%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG087+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 : n009.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 13:57:47 EDT 2023 % Result : Theorem 9.78s 1.99s % Output : Proof 13.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : RNG087+2 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n009.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.32 % CPULimit : 300 % 0.17/0.32 % WCLimit : 300 % 0.17/0.32 % DateTime : Sun Aug 27 02:13:20 EDT 2023 % 0.17/0.32 % CPUTime : % 0.65/0.60 ________ _____ % 0.65/0.60 ___ __ \_________(_)________________________________ % 0.65/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.60 % 0.65/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.60 (2023-06-19) % 0.65/0.60 % 0.65/0.60 (c) Philipp Rümmer, 2009-2023 % 0.65/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.60 Amanda Stjerna. % 0.65/0.60 Free software under BSD-3-Clause. % 0.65/0.60 % 0.65/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.60 % 0.65/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.62 Running up to 7 provers in parallel. % 0.69/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.10/1.14 Prover 4: Preprocessing ... % 3.10/1.14 Prover 1: Preprocessing ... % 3.74/1.18 Prover 5: Preprocessing ... % 3.74/1.18 Prover 3: Preprocessing ... % 3.74/1.18 Prover 0: Preprocessing ... % 3.74/1.18 Prover 6: Preprocessing ... % 3.74/1.18 Prover 2: Preprocessing ... % 7.62/1.73 Prover 1: Constructing countermodel ... % 7.62/1.74 Prover 3: Constructing countermodel ... % 7.62/1.74 Prover 6: Proving ... % 8.69/1.84 Prover 4: Constructing countermodel ... % 8.69/1.86 Prover 2: Proving ... % 8.69/1.88 Prover 5: Proving ... % 9.78/1.98 Prover 0: Proving ... % 9.78/1.98 Prover 3: proved (1357ms) % 9.78/1.99 % 9.78/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.78/1.99 % 9.78/1.99 Prover 2: stopped % 9.78/1.99 Prover 6: stopped % 9.78/1.99 Prover 5: stopped % 9.78/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.78/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.78/1.99 Prover 0: stopped % 9.78/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.78/1.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.78/1.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.95/2.20 Prover 7: Preprocessing ... % 10.95/2.21 Prover 8: Preprocessing ... % 10.95/2.21 Prover 10: Preprocessing ... % 11.64/2.22 Prover 13: Preprocessing ... % 11.64/2.22 Prover 11: Preprocessing ... % 12.17/2.32 Prover 1: Found proof (size 14) % 12.17/2.32 Prover 1: proved (1698ms) % 12.17/2.32 Prover 4: stopped % 12.17/2.33 Prover 10: Constructing countermodel ... % 12.17/2.34 Prover 10: stopped % 12.17/2.36 Prover 8: Warning: ignoring some quantifiers % 12.17/2.37 Prover 8: Constructing countermodel ... % 12.17/2.37 Prover 7: Constructing countermodel ... % 12.87/2.38 Prover 13: Warning: ignoring some quantifiers % 12.87/2.38 Prover 8: stopped % 12.95/2.39 Prover 7: stopped % 12.95/2.39 Prover 13: Constructing countermodel ... % 12.95/2.40 Prover 13: stopped % 13.13/2.45 Prover 11: Constructing countermodel ... % 13.13/2.46 Prover 11: stopped % 13.13/2.46 % 13.13/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.13/2.46 % 13.13/2.47 % SZS output start Proof for theBenchmark % 13.13/2.47 Assumptions after simplification: % 13.13/2.47 --------------------------------- % 13.13/2.47 % 13.13/2.47 (m__) % 13.13/2.50 $i(xy) & $i(xJ) & $i(xI) & ! [v0: $i] : ! [v1: $i] : ( ~ (aElementOf0(v1, % 13.13/2.50 xJ) = 0) | ~ (aElementOf0(v0, xI) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.13/2.50 [v2: $i] : ( ~ (v2 = xy) & sdtpldt0(v0, v1) = v2 & $i(v2))) % 13.13/2.50 % 13.13/2.50 (m__901) % 13.13/2.50 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = % 13.13/2.50 v0 & aElementOf0(xy, v0) = 0 & aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & % 13.13/2.50 $i(v0) & ? [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & % 13.13/2.50 aElementOf0(v1, xI) = 0 & sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ? % 13.13/2.50 [v1: $i] : ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 % 13.13/2.50 & sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1))) % 13.13/2.50 % 13.13/2.50 (function-axioms) % 13.13/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.13/2.50 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 13.13/2.50 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 13.13/2.50 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.13/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.13/2.50 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] : % 13.13/2.50 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) % 13.13/2.50 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 13.13/2.50 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 13.13/2.50 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 13.13/2.50 = v0 | ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: % 13.13/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.13/2.50 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.13/2.50 [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: % 13.13/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.13/2.51 ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0)) % 13.13/2.51 % 13.13/2.51 Further assumptions not needed in the proof: % 13.13/2.51 -------------------------------------------- % 13.13/2.51 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, % 13.13/2.51 mDefSSum, mEOfElem, mElmSort, mMulAsso, mMulComm, mMulMnOne, mMulUnit, mMulZero, % 13.13/2.51 mSetEq, mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, % 13.13/2.51 m__870, m__934 % 13.13/2.51 % 13.13/2.51 Those formulas are unsatisfiable: % 13.13/2.51 --------------------------------- % 13.13/2.51 % 13.13/2.51 Begin of proof % 13.13/2.51 | % 13.57/2.51 | ALPHA: (m__901) implies: % 13.57/2.51 | (1) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & aElementOf0(xy, v0) = 0 & % 13.57/2.51 | aElementOf0(xx, v0) = 0 & aElement0(xz) = 0 & $i(v0) & ? [v1: $i] : % 13.57/2.51 | ? [v2: $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 & % 13.57/2.51 | sdtpldt0(v1, v2) = xy & $i(v2) & $i(v1)) & ? [v1: $i] : ? [v2: % 13.57/2.51 | $i] : (aElementOf0(v2, xJ) = 0 & aElementOf0(v1, xI) = 0 & % 13.57/2.51 | sdtpldt0(v1, v2) = xx & $i(v2) & $i(v1))) % 13.57/2.51 | % 13.57/2.51 | ALPHA: (m__) implies: % 13.57/2.51 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (aElementOf0(v1, xJ) = 0) | ~ % 13.57/2.51 | (aElementOf0(v0, xI) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ( ~ % 13.57/2.51 | (v2 = xy) & sdtpldt0(v0, v1) = v2 & $i(v2))) % 13.57/2.51 | % 13.57/2.51 | ALPHA: (function-axioms) implies: % 13.57/2.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.57/2.51 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 13.57/2.51 | % 13.57/2.51 | DELTA: instantiating (1) with fresh symbol all_27_0 gives: % 13.57/2.51 | (4) sdtpldt1(xI, xJ) = all_27_0 & aElementOf0(xy, all_27_0) = 0 & % 13.57/2.51 | aElementOf0(xx, all_27_0) = 0 & aElement0(xz) = 0 & $i(all_27_0) & ? % 13.57/2.51 | [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI) % 13.57/2.51 | = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0)) & ? [v0: $i] : ? % 13.57/2.51 | [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, xI) = 0 & % 13.57/2.51 | sdtpldt0(v0, v1) = xx & $i(v1) & $i(v0)) % 13.57/2.51 | % 13.57/2.51 | ALPHA: (4) implies: % 13.57/2.51 | (5) ? [v0: $i] : ? [v1: $i] : (aElementOf0(v1, xJ) = 0 & aElementOf0(v0, % 13.57/2.51 | xI) = 0 & sdtpldt0(v0, v1) = xy & $i(v1) & $i(v0)) % 13.57/2.51 | % 13.57/2.51 | DELTA: instantiating (5) with fresh symbols all_29_0, all_29_1 gives: % 13.57/2.51 | (6) aElementOf0(all_29_0, xJ) = 0 & aElementOf0(all_29_1, xI) = 0 & % 13.57/2.51 | sdtpldt0(all_29_1, all_29_0) = xy & $i(all_29_0) & $i(all_29_1) % 13.57/2.51 | % 13.57/2.51 | ALPHA: (6) implies: % 13.57/2.52 | (7) $i(all_29_1) % 13.57/2.52 | (8) $i(all_29_0) % 13.57/2.52 | (9) sdtpldt0(all_29_1, all_29_0) = xy % 13.57/2.52 | (10) aElementOf0(all_29_1, xI) = 0 % 13.57/2.52 | (11) aElementOf0(all_29_0, xJ) = 0 % 13.57/2.52 | % 13.57/2.52 | GROUND_INST: instantiating (2) with all_29_1, all_29_0, simplifying with (7), % 13.57/2.52 | (8), (10), (11) gives: % 13.57/2.52 | (12) ? [v0: $i] : ( ~ (v0 = xy) & sdtpldt0(all_29_1, all_29_0) = v0 & % 13.57/2.52 | $i(v0)) % 13.57/2.52 | % 13.57/2.52 | DELTA: instantiating (12) with fresh symbol all_71_0 gives: % 13.57/2.52 | (13) ~ (all_71_0 = xy) & sdtpldt0(all_29_1, all_29_0) = all_71_0 & % 13.57/2.52 | $i(all_71_0) % 13.57/2.52 | % 13.57/2.52 | ALPHA: (13) implies: % 13.57/2.52 | (14) ~ (all_71_0 = xy) % 13.57/2.52 | (15) sdtpldt0(all_29_1, all_29_0) = all_71_0 % 13.57/2.52 | % 13.57/2.52 | GROUND_INST: instantiating (3) with xy, all_71_0, all_29_0, all_29_1, % 13.57/2.52 | simplifying with (9), (15) gives: % 13.57/2.52 | (16) all_71_0 = xy % 13.57/2.52 | % 13.57/2.52 | REDUCE: (14), (16) imply: % 13.57/2.52 | (17) $false % 13.57/2.52 | % 13.57/2.52 | CLOSE: (17) is inconsistent. % 13.57/2.52 | % 13.57/2.52 End of proof % 13.57/2.52 % SZS output end Proof for theBenchmark % 13.57/2.52 % 13.57/2.52 1916ms %------------------------------------------------------------------------------