%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM137+1 : TPTP v8.1.2. Released v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 : Wed Aug 30 18:44:34 EDT 2023 % Result : Theorem 15.31s 2.77s % Output : Proof 18.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COM137+1 : TPTP v8.1.2. Released v6.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n023.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 13:17:10 EDT 2023 % 0.13/0.34 % CPUTime : % 0.47/0.62 ________ _____ % 0.47/0.62 ___ __ \_________(_)________________________________ % 0.47/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.47/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.47/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.47/0.62 % 0.47/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.47/0.62 (2023-06-19) % 0.47/0.62 % 0.47/0.62 (c) Philipp Rümmer, 2009-2023 % 0.47/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.47/0.62 Amanda Stjerna. % 0.47/0.62 Free software under BSD-3-Clause. % 0.47/0.62 % 0.47/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.47/0.62 % 0.47/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.47/0.63 Running up to 7 provers in parallel. % 0.73/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.07/1.40 Prover 1: Preprocessing ... % 5.07/1.40 Prover 4: Preprocessing ... % 5.50/1.43 Prover 6: Preprocessing ... % 5.50/1.43 Prover 0: Preprocessing ... % 5.50/1.43 Prover 2: Preprocessing ... % 5.50/1.43 Prover 5: Preprocessing ... % 5.50/1.44 Prover 3: Preprocessing ... % 11.77/2.27 Prover 1: Constructing countermodel ... % 11.97/2.28 Prover 6: Proving ... % 11.97/2.28 Prover 3: Constructing countermodel ... % 11.97/2.29 Prover 0: Proving ... % 11.97/2.30 Prover 4: Constructing countermodel ... % 12.31/2.34 Prover 5: Proving ... % 12.98/2.45 Prover 2: Proving ... % 15.31/2.77 Prover 3: proved (2123ms) % 15.31/2.77 % 15.31/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.31/2.77 % 15.31/2.77 Prover 6: stopped % 15.31/2.77 Prover 0: stopped % 15.31/2.77 Prover 2: stopped % 15.31/2.77 Prover 5: stopped % 15.31/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.31/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.31/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.31/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.31/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.74/2.92 Prover 11: Preprocessing ... % 16.87/2.94 Prover 13: Preprocessing ... % 16.87/2.94 Prover 4: Found proof (size 66) % 16.87/2.95 Prover 8: Preprocessing ... % 16.87/2.95 Prover 1: Found proof (size 67) % 16.87/2.96 Prover 1: proved (2317ms) % 16.87/2.96 Prover 4: proved (2315ms) % 16.87/2.96 Prover 7: Preprocessing ... % 16.87/2.96 Prover 10: Preprocessing ... % 16.87/3.01 Prover 11: stopped % 17.51/3.02 Prover 10: stopped % 17.51/3.02 Prover 7: stopped % 17.51/3.07 Prover 13: stopped % 17.89/3.14 Prover 8: Warning: ignoring some quantifiers % 17.89/3.15 Prover 8: Constructing countermodel ... % 17.89/3.16 Prover 8: stopped % 17.89/3.16 % 18.26/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.26/3.16 % 18.26/3.17 % SZS output start Proof for theBenchmark % 18.34/3.18 Assumptions after simplification: % 18.34/3.18 --------------------------------- % 18.34/3.18 % 18.34/3.18 (DIFF-abs-app) % 18.50/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.50/3.22 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~ % 18.50/3.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.50/3.22 % 18.50/3.22 (DIFF-var-app) % 18.50/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) = % 18.50/3.22 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.50/3.22 % 18.50/3.22 (EQ-app) % 18.50/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 18.50/3.22 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 18.50/3.22 ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 18.50/3.22 $i] : ! [v4: $i] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = % 18.50/3.22 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.50/3.22 % 18.50/3.22 (T-Strong-app) % 18.50/3.23 $i(ve2app) & $i(ve1app) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 18.50/3.23 $i] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) % 18.50/3.23 & ~ (v5 = 0) & vtcheck(v6, v0, v4) = 0 & vtcheck(v3, v0, v4) = v7 & % 18.50/3.23 vbind(v1, v2, v3) = v6 & visFreeVar(v1, v0) = v5 & vapp(ve1app, ve2app) = v0 % 18.50/3.23 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.50/3.23 % 18.50/3.23 (T-Strong-app-IH1) % 18.50/3.23 $i(ve1app) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.50/3.23 $i] : ( ~ (vtcheck(v4, ve1app, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 18.50/3.23 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 18.50/3.23 (vtcheck(v2, ve1app, v3) = v6 & visFreeVar(v0, ve1app) = v5 & (v6 = 0 | v5 = % 18.50/3.23 0))) % 18.50/3.23 % 18.50/3.23 (T-Strong-app-IH2) % 18.50/3.23 $i(ve2app) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.50/3.23 $i] : ( ~ (vtcheck(v4, ve2app, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 18.50/3.23 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 18.50/3.23 (vtcheck(v2, ve2app, v3) = v6 & visFreeVar(v0, ve2app) = v5 & (v6 = 0 | v5 = % 18.50/3.23 0))) % 18.50/3.23 % 18.50/3.23 (T-app) % 18.50/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.50/3.23 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~ % 18.50/3.23 (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3) % 18.50/3.23 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.50/3.23 [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0: $i] : ! % 18.50/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 18.50/3.23 int] : (v6 = 0 | ~ (vtcheck(v1, v5, v4) = v6) | ~ (vtcheck(v1, v3, v0) = % 18.50/3.23 0) | ~ (vapp(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 18.50/3.23 $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & varrow(v0, % 18.50/3.23 v4) = v7 & vtcheck(v1, v2, v7) = v8 & $i(v7))) & ! [v0: $i] : ! [v1: % 18.50/3.23 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 18.50/3.23 (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vtcheck(v1, v2, % 18.50/3.23 v5) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.50/3.23 ? [v6: $i] : (vtcheck(v1, v6, v4) = 0 & vapp(v2, v3) = v6 & $i(v6))) % 18.50/3.23 % 18.50/3.23 (T-inv) % 18.50/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 18.50/3.24 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 18.50/3.24 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 18.50/3.24 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: $i] : ? [v15: $i] : ? % 18.50/3.24 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? % 18.50/3.24 [v21: int] : ($i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v9) & $i(v8) & % 18.50/3.24 $i(v7) & $i(v4) & ((v21 = 0 & v19 = v1 & v18 = v0 & varrow(v16, v17) = v1 % 18.50/3.24 & vtcheck(v20, v15, v17) = 0 & vbind(v14, v16, v2) = v20 & vabs(v14, % 18.50/3.24 v16, v15) = v0 & $i(v20)) | (v13 = 0 & v12 = 0 & v10 = v0 & % 18.50/3.24 varrow(v9, v1) = v11 & vtcheck(v2, v8, v9) = 0 & vtcheck(v2, v7, v11) % 18.50/3.24 = 0 & vapp(v7, v8) = v0 & $i(v11)) | (v6 = v3 & v5 = v0 & vlookup(v4, % 18.50/3.24 v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0 & $i(v3))))) % 18.50/3.24 % 18.50/3.24 (isFreeVar2) % 18.50/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 18.50/3.24 int] : (v5 = 0 | v4 = 0 | ~ (visFreeVar(v0, v3) = v5) | ~ (visFreeVar(v0, % 18.50/3.24 v2) = v4) | ~ (visFreeVar(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 18.50/3.24 $i(v1) | ~ $i(v0) | ? [v6: $i] : ( ~ (v6 = v1) & vapp(v2, v3) = v6 & % 18.50/3.24 $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 18.50/3.24 MultipleValueBool] : ! [v5: int] : (v5 = 0 | ~ (visFreeVar(v0, v3) = v4) | % 18.50/3.24 ~ (visFreeVar(v0, v2) = 0) | ~ (visFreeVar(v0, v1) = v5) | ~ $i(v3) | ~ % 18.50/3.24 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ( ~ (v6 = v1) & vapp(v2, v3) % 18.50/3.24 = v6 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.50/3.24 ! [v4: MultipleValueBool] : ! [v5: int] : (v5 = 0 | ~ (visFreeVar(v0, v3) = % 18.50/3.24 0) | ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ~ % 18.50/3.24 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ( ~ (v6 = v1) & % 18.50/3.24 vapp(v2, v3) = v6 & $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.50/3.24 ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~ (visFreeVar(v0, v3) = v4) | ~ % 18.50/3.24 (visFreeVar(v0, v1) = v5) | ~ (vapp(v2, v3) = v1) | ~ $i(v3) | ~ $i(v2) | % 18.50/3.24 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : (visFreeVar(v0, v2) = v6 & ( ~ (v5 = % 18.50/3.24 0) | v6 = 0 | v4 = 0) & (v5 = 0 | ( ~ (v6 = 0) & ~ (v4 = 0))))) & ! % 18.50/3.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: % 18.50/3.24 any] : ( ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = v5) | ~ % 18.50/3.24 (vapp(v2, v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.50/3.24 [v6: any] : (visFreeVar(v0, v3) = v6 & ( ~ (v5 = 0) | v6 = 0 | v4 = 0) & (v5 % 18.50/3.24 = 0 | ( ~ (v6 = 0) & ~ (v4 = 0))))) % 18.50/3.24 % 18.50/3.24 (function-axioms) % 18.50/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 18.50/3.25 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 18.50/3.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.50/3.25 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 18.50/3.25 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 18.50/3.25 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 18.50/3.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 18.50/3.25 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 18.50/3.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 18.50/3.25 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 18.50/3.25 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 18.50/3.25 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.50/3.25 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.50/3.25 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 18.50/3.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 18.50/3.25 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.50/3.25 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 18.50/3.25 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 18.50/3.25 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 18.50/3.25 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 18.50/3.25 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 18.50/3.25 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.50/3.25 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 18.50/3.25 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 18.50/3.25 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.50/3.25 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 18.50/3.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 18.50/3.25 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.50/3.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 18.50/3.25 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 18.50/3.25 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 18.50/3.25 % 18.50/3.25 Further assumptions not needed in the proof: % 18.50/3.25 -------------------------------------------- % 18.50/3.25 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-abs, EQ-abs, % 18.50/3.25 EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, % 18.50/3.25 EQ-var, T-Context-Duplicate, T-Context-Swap, T-Weak, T-abs, T-var, % 18.50/3.25 gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0, isFreeVar1, isSomeExp0, % 18.50/3.25 isSomeExp1, isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, % 18.50/3.25 lookup0, lookup1, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3, % 18.50/3.25 reduce4, reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, % 18.50/3.25 subst5 % 18.50/3.25 % 18.50/3.25 Those formulas are unsatisfiable: % 18.50/3.25 --------------------------------- % 18.50/3.25 % 18.50/3.25 Begin of proof % 18.50/3.25 | % 18.50/3.25 | ALPHA: (EQ-app) implies: % 18.50/3.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.50/3.26 | (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) % 18.50/3.26 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.50/3.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.50/3.26 | (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) % 18.50/3.26 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 18.50/3.26 | % 18.50/3.26 | ALPHA: (isFreeVar2) implies: % 18.71/3.26 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 18.71/3.26 | ! [v5: any] : ( ~ (visFreeVar(v0, v2) = v4) | ~ (visFreeVar(v0, v1) = % 18.71/3.26 | v5) | ~ (vapp(v2, v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 18.71/3.26 | ~ $i(v0) | ? [v6: any] : (visFreeVar(v0, v3) = v6 & ( ~ (v5 = 0) | % 18.71/3.26 | v6 = 0 | v4 = 0) & (v5 = 0 | ( ~ (v6 = 0) & ~ (v4 = 0))))) % 18.71/3.26 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 18.71/3.26 | ! [v5: any] : ( ~ (visFreeVar(v0, v3) = v4) | ~ (visFreeVar(v0, v1) = % 18.71/3.26 | v5) | ~ (vapp(v2, v3) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 18.71/3.26 | ~ $i(v0) | ? [v6: any] : (visFreeVar(v0, v2) = v6 & ( ~ (v5 = 0) | % 18.71/3.26 | v6 = 0 | v4 = 0) & (v5 = 0 | ( ~ (v6 = 0) & ~ (v4 = 0))))) % 18.71/3.26 | % 18.71/3.26 | ALPHA: (T-app) implies: % 18.71/3.26 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.71/3.26 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) % 18.71/3.26 | = v5) | ~ (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = % 18.71/3.26 | 0) | ~ (vapp(v2, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 18.71/3.26 | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, % 18.71/3.26 | v0) = v8)) % 18.71/3.26 | % 18.71/3.26 | ALPHA: (T-Strong-app-IH1) implies: % 18.71/3.26 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 18.71/3.26 | ~ (vtcheck(v4, ve1app, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 18.71/3.26 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 18.71/3.26 | any] : (vtcheck(v2, ve1app, v3) = v6 & visFreeVar(v0, ve1app) = v5 % 18.71/3.26 | & (v6 = 0 | v5 = 0))) % 18.71/3.26 | % 18.71/3.26 | ALPHA: (T-Strong-app-IH2) implies: % 18.71/3.26 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 18.71/3.26 | ~ (vtcheck(v4, ve2app, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 18.71/3.26 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 18.71/3.26 | any] : (vtcheck(v2, ve2app, v3) = v6 & visFreeVar(v0, ve2app) = v5 % 18.71/3.26 | & (v6 = 0 | v5 = 0))) % 18.71/3.26 | % 18.71/3.26 | ALPHA: (T-Strong-app) implies: % 18.71/3.26 | (8) $i(ve1app) % 18.71/3.26 | (9) $i(ve2app) % 18.71/3.27 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 18.71/3.27 | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & ~ (v5 = 0) % 18.71/3.27 | & vtcheck(v6, v0, v4) = 0 & vtcheck(v3, v0, v4) = v7 & vbind(v1, v2, % 18.71/3.27 | v3) = v6 & visFreeVar(v1, v0) = v5 & vapp(ve1app, ve2app) = v0 & % 18.71/3.27 | $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 18.71/3.27 | % 18.71/3.27 | ALPHA: (function-axioms) implies: % 18.71/3.27 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 18.71/3.27 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) % 18.71/3.27 | | ~ (vtcheck(v4, v3, v2) = v0)) % 18.71/3.27 | % 18.71/3.27 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2, % 18.71/3.27 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7 gives: % 18.71/3.27 | (12) ~ (all_56_0 = 0) & ~ (all_56_2 = 0) & vtcheck(all_56_1, all_56_7, % 18.71/3.27 | all_56_3) = 0 & vtcheck(all_56_4, all_56_7, all_56_3) = all_56_0 & % 18.71/3.27 | vbind(all_56_6, all_56_5, all_56_4) = all_56_1 & visFreeVar(all_56_6, % 18.71/3.27 | all_56_7) = all_56_2 & vapp(ve1app, ve2app) = all_56_7 & % 18.71/3.27 | $i(all_56_1) & $i(all_56_3) & $i(all_56_4) & $i(all_56_5) & % 18.71/3.27 | $i(all_56_6) & $i(all_56_7) % 18.71/3.27 | % 18.71/3.27 | ALPHA: (12) implies: % 18.71/3.27 | (13) ~ (all_56_2 = 0) % 18.71/3.27 | (14) ~ (all_56_0 = 0) % 18.71/3.27 | (15) $i(all_56_7) % 18.71/3.27 | (16) $i(all_56_6) % 18.71/3.27 | (17) $i(all_56_5) % 18.71/3.27 | (18) $i(all_56_4) % 18.71/3.27 | (19) $i(all_56_3) % 18.71/3.27 | (20) $i(all_56_1) % 18.71/3.27 | (21) vapp(ve1app, ve2app) = all_56_7 % 18.71/3.27 | (22) visFreeVar(all_56_6, all_56_7) = all_56_2 % 18.71/3.27 | (23) vbind(all_56_6, all_56_5, all_56_4) = all_56_1 % 18.71/3.27 | (24) vtcheck(all_56_4, all_56_7, all_56_3) = all_56_0 % 18.71/3.27 | (25) vtcheck(all_56_1, all_56_7, all_56_3) = 0 % 18.71/3.27 | % 18.71/3.27 | GROUND_INST: instantiating (T-inv) with all_56_7, all_56_3, all_56_1, % 18.71/3.27 | simplifying with (15), (19), (20), (25) gives: % 18.71/3.27 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] : % 18.71/3.27 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] % 18.71/3.27 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 18.71/3.27 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18: % 18.71/3.27 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) & % 18.71/3.27 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_56_3 & v15 = all_56_7 & % 18.71/3.27 | varrow(v13, v14) = all_56_3 & vtcheck(v17, v12, v14) = 0 & % 18.71/3.27 | vbind(v11, v13, all_56_1) = v17 & vabs(v11, v13, v12) = all_56_7 % 18.71/3.27 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_56_7 & varrow(v6, % 18.71/3.27 | all_56_3) = v8 & vtcheck(all_56_1, v5, v6) = 0 & % 18.71/3.27 | vtcheck(all_56_1, v4, v8) = 0 & vapp(v4, v5) = all_56_7 & % 18.71/3.27 | $i(v8)) | (v3 = v0 & v2 = all_56_7 & vlookup(v1, all_56_1) = v0 % 18.71/3.27 | & vsomeType(all_56_3) = v0 & vvar(v1) = all_56_7 & $i(v0)))) % 18.71/3.27 | % 18.71/3.27 | DELTA: instantiating (26) with fresh symbols all_65_0, all_65_1, all_65_2, % 18.71/3.27 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9, % 18.71/3.27 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15, % 18.71/3.27 | all_65_16, all_65_17, all_65_18 gives: % 18.71/3.28 | (27) $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) & % 18.71/3.28 | $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & $i(all_65_17) & % 18.71/3.28 | ((all_65_0 = 0 & all_65_2 = all_56_3 & all_65_3 = all_56_7 & % 18.71/3.28 | varrow(all_65_5, all_65_4) = all_56_3 & vtcheck(all_65_1, % 18.71/3.28 | all_65_6, all_65_4) = 0 & vbind(all_65_7, all_65_5, all_56_1) = % 18.71/3.28 | all_65_1 & vabs(all_65_7, all_65_5, all_65_6) = all_56_7 & % 18.71/3.28 | $i(all_65_1)) | (all_65_8 = 0 & all_65_9 = 0 & all_65_11 = % 18.71/3.28 | all_56_7 & varrow(all_65_12, all_56_3) = all_65_10 & % 18.71/3.28 | vtcheck(all_56_1, all_65_13, all_65_12) = 0 & vtcheck(all_56_1, % 18.71/3.28 | all_65_14, all_65_10) = 0 & vapp(all_65_14, all_65_13) = % 18.71/3.28 | all_56_7 & $i(all_65_10)) | (all_65_15 = all_65_18 & all_65_16 = % 18.71/3.28 | all_56_7 & vlookup(all_65_17, all_56_1) = all_65_18 & % 18.71/3.28 | vsomeType(all_56_3) = all_65_18 & vvar(all_65_17) = all_56_7 & % 18.71/3.28 | $i(all_65_18))) % 18.71/3.28 | % 18.71/3.28 | ALPHA: (27) implies: % 18.71/3.28 | (28) $i(all_65_17) % 18.71/3.28 | (29) $i(all_65_14) % 18.71/3.28 | (30) $i(all_65_13) % 18.71/3.28 | (31) $i(all_65_12) % 18.71/3.28 | (32) $i(all_65_7) % 18.71/3.28 | (33) $i(all_65_6) % 18.71/3.28 | (34) $i(all_65_5) % 18.71/3.28 | (35) (all_65_0 = 0 & all_65_2 = all_56_3 & all_65_3 = all_56_7 & % 18.71/3.28 | varrow(all_65_5, all_65_4) = all_56_3 & vtcheck(all_65_1, all_65_6, % 18.71/3.28 | all_65_4) = 0 & vbind(all_65_7, all_65_5, all_56_1) = all_65_1 & % 18.71/3.28 | vabs(all_65_7, all_65_5, all_65_6) = all_56_7 & $i(all_65_1)) | % 18.71/3.28 | (all_65_8 = 0 & all_65_9 = 0 & all_65_11 = all_56_7 & % 18.71/3.28 | varrow(all_65_12, all_56_3) = all_65_10 & vtcheck(all_56_1, % 18.71/3.28 | all_65_13, all_65_12) = 0 & vtcheck(all_56_1, all_65_14, % 18.71/3.28 | all_65_10) = 0 & vapp(all_65_14, all_65_13) = all_56_7 & % 18.71/3.28 | $i(all_65_10)) | (all_65_15 = all_65_18 & all_65_16 = all_56_7 & % 18.71/3.28 | vlookup(all_65_17, all_56_1) = all_65_18 & vsomeType(all_56_3) = % 18.71/3.28 | all_65_18 & vvar(all_65_17) = all_56_7 & $i(all_65_18)) % 18.71/3.28 | % 18.71/3.28 | BETA: splitting (35) gives: % 18.71/3.28 | % 18.71/3.28 | Case 1: % 18.71/3.28 | | % 18.71/3.28 | | (36) all_65_0 = 0 & all_65_2 = all_56_3 & all_65_3 = all_56_7 & % 18.71/3.28 | | varrow(all_65_5, all_65_4) = all_56_3 & vtcheck(all_65_1, all_65_6, % 18.71/3.28 | | all_65_4) = 0 & vbind(all_65_7, all_65_5, all_56_1) = all_65_1 & % 18.71/3.28 | | vabs(all_65_7, all_65_5, all_65_6) = all_56_7 & $i(all_65_1) % 18.71/3.28 | | % 18.71/3.28 | | ALPHA: (36) implies: % 18.71/3.28 | | (37) vabs(all_65_7, all_65_5, all_65_6) = all_56_7 % 18.71/3.28 | | % 18.71/3.28 | | GROUND_INST: instantiating (DIFF-abs-app) with all_65_7, all_65_5, all_65_6, % 18.71/3.28 | | ve1app, ve2app, all_56_7, simplifying with (8), (9), (21), % 18.71/3.28 | | (32), (33), (34), (37) gives: % 18.71/3.28 | | (38) $false % 18.71/3.28 | | % 18.71/3.28 | | CLOSE: (38) is inconsistent. % 18.71/3.28 | | % 18.71/3.28 | Case 2: % 18.71/3.28 | | % 18.71/3.28 | | (39) (all_65_8 = 0 & all_65_9 = 0 & all_65_11 = all_56_7 & % 18.71/3.28 | | varrow(all_65_12, all_56_3) = all_65_10 & vtcheck(all_56_1, % 18.71/3.28 | | all_65_13, all_65_12) = 0 & vtcheck(all_56_1, all_65_14, % 18.71/3.28 | | all_65_10) = 0 & vapp(all_65_14, all_65_13) = all_56_7 & % 18.71/3.28 | | $i(all_65_10)) | (all_65_15 = all_65_18 & all_65_16 = all_56_7 & % 18.71/3.28 | | vlookup(all_65_17, all_56_1) = all_65_18 & vsomeType(all_56_3) = % 18.71/3.28 | | all_65_18 & vvar(all_65_17) = all_56_7 & $i(all_65_18)) % 18.71/3.28 | | % 18.71/3.28 | | BETA: splitting (39) gives: % 18.71/3.28 | | % 18.71/3.28 | | Case 1: % 18.71/3.28 | | | % 18.71/3.28 | | | (40) all_65_8 = 0 & all_65_9 = 0 & all_65_11 = all_56_7 & % 18.71/3.28 | | | varrow(all_65_12, all_56_3) = all_65_10 & vtcheck(all_56_1, % 18.71/3.28 | | | all_65_13, all_65_12) = 0 & vtcheck(all_56_1, all_65_14, % 18.71/3.28 | | | all_65_10) = 0 & vapp(all_65_14, all_65_13) = all_56_7 & % 18.71/3.28 | | | $i(all_65_10) % 18.71/3.28 | | | % 18.71/3.28 | | | ALPHA: (40) implies: % 18.71/3.28 | | | (41) $i(all_65_10) % 18.71/3.28 | | | (42) vapp(all_65_14, all_65_13) = all_56_7 % 18.71/3.28 | | | (43) vtcheck(all_56_1, all_65_14, all_65_10) = 0 % 18.71/3.28 | | | (44) vtcheck(all_56_1, all_65_13, all_65_12) = 0 % 18.71/3.28 | | | (45) varrow(all_65_12, all_56_3) = all_65_10 % 18.71/3.28 | | | % 18.71/3.28 | | | GROUND_INST: instantiating (2) with ve1app, ve2app, all_65_14, all_65_13, % 18.71/3.28 | | | all_56_7, simplifying with (8), (9), (21), (29), (30), (42) % 18.71/3.28 | | | gives: % 18.71/3.28 | | | (46) all_65_13 = ve2app % 18.71/3.28 | | | % 18.71/3.28 | | | GROUND_INST: instantiating (1) with ve1app, ve2app, all_65_14, all_65_13, % 18.71/3.28 | | | all_56_7, simplifying with (8), (9), (21), (29), (30), (42) % 18.71/3.28 | | | gives: % 18.71/3.29 | | | (47) all_65_14 = ve1app % 18.71/3.29 | | | % 18.71/3.29 | | | REDUCE: (44), (46) imply: % 18.71/3.29 | | | (48) vtcheck(all_56_1, ve2app, all_65_12) = 0 % 18.71/3.29 | | | % 18.71/3.29 | | | REDUCE: (43), (47) imply: % 18.71/3.29 | | | (49) vtcheck(all_56_1, ve1app, all_65_10) = 0 % 18.71/3.29 | | | % 18.71/3.29 | | | GROUND_INST: instantiating (6) with all_56_6, all_56_5, all_56_4, % 18.71/3.29 | | | all_65_10, all_56_1, simplifying with (16), (17), (18), (23), % 18.71/3.29 | | | (41), (49) gives: % 18.71/3.29 | | | (50) ? [v0: any] : ? [v1: any] : (vtcheck(all_56_4, ve1app, % 18.71/3.29 | | | all_65_10) = v1 & visFreeVar(all_56_6, ve1app) = v0 & (v1 = 0 % 18.71/3.29 | | | | v0 = 0)) % 18.71/3.29 | | | % 18.71/3.29 | | | GROUND_INST: instantiating (7) with all_56_6, all_56_5, all_56_4, % 18.71/3.29 | | | all_65_12, all_56_1, simplifying with (16), (17), (18), (23), % 18.71/3.29 | | | (31), (48) gives: % 18.71/3.29 | | | (51) ? [v0: any] : ? [v1: any] : (vtcheck(all_56_4, ve2app, % 18.71/3.29 | | | all_65_12) = v1 & visFreeVar(all_56_6, ve2app) = v0 & (v1 = 0 % 18.71/3.29 | | | | v0 = 0)) % 18.71/3.29 | | | % 18.71/3.29 | | | DELTA: instantiating (51) with fresh symbols all_100_0, all_100_1 gives: % 18.71/3.29 | | | (52) vtcheck(all_56_4, ve2app, all_65_12) = all_100_0 & % 18.71/3.29 | | | visFreeVar(all_56_6, ve2app) = all_100_1 & (all_100_0 = 0 | % 18.71/3.29 | | | all_100_1 = 0) % 18.71/3.29 | | | % 18.71/3.29 | | | ALPHA: (52) implies: % 18.71/3.29 | | | (53) visFreeVar(all_56_6, ve2app) = all_100_1 % 18.71/3.29 | | | (54) vtcheck(all_56_4, ve2app, all_65_12) = all_100_0 % 18.71/3.29 | | | (55) all_100_0 = 0 | all_100_1 = 0 % 18.71/3.29 | | | % 18.71/3.29 | | | DELTA: instantiating (50) with fresh symbols all_102_0, all_102_1 gives: % 18.71/3.29 | | | (56) vtcheck(all_56_4, ve1app, all_65_10) = all_102_0 & % 18.71/3.29 | | | visFreeVar(all_56_6, ve1app) = all_102_1 & (all_102_0 = 0 | % 18.71/3.29 | | | all_102_1 = 0) % 18.71/3.29 | | | % 18.71/3.29 | | | ALPHA: (56) implies: % 18.71/3.29 | | | (57) visFreeVar(all_56_6, ve1app) = all_102_1 % 18.71/3.29 | | | (58) vtcheck(all_56_4, ve1app, all_65_10) = all_102_0 % 18.71/3.29 | | | (59) all_102_0 = 0 | all_102_1 = 0 % 18.71/3.29 | | | % 18.71/3.29 | | | GROUND_INST: instantiating (3) with all_56_6, all_56_7, ve1app, ve2app, % 18.71/3.29 | | | all_102_1, all_56_2, simplifying with (8), (9), (15), (16), % 18.71/3.29 | | | (21), (22), (57) gives: % 18.71/3.29 | | | (60) ? [v0: any] : (visFreeVar(all_56_6, ve2app) = v0 & ( ~ (all_56_2 % 18.71/3.29 | | | = 0) | v0 = 0 | all_102_1 = 0) & (all_56_2 = 0 | ( ~ (v0 = % 18.71/3.29 | | | 0) & ~ (all_102_1 = 0)))) % 18.71/3.29 | | | % 18.71/3.29 | | | GROUND_INST: instantiating (4) with all_56_6, all_56_7, ve1app, ve2app, % 18.71/3.29 | | | all_100_1, all_56_2, simplifying with (8), (9), (15), (16), % 18.71/3.29 | | | (21), (22), (53) gives: % 18.71/3.29 | | | (61) ? [v0: any] : (visFreeVar(all_56_6, ve1app) = v0 & ( ~ (all_56_2 % 18.71/3.29 | | | = 0) | v0 = 0 | all_100_1 = 0) & (all_56_2 = 0 | ( ~ (v0 = % 18.71/3.29 | | | 0) & ~ (all_100_1 = 0)))) % 18.71/3.29 | | | % 18.71/3.29 | | | DELTA: instantiating (61) with fresh symbol all_113_0 gives: % 18.71/3.29 | | | (62) visFreeVar(all_56_6, ve1app) = all_113_0 & ( ~ (all_56_2 = 0) | % 18.71/3.29 | | | all_113_0 = 0 | all_100_1 = 0) & (all_56_2 = 0 | ( ~ (all_113_0 % 18.71/3.29 | | | = 0) & ~ (all_100_1 = 0))) % 18.71/3.29 | | | % 18.71/3.29 | | | ALPHA: (62) implies: % 18.71/3.29 | | | (63) all_56_2 = 0 | ( ~ (all_113_0 = 0) & ~ (all_100_1 = 0)) % 18.71/3.29 | | | % 18.71/3.29 | | | DELTA: instantiating (60) with fresh symbol all_115_0 gives: % 18.71/3.29 | | | (64) visFreeVar(all_56_6, ve2app) = all_115_0 & ( ~ (all_56_2 = 0) | % 18.71/3.29 | | | all_115_0 = 0 | all_102_1 = 0) & (all_56_2 = 0 | ( ~ (all_115_0 % 18.71/3.29 | | | = 0) & ~ (all_102_1 = 0))) % 18.71/3.29 | | | % 18.71/3.29 | | | ALPHA: (64) implies: % 18.71/3.29 | | | (65) all_56_2 = 0 | ( ~ (all_115_0 = 0) & ~ (all_102_1 = 0)) % 18.71/3.29 | | | % 18.71/3.29 | | | BETA: splitting (63) gives: % 18.71/3.29 | | | % 18.71/3.29 | | | Case 1: % 18.71/3.29 | | | | % 18.71/3.29 | | | | (66) all_56_2 = 0 % 18.71/3.29 | | | | % 18.71/3.29 | | | | REDUCE: (13), (66) imply: % 18.71/3.29 | | | | (67) $false % 18.71/3.29 | | | | % 18.71/3.29 | | | | CLOSE: (67) is inconsistent. % 18.71/3.29 | | | | % 18.71/3.29 | | | Case 2: % 18.71/3.29 | | | | % 18.71/3.29 | | | | (68) ~ (all_113_0 = 0) & ~ (all_100_1 = 0) % 18.71/3.29 | | | | % 18.71/3.29 | | | | ALPHA: (68) implies: % 18.71/3.29 | | | | (69) ~ (all_100_1 = 0) % 18.71/3.29 | | | | % 18.71/3.29 | | | | BETA: splitting (55) gives: % 18.71/3.29 | | | | % 18.71/3.29 | | | | Case 1: % 18.71/3.29 | | | | | % 18.71/3.29 | | | | | (70) all_100_0 = 0 % 18.71/3.29 | | | | | % 18.71/3.29 | | | | | REDUCE: (54), (70) imply: % 18.71/3.29 | | | | | (71) vtcheck(all_56_4, ve2app, all_65_12) = 0 % 18.71/3.29 | | | | | % 18.71/3.29 | | | | | BETA: splitting (65) gives: % 18.71/3.29 | | | | | % 18.71/3.29 | | | | | Case 1: % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | (72) all_56_2 = 0 % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | REDUCE: (13), (72) imply: % 18.71/3.29 | | | | | | (73) $false % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | CLOSE: (73) is inconsistent. % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | Case 2: % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | (74) ~ (all_115_0 = 0) & ~ (all_102_1 = 0) % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | ALPHA: (74) implies: % 18.71/3.29 | | | | | | (75) ~ (all_102_1 = 0) % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | BETA: splitting (59) gives: % 18.71/3.29 | | | | | | % 18.71/3.29 | | | | | | Case 1: % 18.71/3.29 | | | | | | | % 18.71/3.29 | | | | | | | (76) all_102_0 = 0 % 18.71/3.29 | | | | | | | % 18.71/3.29 | | | | | | | REDUCE: (58), (76) imply: % 18.71/3.29 | | | | | | | (77) vtcheck(all_56_4, ve1app, all_65_10) = 0 % 18.71/3.29 | | | | | | | % 18.71/3.29 | | | | | | | GROUND_INST: instantiating (5) with all_65_12, all_56_4, ve1app, % 18.71/3.29 | | | | | | | ve2app, all_56_3, all_65_10, all_56_7, all_56_0, % 18.71/3.29 | | | | | | | simplifying with (8), (9), (18), (19), (21), (24), % 18.71/3.29 | | | | | | | (31), (45), (77) gives: % 18.71/3.29 | | | | | | | (78) all_56_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 18.71/3.29 | | | | | | | vtcheck(all_56_4, ve2app, all_65_12) = v0) % 18.71/3.29 | | | | | | | % 18.71/3.30 | | | | | | | BETA: splitting (78) gives: % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | | Case 1: % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | (79) all_56_0 = 0 % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | REDUCE: (14), (79) imply: % 18.71/3.30 | | | | | | | | (80) $false % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | CLOSE: (80) is inconsistent. % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | Case 2: % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_56_4, ve2app, % 18.71/3.30 | | | | | | | | all_65_12) = v0) % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | DELTA: instantiating (81) with fresh symbol all_158_0 gives: % 18.71/3.30 | | | | | | | | (82) ~ (all_158_0 = 0) & vtcheck(all_56_4, ve2app, % 18.71/3.30 | | | | | | | | all_65_12) = all_158_0 % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | ALPHA: (82) implies: % 18.71/3.30 | | | | | | | | (83) ~ (all_158_0 = 0) % 18.71/3.30 | | | | | | | | (84) vtcheck(all_56_4, ve2app, all_65_12) = all_158_0 % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_158_0, all_65_12, % 18.71/3.30 | | | | | | | | ve2app, all_56_4, simplifying with (71), (84) % 18.71/3.30 | | | | | | | | gives: % 18.71/3.30 | | | | | | | | (85) all_158_0 = 0 % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | REDUCE: (83), (85) imply: % 18.71/3.30 | | | | | | | | (86) $false % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | | CLOSE: (86) is inconsistent. % 18.71/3.30 | | | | | | | | % 18.71/3.30 | | | | | | | End of split % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | Case 2: % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | | (87) all_102_1 = 0 % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | | REDUCE: (75), (87) imply: % 18.71/3.30 | | | | | | | (88) $false % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | | CLOSE: (88) is inconsistent. % 18.71/3.30 | | | | | | | % 18.71/3.30 | | | | | | End of split % 18.71/3.30 | | | | | | % 18.71/3.30 | | | | | End of split % 18.71/3.30 | | | | | % 18.71/3.30 | | | | Case 2: % 18.71/3.30 | | | | | % 18.71/3.30 | | | | | (89) all_100_1 = 0 % 18.71/3.30 | | | | | % 18.71/3.30 | | | | | REDUCE: (69), (89) imply: % 18.71/3.30 | | | | | (90) $false % 18.71/3.30 | | | | | % 18.71/3.30 | | | | | CLOSE: (90) is inconsistent. % 18.71/3.30 | | | | | % 18.71/3.30 | | | | End of split % 18.71/3.30 | | | | % 18.71/3.30 | | | End of split % 18.71/3.30 | | | % 18.71/3.30 | | Case 2: % 18.71/3.30 | | | % 18.71/3.30 | | | (91) all_65_15 = all_65_18 & all_65_16 = all_56_7 & vlookup(all_65_17, % 18.71/3.30 | | | all_56_1) = all_65_18 & vsomeType(all_56_3) = all_65_18 & % 18.71/3.30 | | | vvar(all_65_17) = all_56_7 & $i(all_65_18) % 18.71/3.30 | | | % 18.71/3.30 | | | ALPHA: (91) implies: % 18.71/3.30 | | | (92) vvar(all_65_17) = all_56_7 % 18.71/3.30 | | | % 18.71/3.30 | | | GROUND_INST: instantiating (DIFF-var-app) with all_65_17, ve1app, ve2app, % 18.71/3.30 | | | all_56_7, simplifying with (8), (9), (21), (28), (92) gives: % 18.71/3.30 | | | (93) $false % 18.71/3.30 | | | % 18.71/3.30 | | | CLOSE: (93) is inconsistent. % 18.71/3.30 | | | % 18.71/3.30 | | End of split % 18.71/3.30 | | % 18.71/3.30 | End of split % 18.71/3.30 | % 18.71/3.30 End of proof % 18.71/3.30 % SZS output end Proof for theBenchmark % 18.71/3.30 % 18.71/3.30 2678ms %------------------------------------------------------------------------------