%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM267_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 : n005.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 06:21:39 PM UTC 2026 % Result : Theorem 36.89s 5.61s % Output : Proof 49.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM267_1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Mon May 4 20:01:00 EDT 2026 % 0.17/0.34 % 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/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.62 Running up to 7 provers in parallel. % 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 9.73/2.05 Prover 4: Preprocessing ... % 9.73/2.06 Prover 1: Preprocessing ... % 10.37/2.11 Prover 6: Preprocessing ... % 10.37/2.11 Prover 2: Preprocessing ... % 10.37/2.11 Prover 0: Preprocessing ... % 10.37/2.11 Prover 3: Preprocessing ... % 10.37/2.11 Prover 5: Preprocessing ... % 24.76/4.06 Prover 1: Warning: ignoring some quantifiers % 26.19/4.28 Prover 1: Constructing countermodel ... % 26.92/4.31 Prover 3: Warning: ignoring some quantifiers % 26.92/4.33 Prover 6: Proving ... % 26.92/4.35 Prover 3: Constructing countermodel ... % 26.92/4.40 Prover 5: Proving ... % 29.16/4.63 Prover 4: Warning: ignoring some quantifiers % 29.93/4.74 Prover 4: Constructing countermodel ... % 31.46/4.94 Prover 0: Proving ... % 34.58/5.32 Prover 2: Proving ... % 36.89/5.61 Prover 5: proved (4967ms) % 36.89/5.61 % 36.89/5.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.89/5.61 % 36.89/5.62 Prover 6: stopped % 36.89/5.62 Prover 3: stopped % 36.89/5.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 36.89/5.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 36.89/5.64 Prover 2: stopped % 36.89/5.65 Prover 0: stopped % 36.89/5.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 36.89/5.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 36.89/5.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 40.84/6.16 Prover 7: Preprocessing ... % 41.44/6.27 Prover 13: Preprocessing ... % 42.19/6.30 Prover 10: Preprocessing ... % 42.19/6.31 Prover 11: Preprocessing ... % 42.19/6.32 Prover 8: Preprocessing ... % 46.08/6.83 Prover 4: Found proof (size 21) % 46.08/6.84 Prover 4: proved (6195ms) % 46.08/6.84 Prover 7: stopped % 46.08/6.84 Prover 1: stopped % 46.08/6.85 Prover 11: stopped % 46.08/6.89 Prover 13: stopped % 47.34/7.09 Prover 8: Warning: ignoring some quantifiers % 47.87/7.12 Prover 8: Constructing countermodel ... % 47.87/7.14 Prover 8: stopped % 48.64/7.39 Prover 10: Warning: ignoring some quantifiers % 49.04/7.44 Prover 10: Constructing countermodel ... % 49.04/7.46 Prover 10: stopped % 49.04/7.46 % 49.04/7.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 49.04/7.46 % 49.04/7.47 % SZS output start Proof for theBenchmark % 49.48/7.51 Assumptions after simplification: % 49.48/7.51 --------------------------------- % 49.48/7.51 % 49.48/7.51 (Progress-qsingle-defquestion) % 49.48/7.56 ? [v0: vQMap] : ? [v1: vAType] : ? [v2: vATMap] : ? [v3: vATMap] : ? [v4: % 49.48/7.56 vLabel] : ? [v5: vAnsMap] : ? [v6: vQID] : ? [v7: vEntry] : ? [v8: % 49.48/7.56 vQuestionnaire] : ? [v9: int] : ? [v10: vATMap] : ? [v11: vATMap] : ? % 49.48/7.56 [v12: vMapConf] : ? [v13: vMapConf] : ? [v14: vOptQConf] : ( ~ (v9 = 0) & % 49.48/7.56 vptcheck(v12, v8, v13) = 0 & vtypeQM(v0) = v11 & vtypeAM(v5) = v10 & % 49.48/7.56 vreduce(v8, v5, v0) = v14 & visValue(v8) = v9 & vqsingle(v7) = v8 & vMC(v10, % 49.48/7.56 v11) = v12 & vMC(v2, v3) = v13 & vdefquestion(v6, v4, v1) = v7 & % 49.48/7.56 vAType(v1) & vLabel(v4) & vQID(v6) & vQMap(v0) & vAnsMap(v5) & % 49.48/7.56 vOptQConf(v14) & vQuestionnaire(v8) & vATMap(v11) & vATMap(v10) & vATMap(v3) % 49.48/7.56 & vATMap(v2) & vMapConf(v13) & vMapConf(v12) & vEntry(v7) & ! [v15: % 49.48/7.56 vAnsMap] : ! [v16: vQMap] : ! [v17: vQuestionnaire] : ! [v18: vQConf] : % 49.48/7.56 ( ~ (vQC(v15, v16, v17) = v18) | ~ vQMap(v16) | ~ vAnsMap(v15) | ~ % 49.48/7.56 vQuestionnaire(v17) | ? [v19: vOptQConf] : ( ~ (v19 = v14) & % 49.48/7.56 vsomeQConf(v18) = v19 & vOptQConf(v19)))) % 49.48/7.56 % 49.48/7.56 (Tqempty_inv2) % 49.48/7.56 vQuestionnaire(vqempty) & ! [v0: vATMap] : ! [v1: vATMap] : ! [v2: vATMap] % 49.48/7.56 : ! [v3: vATMap] : ! [v4: vMapConf] : ! [v5: vMapConf] : (v3 = v1 | ~ % 49.48/7.56 (vptcheck(v4, vqempty, v5) = 0) | ~ (vMC(v2, v3) = v5) | ~ (vMC(v0, v1) = % 49.48/7.56 v4) | ~ vATMap(v3) | ~ vATMap(v2) | ~ vATMap(v1) | ~ vATMap(v0)) % 49.48/7.56 % 49.48/7.56 (reduce-5) % 49.48/7.57 vQuestionnaire(vqempty) & ! [v0: vQMap] : ! [v1: vAType] : ! [v2: vLabel] : % 49.48/7.57 ! [v3: vAnsMap] : ! [v4: vQID] : ! [v5: vEntry] : ! [v6: vQuestionnaire] : % 49.48/7.57 ! [v7: vOptQConf] : ( ~ (vreduce(v6, v3, v0) = v7) | ~ (vqsingle(v5) = v6) | % 49.48/7.57 ~ (vdefquestion(v4, v2, v1) = v5) | ~ vAType(v1) | ~ vLabel(v2) | ~ % 49.48/7.57 vQID(v4) | ~ vQMap(v0) | ~ vAnsMap(v3) | ? [v8: vQMap] : ? [v9: vQConf] % 49.48/7.57 : (vQC(v3, v8, vqempty) = v9 & vsomeQConf(v9) = v7 & vqmbind(v4, v2, v1, v0) % 49.48/7.57 = v8 & vQMap(v8) & vOptQConf(v7) & vQConf(v9))) & ! [v0: vQMap] : ! [v1: % 49.48/7.57 vAType] : ! [v2: vLabel] : ! [v3: vAnsMap] : ! [v4: vQID] : ! [v5: % 49.48/7.57 vQMap] : ! [v6: vQConf] : ( ~ (vQC(v3, v5, vqempty) = v6) | ~ (vqmbind(v4, % 49.48/7.57 v2, v1, v0) = v5) | ~ vAType(v1) | ~ vLabel(v2) | ~ vQID(v4) | ~ % 49.48/7.57 vQMap(v0) | ~ vAnsMap(v3) | ? [v7: vEntry] : ? [v8: vQuestionnaire] : ? % 49.48/7.57 [v9: vOptQConf] : (vreduce(v8, v3, v0) = v9 & vsomeQConf(v6) = v9 & % 49.48/7.57 vqsingle(v7) = v8 & vdefquestion(v4, v2, v1) = v7 & vOptQConf(v9) & % 49.48/7.57 vQuestionnaire(v8) & vEntry(v7))) % 49.48/7.57 % 49.48/7.57 (reduce-8) % 49.48/7.57 vQuestionnaire(vqempty) & ! [v0: vQuestionnaire] : ! [v1: vAnsMap] : ! [v2: % 49.48/7.57 vQMap] : ! [v3: vQuestionnaire] : ! [v4: vOptQConf] : ( ~ (vreduce(v3, v1, % 49.48/7.57 v2) = v4) | ~ (vqseq(vqempty, v0) = v3) | ~ vQMap(v2) | ~ vAnsMap(v1) % 49.48/7.57 | ~ vQuestionnaire(v0) | ? [v5: vQConf] : (vQC(v1, v2, v0) = v5 & % 49.48/7.57 vsomeQConf(v5) = v4 & vOptQConf(v4) & vQConf(v5))) & ! [v0: % 49.48/7.57 vQuestionnaire] : ! [v1: vAnsMap] : ! [v2: vQMap] : ! [v3: vQConf] : ( ~ % 49.48/7.57 (vQC(v1, v2, v0) = v3) | ~ vQMap(v2) | ~ vAnsMap(v1) | ~ % 49.48/7.57 vQuestionnaire(v0) | ? [v4: vQuestionnaire] : ? [v5: vOptQConf] : % 49.48/7.57 (vreduce(v4, v1, v2) = v5 & vsomeQConf(v3) = v5 & vqseq(vqempty, v0) = v4 & % 49.48/7.57 vOptQConf(v5) & vQuestionnaire(v4))) % 49.48/7.57 % 49.48/7.57 (function-axioms) % 49.48/7.60 ! [v0: vQMap] : ! [v1: vQMap] : ! [v2: vQMap] : ! [v3: vAType] : ! [v4: % 49.48/7.60 vLabel] : ! [v5: vQID] : (v1 = v0 | ~ (vqmbind(v5, v4, v3, v2) = v1) | ~ % 49.48/7.60 (vqmbind(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 49.48/7.60 MultipleValueBool] : ! [v2: vMapConf] : ! [v3: vQuestionnaire] : ! [v4: % 49.48/7.60 vMapConf] : (v1 = v0 | ~ (vptcheck(v4, v3, v2) = v1) | ~ (vptcheck(v4, v3, % 49.48/7.60 v2) = v0)) & ! [v0: vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : % 49.48/7.60 ! [v3: vAType] : ! [v4: vBinOpT] : (v1 = v0 | ~ (vcheckBinOp(v4, v3, v2) = % 49.48/7.60 v1) | ~ (vcheckBinOp(v4, v3, v2) = v0)) & ! [v0: vOptQConf] : ! [v1: % 49.96/7.60 vOptQConf] : ! [v2: vQMap] : ! [v3: vAnsMap] : ! [v4: vQuestionnaire] : % 49.96/7.60 (v1 = v0 | ~ (vreduce(v4, v3, v2) = v1) | ~ (vreduce(v4, v3, v2) = v0)) & ! % 49.96/7.60 [v0: vOptExp] : ! [v1: vOptExp] : ! [v2: vAval] : ! [v3: vAval] : ! [v4: % 49.96/7.60 vBinOpT] : (v1 = v0 | ~ (vevalBinOp(v4, v3, v2) = v1) | ~ (vevalBinOp(v4, % 49.96/7.60 v3, v2) = v0)) & ! [v0: vQConf] : ! [v1: vQConf] : ! [v2: % 49.96/7.60 vQuestionnaire] : ! [v3: vQMap] : ! [v4: vAnsMap] : (v1 = v0 | ~ (vQC(v4, % 49.96/7.60 v3, v2) = v1) | ~ (vQC(v4, v3, v2) = v0)) & ! [v0: vATMap] : ! [v1: % 49.96/7.60 vATMap] : ! [v2: vATMap] : ! [v3: vAType] : ! [v4: vQID] : (v1 = v0 | ~ % 49.96/7.60 (vatmbind(v4, v3, v2) = v1) | ~ (vatmbind(v4, v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptQuestion] : ! [v1: vOptQuestion] : ! [v2: vAType] : ! [v3: vLabel] : % 49.96/7.60 ! [v4: vQID] : (v1 = v0 | ~ (vsomeQuestion(v4, v3, v2) = v1) | ~ % 49.96/7.60 (vsomeQuestion(v4, v3, v2) = v0)) & ! [v0: vAnsMap] : ! [v1: vAnsMap] : ! % 49.96/7.60 [v2: vAnsMap] : ! [v3: vAval] : ! [v4: vQID] : (v1 = v0 | ~ (vabind(v4, v3, % 49.96/7.60 v2) = v1) | ~ (vabind(v4, v3, v2) = v0)) & ! [v0: vQuestionnaire] : ! % 49.96/7.60 [v1: vQuestionnaire] : ! [v2: vQuestionnaire] : ! [v3: vQuestionnaire] : ! % 49.96/7.60 [v4: vExp] : (v1 = v0 | ~ (vqcond(v4, v3, v2) = v1) | ~ (vqcond(v4, v3, v2) % 49.96/7.60 = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vExp] : ! [v3: vBinOpT] % 49.96/7.60 : ! [v4: vExp] : (v1 = v0 | ~ (vbinop(v4, v3, v2) = v1) | ~ (vbinop(v4, v3, % 49.96/7.60 v2) = v0)) & ! [v0: vEntry] : ! [v1: vEntry] : ! [v2: vAType] : ! % 49.96/7.60 [v3: vLabel] : ! [v4: vQID] : (v1 = v0 | ~ (vdefquestion(v4, v3, v2) = v1) | % 49.96/7.60 ~ (vdefquestion(v4, v3, v2) = v0)) & ! [v0: vEntry] : ! [v1: vEntry] : ! % 49.96/7.60 [v2: vExp] : ! [v3: vAType] : ! [v4: vQID] : (v1 = v0 | ~ (vvalue(v4, v3, % 49.96/7.60 v2) = v1) | ~ (vvalue(v4, v3, v2) = v0)) & ! [v0: vEntry] : ! [v1: % 49.96/7.60 vEntry] : ! [v2: vAType] : ! [v3: vLabel] : ! [v4: vQID] : (v1 = v0 | ~ % 49.96/7.60 (vquestion(v4, v3, v2) = v1) | ~ (vquestion(v4, v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptAType] : ! [v1: vOptAType] : ! [v2: vExp] : ! [v3: vATMap] : (v1 = v0 % 49.96/7.60 | ~ (vecheck(v3, v2) = v1) | ~ (vecheck(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : ! [v3: vUnOpT] : (v1 = % 49.96/7.60 v0 | ~ (vcheckUnOp(v3, v2) = v1) | ~ (vcheckUnOp(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vATMap] : ! [v1: vATMap] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = v0 | % 49.96/7.60 ~ (vintersectATM(v3, v2) = v1) | ~ (vintersectATM(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vATMap] : ! [v1: vATMap] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = v0 | % 49.96/7.60 ~ (vappendATMap(v3, v2) = v1) | ~ (vappendATMap(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptAType] : ! [v1: vOptAType] : ! [v2: vATMap] : ! [v3: vQID] : (v1 = v0 % 49.96/7.60 | ~ (vlookupATMap(v3, v2) = v1) | ~ (vlookupATMap(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptExp] : ! [v1: vOptExp] : ! [v2: vAnsMap] : ! [v3: vExp] : (v1 = v0 | % 49.96/7.60 ~ (vreduceExp(v3, v2) = v1) | ~ (vreduceExp(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptExp] : ! [v1: vOptExp] : ! [v2: vAval] : ! [v3: vUnOpT] : (v1 = v0 | % 49.96/7.60 ~ (vevalUnOp(v3, v2) = v1) | ~ (vevalUnOp(v3, v2) = v0)) & ! [v0: vAval] : % 49.96/7.60 ! [v1: vAval] : ! [v2: vAType] : ! [v3: vLabel] : (v1 = v0 | ~ % 49.96/7.60 (vgetAnswer(v3, v2) = v1) | ~ (vgetAnswer(v3, v2) = v0)) & ! [v0: vQConf] % 49.96/7.60 : ! [v1: vQConf] : ! [v2: vQuestionnaire] : ! [v3: vQConf] : (v1 = v0 | ~ % 49.96/7.60 (vqcappend(v3, v2) = v1) | ~ (vqcappend(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vOptQuestion] : ! [v1: vOptQuestion] : ! [v2: vQMap] : ! [v3: vQID] : (v1 % 49.96/7.60 = v0 | ~ (vlookupQMap(v3, v2) = v1) | ~ (vlookupQMap(v3, v2) = v0)) & ! % 49.96/7.60 [v0: vAnsMap] : ! [v1: vAnsMap] : ! [v2: vAnsMap] : ! [v3: vAnsMap] : (v1 = % 49.96/7.60 v0 | ~ (vappendAnsMap(v3, v2) = v1) | ~ (vappendAnsMap(v3, v2) = v0)) & ! % 49.96/7.60 [v0: vOptAval] : ! [v1: vOptAval] : ! [v2: vAnsMap] : ! [v3: vQID] : (v1 = % 49.96/7.60 v0 | ~ (vlookupAnsMap(v3, v2) = v1) | ~ (vlookupAnsMap(v3, v2) = v0)) & ! % 49.96/7.60 [v0: vATList] : ! [v1: vATList] : ! [v2: vATList] : ! [v3: vATList] : (v1 = % 49.96/7.60 v0 | ~ (vappend(v3, v2) = v1) | ~ (vappend(v3, v2) = v0)) & ! [v0: vnat] % 49.96/7.60 : ! [v1: vnat] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vdivide(v3, % 49.96/7.60 v2) = v1) | ~ (vdivide(v3, v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : % 49.96/7.60 ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vmultiply(v3, v2) = v1) | ~ % 49.96/7.60 (vmultiply(v3, v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : ! [v2: vnat] : % 49.96/7.60 ! [v3: vnat] : (v1 = v0 | ~ (vminus(v3, v2) = v1) | ~ (vminus(v3, v2) = v0)) % 49.96/7.60 & ! [v0: vnat] : ! [v1: vnat] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | % 49.96/7.60 ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: % 49.96/7.60 vYN] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vlt(v3, v2) = v1) | ~ % 49.96/7.60 (vlt(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! [v2: vnat] : ! [v3: % 49.96/7.60 vnat] : (v1 = v0 | ~ (vgt(v3, v2) = v1) | ~ (vgt(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vYN] : ! [v1: vYN] : ! [v2: vYN] : ! [v3: vYN] : (v1 = v0 | ~ (vor(v3, % 49.96/7.60 v2) = v1) | ~ (vor(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! % 49.96/7.60 [v2: vYN] : ! [v3: vYN] : (v1 = v0 | ~ (vand(v3, v2) = v1) | ~ (vand(v3, % 49.96/7.60 v2) = v0)) & ! [v0: vstring] : ! [v1: vstring] : ! [v2: vstring] : ! % 49.96/7.60 [v3: vchar] : (v1 = v0 | ~ (vscons(v3, v2) = v1) | ~ (vscons(v3, v2) = v0)) % 49.96/7.60 & ! [v0: vATList] : ! [v1: vATList] : ! [v2: vATList] : ! [v3: vAType] : % 49.96/7.60 (v1 = v0 | ~ (vatcons(v3, v2) = v1) | ~ (vatcons(v3, v2) = v0)) & ! [v0: % 49.96/7.60 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQuestionnaire] : ! % 49.96/7.60 [v3: vGID] : (v1 = v0 | ~ (vqgroup(v3, v2) = v1) | ~ (vqgroup(v3, v2) = v0)) % 49.96/7.60 & ! [v0: vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQuestionnaire] % 49.96/7.60 : ! [v3: vQuestionnaire] : (v1 = v0 | ~ (vqseq(v3, v2) = v1) | ~ (vqseq(v3, % 49.96/7.60 v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vExp] : ! [v3: % 49.96/7.60 vUnOpT] : (v1 = v0 | ~ (vunop(v3, v2) = v1) | ~ (vunop(v3, v2) = v0)) & ! % 49.96/7.60 [v0: vMapConf] : ! [v1: vMapConf] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = % 49.96/7.60 v0 | ~ (vMC(v3, v2) = v1) | ~ (vMC(v3, v2) = v0)) & ! [v0: vATMap] : ! % 49.96/7.60 [v1: vATMap] : ! [v2: vQMap] : (v1 = v0 | ~ (vtypeQM(v2) = v1) | ~ % 49.96/7.60 (vtypeQM(v2) = v0)) & ! [v0: vATMap] : ! [v1: vATMap] : ! [v2: vAnsMap] : % 49.96/7.60 (v1 = v0 | ~ (vtypeAM(v2) = v1) | ~ (vtypeAM(v2) = v0)) & ! [v0: % 49.96/7.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptMapConf] : (v1 % 49.96/7.60 = v0 | ~ (visSomeMapConf(v2) = v1) | ~ (visSomeMapConf(v2) = v0)) & ! % 49.96/7.60 [v0: vstring] : ! [v1: vstring] : ! [v2: vLabel] : (v1 = v0 | ~ % 49.96/7.60 (vaskText(v2) = v1) | ~ (vaskText(v2) = v0)) & ! [v0: vnat] : ! [v1: % 49.96/7.60 vnat] : ! [v2: vLabel] : (v1 = v0 | ~ (vaskNumber(v2) = v1) | ~ % 49.96/7.60 (vaskNumber(v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! [v2: vLabel] : (v1 % 49.96/7.60 = v0 | ~ (vaskYesNo(v2) = v1) | ~ (vaskYesNo(v2) = v0)) & ! [v0: % 49.96/7.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vExp] : (v1 = v0 | % 49.96/7.60 ~ (vexpIsValue(v2) = v1) | ~ (vexpIsValue(v2) = v0)) & ! [v0: % 49.96/7.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptExp] : (v1 = % 49.96/7.60 v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: % 49.96/7.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptQConf] : (v1 = % 49.96/7.60 v0 | ~ (visSomeQC(v2) = v1) | ~ (visSomeQC(v2) = v0)) & ! [v0: % 49.96/7.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vQuestionnaire] : % 49.96/7.60 (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) & ! [v0: % 49.96/7.60 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQConf] : (v1 = v0 | ~ % 49.96/7.60 (vgetQuest(v2) = v1) | ~ (vgetQuest(v2) = v0)) & ! [v0: vQMap] : ! [v1: % 49.96/7.60 vQMap] : ! [v2: vQConf] : (v1 = v0 | ~ (vgetQM(v2) = v1) | ~ (vgetQM(v2) % 49.96/7.60 = v0)) & ! [v0: vAnsMap] : ! [v1: vAnsMap] : ! [v2: vQConf] : (v1 = v0 % 49.96/7.60 | ~ (vgetAM(v2) = v1) | ~ (vgetAM(v2) = v0)) & ! [v0: MultipleValueBool] % 49.96/7.60 : ! [v1: MultipleValueBool] : ! [v2: vOptQuestion] : (v1 = v0 | ~ % 49.96/7.60 (visSomeQuestion(v2) = v1) | ~ (visSomeQuestion(v2) = v0)) & ! [v0: % 49.96/7.60 vAType] : ! [v1: vAType] : ! [v2: vAval] : (v1 = v0 | ~ (vtypeOf(v2) = % 49.96/7.60 v1) | ~ (vtypeOf(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 49.96/7.60 MultipleValueBool] : ! [v2: vOptAType] : (v1 = v0 | ~ (visSomeAType(v2) = % 49.96/7.60 v1) | ~ (visSomeAType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 49.96/7.60 MultipleValueBool] : ! [v2: vOptAval] : (v1 = v0 | ~ (visSomeAval(v2) = % 49.96/7.60 v1) | ~ (visSomeAval(v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : ! [v2: % 49.96/7.60 vnat] : (v1 = v0 | ~ (vpred(v2) = v1) | ~ (vpred(v2) = v0)) & ! [v0: vYN] % 49.96/7.60 : ! [v1: vYN] : ! [v2: vYN] : (v1 = v0 | ~ (vnot(v2) = v1) | ~ (vnot(v2) = % 49.96/7.60 v0)) & ! [v0: vMapConf] : ! [v1: vMapConf] : ! [v2: vOptMapConf] : (v1 % 49.96/7.60 = v0 | ~ (vgetMapConf(v2) = v1) | ~ (vgetMapConf(v2) = v0)) & ! [v0: % 49.96/7.60 vAval] : ! [v1: vAval] : ! [v2: vExp] : (v1 = v0 | ~ (vgetExpValue(v2) = % 49.96/7.60 v1) | ~ (vgetExpValue(v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! % 49.96/7.60 [v2: vOptExp] : (v1 = v0 | ~ (vgetExp(v2) = v1) | ~ (vgetExp(v2) = v0)) & ! % 49.96/7.60 [v0: vQConf] : ! [v1: vQConf] : ! [v2: vOptQConf] : (v1 = v0 | ~ % 49.96/7.60 (vgetQC(v2) = v1) | ~ (vgetQC(v2) = v0)) & ! [v0: vAType] : ! [v1: % 49.96/7.60 vAType] : ! [v2: vOptQuestion] : (v1 = v0 | ~ (vgetQuestionAType(v2) = v1) % 49.96/7.60 | ~ (vgetQuestionAType(v2) = v0)) & ! [v0: vLabel] : ! [v1: vLabel] : ! % 49.96/7.60 [v2: vOptQuestion] : (v1 = v0 | ~ (vgetQuestionLabel(v2) = v1) | ~ % 49.96/7.60 (vgetQuestionLabel(v2) = v0)) & ! [v0: vQID] : ! [v1: vQID] : ! [v2: % 49.96/7.60 vOptQuestion] : (v1 = v0 | ~ (vgetQuestionQID(v2) = v1) | ~ % 49.96/7.60 (vgetQuestionQID(v2) = v0)) & ! [v0: vAType] : ! [v1: vAType] : ! [v2: % 49.96/7.60 vOptAType] : (v1 = v0 | ~ (vgetAType(v2) = v1) | ~ (vgetAType(v2) = v0)) & % 49.96/7.60 ! [v0: vAval] : ! [v1: vAval] : ! [v2: vOptAval] : (v1 = v0 | ~ % 49.96/7.60 (vgetAval(v2) = v1) | ~ (vgetAval(v2) = v0)) & ! [v0: vOptAval] : ! [v1: % 49.96/7.60 vOptAval] : ! [v2: vAval] : (v1 = v0 | ~ (vsomeAval(v2) = v1) | ~ % 49.96/7.60 (vsomeAval(v2) = v0)) & ! [v0: vQID] : ! [v1: vQID] : ! [v2: vQID] : (v1 % 49.96/7.60 = v0 | ~ (venumQID(v2) = v1) | ~ (venumQID(v2) = v0)) & ! [v0: % 49.96/7.60 vOptMapConf] : ! [v1: vOptMapConf] : ! [v2: vMapConf] : (v1 = v0 | ~ % 49.96/7.60 (vsomeMapConf(v2) = v1) | ~ (vsomeMapConf(v2) = v0)) & ! [v0: vGID] : ! % 49.96/7.60 [v1: vGID] : ! [v2: vGID] : (v1 = v0 | ~ (venumGID(v2) = v1) | ~ % 49.96/7.60 (venumGID(v2) = v0)) & ! [v0: vOptExp] : ! [v1: vOptExp] : ! [v2: vExp] : % 49.96/7.60 (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0: vAval] : % 49.96/7.60 ! [v1: vAval] : ! [v2: vstring] : (v1 = v0 | ~ (vT(v2) = v1) | ~ (vT(v2) = % 49.96/7.60 v0)) & ! [v0: vAval] : ! [v1: vAval] : ! [v2: vnat] : (v1 = v0 | ~ % 49.96/7.60 (vNum(v2) = v1) | ~ (vNum(v2) = v0)) & ! [v0: vAval] : ! [v1: vAval] : ! % 49.96/7.60 [v2: vYN] : (v1 = v0 | ~ (vB(v2) = v1) | ~ (vB(v2) = v0)) & ! [v0: % 49.96/7.60 vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : (v1 = v0 | ~ % 49.96/7.60 (vsomeAType(v2) = v1) | ~ (vsomeAType(v2) = v0)) & ! [v0: vOptQConf] : ! % 49.96/7.60 [v1: vOptQConf] : ! [v2: vQConf] : (v1 = v0 | ~ (vsomeQConf(v2) = v1) | ~ % 49.96/7.60 (vsomeQConf(v2) = v0)) & ! [v0: vchar] : ! [v1: vchar] : ! [v2: vchar] : % 49.96/7.60 (v1 = v0 | ~ (venumchar(v2) = v1) | ~ (venumchar(v2) = v0)) & ! [v0: % 49.96/7.60 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vEntry] : (v1 = v0 | ~ % 49.96/7.60 (vqsingle(v2) = v1) | ~ (vqsingle(v2) = v0)) & ! [v0: vnat] : ! [v1: % 49.96/7.60 vnat] : ! [v2: vnat] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = % 49.96/7.60 v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vQID] : (v1 = v0 | ~ % 49.96/7.60 (vqvar(v2) = v1) | ~ (vqvar(v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! % 49.96/7.60 [v2: vAval] : (v1 = v0 | ~ (vconstant(v2) = v1) | ~ (vconstant(v2) = v0)) & % 49.96/7.60 ! [v0: vLabel] : ! [v1: vLabel] : ! [v2: vLabel] : (v1 = v0 | ~ % 49.96/7.60 (venumLabel(v2) = v1) | ~ (venumLabel(v2) = v0)) & ! [v0: vEntry] : ! % 49.96/7.60 [v1: vEntry] : ! [v2: vQID] : (v1 = v0 | ~ (vask(v2) = v1) | ~ (vask(v2) = % 49.96/7.60 v0)) % 49.96/7.60 % 49.96/7.60 Further assumptions not needed in the proof: % 49.96/7.60 -------------------------------------------- % 49.96/7.60 DIFF-B-Num, DIFF-B-T, DIFF-Num-T, DIFF-Number-Text, DIFF-YesNo-Number, % 49.96/7.60 DIFF-YesNo-Text, DIFF-addop-andop, DIFF-addop-divop, DIFF-addop-eqop, % 49.96/7.60 DIFF-addop-gtop, DIFF-addop-ltop, DIFF-addop-mulop, DIFF-addop-orop, % 49.96/7.60 DIFF-addop-subop, DIFF-aempty-abind, DIFF-andop-orop, DIFF-atempty-atcons, % 49.96/7.60 DIFF-atmempty-atmbind, DIFF-binop-unop, DIFF-constant-binop, DIFF-constant-qvar, % 49.96/7.60 DIFF-constant-unop, DIFF-defquestion-ask, DIFF-divop-andop, DIFF-divop-eqop, % 49.96/7.60 DIFF-divop-gtop, DIFF-divop-ltop, DIFF-divop-orop, DIFF-eqop-andop, % 49.96/7.60 DIFF-eqop-gtop, DIFF-eqop-ltop, DIFF-eqop-orop, DIFF-gtop-andop, DIFF-gtop-ltop, % 49.96/7.60 DIFF-gtop-orop, DIFF-initGID-enumGID, DIFF-initLabel-enumLabel, % 49.96/7.60 DIFF-initQID-enumQID, DIFF-initchar-enumchar, DIFF-ltop-andop, DIFF-ltop-orop, % 49.96/7.60 DIFF-mulop-andop, DIFF-mulop-divop, DIFF-mulop-eqop, DIFF-mulop-gtop, % 49.96/7.60 DIFF-mulop-ltop, DIFF-mulop-orop, DIFF-noAType-someAType, DIFF-noAval-someAval, % 49.96/7.60 DIFF-noExp-someExp, DIFF-noMapConf-someMapConf, DIFF-noQConf-someQConf, % 49.96/7.60 DIFF-noQuestion-someQuestion, DIFF-qcond-qgroup, DIFF-qempty-qcond, % 49.96/7.60 DIFF-qempty-qgroup, DIFF-qempty-qseq, DIFF-qempty-qsingle, DIFF-qmempty-qmbind, % 49.96/7.60 DIFF-qseq-qcond, DIFF-qseq-qgroup, DIFF-qsingle-qcond, DIFF-qsingle-qgroup, % 49.96/7.60 DIFF-qsingle-qseq, DIFF-question-ask, DIFF-question-defquestion, % 49.96/7.60 DIFF-question-value, DIFF-qvar-binop, DIFF-qvar-unop, DIFF-sempty-scons, % 49.96/7.60 DIFF-subop-andop, DIFF-subop-divop, DIFF-subop-eqop, DIFF-subop-gtop, % 49.96/7.60 DIFF-subop-ltop, DIFF-subop-mulop, DIFF-subop-orop, DIFF-value-ask, % 49.96/7.60 DIFF-value-defquestion, DIFF-yes-no, DIFF-zero-succ, EQ-B, EQ-MC, EQ-Num, EQ-QC, % 49.96/7.60 EQ-T, EQ-abind, EQ-ask, EQ-atcons, EQ-atmbind, EQ-binop, EQ-constant, % 49.96/7.60 EQ-defquestion, EQ-enumGID, EQ-enumLabel, EQ-enumQID, EQ-enumchar, EQ-qcond, % 49.96/7.60 EQ-qgroup, EQ-qmbind, EQ-qseq, EQ-qsingle, EQ-question, EQ-qvar, EQ-scons, % 49.96/7.60 EQ-someAType, EQ-someAval, EQ-someExp, EQ-someMapConf, EQ-someQConf, % 49.96/7.60 EQ-someQuestion, EQ-succ, EQ-unop, EQ-value, Task, Task_inv1, Task_inv2, % 49.96/7.60 Task_inv3, Task_inv4, Tdefquestion, Tdefquestion_inv1, Tdefquestion_inv2, % 49.96/7.60 Tdefquestion_inv3, Tqcond, Tqcond_inv1, Tqcond_inv2, Tqcond_inv3, Tqcond_inv4, % 49.96/7.60 Tqcond_inv5, Tqcond_inv6, Tqcond_inv7, Tqempty, Tqempty_inv1, Tqgroup, % 49.96/7.60 Tqgroup_inv, Tqseq, Tqseq_inv1, Tqseq_inv2, Tqseq_inv3, Tqseq_inv4, Tquestion, % 49.96/7.60 Tquestion_inv1, Tquestion_inv2, Tquestion_inv3, Tvalue, Tvalue_inv1, % 49.96/7.60 Tvalue_inv2, Tvalue_inv3, Tvalue_inv4, and-0, and-1, and-INV, append-0, % 49.96/7.60 append-1, append-INV, appendATMap-0, appendATMap-1, appendATMap-INV, % 49.96/7.60 appendAnsMap-0, appendAnsMap-1, appendAnsMap-INV, checkBinOp-0, checkBinOp-1, % 49.96/7.60 checkBinOp-2, checkBinOp-3, checkBinOp-4, checkBinOp-5, checkBinOp-6, % 49.96/7.60 checkBinOp-7, checkBinOp-8, checkBinOp-9, checkBinOp-INV, checkUnOp-0, % 49.96/7.60 checkUnOp-1, checkUnOp-INV, divide-0, divide-1, divide-INV, dom-ATList, % 49.96/7.60 dom-ATMap, dom-AType, dom-AnsMap, dom-Aval, dom-BinOpT, dom-Entry, dom-Exp, % 49.96/7.60 dom-MapConf, dom-OptAType, dom-OptAval, dom-OptExp, dom-OptMapConf, % 49.96/7.60 dom-OptQConf, dom-OptQuestion, dom-QConf, dom-QMap, dom-Questionnaire, % 49.96/7.60 dom-UnOpT, dom-YN, dom-nat, dom-string, echeck-0, echeck-1, echeck-2, echeck-3, % 49.96/7.60 echeck-4, echeck-5, echeck-6, echeck-7, echeck-INV, evalBinOp-0, evalBinOp-1, % 49.96/7.60 evalBinOp-10, evalBinOp-2, evalBinOp-3, evalBinOp-4, evalBinOp-5, evalBinOp-6, % 49.96/7.60 evalBinOp-7, evalBinOp-8, evalBinOp-9, evalBinOp-INV, evalUnOp-0, evalUnOp-1, % 49.96/7.60 evalUnOp-INV, expIsValue-0, expIsValue-1, expIsValue-false-INV, % 49.96/7.60 expIsValue-true-INV, getAM-0, getAM-INV, getAType-0, getAnswer-0, getAnswer-1, % 49.96/7.60 getAnswer-2, getAnswer-INV, getAval-0, getExp-0, getExpValue-0, getMapConf-0, % 49.96/7.60 getQC-0, getQM-0, getQM-INV, getQuest-0, getQuest-INV, getQuestionAType-0, % 49.96/7.60 getQuestionLabel-0, getQuestionQID-0, gt-0, gt-1, gt-2, gt-INV, intersectATM-0, % 49.96/7.60 intersectATM-1, intersectATM-2, intersectATM-INV, isSomeAType-0, isSomeAType-1, % 49.96/7.60 isSomeAType-false-INV, isSomeAType-true-INV, isSomeAval-0, isSomeAval-1, % 49.96/7.60 isSomeAval-false-INV, isSomeAval-true-INV, isSomeExp-0, isSomeExp-1, % 49.96/7.60 isSomeExp-false-INV, isSomeExp-true-INV, isSomeMapConf-0, isSomeMapConf-1, % 49.96/7.60 isSomeMapConf-false-INV, isSomeMapConf-true-INV, isSomeQC-0, isSomeQC-1, % 49.96/7.60 isSomeQC-false-INV, isSomeQC-true-INV, isSomeQuestion-0, isSomeQuestion-1, % 49.96/7.60 isSomeQuestion-false-INV, isSomeQuestion-true-INV, isValue-0, isValue-1, % 49.96/7.60 isValue-false-INV, isValue-true-INV, lookupATMap-0, lookupATMap-1, % 49.96/7.60 lookupATMap-2, lookupATMap-INV, lookupAnsMap-0, lookupAnsMap-1, lookupAnsMap-2, % 49.96/7.60 lookupAnsMap-INV, lookupQMap-0, lookupQMap-1, lookupQMap-2, lookupQMap-INV, % 49.96/7.60 lt-0, lt-1, lt-2, lt-INV, minus-0, minus-1, minus-INV, multiply-0, multiply-1, % 49.96/7.60 multiply-INV, not-0, not-1, not-INV, or-0, or-1, or-INV, plus-0, plus-1, % 49.96/7.60 plus-INV, pred-0, pred-1, pred-INV, qcappend-0, qcappend-INV, reduce-0, % 49.96/7.60 reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, % 49.96/7.60 reduce-2, reduce-3, reduce-4, reduce-6, reduce-7, reduce-9, reduce-INV, % 49.96/7.60 reduceExp-0, reduceExp-1, reduceExp-10, reduceExp-2, reduceExp-3, reduceExp-4, % 49.96/7.60 reduceExp-5, reduceExp-6, reduceExp-7, reduceExp-8, reduceExp-9, reduceExp-INV, % 49.96/7.60 typeAM-0, typeAM-1, typeAM-INV, typeOf-0, typeOf-1, typeOf-2, typeOf-INV, % 49.96/7.60 typeQM-0, typeQM-1, typeQM-INV % 49.96/7.60 % 49.96/7.60 Those formulas are unsatisfiable: % 49.96/7.60 --------------------------------- % 49.96/7.60 % 49.96/7.60 Begin of proof % 49.96/7.60 | % 49.96/7.61 | ALPHA: (reduce-5) implies: % 49.96/7.61 | (1) ! [v0: vQMap] : ! [v1: vAType] : ! [v2: vLabel] : ! [v3: vAnsMap] : % 49.96/7.61 | ! [v4: vQID] : ! [v5: vEntry] : ! [v6: vQuestionnaire] : ! [v7: % 49.96/7.61 | vOptQConf] : ( ~ (vreduce(v6, v3, v0) = v7) | ~ (vqsingle(v5) = v6) % 49.96/7.61 | | ~ (vdefquestion(v4, v2, v1) = v5) | ~ vAType(v1) | ~ vLabel(v2) % 49.96/7.61 | | ~ vQID(v4) | ~ vQMap(v0) | ~ vAnsMap(v3) | ? [v8: vQMap] : ? % 49.96/7.61 | [v9: vQConf] : (vQC(v3, v8, vqempty) = v9 & vsomeQConf(v9) = v7 & % 49.96/7.61 | vqmbind(v4, v2, v1, v0) = v8 & vQMap(v8) & vOptQConf(v7) & % 49.96/7.61 | vQConf(v9))) % 49.96/7.61 | % 49.96/7.61 | ALPHA: (reduce-8) implies: % 49.96/7.61 | (2) ! [v0: vQuestionnaire] : ! [v1: vAnsMap] : ! [v2: vQMap] : ! [v3: % 49.96/7.61 | vQConf] : ( ~ (vQC(v1, v2, v0) = v3) | ~ vQMap(v2) | ~ vAnsMap(v1) % 49.96/7.61 | | ~ vQuestionnaire(v0) | ? [v4: vQuestionnaire] : ? [v5: % 49.96/7.61 | vOptQConf] : (vreduce(v4, v1, v2) = v5 & vsomeQConf(v3) = v5 & % 49.96/7.61 | vqseq(vqempty, v0) = v4 & vOptQConf(v5) & vQuestionnaire(v4))) % 49.96/7.61 | % 49.96/7.61 | ALPHA: (Tqempty_inv2) implies: % 49.96/7.61 | (3) vQuestionnaire(vqempty) % 49.96/7.61 | % 49.96/7.61 | ALPHA: (function-axioms) implies: % 49.96/7.61 | (4) ! [v0: vOptQConf] : ! [v1: vOptQConf] : ! [v2: vQConf] : (v1 = v0 | % 49.96/7.61 | ~ (vsomeQConf(v2) = v1) | ~ (vsomeQConf(v2) = v0)) % 49.96/7.61 | % 49.96/7.61 | DELTA: instantiating (Progress-qsingle-defquestion) with fresh symbols % 49.96/7.61 | all_401_0, all_401_1, all_401_2, all_401_3, all_401_4, all_401_5, % 49.96/7.61 | all_401_6, all_401_7, all_401_8, all_401_9, all_401_10, all_401_11, % 49.96/7.61 | all_401_12, all_401_13, all_401_14 gives: % 49.96/7.61 | (5) ~ (all_401_5 = 0) & vptcheck(all_401_2, all_401_6, all_401_1) = 0 & % 49.96/7.61 | vtypeQM(all_401_14) = all_401_3 & vtypeAM(all_401_9) = all_401_4 & % 49.96/7.61 | vreduce(all_401_6, all_401_9, all_401_14) = all_401_0 & % 49.96/7.61 | visValue(all_401_6) = all_401_5 & vqsingle(all_401_7) = all_401_6 & % 49.96/7.61 | vMC(all_401_4, all_401_3) = all_401_2 & vMC(all_401_12, all_401_11) = % 49.96/7.61 | all_401_1 & vdefquestion(all_401_8, all_401_10, all_401_13) = all_401_7 % 49.96/7.61 | & vAType(all_401_13) & vLabel(all_401_10) & vQID(all_401_8) & % 49.96/7.61 | vQMap(all_401_14) & vAnsMap(all_401_9) & vOptQConf(all_401_0) & % 49.96/7.61 | vQuestionnaire(all_401_6) & vATMap(all_401_3) & vATMap(all_401_4) & % 49.96/7.61 | vATMap(all_401_11) & vATMap(all_401_12) & vMapConf(all_401_1) & % 49.96/7.61 | vMapConf(all_401_2) & vEntry(all_401_7) & ! [v0: vAnsMap] : ! [v1: % 49.96/7.61 | vQMap] : ! [v2: vQuestionnaire] : ! [v3: vQConf] : ( ~ (vQC(v0, v1, % 49.96/7.61 | v2) = v3) | ~ vQMap(v1) | ~ vAnsMap(v0) | ~ vQuestionnaire(v2) % 49.96/7.61 | | ? [v4: any] : ( ~ (v4 = all_401_0) & vsomeQConf(v3) = v4 & % 49.96/7.61 | vOptQConf(v4))) % 49.96/7.61 | % 49.96/7.61 | ALPHA: (5) implies: % 49.96/7.61 | (6) vAnsMap(all_401_9) % 49.96/7.61 | (7) vQMap(all_401_14) % 49.96/7.61 | (8) vQID(all_401_8) % 49.96/7.61 | (9) vLabel(all_401_10) % 49.96/7.61 | (10) vAType(all_401_13) % 49.96/7.61 | (11) vdefquestion(all_401_8, all_401_10, all_401_13) = all_401_7 % 49.96/7.61 | (12) vqsingle(all_401_7) = all_401_6 % 49.96/7.61 | (13) vreduce(all_401_6, all_401_9, all_401_14) = all_401_0 % 49.96/7.61 | (14) ! [v0: vAnsMap] : ! [v1: vQMap] : ! [v2: vQuestionnaire] : ! [v3: % 49.96/7.61 | vQConf] : ( ~ (vQC(v0, v1, v2) = v3) | ~ vQMap(v1) | ~ vAnsMap(v0) % 49.96/7.61 | | ~ vQuestionnaire(v2) | ? [v4: any] : ( ~ (v4 = all_401_0) & % 49.96/7.61 | vsomeQConf(v3) = v4 & vOptQConf(v4))) % 49.96/7.61 | % 49.96/7.62 | GROUND_INST: instantiating (1) with all_401_14, all_401_13, all_401_10, % 49.96/7.62 | all_401_9, all_401_8, all_401_7, all_401_6, all_401_0, % 49.96/7.62 | simplifying with (6), (7), (8), (9), (10), (11), (12), (13) % 49.96/7.62 | gives: % 49.96/7.62 | (15) ? [v0: vQMap] : ? [v1: vQConf] : (vQC(all_401_9, v0, vqempty) = v1 & % 49.96/7.62 | vsomeQConf(v1) = all_401_0 & vqmbind(all_401_8, all_401_10, % 49.96/7.62 | all_401_13, all_401_14) = v0 & vQMap(v0) & vOptQConf(all_401_0) & % 49.96/7.62 | vQConf(v1)) % 49.96/7.62 | % 49.96/7.62 | DELTA: instantiating (15) with fresh symbols all_437_0, all_437_1 gives: % 49.96/7.62 | (16) vQC(all_401_9, all_437_1, vqempty) = all_437_0 & vsomeQConf(all_437_0) % 49.96/7.62 | = all_401_0 & vqmbind(all_401_8, all_401_10, all_401_13, all_401_14) = % 49.96/7.62 | all_437_1 & vQMap(all_437_1) & vOptQConf(all_401_0) & % 49.96/7.62 | vQConf(all_437_0) % 49.96/7.62 | % 49.96/7.62 | ALPHA: (16) implies: % 49.96/7.62 | (17) vQMap(all_437_1) % 49.96/7.62 | (18) vsomeQConf(all_437_0) = all_401_0 % 49.96/7.62 | (19) vQC(all_401_9, all_437_1, vqempty) = all_437_0 % 49.96/7.62 | % 49.96/7.62 | GROUND_INST: instantiating (2) with vqempty, all_401_9, all_437_1, all_437_0, % 49.96/7.62 | simplifying with (3), (6), (17), (19) gives: % 49.96/7.62 | (20) ? [v0: vQuestionnaire] : ? [v1: vOptQConf] : (vreduce(v0, all_401_9, % 49.96/7.62 | all_437_1) = v1 & vsomeQConf(all_437_0) = v1 & vqseq(vqempty, % 49.96/7.62 | vqempty) = v0 & vOptQConf(v1) & vQuestionnaire(v0)) % 49.96/7.62 | % 49.96/7.62 | GROUND_INST: instantiating (14) with all_401_9, all_437_1, vqempty, all_437_0, % 49.96/7.62 | simplifying with (3), (6), (17), (19) gives: % 49.96/7.62 | (21) ? [v0: any] : ( ~ (v0 = all_401_0) & vsomeQConf(all_437_0) = v0 & % 49.96/7.62 | vOptQConf(v0)) % 49.96/7.62 | % 49.96/7.62 | DELTA: instantiating (21) with fresh symbol all_507_0 gives: % 49.96/7.62 | (22) ~ (all_507_0 = all_401_0) & vsomeQConf(all_437_0) = all_507_0 & % 49.96/7.62 | vOptQConf(all_507_0) % 49.96/7.62 | % 49.96/7.62 | ALPHA: (22) implies: % 49.96/7.62 | (23) ~ (all_507_0 = all_401_0) % 49.96/7.62 | (24) vsomeQConf(all_437_0) = all_507_0 % 49.96/7.62 | % 49.96/7.62 | DELTA: instantiating (20) with fresh symbols all_513_0, all_513_1 gives: % 49.96/7.62 | (25) vreduce(all_513_1, all_401_9, all_437_1) = all_513_0 & % 49.96/7.62 | vsomeQConf(all_437_0) = all_513_0 & vqseq(vqempty, vqempty) = % 49.96/7.62 | all_513_1 & vOptQConf(all_513_0) & vQuestionnaire(all_513_1) % 49.96/7.62 | % 49.96/7.62 | ALPHA: (25) implies: % 49.96/7.62 | (26) vsomeQConf(all_437_0) = all_513_0 % 49.96/7.62 | % 49.96/7.62 | GROUND_INST: instantiating (4) with all_401_0, all_513_0, all_437_0, % 49.96/7.62 | simplifying with (18), (26) gives: % 49.96/7.62 | (27) all_513_0 = all_401_0 % 49.96/7.62 | % 49.96/7.62 | GROUND_INST: instantiating (4) with all_507_0, all_513_0, all_437_0, % 49.96/7.62 | simplifying with (24), (26) gives: % 49.96/7.62 | (28) all_513_0 = all_507_0 % 49.96/7.62 | % 49.96/7.62 | COMBINE_EQS: (27), (28) imply: % 49.96/7.62 | (29) all_507_0 = all_401_0 % 49.96/7.62 | % 49.96/7.62 | REDUCE: (23), (29) imply: % 49.96/7.62 | (30) $false % 49.96/7.62 | % 49.96/7.62 | CLOSE: (30) is inconsistent. % 49.96/7.62 | % 49.96/7.62 End of proof % 49.96/7.62 % SZS output end Proof for theBenchmark % 49.96/7.62 % 49.96/7.62 7013ms %------------------------------------------------------------------------------