%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM275_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 06:21:40 PM UTC 2026 % Result : Theorem 33.63s 5.12s % Output : Proof 48.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM275_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 20:09:30 EDT 2026 % 0.17/0.34 % CPUTime : % 0.50/0.61 ________ _____ % 0.50/0.61 ___ __ \_________(_)________________________________ % 0.50/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.61 % 0.50/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.61 (2023-06-19) % 0.50/0.61 % 0.50/0.61 (c) Philipp Rümmer, 2009-2023 % 0.50/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.61 Amanda Stjerna. % 0.50/0.61 Free software under BSD-3-Clause. % 0.50/0.61 % 0.50/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.61 % 0.50/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.63 Running up to 7 provers in parallel. % 0.67/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 9.24/1.91 Prover 4: Preprocessing ... % 9.24/1.93 Prover 1: Preprocessing ... % 9.24/1.95 Prover 3: Preprocessing ... % 9.24/1.95 Prover 6: Preprocessing ... % 9.24/1.95 Prover 2: Preprocessing ... % 9.24/1.95 Prover 0: Preprocessing ... % 9.24/1.96 Prover 5: Preprocessing ... % 22.54/3.69 Prover 3: Warning: ignoring some quantifiers % 23.27/3.70 Prover 1: Warning: ignoring some quantifiers % 23.27/3.74 Prover 3: Constructing countermodel ... % 23.27/3.78 Prover 6: Proving ... % 24.04/3.82 Prover 1: Constructing countermodel ... % 25.70/4.07 Prover 5: Proving ... % 27.14/4.26 Prover 4: Warning: ignoring some quantifiers % 27.94/4.38 Prover 4: Constructing countermodel ... % 29.51/4.52 Prover 0: Proving ... % 31.88/4.89 Prover 2: Proving ... % 33.63/5.12 Prover 5: proved (4478ms) % 33.63/5.12 % 33.63/5.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 33.63/5.12 % 34.43/5.12 Prover 2: stopped % 34.43/5.12 Prover 3: stopped % 34.43/5.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 34.43/5.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 34.43/5.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 34.43/5.14 Prover 6: stopped % 34.43/5.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 34.43/5.17 Prover 0: stopped % 34.43/5.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 38.94/5.77 Prover 8: Preprocessing ... % 39.72/5.86 Prover 11: Preprocessing ... % 39.72/5.86 Prover 7: Preprocessing ... % 39.72/5.86 Prover 13: Preprocessing ... % 39.72/5.86 Prover 10: Preprocessing ... % 42.85/6.29 Prover 4: Found proof (size 38) % 42.85/6.29 Prover 4: proved (5654ms) % 42.85/6.29 Prover 1: stopped % 44.44/6.43 Prover 8: Warning: ignoring some quantifiers % 44.44/6.48 Prover 8: Constructing countermodel ... % 45.24/6.50 Prover 8: stopped % 46.65/6.72 Prover 10: Warning: ignoring some quantifiers % 46.65/6.76 Prover 7: Warning: ignoring some quantifiers % 46.65/6.77 Prover 10: Constructing countermodel ... % 46.65/6.79 Prover 11: Warning: ignoring some quantifiers % 46.65/6.79 Prover 10: stopped % 47.35/6.81 Prover 7: Constructing countermodel ... % 47.35/6.84 Prover 7: stopped % 47.35/6.84 Prover 11: Constructing countermodel ... % 47.35/6.86 Prover 11: stopped % 47.35/6.87 Prover 13: Warning: ignoring some quantifiers % 47.87/6.92 Prover 13: Constructing countermodel ... % 47.87/6.94 Prover 13: stopped % 47.87/6.94 % 47.87/6.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 47.87/6.94 % 47.87/6.95 % SZS output start Proof for theBenchmark % 47.87/6.96 Assumptions after simplification: % 47.87/6.96 --------------------------------- % 47.87/6.96 % 47.87/6.96 (reduceExp-4) % 47.87/6.99 ! [v0: vExp] : ! [v1: vExp] : ! [v2: vAnsMap] : ! [v3: vBinOpT] : ! [v4: % 47.87/6.99 vOptExp] : ! [v5: vExp] : ! [v6: vExp] : ( ~ (vreduceExp(v1, v2) = v4) | % 47.87/6.99 ~ (vgetExp(v4) = v5) | ~ (vbinop(v0, v3, v5) = v6) | ~ vBinOpT(v3) | ~ % 47.87/6.99 vExp(v1) | ~ vExp(v0) | ~ vAnsMap(v2) | ? [v7: any] : ? [v8: any] : ? % 47.87/6.99 [v9: any] : ? [v10: vExp] : ? [v11: vOptExp] : ? [v12: vOptExp] : % 47.87/6.99 (vreduceExp(v10, v2) = v11 & vexpIsValue(v1) = v8 & vexpIsValue(v0) = v7 & % 47.87/6.99 visSomeExp(v4) = v9 & vsomeExp(v6) = v12 & vbinop(v0, v3, v1) = v10 & % 47.87/6.99 vOptExp(v12) & vOptExp(v11) & vExp(v10) & ( ~ (v9 = 0) | ~ (v7 = 0) | v12 % 47.87/6.99 = v11 | v8 = 0))) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vAnsMap] : % 47.87/6.99 ! [v3: vBinOpT] : ! [v4: vExp] : ! [v5: vOptExp] : ( ~ (vreduceExp(v4, v2) = % 47.87/6.99 v5) | ~ (vbinop(v0, v3, v1) = v4) | ~ vBinOpT(v3) | ~ vExp(v1) | ~ % 47.87/6.99 vExp(v0) | ~ vAnsMap(v2) | ? [v6: any] : ? [v7: any] : ? [v8: vOptExp] : % 47.87/6.99 ? [v9: any] : ? [v10: vExp] : ? [v11: vExp] : ? [v12: vOptExp] : % 47.87/6.99 (vreduceExp(v1, v2) = v8 & vexpIsValue(v1) = v7 & vexpIsValue(v0) = v6 & % 47.87/6.99 visSomeExp(v8) = v9 & vgetExp(v8) = v10 & vsomeExp(v11) = v12 & vbinop(v0, % 47.87/6.99 v3, v10) = v11 & vOptExp(v12) & vOptExp(v8) & vExp(v11) & vExp(v10) & ( % 47.87/6.99 ~ (v9 = 0) | ~ (v6 = 0) | v12 = v5 | v7 = 0))) % 47.87/6.99 % 47.87/6.99 (reduceExpProgress-binop-IH0) % 47.87/7.00 vExp(ve1) & ? [v0: any] : (vexpIsValue(ve1) = v0 & ! [v1: vAnsMap] : ! [v2: % 47.87/7.00 vAType] : ! [v3: vATMap] : ! [v4: vOptAType] : (v0 = 0 | ~ (vecheck(v3, % 47.87/7.00 ve1) = v4) | ~ (vtypeAM(v1) = v3) | ~ (vsomeAType(v2) = v4) | ~ % 47.87/7.00 vAType(v2) | ~ vAnsMap(v1) | ? [v5: vOptExp] : ? [v6: vExp] : % 47.87/7.00 (vreduceExp(ve1, v1) = v5 & vsomeExp(v6) = v5 & vOptExp(v5) & vExp(v6))) & % 47.87/7.00 ! [v1: vAnsMap] : ! [v2: vAType] : ! [v3: vOptAType] : ! [v4: vOptExp] : % 47.87/7.00 (v0 = 0 | ~ (vreduceExp(ve1, v1) = v4) | ~ (vsomeAType(v2) = v3) | ~ % 47.87/7.00 vAType(v2) | ~ vAnsMap(v1) | ? [v5: vATMap] : ? [v6: vOptAType] : ? % 47.87/7.00 [v7: vExp] : ? [v8: vOptExp] : (vExp(v7) & ((v8 = v4 & vsomeExp(v7) = v4 % 47.87/7.00 & vOptExp(v4)) | ( ~ (v6 = v3) & vecheck(v5, ve1) = v6 & vtypeAM(v1) % 47.87/7.00 = v5 & vATMap(v5) & vOptAType(v6)))))) % 47.87/7.00 % 47.87/7.00 (reduceExpProgress-binop-IH1) % 47.87/7.00 vExp(ve2) & ? [v0: any] : (vexpIsValue(ve2) = v0 & ! [v1: vAnsMap] : ! [v2: % 47.87/7.00 vAType] : ! [v3: vATMap] : ! [v4: vOptAType] : (v0 = 0 | ~ (vecheck(v3, % 47.87/7.00 ve2) = v4) | ~ (vtypeAM(v1) = v3) | ~ (vsomeAType(v2) = v4) | ~ % 47.87/7.00 vAType(v2) | ~ vAnsMap(v1) | ? [v5: vOptExp] : ? [v6: vExp] : % 47.87/7.00 (vreduceExp(ve2, v1) = v5 & vsomeExp(v6) = v5 & vOptExp(v5) & vExp(v6))) & % 47.87/7.00 ! [v1: vAnsMap] : ! [v2: vAType] : ! [v3: vOptAType] : ! [v4: vOptExp] : % 47.87/7.00 (v0 = 0 | ~ (vreduceExp(ve2, v1) = v4) | ~ (vsomeAType(v2) = v3) | ~ % 47.87/7.00 vAType(v2) | ~ vAnsMap(v1) | ? [v5: vATMap] : ? [v6: vOptAType] : ? % 47.87/7.00 [v7: vExp] : ? [v8: vOptExp] : (vExp(v7) & ((v8 = v4 & vsomeExp(v7) = v4 % 47.87/7.00 & vOptExp(v4)) | ( ~ (v6 = v3) & vecheck(v5, ve2) = v6 & vtypeAM(v1) % 47.87/7.00 = v5 & vATMap(v5) & vOptAType(v6)))))) % 47.87/7.00 % 47.87/7.00 (reduceExpProgress-binop-expIsValue-True-expIsValue-False-isSomeExp-True) % 47.87/7.00 vExp(ve2) & vExp(ve1) & ? [v0: int] : ? [v1: vAnsMap] : ? [v2: vBinOpT] : % 47.87/7.00 ? [v3: vAType] : ? [v4: vOptExp] : ? [v5: vExp] : ? [v6: int] : ? [v7: % 47.87/7.00 vATMap] : ? [v8: vOptAType] : ? [v9: vOptExp] : ( ~ (v6 = 0) & ~ (v0 = 0) % 47.87/7.00 & vecheck(v7, v5) = v8 & vtypeAM(v1) = v7 & vreduceExp(v5, v1) = v9 & % 47.87/7.00 vreduceExp(ve2, v1) = v4 & vexpIsValue(v5) = v6 & vexpIsValue(ve2) = v0 & % 47.87/7.00 vexpIsValue(ve1) = 0 & visSomeExp(v4) = 0 & vsomeAType(v3) = v8 & % 47.87/7.00 vbinop(ve1, v2, ve2) = v5 & vAType(v3) & vBinOpT(v2) & vOptExp(v9) & % 47.87/7.00 vOptExp(v4) & vExp(v5) & vAnsMap(v1) & vATMap(v7) & vOptAType(v8) & ! [v10: % 47.87/7.00 vExp] : ( ~ (vsomeExp(v10) = v9) | ~ vExp(v10))) % 47.87/7.00 % 47.87/7.00 (function-axioms) % 48.36/7.02 ! [v0: vQMap] : ! [v1: vQMap] : ! [v2: vQMap] : ! [v3: vAType] : ! [v4: % 48.36/7.02 vLabel] : ! [v5: vQID] : (v1 = v0 | ~ (vqmbind(v5, v4, v3, v2) = v1) | ~ % 48.36/7.02 (vqmbind(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.36/7.02 MultipleValueBool] : ! [v2: vMapConf] : ! [v3: vQuestionnaire] : ! [v4: % 48.36/7.02 vMapConf] : (v1 = v0 | ~ (vptcheck(v4, v3, v2) = v1) | ~ (vptcheck(v4, v3, % 48.36/7.02 v2) = v0)) & ! [v0: vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : % 48.36/7.02 ! [v3: vAType] : ! [v4: vBinOpT] : (v1 = v0 | ~ (vcheckBinOp(v4, v3, v2) = % 48.36/7.02 v1) | ~ (vcheckBinOp(v4, v3, v2) = v0)) & ! [v0: vOptQConf] : ! [v1: % 48.36/7.02 vOptQConf] : ! [v2: vQMap] : ! [v3: vAnsMap] : ! [v4: vQuestionnaire] : % 48.36/7.02 (v1 = v0 | ~ (vreduce(v4, v3, v2) = v1) | ~ (vreduce(v4, v3, v2) = v0)) & ! % 48.36/7.02 [v0: vOptExp] : ! [v1: vOptExp] : ! [v2: vAval] : ! [v3: vAval] : ! [v4: % 48.36/7.02 vBinOpT] : (v1 = v0 | ~ (vevalBinOp(v4, v3, v2) = v1) | ~ (vevalBinOp(v4, % 48.36/7.02 v3, v2) = v0)) & ! [v0: vQConf] : ! [v1: vQConf] : ! [v2: % 48.36/7.02 vQuestionnaire] : ! [v3: vQMap] : ! [v4: vAnsMap] : (v1 = v0 | ~ (vQC(v4, % 48.36/7.02 v3, v2) = v1) | ~ (vQC(v4, v3, v2) = v0)) & ! [v0: vATMap] : ! [v1: % 48.36/7.02 vATMap] : ! [v2: vATMap] : ! [v3: vAType] : ! [v4: vQID] : (v1 = v0 | ~ % 48.36/7.02 (vatmbind(v4, v3, v2) = v1) | ~ (vatmbind(v4, v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptQuestion] : ! [v1: vOptQuestion] : ! [v2: vAType] : ! [v3: vLabel] : % 48.36/7.02 ! [v4: vQID] : (v1 = v0 | ~ (vsomeQuestion(v4, v3, v2) = v1) | ~ % 48.36/7.02 (vsomeQuestion(v4, v3, v2) = v0)) & ! [v0: vAnsMap] : ! [v1: vAnsMap] : ! % 48.36/7.02 [v2: vAnsMap] : ! [v3: vAval] : ! [v4: vQID] : (v1 = v0 | ~ (vabind(v4, v3, % 48.36/7.02 v2) = v1) | ~ (vabind(v4, v3, v2) = v0)) & ! [v0: vQuestionnaire] : ! % 48.36/7.02 [v1: vQuestionnaire] : ! [v2: vQuestionnaire] : ! [v3: vQuestionnaire] : ! % 48.36/7.02 [v4: vExp] : (v1 = v0 | ~ (vqcond(v4, v3, v2) = v1) | ~ (vqcond(v4, v3, v2) % 48.36/7.02 = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vExp] : ! [v3: vBinOpT] % 48.36/7.02 : ! [v4: vExp] : (v1 = v0 | ~ (vbinop(v4, v3, v2) = v1) | ~ (vbinop(v4, v3, % 48.36/7.02 v2) = v0)) & ! [v0: vEntry] : ! [v1: vEntry] : ! [v2: vAType] : ! % 48.36/7.02 [v3: vLabel] : ! [v4: vQID] : (v1 = v0 | ~ (vdefquestion(v4, v3, v2) = v1) | % 48.36/7.02 ~ (vdefquestion(v4, v3, v2) = v0)) & ! [v0: vEntry] : ! [v1: vEntry] : ! % 48.36/7.02 [v2: vExp] : ! [v3: vAType] : ! [v4: vQID] : (v1 = v0 | ~ (vvalue(v4, v3, % 48.36/7.02 v2) = v1) | ~ (vvalue(v4, v3, v2) = v0)) & ! [v0: vEntry] : ! [v1: % 48.36/7.02 vEntry] : ! [v2: vAType] : ! [v3: vLabel] : ! [v4: vQID] : (v1 = v0 | ~ % 48.36/7.02 (vquestion(v4, v3, v2) = v1) | ~ (vquestion(v4, v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptAType] : ! [v1: vOptAType] : ! [v2: vExp] : ! [v3: vATMap] : (v1 = v0 % 48.36/7.02 | ~ (vecheck(v3, v2) = v1) | ~ (vecheck(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : ! [v3: vUnOpT] : (v1 = % 48.36/7.02 v0 | ~ (vcheckUnOp(v3, v2) = v1) | ~ (vcheckUnOp(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vATMap] : ! [v1: vATMap] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = v0 | % 48.36/7.02 ~ (vintersectATM(v3, v2) = v1) | ~ (vintersectATM(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vATMap] : ! [v1: vATMap] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = v0 | % 48.36/7.02 ~ (vappendATMap(v3, v2) = v1) | ~ (vappendATMap(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptAType] : ! [v1: vOptAType] : ! [v2: vATMap] : ! [v3: vQID] : (v1 = v0 % 48.36/7.02 | ~ (vlookupATMap(v3, v2) = v1) | ~ (vlookupATMap(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptExp] : ! [v1: vOptExp] : ! [v2: vAnsMap] : ! [v3: vExp] : (v1 = v0 | % 48.36/7.02 ~ (vreduceExp(v3, v2) = v1) | ~ (vreduceExp(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptExp] : ! [v1: vOptExp] : ! [v2: vAval] : ! [v3: vUnOpT] : (v1 = v0 | % 48.36/7.02 ~ (vevalUnOp(v3, v2) = v1) | ~ (vevalUnOp(v3, v2) = v0)) & ! [v0: vAval] : % 48.36/7.02 ! [v1: vAval] : ! [v2: vAType] : ! [v3: vLabel] : (v1 = v0 | ~ % 48.36/7.02 (vgetAnswer(v3, v2) = v1) | ~ (vgetAnswer(v3, v2) = v0)) & ! [v0: vQConf] % 48.36/7.02 : ! [v1: vQConf] : ! [v2: vQuestionnaire] : ! [v3: vQConf] : (v1 = v0 | ~ % 48.36/7.02 (vqcappend(v3, v2) = v1) | ~ (vqcappend(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vOptQuestion] : ! [v1: vOptQuestion] : ! [v2: vQMap] : ! [v3: vQID] : (v1 % 48.36/7.02 = v0 | ~ (vlookupQMap(v3, v2) = v1) | ~ (vlookupQMap(v3, v2) = v0)) & ! % 48.36/7.02 [v0: vAnsMap] : ! [v1: vAnsMap] : ! [v2: vAnsMap] : ! [v3: vAnsMap] : (v1 = % 48.36/7.02 v0 | ~ (vappendAnsMap(v3, v2) = v1) | ~ (vappendAnsMap(v3, v2) = v0)) & ! % 48.36/7.02 [v0: vOptAval] : ! [v1: vOptAval] : ! [v2: vAnsMap] : ! [v3: vQID] : (v1 = % 48.36/7.02 v0 | ~ (vlookupAnsMap(v3, v2) = v1) | ~ (vlookupAnsMap(v3, v2) = v0)) & ! % 48.36/7.02 [v0: vATList] : ! [v1: vATList] : ! [v2: vATList] : ! [v3: vATList] : (v1 = % 48.36/7.02 v0 | ~ (vappend(v3, v2) = v1) | ~ (vappend(v3, v2) = v0)) & ! [v0: vnat] % 48.36/7.02 : ! [v1: vnat] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vdivide(v3, % 48.36/7.02 v2) = v1) | ~ (vdivide(v3, v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : % 48.36/7.02 ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vmultiply(v3, v2) = v1) | ~ % 48.36/7.02 (vmultiply(v3, v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : ! [v2: vnat] : % 48.36/7.02 ! [v3: vnat] : (v1 = v0 | ~ (vminus(v3, v2) = v1) | ~ (vminus(v3, v2) = v0)) % 48.36/7.02 & ! [v0: vnat] : ! [v1: vnat] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | % 48.36/7.02 ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: % 48.36/7.02 vYN] : ! [v2: vnat] : ! [v3: vnat] : (v1 = v0 | ~ (vlt(v3, v2) = v1) | ~ % 48.36/7.02 (vlt(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! [v2: vnat] : ! [v3: % 48.36/7.02 vnat] : (v1 = v0 | ~ (vgt(v3, v2) = v1) | ~ (vgt(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vYN] : ! [v1: vYN] : ! [v2: vYN] : ! [v3: vYN] : (v1 = v0 | ~ (vor(v3, % 48.36/7.02 v2) = v1) | ~ (vor(v3, v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! % 48.36/7.02 [v2: vYN] : ! [v3: vYN] : (v1 = v0 | ~ (vand(v3, v2) = v1) | ~ (vand(v3, % 48.36/7.02 v2) = v0)) & ! [v0: vstring] : ! [v1: vstring] : ! [v2: vstring] : ! % 48.36/7.02 [v3: vchar] : (v1 = v0 | ~ (vscons(v3, v2) = v1) | ~ (vscons(v3, v2) = v0)) % 48.36/7.02 & ! [v0: vATList] : ! [v1: vATList] : ! [v2: vATList] : ! [v3: vAType] : % 48.36/7.02 (v1 = v0 | ~ (vatcons(v3, v2) = v1) | ~ (vatcons(v3, v2) = v0)) & ! [v0: % 48.36/7.02 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQuestionnaire] : ! % 48.36/7.02 [v3: vGID] : (v1 = v0 | ~ (vqgroup(v3, v2) = v1) | ~ (vqgroup(v3, v2) = v0)) % 48.36/7.02 & ! [v0: vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQuestionnaire] % 48.36/7.02 : ! [v3: vQuestionnaire] : (v1 = v0 | ~ (vqseq(v3, v2) = v1) | ~ (vqseq(v3, % 48.36/7.02 v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vExp] : ! [v3: % 48.36/7.02 vUnOpT] : (v1 = v0 | ~ (vunop(v3, v2) = v1) | ~ (vunop(v3, v2) = v0)) & ! % 48.36/7.02 [v0: vMapConf] : ! [v1: vMapConf] : ! [v2: vATMap] : ! [v3: vATMap] : (v1 = % 48.36/7.02 v0 | ~ (vMC(v3, v2) = v1) | ~ (vMC(v3, v2) = v0)) & ! [v0: vATMap] : ! % 48.36/7.02 [v1: vATMap] : ! [v2: vQMap] : (v1 = v0 | ~ (vtypeQM(v2) = v1) | ~ % 48.36/7.02 (vtypeQM(v2) = v0)) & ! [v0: vATMap] : ! [v1: vATMap] : ! [v2: vAnsMap] : % 48.36/7.02 (v1 = v0 | ~ (vtypeAM(v2) = v1) | ~ (vtypeAM(v2) = v0)) & ! [v0: % 48.36/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptMapConf] : (v1 % 48.36/7.02 = v0 | ~ (visSomeMapConf(v2) = v1) | ~ (visSomeMapConf(v2) = v0)) & ! % 48.36/7.02 [v0: vstring] : ! [v1: vstring] : ! [v2: vLabel] : (v1 = v0 | ~ % 48.36/7.02 (vaskText(v2) = v1) | ~ (vaskText(v2) = v0)) & ! [v0: vnat] : ! [v1: % 48.36/7.02 vnat] : ! [v2: vLabel] : (v1 = v0 | ~ (vaskNumber(v2) = v1) | ~ % 48.36/7.02 (vaskNumber(v2) = v0)) & ! [v0: vYN] : ! [v1: vYN] : ! [v2: vLabel] : (v1 % 48.36/7.02 = v0 | ~ (vaskYesNo(v2) = v1) | ~ (vaskYesNo(v2) = v0)) & ! [v0: % 48.36/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vExp] : (v1 = v0 | % 48.36/7.02 ~ (vexpIsValue(v2) = v1) | ~ (vexpIsValue(v2) = v0)) & ! [v0: % 48.36/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptExp] : (v1 = % 48.36/7.02 v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: % 48.36/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vOptQConf] : (v1 = % 48.36/7.02 v0 | ~ (visSomeQC(v2) = v1) | ~ (visSomeQC(v2) = v0)) & ! [v0: % 48.36/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vQuestionnaire] : % 48.36/7.02 (v1 = v0 | ~ (visValue(v2) = v1) | ~ (visValue(v2) = v0)) & ! [v0: % 48.36/7.02 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vQConf] : (v1 = v0 | ~ % 48.36/7.02 (vgetQuest(v2) = v1) | ~ (vgetQuest(v2) = v0)) & ! [v0: vQMap] : ! [v1: % 48.36/7.02 vQMap] : ! [v2: vQConf] : (v1 = v0 | ~ (vgetQM(v2) = v1) | ~ (vgetQM(v2) % 48.36/7.02 = v0)) & ! [v0: vAnsMap] : ! [v1: vAnsMap] : ! [v2: vQConf] : (v1 = v0 % 48.36/7.02 | ~ (vgetAM(v2) = v1) | ~ (vgetAM(v2) = v0)) & ! [v0: MultipleValueBool] % 48.36/7.02 : ! [v1: MultipleValueBool] : ! [v2: vOptQuestion] : (v1 = v0 | ~ % 48.36/7.02 (visSomeQuestion(v2) = v1) | ~ (visSomeQuestion(v2) = v0)) & ! [v0: % 48.36/7.02 vAType] : ! [v1: vAType] : ! [v2: vAval] : (v1 = v0 | ~ (vtypeOf(v2) = % 48.36/7.02 v1) | ~ (vtypeOf(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.36/7.02 MultipleValueBool] : ! [v2: vOptAType] : (v1 = v0 | ~ (visSomeAType(v2) = % 48.36/7.02 v1) | ~ (visSomeAType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.36/7.02 MultipleValueBool] : ! [v2: vOptAval] : (v1 = v0 | ~ (visSomeAval(v2) = % 48.36/7.02 v1) | ~ (visSomeAval(v2) = v0)) & ! [v0: vnat] : ! [v1: vnat] : ! [v2: % 48.36/7.02 vnat] : (v1 = v0 | ~ (vpred(v2) = v1) | ~ (vpred(v2) = v0)) & ! [v0: vYN] % 48.36/7.02 : ! [v1: vYN] : ! [v2: vYN] : (v1 = v0 | ~ (vnot(v2) = v1) | ~ (vnot(v2) = % 48.36/7.02 v0)) & ! [v0: vMapConf] : ! [v1: vMapConf] : ! [v2: vOptMapConf] : (v1 % 48.36/7.02 = v0 | ~ (vgetMapConf(v2) = v1) | ~ (vgetMapConf(v2) = v0)) & ! [v0: % 48.36/7.02 vAval] : ! [v1: vAval] : ! [v2: vExp] : (v1 = v0 | ~ (vgetExpValue(v2) = % 48.36/7.02 v1) | ~ (vgetExpValue(v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! % 48.36/7.02 [v2: vOptExp] : (v1 = v0 | ~ (vgetExp(v2) = v1) | ~ (vgetExp(v2) = v0)) & ! % 48.36/7.02 [v0: vQConf] : ! [v1: vQConf] : ! [v2: vOptQConf] : (v1 = v0 | ~ % 48.36/7.02 (vgetQC(v2) = v1) | ~ (vgetQC(v2) = v0)) & ! [v0: vAType] : ! [v1: % 48.36/7.02 vAType] : ! [v2: vOptQuestion] : (v1 = v0 | ~ (vgetQuestionAType(v2) = v1) % 48.36/7.02 | ~ (vgetQuestionAType(v2) = v0)) & ! [v0: vLabel] : ! [v1: vLabel] : ! % 48.36/7.02 [v2: vOptQuestion] : (v1 = v0 | ~ (vgetQuestionLabel(v2) = v1) | ~ % 48.36/7.02 (vgetQuestionLabel(v2) = v0)) & ! [v0: vQID] : ! [v1: vQID] : ! [v2: % 48.36/7.02 vOptQuestion] : (v1 = v0 | ~ (vgetQuestionQID(v2) = v1) | ~ % 48.36/7.02 (vgetQuestionQID(v2) = v0)) & ! [v0: vAType] : ! [v1: vAType] : ! [v2: % 48.36/7.02 vOptAType] : (v1 = v0 | ~ (vgetAType(v2) = v1) | ~ (vgetAType(v2) = v0)) & % 48.36/7.02 ! [v0: vAval] : ! [v1: vAval] : ! [v2: vOptAval] : (v1 = v0 | ~ % 48.36/7.02 (vgetAval(v2) = v1) | ~ (vgetAval(v2) = v0)) & ! [v0: vOptAval] : ! [v1: % 48.36/7.02 vOptAval] : ! [v2: vAval] : (v1 = v0 | ~ (vsomeAval(v2) = v1) | ~ % 48.36/7.02 (vsomeAval(v2) = v0)) & ! [v0: vQID] : ! [v1: vQID] : ! [v2: vQID] : (v1 % 48.36/7.02 = v0 | ~ (venumQID(v2) = v1) | ~ (venumQID(v2) = v0)) & ! [v0: % 48.36/7.02 vOptMapConf] : ! [v1: vOptMapConf] : ! [v2: vMapConf] : (v1 = v0 | ~ % 48.36/7.02 (vsomeMapConf(v2) = v1) | ~ (vsomeMapConf(v2) = v0)) & ! [v0: vGID] : ! % 48.36/7.02 [v1: vGID] : ! [v2: vGID] : (v1 = v0 | ~ (venumGID(v2) = v1) | ~ % 48.36/7.02 (venumGID(v2) = v0)) & ! [v0: vOptExp] : ! [v1: vOptExp] : ! [v2: vExp] : % 48.36/7.02 (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ (vsomeExp(v2) = v0)) & ! [v0: vAval] : % 48.36/7.02 ! [v1: vAval] : ! [v2: vstring] : (v1 = v0 | ~ (vT(v2) = v1) | ~ (vT(v2) = % 48.36/7.02 v0)) & ! [v0: vAval] : ! [v1: vAval] : ! [v2: vnat] : (v1 = v0 | ~ % 48.36/7.02 (vNum(v2) = v1) | ~ (vNum(v2) = v0)) & ! [v0: vAval] : ! [v1: vAval] : ! % 48.36/7.02 [v2: vYN] : (v1 = v0 | ~ (vB(v2) = v1) | ~ (vB(v2) = v0)) & ! [v0: % 48.36/7.02 vOptAType] : ! [v1: vOptAType] : ! [v2: vAType] : (v1 = v0 | ~ % 48.36/7.02 (vsomeAType(v2) = v1) | ~ (vsomeAType(v2) = v0)) & ! [v0: vOptQConf] : ! % 48.36/7.02 [v1: vOptQConf] : ! [v2: vQConf] : (v1 = v0 | ~ (vsomeQConf(v2) = v1) | ~ % 48.36/7.02 (vsomeQConf(v2) = v0)) & ! [v0: vchar] : ! [v1: vchar] : ! [v2: vchar] : % 48.36/7.02 (v1 = v0 | ~ (venumchar(v2) = v1) | ~ (venumchar(v2) = v0)) & ! [v0: % 48.36/7.02 vQuestionnaire] : ! [v1: vQuestionnaire] : ! [v2: vEntry] : (v1 = v0 | ~ % 48.36/7.02 (vqsingle(v2) = v1) | ~ (vqsingle(v2) = v0)) & ! [v0: vnat] : ! [v1: % 48.36/7.02 vnat] : ! [v2: vnat] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = % 48.36/7.02 v0)) & ! [v0: vExp] : ! [v1: vExp] : ! [v2: vQID] : (v1 = v0 | ~ % 48.36/7.02 (vqvar(v2) = v1) | ~ (vqvar(v2) = v0)) & ! [v0: vExp] : ! [v1: vExp] : ! % 48.36/7.02 [v2: vAval] : (v1 = v0 | ~ (vconstant(v2) = v1) | ~ (vconstant(v2) = v0)) & % 48.36/7.02 ! [v0: vLabel] : ! [v1: vLabel] : ! [v2: vLabel] : (v1 = v0 | ~ % 48.36/7.02 (venumLabel(v2) = v1) | ~ (venumLabel(v2) = v0)) & ! [v0: vEntry] : ! % 48.36/7.02 [v1: vEntry] : ! [v2: vQID] : (v1 = v0 | ~ (vask(v2) = v1) | ~ (vask(v2) = % 48.36/7.02 v0)) % 48.36/7.02 % 48.36/7.02 Further assumptions not needed in the proof: % 48.36/7.02 -------------------------------------------- % 48.36/7.03 DIFF-B-Num, DIFF-B-T, DIFF-Num-T, DIFF-Number-Text, DIFF-YesNo-Number, % 48.36/7.03 DIFF-YesNo-Text, DIFF-addop-andop, DIFF-addop-divop, DIFF-addop-eqop, % 48.36/7.03 DIFF-addop-gtop, DIFF-addop-ltop, DIFF-addop-mulop, DIFF-addop-orop, % 48.36/7.03 DIFF-addop-subop, DIFF-aempty-abind, DIFF-andop-orop, DIFF-atempty-atcons, % 48.36/7.03 DIFF-atmempty-atmbind, DIFF-binop-unop, DIFF-constant-binop, DIFF-constant-qvar, % 48.36/7.03 DIFF-constant-unop, DIFF-defquestion-ask, DIFF-divop-andop, DIFF-divop-eqop, % 48.36/7.03 DIFF-divop-gtop, DIFF-divop-ltop, DIFF-divop-orop, DIFF-eqop-andop, % 48.36/7.03 DIFF-eqop-gtop, DIFF-eqop-ltop, DIFF-eqop-orop, DIFF-gtop-andop, DIFF-gtop-ltop, % 48.36/7.03 DIFF-gtop-orop, DIFF-initGID-enumGID, DIFF-initLabel-enumLabel, % 48.36/7.03 DIFF-initQID-enumQID, DIFF-initchar-enumchar, DIFF-ltop-andop, DIFF-ltop-orop, % 48.36/7.03 DIFF-mulop-andop, DIFF-mulop-divop, DIFF-mulop-eqop, DIFF-mulop-gtop, % 48.36/7.03 DIFF-mulop-ltop, DIFF-mulop-orop, DIFF-noAType-someAType, DIFF-noAval-someAval, % 48.36/7.03 DIFF-noExp-someExp, DIFF-noMapConf-someMapConf, DIFF-noQConf-someQConf, % 48.36/7.03 DIFF-noQuestion-someQuestion, DIFF-qcond-qgroup, DIFF-qempty-qcond, % 48.36/7.03 DIFF-qempty-qgroup, DIFF-qempty-qseq, DIFF-qempty-qsingle, DIFF-qmempty-qmbind, % 48.36/7.03 DIFF-qseq-qcond, DIFF-qseq-qgroup, DIFF-qsingle-qcond, DIFF-qsingle-qgroup, % 48.36/7.03 DIFF-qsingle-qseq, DIFF-question-ask, DIFF-question-defquestion, % 48.36/7.03 DIFF-question-value, DIFF-qvar-binop, DIFF-qvar-unop, DIFF-sempty-scons, % 48.36/7.03 DIFF-subop-andop, DIFF-subop-divop, DIFF-subop-eqop, DIFF-subop-gtop, % 48.36/7.03 DIFF-subop-ltop, DIFF-subop-mulop, DIFF-subop-orop, DIFF-value-ask, % 48.36/7.03 DIFF-value-defquestion, DIFF-yes-no, DIFF-zero-succ, EQ-B, EQ-MC, EQ-Num, EQ-QC, % 48.36/7.03 EQ-T, EQ-abind, EQ-ask, EQ-atcons, EQ-atmbind, EQ-binop, EQ-constant, % 48.36/7.03 EQ-defquestion, EQ-enumGID, EQ-enumLabel, EQ-enumQID, EQ-enumchar, EQ-qcond, % 48.36/7.03 EQ-qgroup, EQ-qmbind, EQ-qseq, EQ-qsingle, EQ-question, EQ-qvar, EQ-scons, % 48.36/7.03 EQ-someAType, EQ-someAval, EQ-someExp, EQ-someMapConf, EQ-someQConf, % 48.36/7.03 EQ-someQuestion, EQ-succ, EQ-unop, EQ-value, Task, Task_inv1, Task_inv2, % 48.36/7.03 Task_inv3, Task_inv4, Tdefquestion, Tdefquestion_inv1, Tdefquestion_inv2, % 48.36/7.03 Tdefquestion_inv3, Tqcond, Tqcond_inv1, Tqcond_inv2, Tqcond_inv3, Tqcond_inv4, % 48.36/7.03 Tqcond_inv5, Tqcond_inv6, Tqcond_inv7, Tqempty, Tqempty_inv1, Tqempty_inv2, % 48.36/7.03 Tqgroup, Tqgroup_inv, Tqseq, Tqseq_inv1, Tqseq_inv2, Tqseq_inv3, Tqseq_inv4, % 48.36/7.03 Tquestion, Tquestion_inv1, Tquestion_inv2, Tquestion_inv3, Tvalue, Tvalue_inv1, % 48.36/7.03 Tvalue_inv2, Tvalue_inv3, Tvalue_inv4, and-0, and-1, and-INV, append-0, % 48.36/7.03 append-1, append-INV, appendATMap-0, appendATMap-1, appendATMap-INV, % 48.36/7.03 appendAnsMap-0, appendAnsMap-1, appendAnsMap-INV, checkBinOp-0, checkBinOp-1, % 48.36/7.03 checkBinOp-2, checkBinOp-3, checkBinOp-4, checkBinOp-5, checkBinOp-6, % 48.36/7.03 checkBinOp-7, checkBinOp-8, checkBinOp-9, checkBinOp-INV, checkUnOp-0, % 48.36/7.03 checkUnOp-1, checkUnOp-INV, divide-0, divide-1, divide-INV, dom-ATList, % 48.36/7.03 dom-ATMap, dom-AType, dom-AnsMap, dom-Aval, dom-BinOpT, dom-Entry, dom-Exp, % 48.36/7.03 dom-MapConf, dom-OptAType, dom-OptAval, dom-OptExp, dom-OptMapConf, % 48.36/7.03 dom-OptQConf, dom-OptQuestion, dom-QConf, dom-QMap, dom-Questionnaire, % 48.36/7.03 dom-UnOpT, dom-YN, dom-nat, dom-string, echeck-0, echeck-1, echeck-2, echeck-3, % 48.36/7.03 echeck-4, echeck-5, echeck-6, echeck-7, echeck-INV, evalBinOp-0, evalBinOp-1, % 48.36/7.03 evalBinOp-10, evalBinOp-2, evalBinOp-3, evalBinOp-4, evalBinOp-5, evalBinOp-6, % 48.36/7.03 evalBinOp-7, evalBinOp-8, evalBinOp-9, evalBinOp-INV, evalUnOp-0, evalUnOp-1, % 48.36/7.03 evalUnOp-INV, expIsValue-0, expIsValue-1, expIsValue-false-INV, % 48.36/7.03 expIsValue-true-INV, getAM-0, getAM-INV, getAType-0, getAnswer-0, getAnswer-1, % 48.36/7.03 getAnswer-2, getAnswer-INV, getAval-0, getExp-0, getExpValue-0, getMapConf-0, % 48.36/7.03 getQC-0, getQM-0, getQM-INV, getQuest-0, getQuest-INV, getQuestionAType-0, % 48.36/7.03 getQuestionLabel-0, getQuestionQID-0, gt-0, gt-1, gt-2, gt-INV, intersectATM-0, % 48.36/7.03 intersectATM-1, intersectATM-2, intersectATM-INV, isSomeAType-0, isSomeAType-1, % 48.36/7.03 isSomeAType-false-INV, isSomeAType-true-INV, isSomeAval-0, isSomeAval-1, % 48.36/7.03 isSomeAval-false-INV, isSomeAval-true-INV, isSomeExp-0, isSomeExp-1, % 48.36/7.03 isSomeExp-false-INV, isSomeExp-true-INV, isSomeMapConf-0, isSomeMapConf-1, % 48.36/7.03 isSomeMapConf-false-INV, isSomeMapConf-true-INV, isSomeQC-0, isSomeQC-1, % 48.36/7.03 isSomeQC-false-INV, isSomeQC-true-INV, isSomeQuestion-0, isSomeQuestion-1, % 48.36/7.03 isSomeQuestion-false-INV, isSomeQuestion-true-INV, isValue-0, isValue-1, % 48.36/7.03 isValue-false-INV, isValue-true-INV, lookupATMap-0, lookupATMap-1, % 48.36/7.03 lookupATMap-2, lookupATMap-INV, lookupAnsMap-0, lookupAnsMap-1, lookupAnsMap-2, % 48.36/7.03 lookupAnsMap-INV, lookupQMap-0, lookupQMap-1, lookupQMap-2, lookupQMap-INV, % 48.36/7.03 lt-0, lt-1, lt-2, lt-INV, minus-0, minus-1, minus-INV, multiply-0, multiply-1, % 48.36/7.03 multiply-INV, not-0, not-1, not-INV, or-0, or-1, or-INV, plus-0, plus-1, % 48.36/7.03 plus-INV, pred-0, pred-1, pred-INV, qcappend-0, qcappend-INV, reduce-0, % 48.36/7.03 reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, % 48.36/7.03 reduce-2, reduce-3, reduce-4, reduce-5, reduce-6, reduce-7, reduce-8, reduce-9, % 48.36/7.03 reduce-INV, reduceExp-0, reduceExp-1, reduceExp-10, reduceExp-2, reduceExp-3, % 48.36/7.03 reduceExp-5, reduceExp-6, reduceExp-7, reduceExp-8, reduceExp-9, reduceExp-INV, % 48.36/7.03 typeAM-0, typeAM-1, typeAM-INV, typeOf-0, typeOf-1, typeOf-2, typeOf-INV, % 48.36/7.03 typeQM-0, typeQM-1, typeQM-INV % 48.36/7.03 % 48.36/7.03 Those formulas are unsatisfiable: % 48.36/7.03 --------------------------------- % 48.36/7.03 % 48.36/7.03 Begin of proof % 48.36/7.03 | % 48.36/7.03 | ALPHA: (reduceExp-4) implies: % 48.36/7.03 | (1) ! [v0: vExp] : ! [v1: vExp] : ! [v2: vAnsMap] : ! [v3: vBinOpT] : % 48.36/7.03 | ! [v4: vExp] : ! [v5: vOptExp] : ( ~ (vreduceExp(v4, v2) = v5) | ~ % 48.36/7.03 | (vbinop(v0, v3, v1) = v4) | ~ vBinOpT(v3) | ~ vExp(v1) | ~ % 48.36/7.03 | vExp(v0) | ~ vAnsMap(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 48.36/7.03 | vOptExp] : ? [v9: any] : ? [v10: vExp] : ? [v11: vExp] : ? % 48.36/7.03 | [v12: vOptExp] : (vreduceExp(v1, v2) = v8 & vexpIsValue(v1) = v7 & % 48.36/7.03 | vexpIsValue(v0) = v6 & visSomeExp(v8) = v9 & vgetExp(v8) = v10 & % 48.36/7.03 | vsomeExp(v11) = v12 & vbinop(v0, v3, v10) = v11 & vOptExp(v12) & % 48.36/7.03 | vOptExp(v8) & vExp(v11) & vExp(v10) & ( ~ (v9 = 0) | ~ (v6 = 0) | % 48.36/7.03 | v12 = v5 | v7 = 0))) % 48.36/7.03 | % 48.36/7.03 | ALPHA: (reduceExpProgress-binop-IH0) implies: % 48.36/7.03 | (2) ? [v0: any] : (vexpIsValue(ve1) = v0 & ! [v1: vAnsMap] : ! [v2: % 48.36/7.03 | vAType] : ! [v3: vATMap] : ! [v4: vOptAType] : (v0 = 0 | ~ % 48.36/7.03 | (vecheck(v3, ve1) = v4) | ~ (vtypeAM(v1) = v3) | ~ % 48.36/7.03 | (vsomeAType(v2) = v4) | ~ vAType(v2) | ~ vAnsMap(v1) | ? [v5: % 48.36/7.03 | vOptExp] : ? [v6: vExp] : (vreduceExp(ve1, v1) = v5 & % 48.36/7.03 | vsomeExp(v6) = v5 & vOptExp(v5) & vExp(v6))) & ! [v1: vAnsMap] : % 48.36/7.03 | ! [v2: vAType] : ! [v3: vOptAType] : ! [v4: vOptExp] : (v0 = 0 | % 48.36/7.03 | ~ (vreduceExp(ve1, v1) = v4) | ~ (vsomeAType(v2) = v3) | ~ % 48.36/7.03 | vAType(v2) | ~ vAnsMap(v1) | ? [v5: vATMap] : ? [v6: vOptAType] % 48.36/7.03 | : ? [v7: vExp] : ? [v8: vOptExp] : (vExp(v7) & ((v8 = v4 & % 48.36/7.03 | vsomeExp(v7) = v4 & vOptExp(v4)) | ( ~ (v6 = v3) & % 48.36/7.03 | vecheck(v5, ve1) = v6 & vtypeAM(v1) = v5 & vATMap(v5) & % 48.36/7.03 | vOptAType(v6)))))) % 48.36/7.03 | % 48.36/7.03 | ALPHA: (reduceExpProgress-binop-IH1) implies: % 48.36/7.03 | (3) ? [v0: any] : (vexpIsValue(ve2) = v0 & ! [v1: vAnsMap] : ! [v2: % 48.36/7.03 | vAType] : ! [v3: vATMap] : ! [v4: vOptAType] : (v0 = 0 | ~ % 48.36/7.03 | (vecheck(v3, ve2) = v4) | ~ (vtypeAM(v1) = v3) | ~ % 48.36/7.04 | (vsomeAType(v2) = v4) | ~ vAType(v2) | ~ vAnsMap(v1) | ? [v5: % 48.36/7.04 | vOptExp] : ? [v6: vExp] : (vreduceExp(ve2, v1) = v5 & % 48.36/7.04 | vsomeExp(v6) = v5 & vOptExp(v5) & vExp(v6))) & ! [v1: vAnsMap] : % 48.36/7.04 | ! [v2: vAType] : ! [v3: vOptAType] : ! [v4: vOptExp] : (v0 = 0 | % 48.36/7.04 | ~ (vreduceExp(ve2, v1) = v4) | ~ (vsomeAType(v2) = v3) | ~ % 48.36/7.04 | vAType(v2) | ~ vAnsMap(v1) | ? [v5: vATMap] : ? [v6: vOptAType] % 48.36/7.04 | : ? [v7: vExp] : ? [v8: vOptExp] : (vExp(v7) & ((v8 = v4 & % 48.36/7.04 | vsomeExp(v7) = v4 & vOptExp(v4)) | ( ~ (v6 = v3) & % 48.36/7.04 | vecheck(v5, ve2) = v6 & vtypeAM(v1) = v5 & vATMap(v5) & % 48.36/7.04 | vOptAType(v6)))))) % 48.36/7.04 | % 48.36/7.04 | ALPHA: (reduceExpProgress-binop-expIsValue-True-expIsValue-False-isSomeExp-True) % 48.36/7.04 | implies: % 48.36/7.04 | (4) vExp(ve1) % 48.36/7.04 | (5) vExp(ve2) % 48.36/7.04 | (6) ? [v0: int] : ? [v1: vAnsMap] : ? [v2: vBinOpT] : ? [v3: vAType] : % 48.36/7.04 | ? [v4: vOptExp] : ? [v5: vExp] : ? [v6: int] : ? [v7: vATMap] : ? % 48.36/7.04 | [v8: vOptAType] : ? [v9: vOptExp] : ( ~ (v6 = 0) & ~ (v0 = 0) & % 48.36/7.04 | vecheck(v7, v5) = v8 & vtypeAM(v1) = v7 & vreduceExp(v5, v1) = v9 & % 48.36/7.04 | vreduceExp(ve2, v1) = v4 & vexpIsValue(v5) = v6 & vexpIsValue(ve2) = % 48.36/7.04 | v0 & vexpIsValue(ve1) = 0 & visSomeExp(v4) = 0 & vsomeAType(v3) = v8 % 48.36/7.04 | & vbinop(ve1, v2, ve2) = v5 & vAType(v3) & vBinOpT(v2) & vOptExp(v9) % 48.36/7.04 | & vOptExp(v4) & vExp(v5) & vAnsMap(v1) & vATMap(v7) & vOptAType(v8) & % 48.36/7.04 | ! [v10: vExp] : ( ~ (vsomeExp(v10) = v9) | ~ vExp(v10))) % 48.36/7.04 | % 48.36/7.04 | ALPHA: (function-axioms) implies: % 48.36/7.04 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 48.36/7.04 | vOptExp] : (v1 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = % 48.36/7.04 | v0)) % 48.36/7.04 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: vExp] % 48.36/7.04 | : (v1 = v0 | ~ (vexpIsValue(v2) = v1) | ~ (vexpIsValue(v2) = v0)) % 48.36/7.04 | (9) ! [v0: vOptExp] : ! [v1: vOptExp] : ! [v2: vAnsMap] : ! [v3: vExp] % 48.36/7.04 | : (v1 = v0 | ~ (vreduceExp(v3, v2) = v1) | ~ (vreduceExp(v3, v2) = % 48.36/7.04 | v0)) % 48.36/7.04 | % 48.36/7.04 | DELTA: instantiating (6) with fresh symbols all_398_0, all_398_1, all_398_2, % 48.36/7.04 | all_398_3, all_398_4, all_398_5, all_398_6, all_398_7, all_398_8, % 48.36/7.04 | all_398_9 gives: % 48.36/7.04 | (10) ~ (all_398_3 = 0) & ~ (all_398_9 = 0) & vecheck(all_398_2, % 48.36/7.04 | all_398_4) = all_398_1 & vtypeAM(all_398_8) = all_398_2 & % 48.36/7.04 | vreduceExp(all_398_4, all_398_8) = all_398_0 & vreduceExp(ve2, % 48.36/7.04 | all_398_8) = all_398_5 & vexpIsValue(all_398_4) = all_398_3 & % 48.36/7.04 | vexpIsValue(ve2) = all_398_9 & vexpIsValue(ve1) = 0 & % 48.36/7.04 | visSomeExp(all_398_5) = 0 & vsomeAType(all_398_6) = all_398_1 & % 48.36/7.04 | vbinop(ve1, all_398_7, ve2) = all_398_4 & vAType(all_398_6) & % 48.36/7.04 | vBinOpT(all_398_7) & vOptExp(all_398_0) & vOptExp(all_398_5) & % 48.36/7.04 | vExp(all_398_4) & vAnsMap(all_398_8) & vATMap(all_398_2) & % 48.36/7.04 | vOptAType(all_398_1) & ! [v0: vExp] : ( ~ (vsomeExp(v0) = all_398_0) % 48.36/7.04 | | ~ vExp(v0)) % 48.36/7.04 | % 48.36/7.04 | ALPHA: (10) implies: % 48.36/7.04 | (11) ~ (all_398_9 = 0) % 48.36/7.04 | (12) vAnsMap(all_398_8) % 48.36/7.04 | (13) vBinOpT(all_398_7) % 48.36/7.04 | (14) vbinop(ve1, all_398_7, ve2) = all_398_4 % 48.36/7.04 | (15) visSomeExp(all_398_5) = 0 % 48.36/7.04 | (16) vexpIsValue(ve1) = 0 % 48.36/7.04 | (17) vexpIsValue(ve2) = all_398_9 % 48.36/7.04 | (18) vreduceExp(ve2, all_398_8) = all_398_5 % 48.36/7.04 | (19) vreduceExp(all_398_4, all_398_8) = all_398_0 % 48.36/7.04 | (20) ! [v0: vExp] : ( ~ (vsomeExp(v0) = all_398_0) | ~ vExp(v0)) % 48.36/7.04 | % 48.36/7.04 | DELTA: instantiating (3) with fresh symbol all_401_0 gives: % 48.36/7.05 | (21) vexpIsValue(ve2) = all_401_0 & ! [v0: vAnsMap] : ! [v1: vAType] : ! % 48.36/7.05 | [v2: vATMap] : ! [v3: vOptAType] : (all_401_0 = 0 | ~ (vecheck(v2, % 48.36/7.05 | ve2) = v3) | ~ (vtypeAM(v0) = v2) | ~ (vsomeAType(v1) = v3) | % 48.36/7.05 | ~ vAType(v1) | ~ vAnsMap(v0) | ? [v4: vOptExp] : ? [v5: vExp] : % 48.36/7.05 | (vreduceExp(ve2, v0) = v4 & vsomeExp(v5) = v4 & vOptExp(v4) & % 48.36/7.05 | vExp(v5))) & ! [v0: vAnsMap] : ! [v1: vAType] : ! [v2: % 48.36/7.05 | vOptAType] : ! [v3: vOptExp] : (all_401_0 = 0 | ~ (vreduceExp(ve2, % 48.36/7.05 | v0) = v3) | ~ (vsomeAType(v1) = v2) | ~ vAType(v1) | ~ % 48.36/7.05 | vAnsMap(v0) | ? [v4: vATMap] : ? [v5: vOptAType] : ? [v6: vExp] : % 48.36/7.05 | ? [v7: vOptExp] : (vExp(v6) & ((v7 = v3 & vsomeExp(v6) = v3 & % 48.36/7.05 | vOptExp(v3)) | ( ~ (v5 = v2) & vecheck(v4, ve2) = v5 & % 48.36/7.05 | vtypeAM(v0) = v4 & vATMap(v4) & vOptAType(v5))))) % 48.36/7.05 | % 48.36/7.05 | ALPHA: (21) implies: % 48.36/7.05 | (22) vexpIsValue(ve2) = all_401_0 % 48.36/7.05 | % 48.36/7.05 | DELTA: instantiating (2) with fresh symbol all_404_0 gives: % 48.36/7.05 | (23) vexpIsValue(ve1) = all_404_0 & ! [v0: vAnsMap] : ! [v1: vAType] : ! % 48.36/7.05 | [v2: vATMap] : ! [v3: vOptAType] : (all_404_0 = 0 | ~ (vecheck(v2, % 48.36/7.05 | ve1) = v3) | ~ (vtypeAM(v0) = v2) | ~ (vsomeAType(v1) = v3) | % 48.36/7.05 | ~ vAType(v1) | ~ vAnsMap(v0) | ? [v4: vOptExp] : ? [v5: vExp] : % 48.36/7.05 | (vreduceExp(ve1, v0) = v4 & vsomeExp(v5) = v4 & vOptExp(v4) & % 48.36/7.05 | vExp(v5))) & ! [v0: vAnsMap] : ! [v1: vAType] : ! [v2: % 48.36/7.05 | vOptAType] : ! [v3: vOptExp] : (all_404_0 = 0 | ~ (vreduceExp(ve1, % 48.36/7.05 | v0) = v3) | ~ (vsomeAType(v1) = v2) | ~ vAType(v1) | ~ % 48.36/7.05 | vAnsMap(v0) | ? [v4: vATMap] : ? [v5: vOptAType] : ? [v6: vExp] : % 48.36/7.05 | ? [v7: vOptExp] : (vExp(v6) & ((v7 = v3 & vsomeExp(v6) = v3 & % 48.36/7.05 | vOptExp(v3)) | ( ~ (v5 = v2) & vecheck(v4, ve1) = v5 & % 48.36/7.05 | vtypeAM(v0) = v4 & vATMap(v4) & vOptAType(v5))))) % 48.36/7.05 | % 48.36/7.05 | ALPHA: (23) implies: % 48.36/7.05 | (24) vexpIsValue(ve1) = all_404_0 % 48.36/7.05 | % 48.36/7.05 | GROUND_INST: instantiating (8) with 0, all_404_0, ve1, simplifying with (16), % 48.36/7.05 | (24) gives: % 48.36/7.05 | (25) all_404_0 = 0 % 48.36/7.05 | % 48.36/7.05 | GROUND_INST: instantiating (8) with all_398_9, all_401_0, ve2, simplifying % 48.36/7.05 | with (17), (22) gives: % 48.36/7.05 | (26) all_401_0 = all_398_9 % 48.36/7.05 | % 48.36/7.05 | GROUND_INST: instantiating (1) with ve1, ve2, all_398_8, all_398_7, all_398_4, % 48.36/7.05 | all_398_0, simplifying with (4), (5), (12), (13), (14), (19) % 48.36/7.05 | gives: % 48.36/7.05 | (27) ? [v0: any] : ? [v1: any] : ? [v2: vOptExp] : ? [v3: any] : ? % 48.36/7.05 | [v4: vExp] : ? [v5: vExp] : ? [v6: vOptExp] : (vreduceExp(ve2, % 48.36/7.05 | all_398_8) = v2 & vexpIsValue(ve2) = v1 & vexpIsValue(ve1) = v0 & % 48.36/7.05 | visSomeExp(v2) = v3 & vgetExp(v2) = v4 & vsomeExp(v5) = v6 & % 48.36/7.05 | vbinop(ve1, all_398_7, v4) = v5 & vOptExp(v6) & vOptExp(v2) & % 48.36/7.05 | vExp(v5) & vExp(v4) & ( ~ (v3 = 0) | ~ (v0 = 0) | v6 = all_398_0 | % 48.36/7.05 | v1 = 0)) % 48.36/7.05 | % 48.36/7.05 | DELTA: instantiating (27) with fresh symbols all_463_0, all_463_1, all_463_2, % 48.36/7.05 | all_463_3, all_463_4, all_463_5, all_463_6 gives: % 48.36/7.05 | (28) vreduceExp(ve2, all_398_8) = all_463_4 & vexpIsValue(ve2) = all_463_5 % 48.36/7.05 | & vexpIsValue(ve1) = all_463_6 & visSomeExp(all_463_4) = all_463_3 & % 48.36/7.05 | vgetExp(all_463_4) = all_463_2 & vsomeExp(all_463_1) = all_463_0 & % 48.36/7.05 | vbinop(ve1, all_398_7, all_463_2) = all_463_1 & vOptExp(all_463_0) & % 48.36/7.05 | vOptExp(all_463_4) & vExp(all_463_1) & vExp(all_463_2) & ( ~ % 48.36/7.05 | (all_463_3 = 0) | ~ (all_463_6 = 0) | all_463_0 = all_398_0 | % 48.36/7.05 | all_463_5 = 0) % 48.36/7.05 | % 48.36/7.05 | ALPHA: (28) implies: % 48.36/7.05 | (29) vExp(all_463_1) % 48.36/7.05 | (30) vsomeExp(all_463_1) = all_463_0 % 48.36/7.05 | (31) visSomeExp(all_463_4) = all_463_3 % 48.36/7.05 | (32) vexpIsValue(ve1) = all_463_6 % 48.36/7.05 | (33) vexpIsValue(ve2) = all_463_5 % 48.36/7.05 | (34) vreduceExp(ve2, all_398_8) = all_463_4 % 48.36/7.05 | (35) ~ (all_463_3 = 0) | ~ (all_463_6 = 0) | all_463_0 = all_398_0 | % 48.36/7.05 | all_463_5 = 0 % 48.36/7.05 | % 48.36/7.05 | GROUND_INST: instantiating (8) with 0, all_463_6, ve1, simplifying with (16), % 48.36/7.05 | (32) gives: % 48.36/7.06 | (36) all_463_6 = 0 % 48.36/7.06 | % 48.36/7.06 | GROUND_INST: instantiating (8) with all_398_9, all_463_5, ve2, simplifying % 48.36/7.06 | with (17), (33) gives: % 48.36/7.06 | (37) all_463_5 = all_398_9 % 48.36/7.06 | % 48.36/7.06 | GROUND_INST: instantiating (9) with all_398_5, all_463_4, all_398_8, ve2, % 48.36/7.06 | simplifying with (18), (34) gives: % 48.36/7.06 | (38) all_463_4 = all_398_5 % 48.36/7.06 | % 48.36/7.06 | REDUCE: (31), (38) imply: % 48.36/7.06 | (39) visSomeExp(all_398_5) = all_463_3 % 48.36/7.06 | % 48.36/7.06 | GROUND_INST: instantiating (7) with 0, all_463_3, all_398_5, simplifying with % 48.36/7.06 | (15), (39) gives: % 48.36/7.06 | (40) all_463_3 = 0 % 48.36/7.06 | % 48.36/7.06 | BETA: splitting (35) gives: % 48.36/7.06 | % 48.36/7.06 | Case 1: % 48.36/7.06 | | % 48.36/7.06 | | (41) ~ (all_463_3 = 0) % 48.36/7.06 | | % 48.36/7.06 | | REDUCE: (40), (41) imply: % 48.36/7.06 | | (42) $false % 48.36/7.06 | | % 48.36/7.06 | | CLOSE: (42) is inconsistent. % 48.36/7.06 | | % 48.36/7.06 | Case 2: % 48.36/7.06 | | % 48.36/7.06 | | (43) ~ (all_463_6 = 0) | all_463_0 = all_398_0 | all_463_5 = 0 % 48.36/7.06 | | % 48.36/7.06 | | BETA: splitting (43) gives: % 48.36/7.06 | | % 48.36/7.06 | | Case 1: % 48.36/7.06 | | | % 48.36/7.06 | | | (44) ~ (all_463_6 = 0) % 48.36/7.06 | | | % 48.36/7.06 | | | REDUCE: (36), (44) imply: % 48.36/7.06 | | | (45) $false % 48.36/7.06 | | | % 48.36/7.06 | | | CLOSE: (45) is inconsistent. % 48.36/7.06 | | | % 48.36/7.06 | | Case 2: % 48.36/7.06 | | | % 48.36/7.06 | | | (46) all_463_0 = all_398_0 | all_463_5 = 0 % 48.36/7.06 | | | % 48.36/7.06 | | | BETA: splitting (46) gives: % 48.36/7.06 | | | % 48.36/7.06 | | | Case 1: % 48.36/7.06 | | | | % 48.36/7.06 | | | | (47) all_463_5 = 0 % 48.36/7.06 | | | | % 48.36/7.06 | | | | COMBINE_EQS: (37), (47) imply: % 48.36/7.06 | | | | (48) all_398_9 = 0 % 48.36/7.06 | | | | % 48.36/7.06 | | | | REDUCE: (11), (48) imply: % 48.36/7.06 | | | | (49) $false % 48.36/7.06 | | | | % 48.36/7.06 | | | | CLOSE: (49) is inconsistent. % 48.36/7.06 | | | | % 48.36/7.06 | | | Case 2: % 48.36/7.06 | | | | % 48.36/7.06 | | | | (50) all_463_0 = all_398_0 % 48.36/7.06 | | | | % 48.36/7.06 | | | | REDUCE: (30), (50) imply: % 48.36/7.06 | | | | (51) vsomeExp(all_463_1) = all_398_0 % 48.36/7.06 | | | | % 48.36/7.06 | | | | GROUND_INST: instantiating (20) with all_463_1, simplifying with (29), % 48.36/7.06 | | | | (51) gives: % 48.36/7.06 | | | | (52) $false % 48.36/7.06 | | | | % 48.36/7.06 | | | | CLOSE: (52) is inconsistent. % 48.36/7.06 | | | | % 48.36/7.06 | | | End of split % 48.36/7.06 | | | % 48.36/7.06 | | End of split % 48.36/7.06 | | % 48.36/7.06 | End of split % 48.36/7.06 | % 48.36/7.06 End of proof % 48.36/7.06 % SZS output end Proof for theBenchmark % 48.36/7.06 % 48.36/7.06 6447ms %------------------------------------------------------------------------------