 16.69/3.06 | % 16.69/3.06 | GROUND_INST: instantiating (mMulComm) with xl, all_38_1, all_33_0, simplifying % 16.69/3.06 | with (2), (6), (17), (19), (28) gives: % 16.69/3.06 | (31) sdtasdt0(all_38_1, xl) = all_33_0 & $i(all_33_0) % 16.69/3.06 | % 16.69/3.06 | ALPHA: (31) implies: % 16.69/3.06 | (32) $i(all_33_0) % 16.69/3.06 | % 16.69/3.06 | GROUND_INST: instantiating (mMulComm) with xl, all_38_0, xm, simplifying with % 16.69/3.06 | (2), (6), (18), (20), (23) gives: % 16.69/3.06 | (33) sdtasdt0(all_38_0, xl) = xm & $i(xm) % 16.69/3.06 | % 16.69/3.06 | ALPHA: (33) implies: % 16.69/3.06 | (34) $i(xm) % 16.69/3.06 | % 16.69/3.06 | GROUND_INST: instantiating (1) with xm, all_33_0, xn, simplifying with (3), % 16.69/3.06 | (4), (8), (12), (29), (30), (32), (34) gives: % 16.69/3.06 | (35) $false % 16.69/3.06 | % 16.69/3.06 | CLOSE: (35) is inconsistent. % 16.69/3.06 | % 16.69/3.06 End of proof % 16.69/3.06 % SZS output end Proof for theBenchmark % 16.69/3.06 % 16.69/3.06 2459ms %------------------------------------------------------------------------------