%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM136+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 : n031.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 16.11s 2.96s % Output : Proof 19.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : COM136+1 : TPTP v8.1.2. Released v6.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n031.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 13:58:26 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.93/1.29 Prover 1: Preprocessing ... % 3.93/1.29 Prover 4: Preprocessing ... % 3.93/1.34 Prover 3: Preprocessing ... % 3.93/1.34 Prover 5: Preprocessing ... % 3.93/1.34 Prover 6: Preprocessing ... % 3.93/1.34 Prover 2: Preprocessing ... % 3.93/1.35 Prover 0: Preprocessing ... % 10.90/2.23 Prover 3: Constructing countermodel ... % 10.90/2.23 Prover 1: Constructing countermodel ... % 10.90/2.24 Prover 4: Constructing countermodel ... % 10.90/2.24 Prover 6: Proving ... % 11.83/2.34 Prover 0: Proving ... % 11.83/2.40 Prover 5: Proving ... % 12.54/2.48 Prover 2: Proving ... % 16.11/2.96 Prover 0: proved (2328ms) % 16.11/2.96 % 16.11/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.11/2.96 % 16.78/2.98 Prover 3: stopped % 16.78/2.98 Prover 5: stopped % 16.78/2.98 Prover 2: stopped % 16.78/2.98 Prover 6: stopped % 16.78/3.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.78/3.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.78/3.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.78/3.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.78/3.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 17.11/3.04 Prover 4: Found proof (size 101) % 17.11/3.04 Prover 4: proved (2402ms) % 17.11/3.04 Prover 1: stopped % 17.82/3.13 Prover 8: Preprocessing ... % 17.82/3.16 Prover 7: Preprocessing ... % 17.82/3.17 Prover 10: Preprocessing ... % 17.82/3.19 Prover 13: Preprocessing ... % 18.37/3.21 Prover 11: Preprocessing ... % 18.37/3.25 Prover 7: stopped % 18.37/3.25 Prover 10: stopped % 18.91/3.27 Prover 11: stopped % 18.91/3.28 Prover 13: stopped % 18.91/3.32 Prover 8: Warning: ignoring some quantifiers % 18.91/3.33 Prover 8: Constructing countermodel ... % 18.91/3.34 Prover 8: stopped % 18.91/3.34 % 18.91/3.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.91/3.34 % 18.91/3.35 % SZS output start Proof for theBenchmark % 18.91/3.36 Assumptions after simplification: % 18.91/3.36 --------------------------------- % 18.91/3.36 % 18.91/3.36 (DIFF-abs-app) % 19.37/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.37/3.38 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~ % 19.37/3.38 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.37/3.38 % 19.37/3.38 (DIFF-var-abs) % 19.37/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 19.37/3.38 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 19.37/3.38 $i(v1) | ~ $i(v0)) % 19.37/3.38 % 19.37/3.38 (EQ-abs) % 19.37/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.37/3.39 $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1, % 19.37/3.39 v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 19.37/3.39 ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 19.37/3.39 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ % 19.37/3.39 (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 19.37/3.39 $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 19.37/3.39 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = % 19.37/3.39 v6) | ~ (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 19.37/3.39 $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.37/3.39 % 19.37/3.39 (EQ-arrow) % 19.37/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 19.37/3.39 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~ $i(v3) | ~ % 19.37/3.39 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.37/3.39 ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ % 19.37/3.39 (varrow(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.37/3.39 % 19.37/3.39 (T-Context-Duplicate) % 19.48/3.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.48/3.39 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (vtcheck(v7, v4, v5) = 0) | ~ % 19.48/3.39 (vbind(v0, v2, v6) = v7) | ~ (vbind(v0, v1, v3) = v6) | ~ $i(v5) | ~ % 19.48/3.39 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : % 19.48/3.39 (vtcheck(v8, v4, v5) = 0 & vbind(v0, v2, v3) = v8 & $i(v8))) % 19.48/3.39 % 19.48/3.39 (T-Context-Swap) % 19.48/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.48/3.40 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | v2 % 19.48/3.40 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~ % 19.48/3.40 (vbind(v0, v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 19.48/3.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ? [v12: % 19.48/3.40 int] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) = % 19.48/3.40 v11 & vbind(v0, v1, v4) = v10 & $i(v11) & $i(v10))) & ! [v0: $i] : ! % 19.48/3.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 19.48/3.40 : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~ (vtcheck(v8, v5, v6) = 0) | ~ % 19.48/3.40 (vbind(v2, v3, v7) = v8) | ~ (vbind(v0, v1, v4) = v7) | ~ $i(v6) | ~ % 19.48/3.40 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: % 19.48/3.40 $i] : ? [v10: $i] : (vtcheck(v10, v5, v6) = 0 & vbind(v2, v3, v4) = v9 & % 19.48/3.40 vbind(v0, v1, v9) = v10 & $i(v10) & $i(v9))) % 19.48/3.40 % 19.48/3.40 (T-Strong-abs) % 19.48/3.40 $i(veabs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 19.48/3.40 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] % 19.48/3.40 : ( ~ (v9 = 0) & ~ (v7 = 0) & vtcheck(v8, v6, v5) = 0 & vtcheck(v2, v6, v5) = % 19.48/3.40 v9 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 & vabs(v3, v4, veabs) % 19.48/3.40 = v6 & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 19.48/3.40 $i(v0)) % 19.48/3.40 % 19.48/3.40 (T-Strong-abs-IH) % 19.48/3.40 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 19.48/3.40 $i] : ( ~ (vtcheck(v4, veabs, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 19.48/3.40 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 19.48/3.40 (vtcheck(v2, veabs, v3) = v6 & visFreeVar(v0, veabs) = v5 & (v6 = 0 | v5 = % 19.48/3.40 0))) % 19.48/3.40 % 19.48/3.40 (T-abs) % 19.48/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.48/3.41 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~ % 19.48/3.41 (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ~ $i(v4) | ~ % 19.48/3.41 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: int] : ( % 19.48/3.41 ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8 & $i(v8))) % 19.48/3.41 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 19.48/3.41 [v5: $i] : ( ~ (vtcheck(v5, v2, v4) = 0) | ~ (vbind(v1, v3, v0) = v5) | ~ % 19.48/3.41 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? % 19.48/3.41 [v7: $i] : (varrow(v3, v4) = v7 & vtcheck(v0, v6, v7) = 0 & vabs(v1, v3, v2) % 19.48/3.41 = v6 & $i(v7) & $i(v6))) % 19.48/3.41 % 19.48/3.41 (T-inv) % 19.48/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~ % 19.48/3.41 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 19.48/3.41 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? % 19.48/3.41 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: $i] : ? [v15: $i] : ? % 19.48/3.41 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? % 19.48/3.41 [v21: int] : ($i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v9) & $i(v8) & % 19.48/3.41 $i(v7) & $i(v4) & ((v21 = 0 & v19 = v1 & v18 = v0 & varrow(v16, v17) = v1 % 19.48/3.41 & vtcheck(v20, v15, v17) = 0 & vbind(v14, v16, v2) = v20 & vabs(v14, % 19.48/3.41 v16, v15) = v0 & $i(v20)) | (v13 = 0 & v12 = 0 & v10 = v0 & % 19.48/3.41 varrow(v9, v1) = v11 & vtcheck(v2, v8, v9) = 0 & vtcheck(v2, v7, v11) % 19.48/3.41 = 0 & vapp(v7, v8) = v0 & $i(v11)) | (v6 = v3 & v5 = v0 & vlookup(v4, % 19.48/3.41 v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0 & $i(v3))))) % 19.48/3.41 % 19.48/3.41 (isFreeVar1) % 19.48/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 19.48/3.41 int] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1, % 19.48/3.41 v2) = v5) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ % 19.48/3.41 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 19.48/3.41 ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (visFreeVar(v1, v4) = % 19.48/3.41 v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) % 19.48/3.41 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] % 19.48/3.41 : ! [v2: $i] : ! [v3: $i] : ! [v4: MultipleValueBool] : ( ~ (visFreeVar(v1, % 19.48/3.41 v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2) | % 19.48/3.41 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.41 % 19.48/3.41 (function-axioms) % 19.48/3.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 19.48/3.42 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0: % 19.48/3.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 19.48/3.42 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3, % 19.48/3.42 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 19.48/3.42 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = % 19.48/3.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 19.48/3.42 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & ! % 19.48/3.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3, % 19.48/3.42 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 19.48/3.42 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~ % 19.48/3.42 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.48/3.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.48/3.42 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : ! % 19.48/3.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~ % 19.48/3.42 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 19.48/3.42 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.48/3.42 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0)) % 19.48/3.42 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 19.48/3.42 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] : % 19.48/3.42 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~ % 19.48/3.42 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 19.48/3.42 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 19.48/3.42 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) = % 19.48/3.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 19.48/3.42 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & ! % 19.48/3.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~ % 19.48/3.42 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.48/3.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~ % 19.48/3.42 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 19.48/3.42 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0)) % 19.48/3.42 % 19.48/3.42 Further assumptions not needed in the proof: % 19.48/3.42 -------------------------------------------- % 19.48/3.42 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-app, EQ-app, % 19.48/3.42 EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Weak, % 19.48/3.42 T-app, T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0, % 19.48/3.42 isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1, isValue0, % 19.48/3.42 isValue1, isValue2, lookup-INV, lookup0, lookup1, lookup2, reduce-INV, reduce0, % 19.48/3.42 reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst-INV, subst0, subst1, % 19.48/3.42 subst2, subst3, subst4, subst5 % 19.48/3.42 % 19.48/3.42 Those formulas are unsatisfiable: % 19.48/3.42 --------------------------------- % 19.48/3.42 % 19.48/3.42 Begin of proof % 19.48/3.42 | % 19.48/3.42 | ALPHA: (EQ-abs) implies: % 19.48/3.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.42 | ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~ % 19.48/3.42 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 19.48/3.42 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.42 | ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~ % 19.48/3.42 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 19.48/3.42 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.42 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.42 | ! [v5: $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ % 19.48/3.42 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 19.48/3.42 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.42 | % 19.48/3.42 | ALPHA: (isFreeVar1) implies: % 19.48/3.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.42 | ! [v5: int] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ % 19.48/3.42 | (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) | % 19.48/3.42 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.42 | % 19.48/3.42 | ALPHA: (T-Context-Swap) implies: % 19.48/3.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.43 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~ % 19.48/3.43 | (vtcheck(v8, v5, v6) = 0) | ~ (vbind(v2, v3, v7) = v8) | ~ % 19.48/3.43 | (vbind(v0, v1, v4) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 19.48/3.43 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10: % 19.48/3.43 | $i] : (vtcheck(v10, v5, v6) = 0 & vbind(v2, v3, v4) = v9 & % 19.48/3.43 | vbind(v0, v1, v9) = v10 & $i(v10) & $i(v9))) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (EQ-arrow) implies: % 19.48/3.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.43 | (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~ % 19.48/3.43 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (T-abs) implies: % 19.48/3.43 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.43 | ! [v5: $i] : ( ~ (vtcheck(v5, v2, v4) = 0) | ~ (vbind(v1, v3, v0) = % 19.48/3.43 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.48/3.43 | ? [v6: $i] : ? [v7: $i] : (varrow(v3, v4) = v7 & vtcheck(v0, v6, v7) % 19.48/3.43 | = 0 & vabs(v1, v3, v2) = v6 & $i(v7) & $i(v6))) % 19.48/3.43 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.43 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4) % 19.48/3.43 | = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) % 19.48/3.43 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: % 19.48/3.43 | $i] : ? [v9: int] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & % 19.48/3.43 | vbind(v1, v3, v0) = v8 & $i(v8))) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (T-Strong-abs-IH) implies: % 19.48/3.43 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 19.48/3.43 | ~ (vtcheck(v4, veabs, v3) = 0) | ~ (vbind(v0, v1, v2) = v4) | ~ % 19.48/3.43 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 19.48/3.43 | any] : (vtcheck(v2, veabs, v3) = v6 & visFreeVar(v0, veabs) = v5 & % 19.48/3.43 | (v6 = 0 | v5 = 0))) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (T-Strong-abs) implies: % 19.48/3.43 | (10) $i(veabs) % 19.48/3.43 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 19.48/3.43 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : % 19.48/3.43 | ( ~ (v9 = 0) & ~ (v7 = 0) & vtcheck(v8, v6, v5) = 0 & vtcheck(v2, v6, % 19.48/3.43 | v5) = v9 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 & % 19.48/3.43 | vabs(v3, v4, veabs) = v6 & $i(v8) & $i(v6) & $i(v5) & $i(v4) & % 19.48/3.43 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (function-axioms) implies: % 19.48/3.43 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 19.48/3.43 | (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0)) % 19.48/3.43 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.48/3.43 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) % 19.48/3.43 | | ~ (vtcheck(v4, v3, v2) = v0)) % 19.48/3.43 | % 19.48/3.43 | DELTA: instantiating (11) with fresh symbols all_55_0, all_55_1, all_55_2, % 19.48/3.43 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, all_55_8, all_55_9 % 19.48/3.43 | gives: % 19.48/3.43 | (14) ~ (all_55_0 = 0) & ~ (all_55_2 = 0) & vtcheck(all_55_1, all_55_3, % 19.48/3.43 | all_55_4) = 0 & vtcheck(all_55_7, all_55_3, all_55_4) = all_55_0 & % 19.48/3.43 | vbind(all_55_9, all_55_8, all_55_7) = all_55_1 & visFreeVar(all_55_9, % 19.48/3.43 | all_55_3) = all_55_2 & vabs(all_55_6, all_55_5, veabs) = all_55_3 & % 19.48/3.43 | $i(all_55_1) & $i(all_55_3) & $i(all_55_4) & $i(all_55_5) & % 19.48/3.43 | $i(all_55_6) & $i(all_55_7) & $i(all_55_8) & $i(all_55_9) % 19.48/3.43 | % 19.48/3.43 | ALPHA: (14) implies: % 19.48/3.44 | (15) ~ (all_55_2 = 0) % 19.48/3.44 | (16) ~ (all_55_0 = 0) % 19.48/3.44 | (17) $i(all_55_9) % 19.48/3.44 | (18) $i(all_55_8) % 19.48/3.44 | (19) $i(all_55_7) % 19.48/3.44 | (20) $i(all_55_6) % 19.48/3.44 | (21) $i(all_55_5) % 19.48/3.44 | (22) $i(all_55_4) % 19.48/3.44 | (23) $i(all_55_3) % 19.48/3.44 | (24) $i(all_55_1) % 19.48/3.44 | (25) vabs(all_55_6, all_55_5, veabs) = all_55_3 % 19.48/3.44 | (26) visFreeVar(all_55_9, all_55_3) = all_55_2 % 19.48/3.44 | (27) vbind(all_55_9, all_55_8, all_55_7) = all_55_1 % 19.48/3.44 | (28) vtcheck(all_55_7, all_55_3, all_55_4) = all_55_0 % 19.48/3.44 | (29) vtcheck(all_55_1, all_55_3, all_55_4) = 0 % 19.48/3.44 | % 19.48/3.44 | GROUND_INST: instantiating (7) with all_55_7, all_55_9, all_55_3, all_55_8, % 19.48/3.44 | all_55_4, all_55_1, simplifying with (17), (18), (19), (22), % 19.48/3.44 | (23), (27), (29) gives: % 19.48/3.44 | (30) ? [v0: $i] : ? [v1: $i] : (varrow(all_55_8, all_55_4) = v1 & % 19.48/3.44 | vtcheck(all_55_7, v0, v1) = 0 & vabs(all_55_9, all_55_8, all_55_3) = % 19.48/3.44 | v0 & $i(v1) & $i(v0)) % 19.48/3.44 | % 19.48/3.44 | GROUND_INST: instantiating (T-inv) with all_55_3, all_55_4, all_55_1, % 19.48/3.44 | simplifying with (22), (23), (24), (29) gives: % 19.48/3.44 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] : % 19.48/3.44 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] % 19.48/3.44 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 19.48/3.44 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18: % 19.48/3.44 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) & % 19.48/3.44 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_55_4 & v15 = all_55_3 & % 19.48/3.44 | varrow(v13, v14) = all_55_4 & vtcheck(v17, v12, v14) = 0 & % 19.48/3.44 | vbind(v11, v13, all_55_1) = v17 & vabs(v11, v13, v12) = all_55_3 % 19.48/3.44 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_55_3 & varrow(v6, % 19.48/3.44 | all_55_4) = v8 & vtcheck(all_55_1, v5, v6) = 0 & % 19.48/3.44 | vtcheck(all_55_1, v4, v8) = 0 & vapp(v4, v5) = all_55_3 & % 19.48/3.44 | $i(v8)) | (v3 = v0 & v2 = all_55_3 & vlookup(v1, all_55_1) = v0 % 19.48/3.44 | & vsomeType(all_55_4) = v0 & vvar(v1) = all_55_3 & $i(v0)))) % 19.48/3.44 | % 19.48/3.44 | DELTA: instantiating (30) with fresh symbols all_62_0, all_62_1 gives: % 19.48/3.44 | (32) varrow(all_55_8, all_55_4) = all_62_0 & vtcheck(all_55_7, all_62_1, % 19.48/3.44 | all_62_0) = 0 & vabs(all_55_9, all_55_8, all_55_3) = all_62_1 & % 19.48/3.44 | $i(all_62_0) & $i(all_62_1) % 19.48/3.44 | % 19.48/3.44 | ALPHA: (32) implies: % 19.48/3.44 | (33) $i(all_62_1) % 19.48/3.44 | (34) $i(all_62_0) % 19.48/3.44 | (35) vabs(all_55_9, all_55_8, all_55_3) = all_62_1 % 19.48/3.44 | (36) vtcheck(all_55_7, all_62_1, all_62_0) = 0 % 19.48/3.44 | (37) varrow(all_55_8, all_55_4) = all_62_0 % 19.48/3.44 | % 19.48/3.44 | DELTA: instantiating (31) with fresh symbols all_64_0, all_64_1, all_64_2, % 19.48/3.44 | all_64_3, all_64_4, all_64_5, all_64_6, all_64_7, all_64_8, all_64_9, % 19.48/3.44 | all_64_10, all_64_11, all_64_12, all_64_13, all_64_14, all_64_15, % 19.48/3.44 | all_64_16, all_64_17, all_64_18 gives: % 19.48/3.44 | (38) $i(all_64_4) & $i(all_64_5) & $i(all_64_6) & $i(all_64_7) & % 19.48/3.44 | $i(all_64_12) & $i(all_64_13) & $i(all_64_14) & $i(all_64_17) & % 19.48/3.45 | ((all_64_0 = 0 & all_64_2 = all_55_4 & all_64_3 = all_55_3 & % 19.48/3.45 | varrow(all_64_5, all_64_4) = all_55_4 & vtcheck(all_64_1, % 19.48/3.45 | all_64_6, all_64_4) = 0 & vbind(all_64_7, all_64_5, all_55_1) = % 19.48/3.45 | all_64_1 & vabs(all_64_7, all_64_5, all_64_6) = all_55_3 & % 19.48/3.45 | $i(all_64_1)) | (all_64_8 = 0 & all_64_9 = 0 & all_64_11 = % 19.48/3.45 | all_55_3 & varrow(all_64_12, all_55_4) = all_64_10 & % 19.48/3.45 | vtcheck(all_55_1, all_64_13, all_64_12) = 0 & vtcheck(all_55_1, % 19.48/3.45 | all_64_14, all_64_10) = 0 & vapp(all_64_14, all_64_13) = % 19.48/3.45 | all_55_3 & $i(all_64_10)) | (all_64_15 = all_64_18 & all_64_16 = % 19.48/3.45 | all_55_3 & vlookup(all_64_17, all_55_1) = all_64_18 & % 19.48/3.45 | vsomeType(all_55_4) = all_64_18 & vvar(all_64_17) = all_55_3 & % 19.48/3.45 | $i(all_64_18))) % 19.48/3.45 | % 19.48/3.45 | ALPHA: (38) implies: % 19.48/3.45 | (39) $i(all_64_17) % 19.48/3.45 | (40) $i(all_64_14) % 19.48/3.45 | (41) $i(all_64_13) % 19.48/3.45 | (42) $i(all_64_7) % 19.48/3.45 | (43) $i(all_64_6) % 19.48/3.45 | (44) $i(all_64_5) % 19.48/3.45 | (45) $i(all_64_4) % 19.48/3.45 | (46) (all_64_0 = 0 & all_64_2 = all_55_4 & all_64_3 = all_55_3 & % 19.48/3.45 | varrow(all_64_5, all_64_4) = all_55_4 & vtcheck(all_64_1, all_64_6, % 19.48/3.45 | all_64_4) = 0 & vbind(all_64_7, all_64_5, all_55_1) = all_64_1 & % 19.48/3.45 | vabs(all_64_7, all_64_5, all_64_6) = all_55_3 & $i(all_64_1)) | % 19.48/3.45 | (all_64_8 = 0 & all_64_9 = 0 & all_64_11 = all_55_3 & % 19.48/3.45 | varrow(all_64_12, all_55_4) = all_64_10 & vtcheck(all_55_1, % 19.48/3.45 | all_64_13, all_64_12) = 0 & vtcheck(all_55_1, all_64_14, % 19.48/3.45 | all_64_10) = 0 & vapp(all_64_14, all_64_13) = all_55_3 & % 19.48/3.45 | $i(all_64_10)) | (all_64_15 = all_64_18 & all_64_16 = all_55_3 & % 19.48/3.45 | vlookup(all_64_17, all_55_1) = all_64_18 & vsomeType(all_55_4) = % 19.48/3.45 | all_64_18 & vvar(all_64_17) = all_55_3 & $i(all_64_18)) % 19.48/3.45 | % 19.48/3.45 | GROUND_INST: instantiating (T-inv) with all_62_1, all_62_0, all_55_7, % 19.48/3.45 | simplifying with (19), (33), (34), (36) gives: % 19.48/3.45 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] : % 19.48/3.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] % 19.48/3.45 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 19.48/3.45 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18: % 19.48/3.45 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) & % 19.48/3.45 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_62_0 & v15 = all_62_1 & % 19.48/3.45 | varrow(v13, v14) = all_62_0 & vtcheck(v17, v12, v14) = 0 & % 19.48/3.45 | vbind(v11, v13, all_55_7) = v17 & vabs(v11, v13, v12) = all_62_1 % 19.48/3.45 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_62_1 & varrow(v6, % 19.48/3.45 | all_62_0) = v8 & vtcheck(all_55_7, v5, v6) = 0 & % 19.48/3.45 | vtcheck(all_55_7, v4, v8) = 0 & vapp(v4, v5) = all_62_1 & % 19.48/3.45 | $i(v8)) | (v3 = v0 & v2 = all_62_1 & vlookup(v1, all_55_7) = v0 % 19.48/3.45 | & vsomeType(all_62_0) = v0 & vvar(v1) = all_62_1 & $i(v0)))) % 19.48/3.45 | % 19.48/3.45 | DELTA: instantiating (47) with fresh symbols all_71_0, all_71_1, all_71_2, % 19.48/3.45 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9, % 19.48/3.45 | all_71_10, all_71_11, all_71_12, all_71_13, all_71_14, all_71_15, % 19.48/3.45 | all_71_16, all_71_17, all_71_18 gives: % 19.48/3.45 | (48) $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & $i(all_71_7) & % 19.48/3.45 | $i(all_71_12) & $i(all_71_13) & $i(all_71_14) & $i(all_71_17) & % 19.48/3.45 | ((all_71_0 = 0 & all_71_2 = all_62_0 & all_71_3 = all_62_1 & % 19.48/3.45 | varrow(all_71_5, all_71_4) = all_62_0 & vtcheck(all_71_1, % 19.48/3.45 | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_55_7) = % 19.48/3.45 | all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_62_1 & % 19.48/3.45 | $i(all_71_1)) | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = % 19.48/3.45 | all_62_1 & varrow(all_71_12, all_62_0) = all_71_10 & % 19.48/3.45 | vtcheck(all_55_7, all_71_13, all_71_12) = 0 & vtcheck(all_55_7, % 19.48/3.45 | all_71_14, all_71_10) = 0 & vapp(all_71_14, all_71_13) = % 19.48/3.45 | all_62_1 & $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = % 19.48/3.45 | all_62_1 & vlookup(all_71_17, all_55_7) = all_71_18 & % 19.48/3.45 | vsomeType(all_62_0) = all_71_18 & vvar(all_71_17) = all_62_1 & % 19.48/3.45 | $i(all_71_18))) % 19.48/3.45 | % 19.48/3.45 | ALPHA: (48) implies: % 19.48/3.45 | (49) $i(all_71_17) % 19.48/3.45 | (50) $i(all_71_14) % 19.48/3.45 | (51) $i(all_71_13) % 19.48/3.45 | (52) $i(all_71_7) % 19.48/3.45 | (53) $i(all_71_6) % 19.48/3.45 | (54) $i(all_71_5) % 19.48/3.45 | (55) $i(all_71_4) % 19.48/3.46 | (56) (all_71_0 = 0 & all_71_2 = all_62_0 & all_71_3 = all_62_1 & % 19.48/3.46 | varrow(all_71_5, all_71_4) = all_62_0 & vtcheck(all_71_1, all_71_6, % 19.48/3.46 | all_71_4) = 0 & vbind(all_71_7, all_71_5, all_55_7) = all_71_1 & % 19.48/3.46 | vabs(all_71_7, all_71_5, all_71_6) = all_62_1 & $i(all_71_1)) | % 19.48/3.46 | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_62_1 & % 19.48/3.46 | varrow(all_71_12, all_62_0) = all_71_10 & vtcheck(all_55_7, % 19.48/3.46 | all_71_13, all_71_12) = 0 & vtcheck(all_55_7, all_71_14, % 19.48/3.46 | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_62_1 & % 19.48/3.46 | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_62_1 & % 19.48/3.46 | vlookup(all_71_17, all_55_7) = all_71_18 & vsomeType(all_62_0) = % 19.48/3.46 | all_71_18 & vvar(all_71_17) = all_62_1 & $i(all_71_18)) % 19.48/3.46 | % 19.48/3.46 | BETA: splitting (46) gives: % 19.48/3.46 | % 19.48/3.46 | Case 1: % 19.48/3.46 | | % 19.48/3.46 | | (57) all_64_0 = 0 & all_64_2 = all_55_4 & all_64_3 = all_55_3 & % 19.48/3.46 | | varrow(all_64_5, all_64_4) = all_55_4 & vtcheck(all_64_1, all_64_6, % 19.48/3.46 | | all_64_4) = 0 & vbind(all_64_7, all_64_5, all_55_1) = all_64_1 & % 19.48/3.46 | | vabs(all_64_7, all_64_5, all_64_6) = all_55_3 & $i(all_64_1) % 19.48/3.46 | | % 19.48/3.46 | | ALPHA: (57) implies: % 19.48/3.46 | | (58) vabs(all_64_7, all_64_5, all_64_6) = all_55_3 % 19.48/3.46 | | (59) vbind(all_64_7, all_64_5, all_55_1) = all_64_1 % 19.48/3.46 | | (60) vtcheck(all_64_1, all_64_6, all_64_4) = 0 % 19.48/3.46 | | (61) varrow(all_64_5, all_64_4) = all_55_4 % 19.48/3.46 | | % 19.48/3.46 | | GROUND_INST: instantiating (3) with all_55_6, all_55_5, veabs, all_64_7, % 19.48/3.46 | | all_64_5, all_64_6, all_55_3, simplifying with (10), (20), % 19.48/3.46 | | (21), (25), (42), (43), (44), (58) gives: % 19.48/3.46 | | (62) all_64_6 = veabs % 19.48/3.46 | | % 19.48/3.46 | | GROUND_INST: instantiating (2) with all_55_6, all_55_5, veabs, all_64_7, % 19.48/3.46 | | all_64_5, all_64_6, all_55_3, simplifying with (10), (20), % 19.48/3.46 | | (21), (25), (42), (43), (44), (58) gives: % 19.48/3.46 | | (63) all_64_5 = all_55_5 % 19.48/3.46 | | % 19.48/3.46 | | GROUND_INST: instantiating (1) with all_55_6, all_55_5, veabs, all_64_7, % 19.48/3.46 | | all_64_5, all_64_6, all_55_3, simplifying with (10), (20), % 19.48/3.46 | | (21), (25), (42), (43), (44), (58) gives: % 19.48/3.46 | | (64) all_64_7 = all_55_6 % 19.48/3.46 | | % 19.48/3.46 | | GROUND_INST: instantiating (5) with all_55_9, all_55_8, all_64_7, all_64_5, % 19.48/3.46 | | all_55_7, all_64_6, all_64_4, all_55_1, all_64_1, simplifying % 19.48/3.46 | | with (17), (18), (19), (27), (42), (43), (44), (45), (59), (60) % 19.48/3.46 | | gives: % 19.48/3.46 | | (65) all_64_7 = all_55_9 | ? [v0: $i] : ? [v1: $i] : (vtcheck(v1, % 19.48/3.46 | | all_64_6, all_64_4) = 0 & vbind(all_64_7, all_64_5, all_55_7) = % 19.48/3.46 | | v0 & vbind(all_55_9, all_55_8, v0) = v1 & $i(v1) & $i(v0)) % 19.48/3.46 | | % 19.48/3.46 | | GROUND_INST: instantiating (8) with all_55_7, all_64_7, all_64_6, all_64_5, % 19.48/3.46 | | all_64_4, all_55_3, all_55_4, all_55_0, simplifying with (19), % 19.48/3.46 | | (28), (42), (43), (44), (45), (58), (61) gives: % 19.48/3.46 | | (66) all_55_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 19.48/3.46 | | vtcheck(v0, all_64_6, all_64_4) = v1 & vbind(all_64_7, all_64_5, % 19.48/3.46 | | all_55_7) = v0 & $i(v0)) % 19.48/3.46 | | % 19.48/3.46 | | REDUCE: (60), (62) imply: % 19.48/3.47 | | (67) vtcheck(all_64_1, veabs, all_64_4) = 0 % 19.48/3.47 | | % 19.48/3.47 | | REDUCE: (59), (63), (64) imply: % 19.48/3.47 | | (68) vbind(all_55_6, all_55_5, all_55_1) = all_64_1 % 19.48/3.47 | | % 19.48/3.47 | | BETA: splitting (66) gives: % 19.48/3.47 | | % 19.48/3.47 | | Case 1: % 19.48/3.47 | | | % 19.48/3.47 | | | (69) all_55_0 = 0 % 19.48/3.47 | | | % 19.48/3.47 | | | REDUCE: (16), (69) imply: % 19.48/3.47 | | | (70) $false % 19.48/3.47 | | | % 19.48/3.47 | | | CLOSE: (70) is inconsistent. % 19.48/3.47 | | | % 19.48/3.47 | | Case 2: % 19.48/3.47 | | | % 19.48/3.47 | | | (71) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & vtcheck(v0, all_64_6, % 19.48/3.47 | | | all_64_4) = v1 & vbind(all_64_7, all_64_5, all_55_7) = v0 & % 19.48/3.47 | | | $i(v0)) % 19.48/3.47 | | | % 19.48/3.47 | | | DELTA: instantiating (71) with fresh symbols all_92_0, all_92_1 gives: % 19.48/3.47 | | | (72) ~ (all_92_0 = 0) & vtcheck(all_92_1, all_64_6, all_64_4) = % 19.48/3.47 | | | all_92_0 & vbind(all_64_7, all_64_5, all_55_7) = all_92_1 & % 19.48/3.47 | | | $i(all_92_1) % 19.48/3.47 | | | % 19.48/3.47 | | | ALPHA: (72) implies: % 19.48/3.47 | | | (73) ~ (all_92_0 = 0) % 19.48/3.47 | | | (74) vbind(all_64_7, all_64_5, all_55_7) = all_92_1 % 19.48/3.47 | | | (75) vtcheck(all_92_1, all_64_6, all_64_4) = all_92_0 % 19.48/3.47 | | | % 19.48/3.47 | | | REDUCE: (62), (75) imply: % 19.48/3.47 | | | (76) vtcheck(all_92_1, veabs, all_64_4) = all_92_0 % 19.48/3.47 | | | % 19.48/3.47 | | | REDUCE: (63), (64), (74) imply: % 19.48/3.47 | | | (77) vbind(all_55_6, all_55_5, all_55_7) = all_92_1 % 19.48/3.47 | | | % 19.48/3.47 | | | BETA: splitting (56) gives: % 19.48/3.47 | | | % 19.48/3.47 | | | Case 1: % 19.48/3.47 | | | | % 19.48/3.47 | | | | (78) all_71_0 = 0 & all_71_2 = all_62_0 & all_71_3 = all_62_1 & % 19.48/3.47 | | | | varrow(all_71_5, all_71_4) = all_62_0 & vtcheck(all_71_1, % 19.48/3.47 | | | | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_55_7) % 19.48/3.47 | | | | = all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_62_1 & % 19.48/3.47 | | | | $i(all_71_1) % 19.48/3.47 | | | | % 19.48/3.47 | | | | ALPHA: (78) implies: % 19.48/3.47 | | | | (79) vabs(all_71_7, all_71_5, all_71_6) = all_62_1 % 19.48/3.47 | | | | (80) vbind(all_71_7, all_71_5, all_55_7) = all_71_1 % 19.48/3.47 | | | | (81) varrow(all_71_5, all_71_4) = all_62_0 % 19.48/3.47 | | | | % 19.48/3.47 | | | | GROUND_INST: instantiating (3) with all_55_9, all_55_8, all_55_3, % 19.48/3.47 | | | | all_71_7, all_71_5, all_71_6, all_62_1, simplifying with % 19.48/3.47 | | | | (17), (18), (23), (35), (52), (53), (54), (79) gives: % 19.48/3.47 | | | | (82) all_71_6 = all_55_3 % 19.48/3.47 | | | | % 19.48/3.47 | | | | GROUND_INST: instantiating (1) with all_55_9, all_55_8, all_55_3, % 19.48/3.47 | | | | all_71_7, all_71_5, all_71_6, all_62_1, simplifying with % 19.48/3.47 | | | | (17), (18), (23), (35), (52), (53), (54), (79) gives: % 19.48/3.47 | | | | (83) all_71_7 = all_55_9 % 19.48/3.47 | | | | % 19.48/3.47 | | | | GROUND_INST: instantiating (6) with all_55_8, all_55_4, all_71_5, % 19.48/3.47 | | | | all_71_4, all_62_0, simplifying with (18), (22), (37), % 19.48/3.47 | | | | (54), (55), (81) gives: % 19.48/3.47 | | | | (84) all_71_5 = all_55_8 % 19.48/3.47 | | | | % 19.48/3.47 | | | | REDUCE: (80), (83), (84) imply: % 19.48/3.47 | | | | (85) vbind(all_55_9, all_55_8, all_55_7) = all_71_1 % 19.48/3.47 | | | | % 19.48/3.47 | | | | GROUND_INST: instantiating (12) with all_55_1, all_71_1, all_55_7, % 19.48/3.47 | | | | all_55_8, all_55_9, simplifying with (27), (85) gives: % 19.48/3.47 | | | | (86) all_71_1 = all_55_1 % 19.48/3.47 | | | | % 19.48/3.47 | | | | BETA: splitting (65) gives: % 19.48/3.47 | | | | % 19.48/3.47 | | | | Case 1: % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | (87) all_64_7 = all_55_9 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | COMBINE_EQS: (64), (87) imply: % 19.48/3.47 | | | | | (88) all_55_6 = all_55_9 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | REDUCE: (68), (88) imply: % 19.48/3.47 | | | | | (89) vbind(all_55_9, all_55_5, all_55_1) = all_64_1 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | REDUCE: (77), (88) imply: % 19.48/3.47 | | | | | (90) vbind(all_55_9, all_55_5, all_55_7) = all_92_1 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | GROUND_INST: instantiating (T-Context-Duplicate) with all_55_9, % 19.48/3.47 | | | | | all_55_8, all_55_5, all_55_7, veabs, all_64_4, all_55_1, % 19.48/3.47 | | | | | all_64_1, simplifying with (10), (17), (18), (19), (21), % 19.48/3.47 | | | | | (27), (45), (67), (89) gives: % 19.48/3.47 | | | | | (91) ? [v0: $i] : (vtcheck(v0, veabs, all_64_4) = 0 & % 19.48/3.47 | | | | | vbind(all_55_9, all_55_5, all_55_7) = v0 & $i(v0)) % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | DELTA: instantiating (91) with fresh symbol all_145_0 gives: % 19.48/3.47 | | | | | (92) vtcheck(all_145_0, veabs, all_64_4) = 0 & vbind(all_55_9, % 19.48/3.47 | | | | | all_55_5, all_55_7) = all_145_0 & $i(all_145_0) % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | ALPHA: (92) implies: % 19.48/3.47 | | | | | (93) vbind(all_55_9, all_55_5, all_55_7) = all_145_0 % 19.48/3.47 | | | | | (94) vtcheck(all_145_0, veabs, all_64_4) = 0 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | GROUND_INST: instantiating (12) with all_92_1, all_145_0, all_55_7, % 19.48/3.47 | | | | | all_55_5, all_55_9, simplifying with (90), (93) gives: % 19.48/3.47 | | | | | (95) all_145_0 = all_92_1 % 19.48/3.47 | | | | | % 19.48/3.47 | | | | | REDUCE: (94), (95) imply: % 19.48/3.48 | | | | | (96) vtcheck(all_92_1, veabs, all_64_4) = 0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (13) with all_92_0, 0, all_64_4, veabs, % 19.48/3.48 | | | | | all_92_1, simplifying with (76), (96) gives: % 19.48/3.48 | | | | | (97) all_92_0 = 0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (73), (97) imply: % 19.48/3.48 | | | | | (98) $false % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | CLOSE: (98) is inconsistent. % 19.48/3.48 | | | | | % 19.48/3.48 | | | | Case 2: % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | (99) ~ (all_64_7 = all_55_9) % 19.48/3.48 | | | | | (100) ? [v0: $i] : ? [v1: $i] : (vtcheck(v1, all_64_6, all_64_4) % 19.48/3.48 | | | | | = 0 & vbind(all_64_7, all_64_5, all_55_7) = v0 & % 19.48/3.48 | | | | | vbind(all_55_9, all_55_8, v0) = v1 & $i(v1) & $i(v0)) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | DELTA: instantiating (100) with fresh symbols all_140_0, all_140_1 % 19.48/3.48 | | | | | gives: % 19.48/3.48 | | | | | (101) vtcheck(all_140_0, all_64_6, all_64_4) = 0 & vbind(all_64_7, % 19.48/3.48 | | | | | all_64_5, all_55_7) = all_140_1 & vbind(all_55_9, all_55_8, % 19.48/3.48 | | | | | all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | ALPHA: (101) implies: % 19.48/3.48 | | | | | (102) $i(all_140_1) % 19.48/3.48 | | | | | (103) vbind(all_55_9, all_55_8, all_140_1) = all_140_0 % 19.48/3.48 | | | | | (104) vbind(all_64_7, all_64_5, all_55_7) = all_140_1 % 19.48/3.48 | | | | | (105) vtcheck(all_140_0, all_64_6, all_64_4) = 0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (64), (99) imply: % 19.48/3.48 | | | | | (106) ~ (all_55_6 = all_55_9) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (62), (105) imply: % 19.48/3.48 | | | | | (107) vtcheck(all_140_0, veabs, all_64_4) = 0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (63), (64), (104) imply: % 19.48/3.48 | | | | | (108) vbind(all_55_6, all_55_5, all_55_7) = all_140_1 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (12) with all_92_1, all_140_1, all_55_7, % 19.48/3.48 | | | | | all_55_5, all_55_6, simplifying with (77), (108) gives: % 19.48/3.48 | | | | | (109) all_140_1 = all_92_1 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (103), (109) imply: % 19.48/3.48 | | | | | (110) vbind(all_55_9, all_55_8, all_92_1) = all_140_0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | REDUCE: (102), (109) imply: % 19.48/3.48 | | | | | (111) $i(all_92_1) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (9) with all_55_9, all_55_8, all_92_1, % 19.48/3.48 | | | | | all_64_4, all_140_0, simplifying with (17), (18), (45), % 19.48/3.48 | | | | | (107), (110), (111) gives: % 19.48/3.48 | | | | | (112) ? [v0: any] : ? [v1: any] : (vtcheck(all_92_1, veabs, % 19.48/3.48 | | | | | all_64_4) = v1 & visFreeVar(all_55_9, veabs) = v0 & (v1 = % 19.48/3.48 | | | | | 0 | v0 = 0)) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | DELTA: instantiating (112) with fresh symbols all_151_0, all_151_1 % 19.48/3.48 | | | | | gives: % 19.48/3.48 | | | | | (113) vtcheck(all_92_1, veabs, all_64_4) = all_151_0 & % 19.48/3.48 | | | | | visFreeVar(all_55_9, veabs) = all_151_1 & (all_151_0 = 0 | % 19.48/3.48 | | | | | all_151_1 = 0) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | ALPHA: (113) implies: % 19.48/3.48 | | | | | (114) visFreeVar(all_55_9, veabs) = all_151_1 % 19.48/3.48 | | | | | (115) vtcheck(all_92_1, veabs, all_64_4) = all_151_0 % 19.48/3.48 | | | | | (116) all_151_0 = 0 | all_151_1 = 0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (13) with all_92_0, all_151_0, all_64_4, % 19.48/3.48 | | | | | veabs, all_92_1, simplifying with (76), (115) gives: % 19.48/3.48 | | | | | (117) all_151_0 = all_92_0 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | BETA: splitting (116) gives: % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | Case 1: % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | (118) all_151_0 = 0 % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | COMBINE_EQS: (117), (118) imply: % 19.48/3.48 | | | | | | (119) all_92_0 = 0 % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | REDUCE: (73), (119) imply: % 19.48/3.48 | | | | | | (120) $false % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | CLOSE: (120) is inconsistent. % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | Case 2: % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | (121) all_151_1 = 0 % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | REDUCE: (114), (121) imply: % 19.48/3.48 | | | | | | (122) visFreeVar(all_55_9, veabs) = 0 % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | GROUND_INST: instantiating (4) with all_55_5, all_55_9, all_55_3, % 19.48/3.48 | | | | | | all_55_6, veabs, all_55_2, simplifying with (10), (17), % 19.48/3.48 | | | | | | (20), (21), (23), (25), (26), (122) gives: % 19.48/3.48 | | | | | | (123) all_55_2 = 0 | all_55_6 = all_55_9 % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | BETA: splitting (123) gives: % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | | Case 1: % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | (124) all_55_2 = 0 % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | REDUCE: (15), (124) imply: % 19.48/3.48 | | | | | | | (125) $false % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | CLOSE: (125) is inconsistent. % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | Case 2: % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | (126) all_55_6 = all_55_9 % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | REDUCE: (106), (126) imply: % 19.48/3.48 | | | | | | | (127) $false % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | | CLOSE: (127) is inconsistent. % 19.48/3.48 | | | | | | | % 19.48/3.48 | | | | | | End of split % 19.48/3.48 | | | | | | % 19.48/3.48 | | | | | End of split % 19.48/3.48 | | | | | % 19.48/3.48 | | | | End of split % 19.48/3.48 | | | | % 19.48/3.48 | | | Case 2: % 19.48/3.48 | | | | % 19.48/3.48 | | | | (128) (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_62_1 & % 19.48/3.48 | | | | varrow(all_71_12, all_62_0) = all_71_10 & vtcheck(all_55_7, % 19.48/3.48 | | | | all_71_13, all_71_12) = 0 & vtcheck(all_55_7, all_71_14, % 19.48/3.48 | | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_62_1 & % 19.48/3.48 | | | | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = % 19.48/3.48 | | | | all_62_1 & vlookup(all_71_17, all_55_7) = all_71_18 & % 19.48/3.48 | | | | vsomeType(all_62_0) = all_71_18 & vvar(all_71_17) = all_62_1 % 19.48/3.48 | | | | & $i(all_71_18)) % 19.48/3.48 | | | | % 19.48/3.48 | | | | BETA: splitting (128) gives: % 19.48/3.48 | | | | % 19.48/3.48 | | | | Case 1: % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | (129) all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_62_1 & % 19.48/3.48 | | | | | varrow(all_71_12, all_62_0) = all_71_10 & vtcheck(all_55_7, % 19.48/3.48 | | | | | all_71_13, all_71_12) = 0 & vtcheck(all_55_7, all_71_14, % 19.48/3.48 | | | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_62_1 & % 19.48/3.48 | | | | | $i(all_71_10) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | ALPHA: (129) implies: % 19.48/3.48 | | | | | (130) vapp(all_71_14, all_71_13) = all_62_1 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_55_9, all_55_8, % 19.48/3.48 | | | | | all_55_3, all_71_14, all_71_13, all_62_1, simplifying % 19.48/3.48 | | | | | with (17), (18), (23), (35), (50), (51), (130) gives: % 19.48/3.48 | | | | | (131) $false % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | CLOSE: (131) is inconsistent. % 19.48/3.48 | | | | | % 19.48/3.48 | | | | Case 2: % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | (132) all_71_15 = all_71_18 & all_71_16 = all_62_1 & % 19.48/3.48 | | | | | vlookup(all_71_17, all_55_7) = all_71_18 & % 19.48/3.48 | | | | | vsomeType(all_62_0) = all_71_18 & vvar(all_71_17) = all_62_1 % 19.48/3.48 | | | | | & $i(all_71_18) % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | ALPHA: (132) implies: % 19.48/3.48 | | | | | (133) vvar(all_71_17) = all_62_1 % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_71_17, all_55_9, % 19.48/3.48 | | | | | all_55_8, all_55_3, all_62_1, simplifying with (17), % 19.48/3.48 | | | | | (18), (23), (35), (49), (133) gives: % 19.48/3.48 | | | | | (134) $false % 19.48/3.48 | | | | | % 19.48/3.48 | | | | | CLOSE: (134) is inconsistent. % 19.48/3.48 | | | | | % 19.48/3.48 | | | | End of split % 19.48/3.48 | | | | % 19.48/3.48 | | | End of split % 19.48/3.48 | | | % 19.48/3.48 | | End of split % 19.48/3.48 | | % 19.48/3.48 | Case 2: % 19.48/3.48 | | % 19.48/3.49 | | (135) (all_64_8 = 0 & all_64_9 = 0 & all_64_11 = all_55_3 & % 19.48/3.49 | | varrow(all_64_12, all_55_4) = all_64_10 & vtcheck(all_55_1, % 19.48/3.49 | | all_64_13, all_64_12) = 0 & vtcheck(all_55_1, all_64_14, % 19.48/3.49 | | all_64_10) = 0 & vapp(all_64_14, all_64_13) = all_55_3 & % 19.48/3.49 | | $i(all_64_10)) | (all_64_15 = all_64_18 & all_64_16 = all_55_3 & % 19.48/3.49 | | vlookup(all_64_17, all_55_1) = all_64_18 & vsomeType(all_55_4) = % 19.48/3.49 | | all_64_18 & vvar(all_64_17) = all_55_3 & $i(all_64_18)) % 19.48/3.49 | | % 19.48/3.49 | | BETA: splitting (135) gives: % 19.48/3.49 | | % 19.48/3.49 | | Case 1: % 19.48/3.49 | | | % 19.48/3.49 | | | (136) all_64_8 = 0 & all_64_9 = 0 & all_64_11 = all_55_3 & % 19.48/3.49 | | | varrow(all_64_12, all_55_4) = all_64_10 & vtcheck(all_55_1, % 19.48/3.49 | | | all_64_13, all_64_12) = 0 & vtcheck(all_55_1, all_64_14, % 19.48/3.49 | | | all_64_10) = 0 & vapp(all_64_14, all_64_13) = all_55_3 & % 19.48/3.49 | | | $i(all_64_10) % 19.48/3.49 | | | % 19.48/3.49 | | | ALPHA: (136) implies: % 19.48/3.49 | | | (137) vapp(all_64_14, all_64_13) = all_55_3 % 19.48/3.49 | | | % 19.48/3.49 | | | GROUND_INST: instantiating (DIFF-abs-app) with all_55_6, all_55_5, veabs, % 19.48/3.49 | | | all_64_14, all_64_13, all_55_3, simplifying with (10), (20), % 19.48/3.49 | | | (21), (25), (40), (41), (137) gives: % 19.48/3.49 | | | (138) $false % 19.48/3.49 | | | % 19.48/3.49 | | | CLOSE: (138) is inconsistent. % 19.48/3.49 | | | % 19.48/3.49 | | Case 2: % 19.48/3.49 | | | % 19.48/3.49 | | | (139) all_64_15 = all_64_18 & all_64_16 = all_55_3 & vlookup(all_64_17, % 19.48/3.49 | | | all_55_1) = all_64_18 & vsomeType(all_55_4) = all_64_18 & % 19.48/3.49 | | | vvar(all_64_17) = all_55_3 & $i(all_64_18) % 19.48/3.49 | | | % 19.48/3.49 | | | ALPHA: (139) implies: % 19.48/3.49 | | | (140) vvar(all_64_17) = all_55_3 % 19.48/3.49 | | | % 19.48/3.49 | | | GROUND_INST: instantiating (DIFF-var-abs) with all_64_17, all_55_6, % 19.48/3.49 | | | all_55_5, veabs, all_55_3, simplifying with (10), (20), (21), % 19.48/3.49 | | | (25), (39), (140) gives: % 19.48/3.49 | | | (141) $false % 19.48/3.49 | | | % 19.48/3.49 | | | CLOSE: (141) is inconsistent. % 19.48/3.49 | | | % 19.48/3.49 | | End of split % 19.48/3.49 | | % 19.48/3.49 | End of split % 19.48/3.49 | % 19.48/3.49 End of proof % 19.48/3.49 % SZS output end Proof for theBenchmark % 19.48/3.49 % 19.48/3.49 2878ms %------------------------------------------------------------------------------