TSTP Solution File: COM123+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM123+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 : n010.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 18:44:31 EDT 2023
% Result : Theorem 13.75s 2.67s
% Output : Proof 17.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM123+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.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 12:55:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.59 ________ _____
% 0.21/0.59 ___ __ \_________(_)________________________________
% 0.21/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.59
% 0.21/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.59 (2023-06-19)
% 0.21/0.59
% 0.21/0.59 (c) Philipp Rümmer, 2009-2023
% 0.21/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.59 Amanda Stjerna.
% 0.21/0.59 Free software under BSD-3-Clause.
% 0.21/0.59
% 0.21/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.59
% 0.21/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.76/1.34 Prover 4: Preprocessing ...
% 3.76/1.34 Prover 1: Preprocessing ...
% 4.49/1.38 Prover 6: Preprocessing ...
% 4.49/1.38 Prover 3: Preprocessing ...
% 4.49/1.38 Prover 2: Preprocessing ...
% 4.49/1.38 Prover 5: Preprocessing ...
% 4.49/1.39 Prover 0: Preprocessing ...
% 10.78/2.21 Prover 1: Constructing countermodel ...
% 10.78/2.23 Prover 3: Constructing countermodel ...
% 10.78/2.25 Prover 6: Proving ...
% 11.44/2.28 Prover 4: Constructing countermodel ...
% 11.64/2.33 Prover 0: Proving ...
% 11.64/2.37 Prover 5: Proving ...
% 12.33/2.43 Prover 2: Proving ...
% 13.75/2.67 Prover 3: proved (2054ms)
% 13.75/2.67
% 13.75/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.75/2.67
% 13.75/2.68 Prover 6: stopped
% 13.75/2.68 Prover 5: stopped
% 13.75/2.68 Prover 0: stopped
% 13.75/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.75/2.69 Prover 2: stopped
% 13.75/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.75/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.75/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.75/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.53/2.84 Prover 13: Preprocessing ...
% 15.53/2.86 Prover 7: Preprocessing ...
% 15.53/2.87 Prover 10: Preprocessing ...
% 15.53/2.87 Prover 8: Preprocessing ...
% 15.53/2.87 Prover 4: Found proof (size 83)
% 15.53/2.87 Prover 4: proved (2255ms)
% 15.53/2.87 Prover 1: stopped
% 15.53/2.87 Prover 11: Preprocessing ...
% 15.97/2.95 Prover 10: stopped
% 15.97/2.95 Prover 7: stopped
% 16.45/2.96 Prover 11: stopped
% 16.50/2.97 Prover 13: stopped
% 16.74/3.03 Prover 8: Warning: ignoring some quantifiers
% 16.91/3.05 Prover 8: Constructing countermodel ...
% 16.91/3.06 Prover 8: stopped
% 16.91/3.06
% 16.91/3.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.91/3.06
% 16.91/3.07 % SZS output start Proof for theBenchmark
% 16.91/3.07 Assumptions after simplification:
% 16.91/3.07 ---------------------------------
% 16.91/3.07
% 16.91/3.07 (DIFF-abs-app)
% 16.91/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.91/3.09 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~
% 16.91/3.09 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.09
% 16.91/3.09 (DIFF-var-abs)
% 16.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 16.91/3.10 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.91/3.10 $i(v1) | ~ $i(v0))
% 16.91/3.10
% 16.91/3.10 (EQ-abs)
% 16.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.91/3.10 $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1,
% 16.91/3.10 v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 16.91/3.10 ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 16.91/3.10 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~
% 16.91/3.10 (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.91/3.10 $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 16.91/3.10 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) =
% 16.91/3.10 v6) | ~ (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 16.91/3.10 $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.10
% 16.91/3.10 (T-Context-Swap)
% 16.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.91/3.10 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | v2
% 16.91/3.10 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~
% 16.91/3.10 (vbind(v0, v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 16.91/3.10 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ? [v12:
% 16.91/3.10 int] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) =
% 16.91/3.10 v11 & vbind(v0, v1, v4) = v10 & $i(v11) & $i(v10))) & ! [v0: $i] : !
% 16.91/3.10 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 16.91/3.10 : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~ (vtcheck(v8, v5, v6) = 0) | ~
% 16.91/3.10 (vbind(v2, v3, v7) = v8) | ~ (vbind(v0, v1, v4) = v7) | ~ $i(v6) | ~
% 16.91/3.10 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 16.91/3.10 $i] : ? [v10: $i] : (vtcheck(v10, v5, v6) = 0 & vbind(v2, v3, v4) = v9 &
% 16.91/3.10 vbind(v0, v1, v9) = v10 & $i(v10) & $i(v9)))
% 16.91/3.10
% 16.91/3.10 (T-Weak)
% 16.91/3.11 $i(vnoType) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 16.91/3.11 $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) |
% 16.91/3.11 ~ (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 16.91/3.11 | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : (vtcheck(v2, v3, v4) = v8 &
% 16.91/3.11 vlookup(v0, v2) = v7 & $i(v7) & ( ~ (v8 = 0) | ~ (v7 = vnoType))))
% 16.91/3.11
% 16.91/3.11 (T-Weak-FreeVar-abs-1)
% 16.91/3.11 $i(veabs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 16.91/3.11 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 16.91/3.11 : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v0) & vtcheck(v8, v6, v5) = v9 &
% 16.91/3.11 vtcheck(v2, v6, v5) = 0 & vbind(v0, v1, v2) = v8 & visFreeVar(v0, v6) = v7 &
% 16.91/3.11 vabs(v3, v4, veabs) = v6 & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 16.91/3.11 $i(v2) & $i(v1) & $i(v0))
% 16.91/3.11
% 16.91/3.11 (T-Weak-FreeVar-abs-IH)
% 16.91/3.11 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 16.91/3.11 $i] : ! [v5: int] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) = v5) | ~
% 16.91/3.11 (vbind(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.91/3.11 ? [v6: any] : ? [v7: any] : (vtcheck(v2, veabs, v3) = v7 & visFreeVar(v0,
% 16.91/3.11 veabs) = v6 & ( ~ (v7 = 0) | v6 = 0)))
% 16.91/3.11
% 16.91/3.11 (T-abs)
% 16.91/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.91/3.11 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~
% 16.91/3.11 (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ~ $i(v4) | ~
% 16.91/3.11 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: int] : (
% 16.91/3.11 ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8 & $i(v8)))
% 16.91/3.11 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 16.91/3.11 [v5: $i] : ( ~ (vtcheck(v5, v2, v4) = 0) | ~ (vbind(v1, v3, v0) = v5) | ~
% 16.91/3.11 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ?
% 16.91/3.11 [v7: $i] : (varrow(v3, v4) = v7 & vtcheck(v0, v6, v7) = 0 & vabs(v1, v3, v2)
% 16.91/3.11 = v6 & $i(v7) & $i(v6)))
% 16.91/3.11
% 16.91/3.11 (T-inv)
% 16.91/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 16.91/3.11 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 16.91/3.11 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 16.91/3.11 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: $i] : ? [v15: $i] : ?
% 16.91/3.11 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ?
% 16.91/3.11 [v21: int] : ($i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v9) & $i(v8) &
% 16.91/3.11 $i(v7) & $i(v4) & ((v21 = 0 & v19 = v1 & v18 = v0 & varrow(v16, v17) = v1
% 16.91/3.11 & vtcheck(v20, v15, v17) = 0 & vbind(v14, v16, v2) = v20 & vabs(v14,
% 16.91/3.11 v16, v15) = v0 & $i(v20)) | (v13 = 0 & v12 = 0 & v10 = v0 &
% 16.91/3.11 varrow(v9, v1) = v11 & vtcheck(v2, v8, v9) = 0 & vtcheck(v2, v7, v11)
% 16.91/3.11 = 0 & vapp(v7, v8) = v0 & $i(v11)) | (v6 = v3 & v5 = v0 & vlookup(v4,
% 16.91/3.11 v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0 & $i(v3)))))
% 16.91/3.11
% 16.91/3.11 (isFreeVar1)
% 16.91/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.91/3.11 int] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~ (visFreeVar(v1,
% 16.91/3.11 v2) = v5) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~
% 16.91/3.11 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.91/3.11 ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (visFreeVar(v1, v4) =
% 16.91/3.11 v5) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4)
% 16.91/3.11 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i]
% 16.91/3.11 : ! [v2: $i] : ! [v3: $i] : ! [v4: MultipleValueBool] : ( ~ (visFreeVar(v1,
% 16.91/3.11 v3) = v4) | ~ (visFreeVar(v1, v2) = 0) | ~ (vabs(v1, v0, v3) = v2) |
% 16.91/3.11 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.11
% 16.91/3.11 (function-axioms)
% 16.91/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 16.91/3.12 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 16.91/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 16.91/3.12 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 16.91/3.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 16.91/3.12 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 16.91/3.12 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 16.91/3.12 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 16.91/3.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 16.91/3.12 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 16.91/3.12 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 16.91/3.12 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.91/3.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.91/3.12 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 16.91/3.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 16.91/3.12 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.91/3.12 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.91/3.12 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 16.91/3.12 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 16.91/3.12 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 16.91/3.12 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 16.91/3.12 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.91/3.12 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.91/3.12 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 16.91/3.12 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.91/3.12 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 16.91/3.12 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 16.91/3.12 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.91/3.12 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 16.91/3.12 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 16.91/3.12 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 16.91/3.12
% 16.91/3.12 Further assumptions not needed in the proof:
% 16.91/3.12 --------------------------------------------
% 16.91/3.12 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, DIFF-var-app, EQ-app,
% 16.91/3.12 EQ-arrow, EQ-bind, EQ-empty, EQ-noExp, EQ-noType, EQ-someExp, EQ-someType,
% 16.91/3.12 EQ-var, T-Context-Duplicate, T-Strong, T-app, T-var, gensym-is-fresh,
% 16.91/3.12 getSomeExp0, getSomeType0, isFreeVar0, isFreeVar2, isSomeExp0, isSomeExp1,
% 16.91/3.12 isSomeType0, isSomeType1, isValue0, isValue1, isValue2, lookup-INV, lookup0,
% 16.91/3.12 lookup1, lookup2, reduce-INV, reduce0, reduce1, reduce2, reduce3, reduce4,
% 16.91/3.12 reduce5, reduce6, subst-INV, subst0, subst1, subst2, subst3, subst4, subst5
% 16.91/3.12
% 16.91/3.12 Those formulas are unsatisfiable:
% 16.91/3.12 ---------------------------------
% 16.91/3.12
% 16.91/3.12 Begin of proof
% 16.91/3.12 |
% 16.91/3.12 | ALPHA: (EQ-abs) implies:
% 16.91/3.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.12 | ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~
% 16.91/3.12 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 16.91/3.12 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.12 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.12 | ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~
% 16.91/3.12 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 16.91/3.12 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.13 | ! [v5: $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~
% 16.91/3.13 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 16.91/3.13 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.13 |
% 16.91/3.13 | ALPHA: (isFreeVar1) implies:
% 16.91/3.13 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.13 | ! [v5: int] : (v5 = 0 | v3 = v1 | ~ (visFreeVar(v1, v4) = 0) | ~
% 16.91/3.13 | (visFreeVar(v1, v2) = v5) | ~ (vabs(v3, v0, v4) = v2) | ~ $i(v4) |
% 16.91/3.13 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 16.91/3.13 |
% 16.91/3.13 | ALPHA: (T-Context-Swap) implies:
% 16.91/3.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.13 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] :
% 16.91/3.13 | (v9 = 0 | v2 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3,
% 16.91/3.13 | v4) = v7) | ~ (vbind(v0, v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) |
% 16.91/3.13 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10:
% 16.91/3.13 | $i] : ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & vtcheck(v11,
% 16.91/3.13 | v5, v6) = v12 & vbind(v2, v3, v10) = v11 & vbind(v0, v1, v4) =
% 16.91/3.13 | v10 & $i(v11) & $i(v10)))
% 16.91/3.13 |
% 16.91/3.13 | ALPHA: (T-abs) implies:
% 16.91/3.13 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.13 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4)
% 16.91/3.13 | = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5)
% 16.91/3.13 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8:
% 16.91/3.13 | $i] : ? [v9: int] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 &
% 16.91/3.13 | vbind(v1, v3, v0) = v8 & $i(v8)))
% 16.91/3.13 |
% 16.91/3.13 | ALPHA: (T-Weak) implies:
% 16.91/3.13 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 16.91/3.13 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) |
% 16.91/3.13 | ~ (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.91/3.13 | $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : (vtcheck(v2, v3,
% 16.91/3.13 | v4) = v8 & vlookup(v0, v2) = v7 & $i(v7) & ( ~ (v8 = 0) | ~ (v7
% 16.91/3.13 | = vnoType))))
% 16.91/3.13 |
% 16.91/3.13 | ALPHA: (T-Weak-FreeVar-abs-IH) implies:
% 17.35/3.13 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.35/3.13 | ! [v5: int] : (v5 = 0 | ~ (vtcheck(v4, veabs, v3) = v5) | ~
% 17.35/3.13 | (vbind(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.35/3.13 | $i(v0) | ? [v6: any] : ? [v7: any] : (vtcheck(v2, veabs, v3) = v7 &
% 17.35/3.13 | visFreeVar(v0, veabs) = v6 & ( ~ (v7 = 0) | v6 = 0)))
% 17.35/3.13 |
% 17.35/3.13 | ALPHA: (T-Weak-FreeVar-abs-1) implies:
% 17.35/3.13 | (9) $i(veabs)
% 17.35/3.13 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 17.35/3.13 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] :
% 17.35/3.13 | ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v0) & vtcheck(v8, v6, v5) = v9 &
% 17.35/3.13 | vtcheck(v2, v6, v5) = 0 & vbind(v0, v1, v2) = v8 & visFreeVar(v0,
% 17.35/3.13 | v6) = v7 & vabs(v3, v4, veabs) = v6 & $i(v8) & $i(v6) & $i(v5) &
% 17.35/3.13 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.35/3.13 |
% 17.35/3.13 | ALPHA: (function-axioms) implies:
% 17.35/3.13 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.35/3.13 | (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 17.35/3.13 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.35/3.13 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1)
% 17.35/3.13 | | ~ (vtcheck(v4, v3, v2) = v0))
% 17.35/3.13 |
% 17.35/3.13 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 17.35/3.13 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9
% 17.35/3.13 | gives:
% 17.35/3.14 | (13) ~ (all_56_0 = 0) & ~ (all_56_2 = 0) & ~ (all_56_6 = all_56_9) &
% 17.35/3.14 | vtcheck(all_56_1, all_56_3, all_56_4) = all_56_0 & vtcheck(all_56_7,
% 17.35/3.14 | all_56_3, all_56_4) = 0 & vbind(all_56_9, all_56_8, all_56_7) =
% 17.35/3.14 | all_56_1 & visFreeVar(all_56_9, all_56_3) = all_56_2 & vabs(all_56_6,
% 17.35/3.14 | all_56_5, veabs) = all_56_3 & $i(all_56_1) & $i(all_56_3) &
% 17.35/3.14 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) &
% 17.35/3.14 | $i(all_56_8) & $i(all_56_9)
% 17.35/3.14 |
% 17.35/3.14 | ALPHA: (13) implies:
% 17.35/3.14 | (14) ~ (all_56_6 = all_56_9)
% 17.35/3.14 | (15) ~ (all_56_2 = 0)
% 17.35/3.14 | (16) ~ (all_56_0 = 0)
% 17.35/3.14 | (17) $i(all_56_9)
% 17.35/3.14 | (18) $i(all_56_8)
% 17.35/3.14 | (19) $i(all_56_7)
% 17.35/3.14 | (20) $i(all_56_6)
% 17.35/3.14 | (21) $i(all_56_5)
% 17.35/3.14 | (22) $i(all_56_4)
% 17.35/3.14 | (23) $i(all_56_3)
% 17.35/3.14 | (24) $i(all_56_1)
% 17.35/3.14 | (25) vabs(all_56_6, all_56_5, veabs) = all_56_3
% 17.35/3.14 | (26) visFreeVar(all_56_9, all_56_3) = all_56_2
% 17.35/3.14 | (27) vbind(all_56_9, all_56_8, all_56_7) = all_56_1
% 17.35/3.14 | (28) vtcheck(all_56_7, all_56_3, all_56_4) = 0
% 17.35/3.14 | (29) vtcheck(all_56_1, all_56_3, all_56_4) = all_56_0
% 17.35/3.14 |
% 17.35/3.14 | GROUND_INST: instantiating (T-inv) with all_56_3, all_56_4, all_56_7,
% 17.35/3.14 | simplifying with (19), (22), (23), (28) gives:
% 17.35/3.14 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 17.35/3.14 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 17.35/3.14 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 17.35/3.14 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18:
% 17.35/3.14 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) &
% 17.35/3.14 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_56_4 & v15 = all_56_3 &
% 17.35/3.14 | varrow(v13, v14) = all_56_4 & vtcheck(v17, v12, v14) = 0 &
% 17.35/3.14 | vbind(v11, v13, all_56_7) = v17 & vabs(v11, v13, v12) = all_56_3
% 17.35/3.14 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_56_3 & varrow(v6,
% 17.35/3.14 | all_56_4) = v8 & vtcheck(all_56_7, v5, v6) = 0 &
% 17.35/3.14 | vtcheck(all_56_7, v4, v8) = 0 & vapp(v4, v5) = all_56_3 &
% 17.35/3.14 | $i(v8)) | (v3 = v0 & v2 = all_56_3 & vlookup(v1, all_56_7) = v0
% 17.35/3.14 | & vsomeType(all_56_4) = v0 & vvar(v1) = all_56_3 & $i(v0))))
% 17.35/3.14 |
% 17.35/3.14 | DELTA: instantiating (30) with fresh symbols all_63_0, all_63_1, all_63_2,
% 17.35/3.14 | all_63_3, all_63_4, all_63_5, all_63_6, all_63_7, all_63_8, all_63_9,
% 17.35/3.14 | all_63_10, all_63_11, all_63_12, all_63_13, all_63_14, all_63_15,
% 17.35/3.14 | all_63_16, all_63_17, all_63_18 gives:
% 17.35/3.14 | (31) $i(all_63_4) & $i(all_63_5) & $i(all_63_6) & $i(all_63_7) &
% 17.35/3.14 | $i(all_63_12) & $i(all_63_13) & $i(all_63_14) & $i(all_63_17) &
% 17.35/3.14 | ((all_63_0 = 0 & all_63_2 = all_56_4 & all_63_3 = all_56_3 &
% 17.35/3.14 | varrow(all_63_5, all_63_4) = all_56_4 & vtcheck(all_63_1,
% 17.35/3.14 | all_63_6, all_63_4) = 0 & vbind(all_63_7, all_63_5, all_56_7) =
% 17.35/3.14 | all_63_1 & vabs(all_63_7, all_63_5, all_63_6) = all_56_3 &
% 17.35/3.14 | $i(all_63_1)) | (all_63_8 = 0 & all_63_9 = 0 & all_63_11 =
% 17.35/3.14 | all_56_3 & varrow(all_63_12, all_56_4) = all_63_10 &
% 17.35/3.14 | vtcheck(all_56_7, all_63_13, all_63_12) = 0 & vtcheck(all_56_7,
% 17.35/3.14 | all_63_14, all_63_10) = 0 & vapp(all_63_14, all_63_13) =
% 17.35/3.14 | all_56_3 & $i(all_63_10)) | (all_63_15 = all_63_18 & all_63_16 =
% 17.35/3.14 | all_56_3 & vlookup(all_63_17, all_56_7) = all_63_18 &
% 17.35/3.14 | vsomeType(all_56_4) = all_63_18 & vvar(all_63_17) = all_56_3 &
% 17.35/3.14 | $i(all_63_18)))
% 17.35/3.14 |
% 17.35/3.14 | ALPHA: (31) implies:
% 17.35/3.14 | (32) $i(all_63_17)
% 17.35/3.14 | (33) $i(all_63_14)
% 17.35/3.14 | (34) $i(all_63_13)
% 17.35/3.14 | (35) $i(all_63_7)
% 17.35/3.14 | (36) $i(all_63_6)
% 17.35/3.14 | (37) $i(all_63_5)
% 17.35/3.14 | (38) $i(all_63_4)
% 17.35/3.15 | (39) (all_63_0 = 0 & all_63_2 = all_56_4 & all_63_3 = all_56_3 &
% 17.35/3.15 | varrow(all_63_5, all_63_4) = all_56_4 & vtcheck(all_63_1, all_63_6,
% 17.35/3.15 | all_63_4) = 0 & vbind(all_63_7, all_63_5, all_56_7) = all_63_1 &
% 17.35/3.15 | vabs(all_63_7, all_63_5, all_63_6) = all_56_3 & $i(all_63_1)) |
% 17.35/3.15 | (all_63_8 = 0 & all_63_9 = 0 & all_63_11 = all_56_3 &
% 17.35/3.15 | varrow(all_63_12, all_56_4) = all_63_10 & vtcheck(all_56_7,
% 17.35/3.15 | all_63_13, all_63_12) = 0 & vtcheck(all_56_7, all_63_14,
% 17.35/3.15 | all_63_10) = 0 & vapp(all_63_14, all_63_13) = all_56_3 &
% 17.35/3.15 | $i(all_63_10)) | (all_63_15 = all_63_18 & all_63_16 = all_56_3 &
% 17.35/3.15 | vlookup(all_63_17, all_56_7) = all_63_18 & vsomeType(all_56_4) =
% 17.35/3.15 | all_63_18 & vvar(all_63_17) = all_56_3 & $i(all_63_18))
% 17.35/3.15 |
% 17.35/3.15 | BETA: splitting (39) gives:
% 17.35/3.15 |
% 17.35/3.15 | Case 1:
% 17.35/3.15 | |
% 17.35/3.15 | | (40) all_63_0 = 0 & all_63_2 = all_56_4 & all_63_3 = all_56_3 &
% 17.35/3.15 | | varrow(all_63_5, all_63_4) = all_56_4 & vtcheck(all_63_1, all_63_6,
% 17.35/3.15 | | all_63_4) = 0 & vbind(all_63_7, all_63_5, all_56_7) = all_63_1 &
% 17.35/3.15 | | vabs(all_63_7, all_63_5, all_63_6) = all_56_3 & $i(all_63_1)
% 17.35/3.15 | |
% 17.35/3.15 | | ALPHA: (40) implies:
% 17.35/3.15 | | (41) vabs(all_63_7, all_63_5, all_63_6) = all_56_3
% 17.35/3.15 | | (42) vbind(all_63_7, all_63_5, all_56_7) = all_63_1
% 17.35/3.15 | | (43) vtcheck(all_63_1, all_63_6, all_63_4) = 0
% 17.35/3.15 | | (44) varrow(all_63_5, all_63_4) = all_56_4
% 17.35/3.15 | |
% 17.35/3.15 | | GROUND_INST: instantiating (3) with all_56_6, all_56_5, veabs, all_63_7,
% 17.35/3.15 | | all_63_5, all_63_6, all_56_3, simplifying with (9), (20), (21),
% 17.35/3.15 | | (25), (35), (36), (37), (41) gives:
% 17.35/3.15 | | (45) all_63_6 = veabs
% 17.35/3.15 | |
% 17.35/3.15 | | GROUND_INST: instantiating (2) with all_56_6, all_56_5, veabs, all_63_7,
% 17.35/3.15 | | all_63_5, all_63_6, all_56_3, simplifying with (9), (20), (21),
% 17.35/3.15 | | (25), (35), (36), (37), (41) gives:
% 17.35/3.15 | | (46) all_63_5 = all_56_5
% 17.35/3.15 | |
% 17.35/3.15 | | GROUND_INST: instantiating (1) with all_56_6, all_56_5, veabs, all_63_7,
% 17.35/3.15 | | all_63_5, all_63_6, all_56_3, simplifying with (9), (20), (21),
% 17.35/3.15 | | (25), (35), (36), (37), (41) gives:
% 17.35/3.15 | | (47) all_63_7 = all_56_6
% 17.35/3.15 | |
% 17.35/3.15 | | GROUND_INST: instantiating (6) with all_56_1, all_63_7, all_63_6, all_63_5,
% 17.35/3.15 | | all_63_4, all_56_3, all_56_4, all_56_0, simplifying with (24),
% 17.35/3.15 | | (29), (35), (36), (37), (38), (41), (44) gives:
% 17.35/3.15 | | (48) all_56_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 17.35/3.15 | | vtcheck(v0, all_63_6, all_63_4) = v1 & vbind(all_63_7, all_63_5,
% 17.35/3.15 | | all_56_1) = v0 & $i(v0))
% 17.35/3.15 | |
% 17.35/3.15 | | REDUCE: (43), (45) imply:
% 17.35/3.15 | | (49) vtcheck(all_63_1, veabs, all_63_4) = 0
% 17.35/3.15 | |
% 17.35/3.15 | | REDUCE: (42), (46), (47) imply:
% 17.35/3.15 | | (50) vbind(all_56_6, all_56_5, all_56_7) = all_63_1
% 17.35/3.15 | |
% 17.35/3.15 | | BETA: splitting (48) gives:
% 17.35/3.16 | |
% 17.35/3.16 | | Case 1:
% 17.35/3.16 | | |
% 17.35/3.16 | | | (51) all_56_0 = 0
% 17.35/3.16 | | |
% 17.35/3.16 | | | REDUCE: (16), (51) imply:
% 17.35/3.16 | | | (52) $false
% 17.35/3.16 | | |
% 17.35/3.16 | | | CLOSE: (52) is inconsistent.
% 17.35/3.16 | | |
% 17.35/3.16 | | Case 2:
% 17.35/3.16 | | |
% 17.35/3.16 | | | (53) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & vtcheck(v0, all_63_6,
% 17.35/3.16 | | | all_63_4) = v1 & vbind(all_63_7, all_63_5, all_56_1) = v0 &
% 17.35/3.16 | | | $i(v0))
% 17.35/3.16 | | |
% 17.35/3.16 | | | DELTA: instantiating (53) with fresh symbols all_107_0, all_107_1 gives:
% 17.35/3.16 | | | (54) ~ (all_107_0 = 0) & vtcheck(all_107_1, all_63_6, all_63_4) =
% 17.35/3.16 | | | all_107_0 & vbind(all_63_7, all_63_5, all_56_1) = all_107_1 &
% 17.35/3.16 | | | $i(all_107_1)
% 17.35/3.16 | | |
% 17.35/3.16 | | | ALPHA: (54) implies:
% 17.35/3.16 | | | (55) ~ (all_107_0 = 0)
% 17.35/3.16 | | | (56) vbind(all_63_7, all_63_5, all_56_1) = all_107_1
% 17.35/3.16 | | | (57) vtcheck(all_107_1, all_63_6, all_63_4) = all_107_0
% 17.35/3.16 | | |
% 17.35/3.16 | | | REDUCE: (45), (57) imply:
% 17.35/3.16 | | | (58) vtcheck(all_107_1, veabs, all_63_4) = all_107_0
% 17.35/3.16 | | |
% 17.35/3.16 | | | REDUCE: (46), (47), (56) imply:
% 17.35/3.16 | | | (59) vbind(all_56_6, all_56_5, all_56_1) = all_107_1
% 17.35/3.16 | | |
% 17.35/3.16 | | | GROUND_INST: instantiating (5) with all_56_6, all_56_5, all_56_9,
% 17.35/3.16 | | | all_56_8, all_56_7, veabs, all_63_4, all_56_1, all_107_1,
% 17.35/3.16 | | | all_107_0, simplifying with (9), (17), (18), (19), (20),
% 17.35/3.16 | | | (21), (27), (38), (58), (59) gives:
% 17.35/3.16 | | | (60) all_107_0 = 0 | all_56_6 = all_56_9 | ? [v0: $i] : ? [v1: $i] :
% 17.35/3.16 | | | ? [v2: int] : ( ~ (v2 = 0) & vtcheck(v1, veabs, all_63_4) = v2 &
% 17.35/3.16 | | | vbind(all_56_6, all_56_5, all_56_7) = v0 & vbind(all_56_9,
% 17.35/3.16 | | | all_56_8, v0) = v1 & $i(v1) & $i(v0))
% 17.35/3.16 | | |
% 17.35/3.16 | | | BETA: splitting (60) gives:
% 17.35/3.16 | | |
% 17.35/3.16 | | | Case 1:
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | (61) all_107_0 = 0
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | REDUCE: (55), (61) imply:
% 17.35/3.16 | | | | (62) $false
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | CLOSE: (62) is inconsistent.
% 17.35/3.16 | | | |
% 17.35/3.16 | | | Case 2:
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | (63) all_56_6 = all_56_9 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] :
% 17.35/3.16 | | | | ( ~ (v2 = 0) & vtcheck(v1, veabs, all_63_4) = v2 &
% 17.35/3.16 | | | | vbind(all_56_6, all_56_5, all_56_7) = v0 & vbind(all_56_9,
% 17.35/3.16 | | | | all_56_8, v0) = v1 & $i(v1) & $i(v0))
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | BETA: splitting (63) gives:
% 17.35/3.16 | | | |
% 17.35/3.16 | | | | Case 1:
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | (64) all_56_6 = all_56_9
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | REDUCE: (14), (64) imply:
% 17.35/3.16 | | | | | (65) $false
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | CLOSE: (65) is inconsistent.
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | Case 2:
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 17.35/3.16 | | | | | vtcheck(v1, veabs, all_63_4) = v2 & vbind(all_56_6,
% 17.35/3.16 | | | | | all_56_5, all_56_7) = v0 & vbind(all_56_9, all_56_8, v0) =
% 17.35/3.16 | | | | | v1 & $i(v1) & $i(v0))
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | DELTA: instantiating (66) with fresh symbols all_134_0, all_134_1,
% 17.35/3.16 | | | | | all_134_2 gives:
% 17.35/3.16 | | | | | (67) ~ (all_134_0 = 0) & vtcheck(all_134_1, veabs, all_63_4) =
% 17.35/3.16 | | | | | all_134_0 & vbind(all_56_6, all_56_5, all_56_7) = all_134_2 &
% 17.35/3.16 | | | | | vbind(all_56_9, all_56_8, all_134_2) = all_134_1 &
% 17.35/3.16 | | | | | $i(all_134_1) & $i(all_134_2)
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | ALPHA: (67) implies:
% 17.35/3.16 | | | | | (68) ~ (all_134_0 = 0)
% 17.35/3.16 | | | | | (69) $i(all_134_2)
% 17.35/3.16 | | | | | (70) vbind(all_56_9, all_56_8, all_134_2) = all_134_1
% 17.35/3.16 | | | | | (71) vbind(all_56_6, all_56_5, all_56_7) = all_134_2
% 17.35/3.16 | | | | | (72) vtcheck(all_134_1, veabs, all_63_4) = all_134_0
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | GROUND_INST: instantiating (11) with all_63_1, all_134_2, all_56_7,
% 17.35/3.16 | | | | | all_56_5, all_56_6, simplifying with (50), (71) gives:
% 17.35/3.16 | | | | | (73) all_134_2 = all_63_1
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | REDUCE: (70), (73) imply:
% 17.35/3.16 | | | | | (74) vbind(all_56_9, all_56_8, all_63_1) = all_134_1
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | REDUCE: (69), (73) imply:
% 17.35/3.16 | | | | | (75) $i(all_63_1)
% 17.35/3.16 | | | | |
% 17.35/3.16 | | | | | GROUND_INST: instantiating (7) with all_56_9, all_56_8, all_63_1,
% 17.35/3.16 | | | | | veabs, all_63_4, all_134_1, all_134_0, simplifying with
% 17.35/3.16 | | | | | (9), (17), (18), (38), (72), (74), (75) gives:
% 17.35/3.17 | | | | | (76) all_134_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 17.35/3.17 | | | | | (vtcheck(all_63_1, veabs, all_63_4) = v1 & vlookup(all_56_9,
% 17.35/3.17 | | | | | all_63_1) = v0 & $i(v0) & ( ~ (v1 = 0) | ~ (v0 =
% 17.35/3.17 | | | | | vnoType)))
% 17.35/3.17 | | | | |
% 17.35/3.17 | | | | | GROUND_INST: instantiating (8) with all_56_9, all_56_8, all_63_1,
% 17.35/3.17 | | | | | all_63_4, all_134_1, all_134_0, simplifying with (17),
% 17.35/3.17 | | | | | (18), (38), (72), (74), (75) gives:
% 17.35/3.17 | | | | | (77) all_134_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.35/3.17 | | | | | (vtcheck(all_63_1, veabs, all_63_4) = v1 &
% 17.35/3.17 | | | | | visFreeVar(all_56_9, veabs) = v0 & ( ~ (v1 = 0) | v0 = 0))
% 17.35/3.17 | | | | |
% 17.35/3.17 | | | | | BETA: splitting (77) gives:
% 17.35/3.17 | | | | |
% 17.35/3.17 | | | | | Case 1:
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | (78) all_134_0 = 0
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | REDUCE: (68), (78) imply:
% 17.35/3.17 | | | | | | (79) $false
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | CLOSE: (79) is inconsistent.
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | Case 2:
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | (80) ? [v0: any] : ? [v1: any] : (vtcheck(all_63_1, veabs,
% 17.35/3.17 | | | | | | all_63_4) = v1 & visFreeVar(all_56_9, veabs) = v0 & ( ~
% 17.35/3.17 | | | | | | (v1 = 0) | v0 = 0))
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | DELTA: instantiating (80) with fresh symbols all_151_0, all_151_1
% 17.35/3.17 | | | | | | gives:
% 17.35/3.17 | | | | | | (81) vtcheck(all_63_1, veabs, all_63_4) = all_151_0 &
% 17.35/3.17 | | | | | | visFreeVar(all_56_9, veabs) = all_151_1 & ( ~ (all_151_0 =
% 17.35/3.17 | | | | | | 0) | all_151_1 = 0)
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | ALPHA: (81) implies:
% 17.35/3.17 | | | | | | (82) visFreeVar(all_56_9, veabs) = all_151_1
% 17.35/3.17 | | | | | | (83) vtcheck(all_63_1, veabs, all_63_4) = all_151_0
% 17.35/3.17 | | | | | | (84) ~ (all_151_0 = 0) | all_151_1 = 0
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | BETA: splitting (76) gives:
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | | Case 1:
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | (85) all_134_0 = 0
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | REDUCE: (68), (85) imply:
% 17.35/3.17 | | | | | | | (86) $false
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | CLOSE: (86) is inconsistent.
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | Case 2:
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | (87) ? [v0: $i] : ? [v1: any] : (vtcheck(all_63_1, veabs,
% 17.35/3.17 | | | | | | | all_63_4) = v1 & vlookup(all_56_9, all_63_1) = v0 &
% 17.35/3.17 | | | | | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | DELTA: instantiating (87) with fresh symbols all_156_0, all_156_1
% 17.35/3.17 | | | | | | | gives:
% 17.35/3.17 | | | | | | | (88) vtcheck(all_63_1, veabs, all_63_4) = all_156_0 &
% 17.35/3.17 | | | | | | | vlookup(all_56_9, all_63_1) = all_156_1 & $i(all_156_1) &
% 17.35/3.17 | | | | | | | ( ~ (all_156_0 = 0) | ~ (all_156_1 = vnoType))
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | ALPHA: (88) implies:
% 17.35/3.17 | | | | | | | (89) vtcheck(all_63_1, veabs, all_63_4) = all_156_0
% 17.35/3.17 | | | | | | | (90) ~ (all_156_0 = 0) | ~ (all_156_1 = vnoType)
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | GROUND_INST: instantiating (12) with 0, all_156_0, all_63_4,
% 17.35/3.17 | | | | | | | veabs, all_63_1, simplifying with (49), (89) gives:
% 17.35/3.17 | | | | | | | (91) all_156_0 = 0
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | GROUND_INST: instantiating (12) with all_151_0, all_156_0,
% 17.35/3.17 | | | | | | | all_63_4, veabs, all_63_1, simplifying with (83),
% 17.35/3.17 | | | | | | | (89) gives:
% 17.35/3.17 | | | | | | | (92) all_156_0 = all_151_0
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | COMBINE_EQS: (91), (92) imply:
% 17.35/3.17 | | | | | | | (93) all_151_0 = 0
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | BETA: splitting (84) gives:
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | | Case 1:
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | (94) ~ (all_151_0 = 0)
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | REDUCE: (93), (94) imply:
% 17.35/3.17 | | | | | | | | (95) $false
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | CLOSE: (95) is inconsistent.
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | Case 2:
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | (96) all_151_1 = 0
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | REDUCE: (82), (96) imply:
% 17.35/3.17 | | | | | | | | (97) visFreeVar(all_56_9, veabs) = 0
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | BETA: splitting (90) gives:
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | | Case 1:
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | (98) ~ (all_156_0 = 0)
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | REDUCE: (91), (98) imply:
% 17.35/3.17 | | | | | | | | | (99) $false
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | CLOSE: (99) is inconsistent.
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | Case 2:
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | GROUND_INST: instantiating (4) with all_56_5, all_56_9,
% 17.35/3.17 | | | | | | | | | all_56_3, all_56_6, veabs, all_56_2, simplifying
% 17.35/3.17 | | | | | | | | | with (9), (17), (20), (21), (23), (25), (26), (97)
% 17.35/3.17 | | | | | | | | | gives:
% 17.35/3.17 | | | | | | | | | (100) all_56_2 = 0 | all_56_6 = all_56_9
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | BETA: splitting (100) gives:
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | | Case 1:
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | (101) all_56_2 = 0
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | REDUCE: (15), (101) imply:
% 17.35/3.17 | | | | | | | | | | (102) $false
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | CLOSE: (102) is inconsistent.
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | Case 2:
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | (103) all_56_6 = all_56_9
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | REDUCE: (14), (103) imply:
% 17.35/3.17 | | | | | | | | | | (104) $false
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | | CLOSE: (104) is inconsistent.
% 17.35/3.17 | | | | | | | | | |
% 17.35/3.17 | | | | | | | | | End of split
% 17.35/3.17 | | | | | | | | |
% 17.35/3.17 | | | | | | | | End of split
% 17.35/3.17 | | | | | | | |
% 17.35/3.17 | | | | | | | End of split
% 17.35/3.17 | | | | | | |
% 17.35/3.17 | | | | | | End of split
% 17.35/3.17 | | | | | |
% 17.35/3.17 | | | | | End of split
% 17.35/3.17 | | | | |
% 17.35/3.17 | | | | End of split
% 17.35/3.17 | | | |
% 17.35/3.17 | | | End of split
% 17.35/3.17 | | |
% 17.35/3.17 | | End of split
% 17.35/3.17 | |
% 17.35/3.17 | Case 2:
% 17.35/3.17 | |
% 17.35/3.17 | | (105) (all_63_8 = 0 & all_63_9 = 0 & all_63_11 = all_56_3 &
% 17.35/3.17 | | varrow(all_63_12, all_56_4) = all_63_10 & vtcheck(all_56_7,
% 17.35/3.17 | | all_63_13, all_63_12) = 0 & vtcheck(all_56_7, all_63_14,
% 17.35/3.17 | | all_63_10) = 0 & vapp(all_63_14, all_63_13) = all_56_3 &
% 17.35/3.17 | | $i(all_63_10)) | (all_63_15 = all_63_18 & all_63_16 = all_56_3 &
% 17.35/3.17 | | vlookup(all_63_17, all_56_7) = all_63_18 & vsomeType(all_56_4) =
% 17.35/3.17 | | all_63_18 & vvar(all_63_17) = all_56_3 & $i(all_63_18))
% 17.35/3.17 | |
% 17.35/3.17 | | BETA: splitting (105) gives:
% 17.35/3.17 | |
% 17.35/3.17 | | Case 1:
% 17.35/3.17 | | |
% 17.35/3.18 | | | (106) all_63_8 = 0 & all_63_9 = 0 & all_63_11 = all_56_3 &
% 17.35/3.18 | | | varrow(all_63_12, all_56_4) = all_63_10 & vtcheck(all_56_7,
% 17.35/3.18 | | | all_63_13, all_63_12) = 0 & vtcheck(all_56_7, all_63_14,
% 17.35/3.18 | | | all_63_10) = 0 & vapp(all_63_14, all_63_13) = all_56_3 &
% 17.35/3.18 | | | $i(all_63_10)
% 17.35/3.18 | | |
% 17.35/3.18 | | | ALPHA: (106) implies:
% 17.35/3.18 | | | (107) vapp(all_63_14, all_63_13) = all_56_3
% 17.35/3.18 | | |
% 17.35/3.18 | | | GROUND_INST: instantiating (DIFF-abs-app) with all_56_6, all_56_5, veabs,
% 17.35/3.18 | | | all_63_14, all_63_13, all_56_3, simplifying with (9), (20),
% 17.35/3.18 | | | (21), (25), (33), (34), (107) gives:
% 17.35/3.18 | | | (108) $false
% 17.35/3.18 | | |
% 17.35/3.18 | | | CLOSE: (108) is inconsistent.
% 17.35/3.18 | | |
% 17.35/3.18 | | Case 2:
% 17.35/3.18 | | |
% 17.35/3.18 | | | (109) all_63_15 = all_63_18 & all_63_16 = all_56_3 & vlookup(all_63_17,
% 17.35/3.18 | | | all_56_7) = all_63_18 & vsomeType(all_56_4) = all_63_18 &
% 17.35/3.18 | | | vvar(all_63_17) = all_56_3 & $i(all_63_18)
% 17.35/3.18 | | |
% 17.35/3.18 | | | ALPHA: (109) implies:
% 17.35/3.18 | | | (110) vvar(all_63_17) = all_56_3
% 17.35/3.18 | | |
% 17.35/3.18 | | | GROUND_INST: instantiating (DIFF-var-abs) with all_63_17, all_56_6,
% 17.35/3.18 | | | all_56_5, veabs, all_56_3, simplifying with (9), (20), (21),
% 17.35/3.18 | | | (25), (32), (110) gives:
% 17.35/3.18 | | | (111) $false
% 17.35/3.18 | | |
% 17.35/3.18 | | | CLOSE: (111) is inconsistent.
% 17.35/3.18 | | |
% 17.35/3.18 | | End of split
% 17.35/3.18 | |
% 17.35/3.18 | End of split
% 17.35/3.18 |
% 17.35/3.18 End of proof
% 17.35/3.18 % SZS output end Proof for theBenchmark
% 17.35/3.18
% 17.35/3.18 2584ms
%------------------------------------------------------------------------------