%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM310_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 : Tue May 5 06:21:44 PM UTC 2026 % Result : Theorem 26.74s 4.18s % Output : Proof 37.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : COM310_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.06 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.24 % Computer : n012.cluster.edu % 0.07/0.24 % Model : x86_64 x86_64 % 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.24 % Memory : 8042.1875MB % 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.24 % CPULimit : 300 % 0.07/0.24 % WCLimit : 300 % 0.07/0.24 % DateTime : Mon May 4 20:48:30 EDT 2026 % 0.07/0.25 % CPUTime : % 0.19/0.42 ________ _____ % 0.19/0.42 ___ __ \_________(_)________________________________ % 0.19/0.42 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.42 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.42 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.42 % 0.19/0.42 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.42 (2023-06-19) % 0.19/0.42 % 0.19/0.42 (c) Philipp Rümmer, 2009-2023 % 0.19/0.42 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.42 Amanda Stjerna. % 0.19/0.42 Free software under BSD-3-Clause. % 0.19/0.42 % 0.19/0.42 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.42 % 0.19/0.42 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.38/0.43 Running up to 7 provers in parallel. % 0.38/0.44 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.38/0.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.38/0.44 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.38/0.44 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.38/0.44 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.38/0.44 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.38/0.44 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.77/1.69 Prover 0: Preprocessing ... % 7.77/1.69 Prover 3: Preprocessing ... % 8.45/1.70 Prover 5: Preprocessing ... % 8.45/1.72 Prover 6: Preprocessing ... % 8.45/1.72 Prover 4: Preprocessing ... % 8.45/1.72 Prover 1: Preprocessing ... % 8.45/1.74 Prover 2: Preprocessing ... % 23.56/3.75 Prover 1: Warning: ignoring some quantifiers % 24.34/3.81 Prover 3: Warning: ignoring some quantifiers % 24.34/3.82 Prover 1: Constructing countermodel ... % 24.34/3.82 Prover 6: Proving ... % 24.34/3.84 Prover 4: Warning: ignoring some quantifiers % 24.34/3.85 Prover 3: Constructing countermodel ... % 24.34/3.89 Prover 0: Proving ... % 25.10/3.91 Prover 4: Constructing countermodel ... % 26.74/4.18 Prover 5: Proving ... % 26.74/4.18 Prover 3: proved (3740ms) % 26.74/4.18 % 26.74/4.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.74/4.18 % 26.74/4.19 Prover 5: stopped % 26.74/4.19 Prover 6: stopped % 27.33/4.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 27.33/4.20 Prover 0: stopped % 27.33/4.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 27.33/4.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.33/4.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 28.06/4.37 Prover 2: Proving ... % 28.06/4.37 Prover 2: stopped % 28.06/4.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 31.81/4.85 Prover 1: Found proof (size 35) % 31.81/4.86 Prover 1: proved (4416ms) % 31.81/4.86 Prover 10: Preprocessing ... % 31.81/4.86 Prover 4: stopped % 32.59/4.94 Prover 7: Preprocessing ... % 32.59/4.94 Prover 11: Preprocessing ... % 32.59/4.94 Prover 8: Preprocessing ... % 33.46/5.02 Prover 13: Preprocessing ... % 34.90/5.22 Prover 10: stopped % 34.90/5.25 Prover 11: stopped % 34.90/5.27 Prover 7: stopped % 35.57/5.34 Prover 13: stopped % 36.43/5.54 Prover 8: Warning: ignoring some quantifiers % 36.43/5.58 Prover 8: Constructing countermodel ... % 36.43/5.59 Prover 8: stopped % 36.43/5.59 % 36.43/5.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.43/5.59 % 36.85/5.60 % SZS output start Proof for theBenchmark % 36.85/5.61 Assumptions after simplification: % 36.85/5.61 --------------------------------- % 36.85/5.61 % 36.85/5.61 (EQ-tcons) % 36.85/5.64 ! [v0: vRow] : ! [v1: vRawTable] : ! [v2: vRow] : ! [v3: vRawTable] : ! % 36.85/5.64 [v4: vRawTable] : ( ~ (vtcons(v2, v3) = v4) | ~ (vtcons(v0, v1) = v4) | ~ % 36.85/5.64 vRawTable(v3) | ~ vRawTable(v1) | ~ vRow(v2) | ~ vRow(v0) | (v3 = v1 & v2 % 36.85/5.64 = v0)) % 36.85/5.64 % 36.85/5.64 (projectEmptyCol-1) % 36.85/5.64 vRow(vrempty) & ! [v0: vRow] : ! [v1: vRawTable] : ! [v2: vRawTable] : ( ~ % 36.85/5.64 (vtcons(v0, v1) = v2) | ~ vRawTable(v1) | ~ vRow(v0) | ? [v3: vRawTable] % 36.85/5.64 : ? [v4: vRawTable] : (vprojectEmptyCol(v2) = v3 & vprojectEmptyCol(v1) = % 36.85/5.64 v4 & vtcons(vrempty, v4) = v3 & vRawTable(v4) & vRawTable(v3))) % 36.85/5.64 % 36.85/5.64 (projectEmptyCol-INV) % 36.85/5.64 vRawTable(vtempty) & vRow(vrempty) & ! [v0: vRawTable] : ! [v1: vRawTable] : % 36.85/5.64 ( ~ (vprojectEmptyCol(v0) = v1) | ~ vRawTable(v0) | ? [v2: vRow] : ? [v3: % 36.85/5.64 vRawTable] : ? [v4: vRawTable] : (vprojectEmptyCol(v3) = v4 & vtcons(v2, % 36.85/5.64 v3) = v0 & vtcons(vrempty, v4) = v1 & vRawTable(v4) & vRawTable(v3) & % 36.85/5.64 vRawTable(v1) & vRow(v2)) | (v1 = vtempty & v0 = vtempty)) % 36.85/5.64 % 36.85/5.64 (welltypedEmptyProjection-tcons) % 36.85/5.64 vTType(vttempty) & vRawTable(vrt2) & ? [v0: vRow] : ? [v1: vRawTable] : ? % 36.85/5.64 [v2: vRawTable] : ? [v3: int] : ( ~ (v3 = 0) & vprojectEmptyCol(v1) = v2 & % 36.85/5.64 vwelltypedRawtable(vttempty, v2) = v3 & vtcons(v0, vrt2) = v1 & % 36.85/5.64 vRawTable(v2) & vRawTable(v1) & vRow(v0)) % 36.85/5.64 % 36.85/5.64 (welltypedEmptyProjection-tcons-IH0) % 36.85/5.64 vTType(vttempty) & vRawTable(vrt2) & ? [v0: vRawTable] : % 36.85/5.64 (vprojectEmptyCol(vrt2) = v0 & vwelltypedRawtable(vttempty, v0) = 0 & % 36.85/5.64 vRawTable(v0)) % 36.85/5.64 % 36.85/5.64 (welltypedRawtable-false-INV) % 36.85/5.65 ! [v0: vTType] : ! [v1: vRawTable] : ! [v2: int] : (v2 = 0 | ~ % 36.85/5.65 (vwelltypedRawtable(v0, v1) = v2) | ~ vTType(v0) | ~ vRawTable(v1) | ? % 36.85/5.65 [v3: vRow] : ? [v4: vRawTable] : ? [v5: any] : ? [v6: any] : % 36.85/5.65 (vwelltypedRawtable(v0, v4) = v6 & vwelltypedRow(v0, v3) = v5 & vtcons(v3, % 36.85/5.65 v4) = v1 & vRawTable(v4) & vRow(v3) & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 36.85/5.65 % 36.85/5.65 (welltypedRow-0) % 36.85/5.65 vwelltypedRow(vttempty, vrempty) = 0 & vTType(vttempty) & vRow(vrempty) % 36.85/5.65 % 36.85/5.65 (function-axioms) % 36.85/5.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vTType] : ! % 36.85/5.67 [v3: vQuery] : ! [v4: vTTContext] : (v1 = v0 | ~ (vptcheck(v4, v3, v2) = v1) % 36.85/5.67 | ~ (vptcheck(v4, v3, v2) = v0)) & ! [v0: vRawTable] : ! [v1: vRawTable] % 36.85/5.67 : ! [v2: vPred] : ! [v3: vAttrL] : ! [v4: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vfilterRows(v4, v3, v2) = v1) | ~ (vfilterRows(v4, v3, v2) = v0)) & ! % 36.85/5.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vRow] : ! [v3: % 36.85/5.67 vAttrL] : ! [v4: vPred] : (v1 = v0 | ~ (vfilterSingleRow(v4, v3, v2) = v1) % 36.85/5.67 | ~ (vfilterSingleRow(v4, v3, v2) = v0)) & ! [v0: vOptVal] : ! [v1: % 36.85/5.67 vOptVal] : ! [v2: vRow] : ! [v3: vAttrL] : ! [v4: vExp] : (v1 = v0 | ~ % 36.85/5.67 (vevalExpRow(v4, v3, v2) = v1) | ~ (vevalExpRow(v4, v3, v2) = v0)) & ! % 36.85/5.67 [v0: vOptRawTable] : ! [v1: vOptRawTable] : ! [v2: vRawTable] : ! [v3: % 36.85/5.67 vAttrL] : ! [v4: vAttrL] : (v1 = v0 | ~ (vprojectCols(v4, v3, v2) = v1) | % 36.85/5.67 ~ (vprojectCols(v4, v3, v2) = v0)) & ! [v0: vOptRawTable] : ! [v1: % 36.85/5.67 vOptRawTable] : ! [v2: vRawTable] : ! [v3: vAttrL] : ! [v4: vName] : (v1 % 36.85/5.67 = v0 | ~ (vfindCol(v4, v3, v2) = v1) | ~ (vfindCol(v4, v3, v2) = v0)) & ! % 36.85/5.67 [v0: vTStore] : ! [v1: vTStore] : ! [v2: vTStore] : ! [v3: vTable] : ! % 36.85/5.67 [v4: vName] : (v1 = v0 | ~ (vbindStore(v4, v3, v2) = v1) | ~ (vbindStore(v4, % 36.85/5.67 v3, v2) = v0)) & ! [v0: vTTContext] : ! [v1: vTTContext] : ! [v2: % 36.85/5.67 vTTContext] : ! [v3: vTType] : ! [v4: vName] : (v1 = v0 | ~ % 36.85/5.67 (vbindContext(v4, v3, v2) = v1) | ~ (vbindContext(v4, v3, v2) = v0)) & ! % 36.85/5.67 [v0: vTType] : ! [v1: vTType] : ! [v2: vTType] : ! [v3: vFType] : ! [v4: % 36.85/5.67 vName] : (v1 = v0 | ~ (vttcons(v4, v3, v2) = v1) | ~ (vttcons(v4, v3, v2) % 36.85/5.67 = v0)) & ! [v0: vQuery] : ! [v1: vQuery] : ! [v2: vPred] : ! [v3: % 36.85/5.67 vName] : ! [v4: vSelect] : (v1 = v0 | ~ (vselectFromWhere(v4, v3, v2) = % 36.85/5.67 v1) | ~ (vselectFromWhere(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] % 36.85/5.67 : ! [v1: MultipleValueBool] : ! [v2: vTTContext] : ! [v3: vTStore] : (v1 = % 36.85/5.67 v0 | ~ (vstoreContextConsistent(v3, v2) = v1) | ~ % 36.85/5.67 (vstoreContextConsistent(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 36.85/5.67 [v1: MultipleValueBool] : ! [v2: vTType] : ! [v3: vPred] : (v1 = v0 | ~ % 36.85/5.67 (vtcheckPred(v3, v2) = v1) | ~ (vtcheckPred(v3, v2) = v0)) & ! [v0: % 36.85/5.67 vOptFType] : ! [v1: vOptFType] : ! [v2: vTType] : ! [v3: vExp] : (v1 = v0 % 36.85/5.67 | ~ (vtypeOfExp(v3, v2) = v1) | ~ (vtypeOfExp(v3, v2) = v0)) & ! [v0: % 36.85/5.67 vOptTType] : ! [v1: vOptTType] : ! [v2: vTType] : ! [v3: vSelect] : (v1 = % 36.85/5.67 v0 | ~ (vprojectType(v3, v2) = v1) | ~ (vprojectType(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vOptTType] : ! [v1: vOptTType] : ! [v2: vTType] : ! [v3: vAttrL] : (v1 % 36.85/5.67 = v0 | ~ (vprojectTypeAttrL(v3, v2) = v1) | ~ (vprojectTypeAttrL(v3, v2) = % 36.85/5.67 v0)) & ! [v0: vOptFType] : ! [v1: vOptFType] : ! [v2: vTType] : ! [v3: % 36.85/5.67 vName] : (v1 = v0 | ~ (vfindColType(v3, v2) = v1) | ~ (vfindColType(v3, % 36.85/5.67 v2) = v0)) & ! [v0: vOptQuery] : ! [v1: vOptQuery] : ! [v2: vTStore] % 36.85/5.67 : ! [v3: vQuery] : (v1 = v0 | ~ (vreduce(v3, v2) = v1) | ~ (vreduce(v3, v2) % 36.85/5.67 = v0)) & ! [v0: vTable] : ! [v1: vTable] : ! [v2: vPred] : ! [v3: % 36.85/5.67 vTable] : (v1 = v0 | ~ (vfilterTable(v3, v2) = v1) | ~ (vfilterTable(v3, % 36.85/5.67 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 36.85/5.67 ! [v2: vVal] : ! [v3: vVal] : (v1 = v0 | ~ (vlessThan(v3, v2) = v1) | ~ % 36.85/5.67 (vlessThan(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.85/5.67 MultipleValueBool] : ! [v2: vVal] : ! [v3: vVal] : (v1 = v0 | ~ % 36.85/5.67 (vgreaterThan(v3, v2) = v1) | ~ (vgreaterThan(v3, v2) = v0)) & ! [v0: % 36.85/5.67 vOptTable] : ! [v1: vOptTable] : ! [v2: vTable] : ! [v3: vSelect] : (v1 = % 36.85/5.67 v0 | ~ (vprojectTable(v3, v2) = v1) | ~ (vprojectTable(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vOptTType] : ! [v1: vOptTType] : ! [v2: vTTContext] : ! [v3: vName] : % 36.85/5.67 (v1 = v0 | ~ (vlookupContext(v3, v2) = v1) | ~ (vlookupContext(v3, v2) = % 36.85/5.67 v0)) & ! [v0: vOptTable] : ! [v1: vOptTable] : ! [v2: vTStore] : ! % 36.85/5.67 [v3: vName] : (v1 = v0 | ~ (vlookupStore(v3, v2) = v1) | ~ (vlookupStore(v3, % 36.85/5.67 v2) = v0)) & ! [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: % 36.85/5.67 vRawTable] : ! [v3: vRawTable] : (v1 = v0 | ~ (vrawDifference(v3, v2) = % 36.85/5.67 v1) | ~ (vrawDifference(v3, v2) = v0)) & ! [v0: vRawTable] : ! [v1: % 36.85/5.67 vRawTable] : ! [v2: vRawTable] : ! [v3: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vrawIntersection(v3, v2) = v1) | ~ (vrawIntersection(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : ! [v3: vRawTable] % 36.85/5.67 : (v1 = v0 | ~ (vrawUnion(v3, v2) = v1) | ~ (vrawUnion(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : ! [v3: vRawTable] % 36.85/5.67 : (v1 = v0 | ~ (vattachColToFrontRaw(v3, v2) = v1) | ~ % 36.85/5.67 (vattachColToFrontRaw(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.85/5.67 MultipleValueBool] : ! [v2: vRawTable] : ! [v3: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vsameLength(v3, v2) = v1) | ~ (vsameLength(v3, v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vRawTable] : ! % 36.85/5.67 [v3: vRow] : (v1 = v0 | ~ (vrowIn(v3, v2) = v1) | ~ (vrowIn(v3, v2) = v0)) & % 36.85/5.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vTable] : ! % 36.85/5.67 [v3: vTType] : (v1 = v0 | ~ (vwelltypedtable(v3, v2) = v1) | ~ % 36.85/5.67 (vwelltypedtable(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.85/5.67 MultipleValueBool] : ! [v2: vRawTable] : ! [v3: vTType] : (v1 = v0 | ~ % 36.85/5.67 (vwelltypedRawtable(v3, v2) = v1) | ~ (vwelltypedRawtable(v3, v2) = v0)) & % 36.85/5.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vRow] : ! % 36.85/5.67 [v3: vTType] : (v1 = v0 | ~ (vwelltypedRow(v3, v2) = v1) | ~ % 36.85/5.67 (vwelltypedRow(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.85/5.67 MultipleValueBool] : ! [v2: vAttrL] : ! [v3: vTType] : (v1 = v0 | ~ % 36.85/5.67 (vmatchingAttrL(v3, v2) = v1) | ~ (vmatchingAttrL(v3, v2) = v0)) & ! [v0: % 36.85/5.67 vAttrL] : ! [v1: vAttrL] : ! [v2: vAttrL] : ! [v3: vAttrL] : (v1 = v0 | % 36.85/5.67 ~ (vappend(v3, v2) = v1) | ~ (vappend(v3, v2) = v0)) & ! [v0: vAttrL] : ! % 36.85/5.67 [v1: vAttrL] : ! [v2: vAttrL] : ! [v3: vName] : (v1 = v0 | ~ (vacons(v3, % 36.85/5.67 v2) = v1) | ~ (vacons(v3, v2) = v0)) & ! [v0: vPred] : ! [v1: vPred] % 36.85/5.67 : ! [v2: vExp] : ! [v3: vExp] : (v1 = v0 | ~ (vlt(v3, v2) = v1) | ~ % 36.85/5.67 (vlt(v3, v2) = v0)) & ! [v0: vPred] : ! [v1: vPred] : ! [v2: vExp] : ! % 36.85/5.67 [v3: vExp] : (v1 = v0 | ~ (vgt(v3, v2) = v1) | ~ (vgt(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vPred] : ! [v1: vPred] : ! [v2: vExp] : ! [v3: vExp] : (v1 = v0 | ~ % 36.85/5.67 (veq(v3, v2) = v1) | ~ (veq(v3, v2) = v0)) & ! [v0: vPred] : ! [v1: % 36.85/5.67 vPred] : ! [v2: vPred] : ! [v3: vPred] : (v1 = v0 | ~ (vand(v3, v2) = v1) % 36.85/5.67 | ~ (vand(v3, v2) = v0)) & ! [v0: vTable] : ! [v1: vTable] : ! [v2: % 36.85/5.67 vRawTable] : ! [v3: vAttrL] : (v1 = v0 | ~ (vtable(v3, v2) = v1) | ~ % 36.85/5.67 (vtable(v3, v2) = v0)) & ! [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: % 36.85/5.67 vRawTable] : ! [v3: vRow] : (v1 = v0 | ~ (vtcons(v3, v2) = v1) | ~ % 36.85/5.67 (vtcons(v3, v2) = v0)) & ! [v0: vRow] : ! [v1: vRow] : ! [v2: vRow] : ! % 36.85/5.67 [v3: vVal] : (v1 = v0 | ~ (vrcons(v3, v2) = v1) | ~ (vrcons(v3, v2) = v0)) & % 36.85/5.67 ! [v0: vQuery] : ! [v1: vQuery] : ! [v2: vQuery] : ! [v3: vQuery] : (v1 = % 36.85/5.67 v0 | ~ (vDifference(v3, v2) = v1) | ~ (vDifference(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vQuery] : ! [v1: vQuery] : ! [v2: vQuery] : ! [v3: vQuery] : (v1 = v0 % 36.85/5.67 | ~ (vIntersection(v3, v2) = v1) | ~ (vIntersection(v3, v2) = v0)) & ! % 36.85/5.67 [v0: vQuery] : ! [v1: vQuery] : ! [v2: vQuery] : ! [v3: vQuery] : (v1 = v0 % 36.85/5.67 | ~ (vUnion(v3, v2) = v1) | ~ (vUnion(v3, v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptFType] : (v1 = % 36.85/5.67 v0 | ~ (visSomeFType(v2) = v1) | ~ (visSomeFType(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptVal] : (v1 = % 36.85/5.67 v0 | ~ (visSomeVal(v2) = v1) | ~ (visSomeVal(v2) = v0)) & ! [v0: % 36.85/5.67 vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vprojectEmptyCol(v2) = v1) | ~ (vprojectEmptyCol(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptQuery] : (v1 = % 36.85/5.67 v0 | ~ (visSomeQuery(v2) = v1) | ~ (visSomeQuery(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vQuery] : (v1 = v0 % 36.85/5.67 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptTType] : (v1 = % 36.85/5.67 v0 | ~ (visSomeTType(v2) = v1) | ~ (visSomeTType(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptTable] : (v1 = % 36.85/5.67 v0 | ~ (visSomeTable(v2) = v1) | ~ (visSomeTable(v2) = v0)) & ! [v0: % 36.85/5.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptRawTable] : % 36.85/5.67 (v1 = v0 | ~ (visSomeRawTable(v2) = v1) | ~ (visSomeRawTable(v2) = v0)) & ! % 36.85/5.67 [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vdropFirstColRaw(v2) = v1) | ~ (vdropFirstColRaw(v2) = v0)) & ! [v0: % 36.85/5.67 vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : (v1 = v0 | ~ % 36.85/5.67 (vprojectFirstRaw(v2) = v1) | ~ (vprojectFirstRaw(v2) = v0)) & ! [v0: % 36.85/5.67 vFType] : ! [v1: vFType] : ! [v2: vVal] : (v1 = v0 | ~ (vfieldType(v2) = % 36.85/5.67 v1) | ~ (vfieldType(v2) = v0)) & ! [v0: vAttrL] : ! [v1: vAttrL] : ! % 36.85/5.67 [v2: vTable] : (v1 = v0 | ~ (vgetAttrL(v2) = v1) | ~ (vgetAttrL(v2) = v0)) & % 36.85/5.67 ! [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: vTable] : (v1 = v0 | ~ % 36.85/5.67 (vgetRaw(v2) = v1) | ~ (vgetRaw(v2) = v0)) & ! [v0: vFType] : ! [v1: % 36.85/5.67 vFType] : ! [v2: vOptFType] : (v1 = v0 | ~ (vgetFType(v2) = v1) | ~ % 36.85/5.67 (vgetFType(v2) = v0)) & ! [v0: vVal] : ! [v1: vVal] : ! [v2: vOptVal] : % 36.85/5.67 (v1 = v0 | ~ (vgetVal(v2) = v1) | ~ (vgetVal(v2) = v0)) & ! [v0: vQuery] : % 36.85/5.67 ! [v1: vQuery] : ! [v2: vOptQuery] : (v1 = v0 | ~ (vgetQuery(v2) = v1) | ~ % 36.85/5.67 (vgetQuery(v2) = v0)) & ! [v0: vTType] : ! [v1: vTType] : ! [v2: % 36.85/5.67 vOptTType] : (v1 = v0 | ~ (vgetTType(v2) = v1) | ~ (vgetTType(v2) = v0)) & % 36.85/5.67 ! [v0: vTable] : ! [v1: vTable] : ! [v2: vOptTable] : (v1 = v0 | ~ % 36.85/5.67 (vgetTable(v2) = v1) | ~ (vgetTable(v2) = v0)) & ! [v0: vRawTable] : ! % 36.85/5.67 [v1: vRawTable] : ! [v2: vOptRawTable] : (v1 = v0 | ~ (vgetRawTable(v2) = % 36.85/5.67 v1) | ~ (vgetRawTable(v2) = v0)) & ! [v0: vOptFType] : ! [v1: % 36.85/5.67 vOptFType] : ! [v2: vFType] : (v1 = v0 | ~ (vsomeFType(v2) = v1) | ~ % 36.85/5.67 (vsomeFType(v2) = v0)) & ! [v0: vVal] : ! [v1: vVal] : ! [v2: vVal] : (v1 % 36.85/5.67 = v0 | ~ (venumVal(v2) = v1) | ~ (venumVal(v2) = v0)) & ! [v0: vPred] : % 36.85/5.67 ! [v1: vPred] : ! [v2: vPred] : (v1 = v0 | ~ (vnot(v2) = v1) | ~ (vnot(v2) % 36.85/5.67 = v0)) & ! [v0: vOptVal] : ! [v1: vOptVal] : ! [v2: vVal] : (v1 = v0 | % 36.85/5.67 ~ (vsomeVal(v2) = v1) | ~ (vsomeVal(v2) = v0)) & ! [v0: vExp] : ! [v1: % 36.85/5.67 vExp] : ! [v2: vName] : (v1 = v0 | ~ (vlookup(v2) = v1) | ~ (vlookup(v2) % 36.85/5.67 = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vVal] : (v1 = v0 | ~ % 36.85/5.67 (vconstant(v2) = v1) | ~ (vconstant(v2) = v0)) & ! [v0: vName] : ! [v1: % 36.85/5.67 vName] : ! [v2: vName] : (v1 = v0 | ~ (venumName(v2) = v1) | ~ % 36.85/5.67 (venumName(v2) = v0)) & ! [v0: vOptQuery] : ! [v1: vOptQuery] : ! [v2: % 36.85/5.67 vQuery] : (v1 = v0 | ~ (vsomeQuery(v2) = v1) | ~ (vsomeQuery(v2) = v0)) & % 36.85/5.67 ! [v0: vFType] : ! [v1: vFType] : ! [v2: vFType] : (v1 = v0 | ~ % 36.85/5.67 (venumFType(v2) = v1) | ~ (venumFType(v2) = v0)) & ! [v0: vOptTType] : ! % 36.85/5.67 [v1: vOptTType] : ! [v2: vTType] : (v1 = v0 | ~ (vsomeTType(v2) = v1) | ~ % 36.85/5.67 (vsomeTType(v2) = v0)) & ! [v0: vOptRawTable] : ! [v1: vOptRawTable] : ! % 36.85/5.67 [v2: vRawTable] : (v1 = v0 | ~ (vsomeRawTable(v2) = v1) | ~ % 36.85/5.67 (vsomeRawTable(v2) = v0)) & ! [v0: vOptTable] : ! [v1: vOptTable] : ! % 36.85/5.67 [v2: vTable] : (v1 = v0 | ~ (vsomeTable(v2) = v1) | ~ (vsomeTable(v2) = v0)) % 36.85/5.67 & ! [v0: vQuery] : ! [v1: vQuery] : ! [v2: vTable] : (v1 = v0 | ~ % 36.85/5.67 (vtvalue(v2) = v1) | ~ (vtvalue(v2) = v0)) & ! [v0: vSelect] : ! [v1: % 36.85/5.67 vSelect] : ! [v2: vAttrL] : (v1 = v0 | ~ (vlist(v2) = v1) | ~ (vlist(v2) % 36.85/5.67 = v0)) % 36.85/5.67 % 36.85/5.67 Further assumptions not needed in the proof: % 36.85/5.67 -------------------------------------------- % 36.85/5.67 DIFF-Intersection-Difference, DIFF-Union-Difference, DIFF-Union-Intersection, % 36.85/5.67 DIFF-aempty-acons, DIFF-all-list, DIFF-and-eq, DIFF-and-gt, DIFF-and-lt, % 36.85/5.68 DIFF-and-not, DIFF-constant-lookup, DIFF-emptyContext-bindContext, % 36.85/5.68 DIFF-emptyStore-bindStore, DIFF-eq-gt, DIFF-eq-lt, DIFF-gt-lt, % 36.85/5.68 DIFF-initFType-enumFType, DIFF-initName-enumName, DIFF-initVal-enumVal, % 36.85/5.68 DIFF-noFType-someFType, DIFF-noQuery-someQuery, DIFF-noRawTable-someRawTable, % 36.85/5.68 DIFF-noTType-someTType, DIFF-noTable-someTable, DIFF-noVal-someVal, DIFF-not-eq, % 36.85/5.68 DIFF-not-gt, DIFF-not-lt, DIFF-ptrue-and, DIFF-ptrue-eq, DIFF-ptrue-gt, % 36.85/5.68 DIFF-ptrue-lt, DIFF-ptrue-not, DIFF-rempty-rcons, % 36.85/5.68 DIFF-selectFromWhere-Difference, DIFF-selectFromWhere-Intersection, % 36.85/5.68 DIFF-selectFromWhere-Union, DIFF-tempty-tcons, DIFF-ttempty-ttcons, % 36.85/5.68 DIFF-tvalue-Difference, DIFF-tvalue-Intersection, DIFF-tvalue-Union, % 36.85/5.68 DIFF-tvalue-selectFromWhere, EQ-Difference, EQ-Intersection, EQ-Union, EQ-acons, % 36.85/5.68 EQ-and, EQ-bindContext, EQ-bindStore, EQ-constant, EQ-enumFType, EQ-enumName, % 36.85/5.68 EQ-enumVal, EQ-eq, EQ-gt, EQ-list, EQ-lookup, EQ-lt, EQ-not, EQ-rcons, % 36.85/5.68 EQ-selectFromWhere, EQ-someFType, EQ-someQuery, EQ-someRawTable, EQ-someTType, % 36.85/5.68 EQ-someTable, EQ-someVal, EQ-table, EQ-ttcons, EQ-tvalue, TDifference, % 36.85/5.68 TDifference_inv1, TDifference_inv2, TIntersection, TIntersection_inv1, % 36.85/5.68 TIntersection_inv2, TSelectFromWhere, TSelectFromWhere_inv, TTTContextDuplicate, % 36.85/5.68 TTTContextSwap, TUnion, TUnion_inv1, TUnion_inv2, Ttvalue, Ttvalue_inv, % 36.85/5.68 append-0, append-1, append-INV, attachColToFrontRaw-0, attachColToFrontRaw-1, % 36.85/5.68 attachColToFrontRaw-2, attachColToFrontRaw-INV, dom-AttrL, dom-Exp, % 36.85/5.68 dom-OptFType, dom-OptQuery, dom-OptRawTable, dom-OptTType, dom-OptTable, % 36.85/5.68 dom-OptVal, dom-Pred, dom-Query, dom-RawTable, dom-Row, dom-Select, dom-TStore, % 36.85/5.68 dom-TTContext, dom-TType, dom-Table, dropFirstColRaw-0, dropFirstColRaw-1, % 36.85/5.68 dropFirstColRaw-2, dropFirstColRaw-INV, evalExpRow-0, evalExpRow-1, % 36.85/5.68 evalExpRow-2, evalExpRow-3, evalExpRow-INV, filterRows-0, filterRows-1, % 36.85/5.68 filterRows-2, filterRows-INV, filterSingleRow-0, filterSingleRow-1, % 36.85/5.68 filterSingleRow-2, filterSingleRow-3, filterSingleRow-4, filterSingleRow-5, % 36.85/5.68 filterSingleRow-false-INV, filterSingleRow-true-INV, filterTable-0, % 36.85/5.68 filterTable-INV, findCol-0, findCol-1, findCol-2, findCol-INV, findColType-0, % 36.85/5.68 findColType-1, findColType-2, findColType-INV, getAttrL-0, getAttrL-INV, % 36.85/5.68 getFType-0, getQuery-0, getRaw-0, getRaw-INV, getRawTable-0, getTType-0, % 36.85/5.68 getTable-0, getVal-0, isSomeFType-0, isSomeFType-1, isSomeFType-false-INV, % 36.85/5.68 isSomeFType-true-INV, isSomeQuery-0, isSomeQuery-1, isSomeQuery-false-INV, % 36.85/5.68 isSomeQuery-true-INV, isSomeRawTable-0, isSomeRawTable-1, % 36.85/5.68 isSomeRawTable-false-INV, isSomeRawTable-true-INV, isSomeTType-0, isSomeTType-1, % 36.85/5.68 isSomeTType-false-INV, isSomeTType-true-INV, isSomeTable-0, isSomeTable-1, % 36.85/5.68 isSomeTable-false-INV, isSomeTable-true-INV, isSomeVal-0, isSomeVal-1, % 36.85/5.68 isSomeVal-false-INV, isSomeVal-true-INV, isValue-0, isValue-1, isValue-2, % 36.85/5.68 isValue-3, isValue-4, isValue-false-INV, isValue-true-INV, lookupContext-0, % 36.85/5.68 lookupContext-1, lookupContext-2, lookupContext-INV, lookupStore-0, % 36.85/5.68 lookupStore-1, lookupStore-2, lookupStore-INV, matchingAttrL-0, matchingAttrL-1, % 36.85/5.68 matchingAttrL-2, matchingAttrL-false-INV, matchingAttrL-true-INV, projectCols-0, % 36.85/5.68 projectCols-1, projectCols-2, projectCols-INV, projectEmptyCol-0, % 36.85/5.68 projectFirstRaw-0, projectFirstRaw-1, projectFirstRaw-2, projectFirstRaw-INV, % 36.85/5.68 projectTable-0, projectTable-1, projectTable-2, projectTable-INV, projectType-0, % 36.85/5.68 projectType-1, projectType-INV, projectTypeAttrL-0, projectTypeAttrL-1, % 36.85/5.68 projectTypeAttrL-2, projectTypeAttrL-INV, rawDifference-0, rawDifference-1, % 36.85/5.68 rawDifference-2, rawDifference-3, rawDifference-4, rawDifference-INV, % 36.85/5.68 rawIntersection-0, rawIntersection-1, rawIntersection-2, rawIntersection-3, % 36.85/5.68 rawIntersection-4, rawIntersection-INV, rawUnion-0, rawUnion-1, rawUnion-2, % 36.85/5.68 rawUnion-INV, reduce-0, reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, % 36.85/5.68 reduce-14, reduce-15, reduce-16, reduce-17, reduce-18, reduce-2, reduce-3, % 36.85/5.68 reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, reduce-INV, rowIn-0, % 36.85/5.68 rowIn-1, rowIn-false-INV, rowIn-true-INV, sameLength-0, sameLength-1, % 36.85/5.68 sameLength-2, sameLength-false-INV, sameLength-true-INV, % 36.85/5.68 storeContextConsistent-0, storeContextConsistent-1, storeContextConsistent-2, % 36.85/5.68 storeContextConsistent-false-INV, storeContextConsistent-true-INV, tcheckPred-0, % 36.85/5.68 tcheckPred-1, tcheckPred-2, tcheckPred-3, tcheckPred-4, tcheckPred-5, % 36.85/5.68 tcheckPred-false-INV, tcheckPred-true-INV, typeOfExp-0, typeOfExp-1, % 36.85/5.68 typeOfExp-2, typeOfExp-3, typeOfExp-INV, welltypedRawtable-0, % 36.85/5.68 welltypedRawtable-1, welltypedRawtable-true-INV, welltypedRow-1, welltypedRow-2, % 36.85/5.68 welltypedRow-false-INV, welltypedRow-true-INV, welltypedtable-0, % 36.85/5.68 welltypedtable-false-INV, welltypedtable-true-INV % 36.85/5.68 % 36.85/5.68 Those formulas are unsatisfiable: % 36.85/5.68 --------------------------------- % 36.85/5.68 % 36.85/5.68 Begin of proof % 36.85/5.68 | % 36.85/5.68 | ALPHA: (welltypedRow-0) implies: % 36.85/5.68 | (1) vwelltypedRow(vttempty, vrempty) = 0 % 36.85/5.68 | % 36.85/5.68 | ALPHA: (projectEmptyCol-1) implies: % 36.85/5.68 | (2) ! [v0: vRow] : ! [v1: vRawTable] : ! [v2: vRawTable] : ( ~ % 36.85/5.68 | (vtcons(v0, v1) = v2) | ~ vRawTable(v1) | ~ vRow(v0) | ? [v3: % 36.85/5.68 | vRawTable] : ? [v4: vRawTable] : (vprojectEmptyCol(v2) = v3 & % 36.85/5.68 | vprojectEmptyCol(v1) = v4 & vtcons(vrempty, v4) = v3 & % 36.85/5.68 | vRawTable(v4) & vRawTable(v3))) % 36.85/5.68 | % 36.85/5.68 | ALPHA: (projectEmptyCol-INV) implies: % 36.85/5.68 | (3) vRow(vrempty) % 36.85/5.68 | % 36.85/5.68 | ALPHA: (welltypedEmptyProjection-tcons-IH0) implies: % 36.85/5.68 | (4) ? [v0: vRawTable] : (vprojectEmptyCol(vrt2) = v0 & % 36.85/5.68 | vwelltypedRawtable(vttempty, v0) = 0 & vRawTable(v0)) % 36.85/5.68 | % 36.85/5.68 | ALPHA: (welltypedEmptyProjection-tcons) implies: % 36.85/5.68 | (5) vRawTable(vrt2) % 36.85/5.68 | (6) vTType(vttempty) % 36.85/5.68 | (7) ? [v0: vRow] : ? [v1: vRawTable] : ? [v2: vRawTable] : ? [v3: int] % 36.85/5.68 | : ( ~ (v3 = 0) & vprojectEmptyCol(v1) = v2 & % 36.85/5.68 | vwelltypedRawtable(vttempty, v2) = v3 & vtcons(v0, vrt2) = v1 & % 36.85/5.68 | vRawTable(v2) & vRawTable(v1) & vRow(v0)) % 36.85/5.68 | % 36.85/5.68 | ALPHA: (function-axioms) implies: % 36.85/5.68 | (8) ! [v0: vRawTable] : ! [v1: vRawTable] : ! [v2: vRawTable] : (v1 = v0 % 36.85/5.68 | | ~ (vprojectEmptyCol(v2) = v1) | ~ (vprojectEmptyCol(v2) = v0)) % 36.85/5.68 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vRow] % 36.85/5.68 | : ! [v3: vTType] : (v1 = v0 | ~ (vwelltypedRow(v3, v2) = v1) | ~ % 36.85/5.68 | (vwelltypedRow(v3, v2) = v0)) % 36.85/5.68 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 36.85/5.68 | vRawTable] : ! [v3: vTType] : (v1 = v0 | ~ (vwelltypedRawtable(v3, % 36.85/5.68 | v2) = v1) | ~ (vwelltypedRawtable(v3, v2) = v0)) % 36.85/5.68 | % 36.85/5.68 | DELTA: instantiating (4) with fresh symbol all_313_0 gives: % 36.85/5.69 | (11) vprojectEmptyCol(vrt2) = all_313_0 & vwelltypedRawtable(vttempty, % 36.85/5.69 | all_313_0) = 0 & vRawTable(all_313_0) % 36.85/5.69 | % 36.85/5.69 | ALPHA: (11) implies: % 36.85/5.69 | (12) vwelltypedRawtable(vttempty, all_313_0) = 0 % 36.85/5.69 | (13) vprojectEmptyCol(vrt2) = all_313_0 % 36.85/5.69 | % 36.85/5.69 | DELTA: instantiating (7) with fresh symbols all_333_0, all_333_1, all_333_2, % 36.85/5.69 | all_333_3 gives: % 36.85/5.69 | (14) ~ (all_333_0 = 0) & vprojectEmptyCol(all_333_2) = all_333_1 & % 36.85/5.69 | vwelltypedRawtable(vttempty, all_333_1) = all_333_0 & % 36.85/5.69 | vtcons(all_333_3, vrt2) = all_333_2 & vRawTable(all_333_1) & % 36.85/5.69 | vRawTable(all_333_2) & vRow(all_333_3) % 36.85/5.69 | % 36.85/5.69 | ALPHA: (14) implies: % 36.85/5.69 | (15) ~ (all_333_0 = 0) % 36.85/5.69 | (16) vRow(all_333_3) % 36.85/5.69 | (17) vRawTable(all_333_1) % 36.85/5.69 | (18) vtcons(all_333_3, vrt2) = all_333_2 % 36.85/5.69 | (19) vwelltypedRawtable(vttempty, all_333_1) = all_333_0 % 36.85/5.69 | (20) vprojectEmptyCol(all_333_2) = all_333_1 % 36.85/5.69 | % 36.85/5.69 | GROUND_INST: instantiating (2) with all_333_3, vrt2, all_333_2, simplifying % 36.85/5.69 | with (5), (16), (18) gives: % 36.85/5.69 | (21) ? [v0: vRawTable] : ? [v1: vRawTable] : (vprojectEmptyCol(all_333_2) % 36.85/5.69 | = v0 & vprojectEmptyCol(vrt2) = v1 & vtcons(vrempty, v1) = v0 & % 36.85/5.69 | vRawTable(v1) & vRawTable(v0)) % 36.85/5.69 | % 36.85/5.69 | GROUND_INST: instantiating (welltypedRawtable-false-INV) with vttempty, % 36.85/5.69 | all_333_1, all_333_0, simplifying with (6), (17), (19) gives: % 36.85/5.69 | (22) all_333_0 = 0 | ? [v0: vRow] : ? [v1: vRawTable] : ? [v2: any] : ? % 36.85/5.69 | [v3: any] : (vwelltypedRawtable(vttempty, v1) = v3 & % 36.85/5.69 | vwelltypedRow(vttempty, v0) = v2 & vtcons(v0, v1) = all_333_1 & % 36.85/5.69 | vRawTable(v1) & vRow(v0) & ( ~ (v3 = 0) | ~ (v2 = 0))) % 36.85/5.69 | % 36.85/5.69 | DELTA: instantiating (21) with fresh symbols all_356_0, all_356_1 gives: % 36.85/5.69 | (23) vprojectEmptyCol(all_333_2) = all_356_1 & vprojectEmptyCol(vrt2) = % 36.85/5.69 | all_356_0 & vtcons(vrempty, all_356_0) = all_356_1 & % 36.85/5.69 | vRawTable(all_356_0) & vRawTable(all_356_1) % 36.85/5.69 | % 36.85/5.69 | ALPHA: (23) implies: % 36.85/5.69 | (24) vRawTable(all_356_0) % 36.85/5.69 | (25) vtcons(vrempty, all_356_0) = all_356_1 % 36.85/5.69 | (26) vprojectEmptyCol(vrt2) = all_356_0 % 36.85/5.69 | (27) vprojectEmptyCol(all_333_2) = all_356_1 % 36.85/5.69 | % 36.85/5.69 | BETA: splitting (22) gives: % 36.85/5.69 | % 36.85/5.69 | Case 1: % 36.85/5.69 | | % 36.85/5.69 | | (28) all_333_0 = 0 % 36.85/5.69 | | % 36.85/5.69 | | REDUCE: (15), (28) imply: % 36.85/5.69 | | (29) $false % 36.85/5.69 | | % 36.85/5.69 | | CLOSE: (29) is inconsistent. % 36.85/5.69 | | % 36.85/5.69 | Case 2: % 36.85/5.69 | | % 36.85/5.69 | | (30) ? [v0: vRow] : ? [v1: vRawTable] : ? [v2: any] : ? [v3: any] : % 36.85/5.69 | | (vwelltypedRawtable(vttempty, v1) = v3 & vwelltypedRow(vttempty, v0) % 36.85/5.69 | | = v2 & vtcons(v0, v1) = all_333_1 & vRawTable(v1) & vRow(v0) & ( ~ % 36.85/5.69 | | (v3 = 0) | ~ (v2 = 0))) % 36.85/5.69 | | % 36.85/5.69 | | DELTA: instantiating (30) with fresh symbols all_368_0, all_368_1, % 36.85/5.69 | | all_368_2, all_368_3 gives: % 36.85/5.69 | | (31) vwelltypedRawtable(vttempty, all_368_2) = all_368_0 & % 36.85/5.69 | | vwelltypedRow(vttempty, all_368_3) = all_368_1 & vtcons(all_368_3, % 36.85/5.69 | | all_368_2) = all_333_1 & vRawTable(all_368_2) & vRow(all_368_3) & % 36.85/5.69 | | ( ~ (all_368_0 = 0) | ~ (all_368_1 = 0)) % 36.85/5.69 | | % 36.85/5.69 | | ALPHA: (31) implies: % 36.85/5.69 | | (32) vRow(all_368_3) % 36.85/5.70 | | (33) vRawTable(all_368_2) % 36.85/5.70 | | (34) vtcons(all_368_3, all_368_2) = all_333_1 % 36.85/5.70 | | (35) vwelltypedRow(vttempty, all_368_3) = all_368_1 % 36.85/5.70 | | (36) vwelltypedRawtable(vttempty, all_368_2) = all_368_0 % 36.85/5.70 | | (37) ~ (all_368_0 = 0) | ~ (all_368_1 = 0) % 36.85/5.70 | | % 36.85/5.70 | | GROUND_INST: instantiating (8) with all_313_0, all_356_0, vrt2, simplifying % 36.85/5.70 | | with (13), (26) gives: % 36.85/5.70 | | (38) all_356_0 = all_313_0 % 36.85/5.70 | | % 37.32/5.70 | | GROUND_INST: instantiating (8) with all_333_1, all_356_1, all_333_2, % 37.32/5.70 | | simplifying with (20), (27) gives: % 37.32/5.70 | | (39) all_356_1 = all_333_1 % 37.32/5.70 | | % 37.32/5.70 | | REDUCE: (25), (38), (39) imply: % 37.32/5.70 | | (40) vtcons(vrempty, all_313_0) = all_333_1 % 37.32/5.70 | | % 37.32/5.70 | | REDUCE: (24), (38) imply: % 37.32/5.70 | | (41) vRawTable(all_313_0) % 37.32/5.70 | | % 37.32/5.70 | | GROUND_INST: instantiating (EQ-tcons) with vrempty, all_313_0, all_368_3, % 37.32/5.70 | | all_368_2, all_333_1, simplifying with (3), (32), (33), (34), % 37.32/5.70 | | (40), (41) gives: % 37.32/5.70 | | (42) all_368_2 = all_313_0 & all_368_3 = vrempty % 37.32/5.70 | | % 37.32/5.70 | | ALPHA: (42) implies: % 37.32/5.70 | | (43) all_368_3 = vrempty % 37.32/5.70 | | (44) all_368_2 = all_313_0 % 37.32/5.70 | | % 37.32/5.70 | | REDUCE: (36), (44) imply: % 37.32/5.70 | | (45) vwelltypedRawtable(vttempty, all_313_0) = all_368_0 % 37.32/5.70 | | % 37.32/5.70 | | REDUCE: (35), (43) imply: % 37.32/5.70 | | (46) vwelltypedRow(vttempty, vrempty) = all_368_1 % 37.32/5.70 | | % 37.32/5.70 | | GROUND_INST: instantiating (9) with 0, all_368_1, vrempty, vttempty, % 37.32/5.70 | | simplifying with (1), (46) gives: % 37.32/5.70 | | (47) all_368_1 = 0 % 37.32/5.70 | | % 37.32/5.70 | | GROUND_INST: instantiating (10) with 0, all_368_0, all_313_0, vttempty, % 37.32/5.70 | | simplifying with (12), (45) gives: % 37.32/5.70 | | (48) all_368_0 = 0 % 37.32/5.70 | | % 37.32/5.70 | | BETA: splitting (37) gives: % 37.32/5.70 | | % 37.32/5.70 | | Case 1: % 37.32/5.70 | | | % 37.32/5.70 | | | (49) ~ (all_368_0 = 0) % 37.32/5.70 | | | % 37.32/5.70 | | | REDUCE: (48), (49) imply: % 37.32/5.70 | | | (50) $false % 37.32/5.70 | | | % 37.32/5.70 | | | CLOSE: (50) is inconsistent. % 37.32/5.70 | | | % 37.32/5.70 | | Case 2: % 37.32/5.70 | | | % 37.32/5.70 | | | (51) ~ (all_368_1 = 0) % 37.32/5.70 | | | % 37.32/5.70 | | | REDUCE: (47), (51) imply: % 37.32/5.70 | | | (52) $false % 37.32/5.70 | | | % 37.32/5.70 | | | CLOSE: (52) is inconsistent. % 37.32/5.70 | | | % 37.32/5.70 | | End of split % 37.32/5.70 | | % 37.32/5.70 | End of split % 37.32/5.70 | % 37.32/5.70 End of proof % 37.32/5.70 % SZS output end Proof for theBenchmark % 37.32/5.70 % 37.32/5.70 5277ms %------------------------------------------------------------------------------