TSTP Solution File: COM131+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM131+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 : n007.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 18:44:33 EDT 2023
% Result : Theorem 48.86s 7.04s
% Output : Proof 50.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM131+1 : TPTP v8.1.2. Released v6.4.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 12:56:13 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.60/0.60 ________ _____
% 0.60/0.60 ___ __ \_________(_)________________________________
% 0.60/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.60
% 0.60/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.60 (2023-06-19)
% 0.60/0.60
% 0.60/0.60 (c) Philipp Rümmer, 2009-2023
% 0.60/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.60 Amanda Stjerna.
% 0.60/0.60 Free software under BSD-3-Clause.
% 0.60/0.60
% 0.60/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.60
% 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.61 Running up to 7 provers in parallel.
% 0.60/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.60/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.60/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.60/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.60/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.60/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.60/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.23/1.43 Prover 1: Preprocessing ...
% 5.23/1.43 Prover 4: Preprocessing ...
% 5.93/1.46 Prover 3: Preprocessing ...
% 5.93/1.46 Prover 2: Preprocessing ...
% 5.93/1.46 Prover 6: Preprocessing ...
% 5.93/1.46 Prover 5: Preprocessing ...
% 5.93/1.46 Prover 0: Preprocessing ...
% 11.57/2.26 Prover 1: Constructing countermodel ...
% 11.57/2.26 Prover 6: Proving ...
% 12.12/2.28 Prover 3: Constructing countermodel ...
% 12.12/2.32 Prover 4: Constructing countermodel ...
% 12.73/2.37 Prover 0: Proving ...
% 12.85/2.39 Prover 5: Proving ...
% 13.13/2.47 Prover 2: Proving ...
% 48.86/7.03 Prover 4: Found proof (size 517)
% 48.86/7.04 Prover 4: proved (6417ms)
% 48.86/7.04 Prover 3: stopped
% 48.86/7.04 Prover 0: stopped
% 48.86/7.04 Prover 5: stopped
% 48.86/7.04 Prover 1: stopped
% 48.86/7.04 Prover 2: stopped
% 48.86/7.04 Prover 6: stopped
% 48.86/7.04
% 48.86/7.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.86/7.04
% 49.35/7.06 % SZS output start Proof for theBenchmark
% 49.39/7.07 Assumptions after simplification:
% 49.39/7.07 ---------------------------------
% 49.39/7.07
% 49.39/7.07 (DIFF-abs-app)
% 49.39/7.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.39/7.09 $i] : ( ~ (vapp(v3, v4) = v5) | ~ (vabs(v0, v1, v2) = v5) | ~ $i(v4) | ~
% 49.39/7.09 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.39/7.09
% 49.39/7.09 (DIFF-var-abs)
% 49.39/7.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 49.39/7.09 (vabs(v1, v2, v3) = v4) | ~ (vvar(v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 49.39/7.09 $i(v1) | ~ $i(v0))
% 49.39/7.09
% 49.39/7.09 (DIFF-var-app)
% 49.39/7.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vapp(v1, v2) =
% 49.39/7.10 v3) | ~ (vvar(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.39/7.10
% 49.39/7.10 (EQ-abs)
% 49.39/7.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.39/7.10 $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~ (vabs(v0, v1,
% 49.39/7.10 v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 49.39/7.10 ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 49.39/7.10 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~
% 49.39/7.10 (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 49.39/7.10 $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 49.39/7.10 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) =
% 49.39/7.10 v6) | ~ (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.39/7.10 $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.39/7.10
% 49.39/7.10 (EQ-app)
% 49.39/7.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 49.39/7.10 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 49.39/7.10 ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 49.39/7.10 $i] : ! [v4: $i] : (v2 = v0 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) =
% 49.39/7.10 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.39/7.10
% 49.39/7.10 (EQ-arrow)
% 49.59/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 49.59/7.11 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~ $i(v3) | ~
% 49.59/7.11 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 49.59/7.11 ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~
% 49.59/7.11 (varrow(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.59/7.11
% 49.59/7.11 (T-Context-Swap)
% 49.59/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.59/7.11 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] : (v9 = 0 | v2
% 49.59/7.11 = v0 | ~ (vtcheck(v8, v5, v6) = v9) | ~ (vbind(v2, v3, v4) = v7) | ~
% 49.59/7.11 (vbind(v0, v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 49.59/7.11 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: $i] : ? [v11: $i] : ? [v12:
% 49.59/7.11 int] : ( ~ (v12 = 0) & vtcheck(v11, v5, v6) = v12 & vbind(v2, v3, v10) =
% 49.59/7.11 v11 & vbind(v0, v1, v4) = v10 & $i(v11) & $i(v10))) & ! [v0: $i] : !
% 49.59/7.11 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 49.59/7.11 : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~ (vtcheck(v8, v5, v6) = 0) | ~
% 49.59/7.11 (vbind(v2, v3, v7) = v8) | ~ (vbind(v0, v1, v4) = v7) | ~ $i(v6) | ~
% 49.59/7.11 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 49.59/7.11 $i] : ? [v10: $i] : (vtcheck(v10, v5, v6) = 0 & vbind(v2, v3, v4) = v9 &
% 49.59/7.11 vbind(v0, v1, v9) = v10 & $i(v10) & $i(v9)))
% 49.59/7.11
% 49.59/7.11 (T-Strong)
% 49.59/7.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.59/7.11 $i] : ( ~ (vtcheck(v5, v3, v4) = 0) | ~ (vbind(v0, v1, v2) = v5) | ~
% 49.59/7.11 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 49.59/7.11 [v7: any] : (vtcheck(v2, v3, v4) = v7 & visFreeVar(v0, v3) = v6 & (v7 = 0 |
% 49.59/7.11 v6 = 0)))
% 49.59/7.11
% 49.59/7.11 (T-Weak)
% 49.59/7.11 $i(vnoType) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 49.59/7.11 $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) |
% 49.59/7.11 ~ (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 49.59/7.11 | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : (vtcheck(v2, v3, v4) = v8 &
% 49.59/7.11 vlookup(v0, v2) = v7 & $i(v7) & ( ~ (v8 = 0) | ~ (v7 = vnoType))))
% 49.59/7.11
% 49.59/7.11 (T-Weak-FreeVar)
% 49.59/7.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.59/7.12 $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~ (vbind(v0,
% 49.59/7.12 v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 49.59/7.12 $i(v0) | ? [v7: any] : ? [v8: any] : (vtcheck(v2, v3, v4) = v8 &
% 49.59/7.12 visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0)))
% 49.59/7.12
% 49.59/7.12 (T-abs)
% 49.59/7.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.59/7.12 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4) = v6) | ~
% 49.59/7.12 (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5) | ~ $i(v4) | ~
% 49.59/7.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: int] : (
% 49.59/7.12 ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 & vbind(v1, v3, v0) = v8 & $i(v8)))
% 49.59/7.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 49.59/7.12 [v5: $i] : ( ~ (vtcheck(v5, v2, v4) = 0) | ~ (vbind(v1, v3, v0) = v5) | ~
% 49.59/7.12 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ?
% 49.59/7.12 [v7: $i] : (varrow(v3, v4) = v7 & vtcheck(v0, v6, v7) = 0 & vabs(v1, v3, v2)
% 49.59/7.12 = v6 & $i(v7) & $i(v6)))
% 49.59/7.12
% 49.59/7.12 (T-app)
% 49.59/7.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 49.59/7.12 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v0, v4) = v5) | ~
% 49.59/7.12 (vtcheck(v1, v6, v4) = v7) | ~ (vtcheck(v1, v2, v5) = 0) | ~ (vapp(v2, v3)
% 49.59/7.12 = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 49.59/7.12 [v8: int] : ( ~ (v8 = 0) & vtcheck(v1, v3, v0) = v8)) & ! [v0: $i] : !
% 49.59/7.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 49.59/7.12 int] : (v6 = 0 | ~ (vtcheck(v1, v5, v4) = v6) | ~ (vtcheck(v1, v3, v0) =
% 49.59/7.12 0) | ~ (vapp(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 49.59/7.12 $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & varrow(v0,
% 49.59/7.12 v4) = v7 & vtcheck(v1, v2, v7) = v8 & $i(v7))) & ! [v0: $i] : ! [v1:
% 49.59/7.12 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 49.59/7.12 (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vtcheck(v1, v2,
% 49.59/7.12 v5) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 49.59/7.12 ? [v6: $i] : (vtcheck(v1, v6, v4) = 0 & vapp(v2, v3) = v6 & $i(v6)))
% 49.59/7.12
% 49.59/7.12 (T-inv)
% 49.59/7.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vtcheck(v2, v0, v1) = 0) | ~
% 49.59/7.12 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 49.59/7.12 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 49.59/7.12 [v11: $i] : ? [v12: int] : ? [v13: int] : ? [v14: $i] : ? [v15: $i] : ?
% 49.59/7.12 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: $i] : ?
% 49.59/7.12 [v21: int] : ($i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v9) & $i(v8) &
% 49.59/7.12 $i(v7) & $i(v4) & ((v21 = 0 & v19 = v1 & v18 = v0 & varrow(v16, v17) = v1
% 49.59/7.12 & vtcheck(v20, v15, v17) = 0 & vbind(v14, v16, v2) = v20 & vabs(v14,
% 49.59/7.12 v16, v15) = v0 & $i(v20)) | (v13 = 0 & v12 = 0 & v10 = v0 &
% 49.59/7.12 varrow(v9, v1) = v11 & vtcheck(v2, v8, v9) = 0 & vtcheck(v2, v7, v11)
% 49.59/7.12 = 0 & vapp(v7, v8) = v0 & $i(v11)) | (v6 = v3 & v5 = v0 & vlookup(v4,
% 49.59/7.12 v2) = v3 & vsomeType(v1) = v3 & vvar(v4) = v0 & $i(v3)))))
% 49.59/7.12
% 49.59/7.12 (T-subst-IH-abs)
% 49.59/7.13 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 49.59/7.13 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vsubst(v2,
% 49.59/7.13 v3, veabs) = v6) | ~ (vtcheck(v5, veabs, v4) = 0) | ~ (vtcheck(v1, v6,
% 49.59/7.13 v4) = v7) | ~ (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.59/7.13 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & vtcheck(v1,
% 49.59/7.13 v3, v0) = v8)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 49.59/7.13 ! [v4: $i] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vsubst(v2, v3, veabs)
% 49.59/7.13 = v5) | ~ (vtcheck(v1, v5, v4) = v6) | ~ (vtcheck(v1, v3, v0) = 0) | ~
% 49.59/7.13 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ?
% 49.59/7.13 [v8: int] : ( ~ (v8 = 0) & vtcheck(v7, veabs, v4) = v8 & vbind(v2, v0, v1) =
% 49.59/7.13 v7 & $i(v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 49.59/7.13 [v4: $i] : ! [v5: $i] : ( ~ (vtcheck(v5, veabs, v4) = 0) | ~ (vtcheck(v1,
% 49.59/7.13 v3, v0) = 0) | ~ (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.59/7.13 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vsubst(v2, v3, veabs) = v6 &
% 49.59/7.13 vtcheck(v1, v6, v4) = 0 & $i(v6)))
% 49.59/7.13
% 49.59/7.13 (T-subst-abs-2)
% 49.59/7.13 $i(veabs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 49.59/7.13 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] :
% 49.59/7.13 ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) & ~ (v7 = 0) & ~ (v4 = v2) &
% 49.59/7.13 vsubst(v2, v3, v9) = v10 & vtcheck(v8, v9, v6) = 0 & vtcheck(v1, v10, v6) =
% 49.59/7.13 v11 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0, v1) = v8 & visFreeVar(v4, v3)
% 49.59/7.13 = v7 & vabs(v4, v5, veabs) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v6) &
% 49.59/7.13 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 49.59/7.13
% 49.59/7.13 (lookup-INV)
% 49.59/7.13 $i(vnoType) & $i(vempty) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 49.59/7.13 (vlookup(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 49.59/7.13 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 49.59/7.13 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 49.59/7.13 $i] : ? [v15: $i] : ($i(v15) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 49.59/7.13 $i(v6) & $i(v5) & $i(v4) & $i(v3) & ((v15 = v0 & v2 = vnoType & v1 =
% 49.59/7.13 vempty) | (v14 = v2 & v13 = v1 & v11 = v0 & v10 = v0 & vsomeType(v12)
% 49.59/7.13 = v2 & vbind(v0, v12, v9) = v1) | (v8 = v2 & v7 = v1 & v5 = v0 & ~
% 49.59/7.13 (v4 = v0) & vlookup(v0, v6) = v2 & vbind(v4, v3, v6) = v1))))
% 49.59/7.13
% 49.59/7.13 (subst-INV)
% 49.59/7.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsubst(v0, v1,
% 49.59/7.14 v2) = v3) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i]
% 49.59/7.14 : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 49.59/7.14 [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ?
% 49.59/7.14 [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ?
% 49.59/7.14 [v20: int] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ?
% 49.59/7.14 [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ?
% 49.59/7.14 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ?
% 49.59/7.14 [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? [v38: $i] : ? [v39: $i] : ?
% 49.59/7.14 [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? [v43: $i] : ? [v44: $i] : ?
% 49.59/7.14 [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? [v48: $i] : ? [v49: $i] : ?
% 49.59/7.14 [v50: $i] : ($i(v49) & $i(v48) & $i(v47) & $i(v45) & $i(v44) & $i(v43) &
% 49.59/7.14 $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v33) & $i(v32) & $i(v31) &
% 49.59/7.14 $i(v30) & $i(v29) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 49.59/7.14 $i(v13) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ((v50 = v2 & v49 =
% 49.59/7.14 v1 & v48 = v0 & v47 = v0 & v3 = v1 & vvar(v0) = v2) | (v46 = v2 & v44
% 49.59/7.14 = v0 & v43 = v1 & v3 = v2 & ~ (v45 = v0) & vvar(v45) = v2) | (v42 =
% 49.59/7.14 v3 & v39 = v2 & v37 = v1 & v36 = v0 & vsubst(v0, v1, v38) = v41 &
% 49.59/7.14 vsubst(v0, v1, v35) = v40 & vapp(v40, v41) = v3 & vapp(v35, v38) = v2
% 49.59/7.14 & $i(v41) & $i(v40)) | (v34 = v2 & v31 = v0 & v30 = v0 & v29 = v1 & v3
% 49.59/7.14 = v2 & vabs(v0, v32, v33) = v2) | (v28 = v3 & v24 = v17 & v20 = 0 &
% 49.59/7.14 v19 = v2 & v14 = v1 & v13 = v0 & ~ (v16 = v0) & vsubst(v16, v25, v18)
% 49.59/7.14 = v26 & vsubst(v0, v1, v27) = v3 & vgensym(v23) = v17 &
% 49.59/7.14 visFreeVar(v16, v1) = 0 & vapp(v21, v22) = v23 & vapp(v1, v18) = v21 &
% 49.59/7.14 vabs(v17, v15, v26) = v27 & vabs(v16, v15, v18) = v2 & vvar(v17) = v25
% 49.59/7.14 & vvar(v0) = v22 & $i(v27) & $i(v26) & $i(v25) & $i(v23) & $i(v22) &
% 49.59/7.14 $i(v21)) | (v12 = v3 & v9 = v2 & v7 = v1 & v6 = v0 & ~ (v10 = 0) & ~
% 49.59/7.14 (v4 = v0) & vsubst(v0, v1, v8) = v11 & visFreeVar(v4, v1) = v10 &
% 49.59/7.14 vabs(v4, v5, v11) = v3 & vabs(v4, v5, v8) = v2 & $i(v11)))))
% 49.59/7.14
% 49.59/7.14 (function-axioms)
% 49.75/7.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 49.75/7.14 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 49.75/7.14 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 49.75/7.14 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 49.75/7.14 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 49.75/7.14 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 49.75/7.14 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 49.75/7.14 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 49.75/7.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 49.75/7.14 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 49.75/7.14 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 49.75/7.14 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 49.75/7.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 49.75/7.14 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 49.75/7.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 49.75/7.14 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 49.75/7.14 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 49.75/7.14 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 49.75/7.14 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 49.75/7.14 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 49.75/7.14 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 49.75/7.14 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 49.75/7.14 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 49.75/7.14 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 49.75/7.14 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 49.75/7.14 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 49.75/7.14 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 49.75/7.14 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 49.75/7.14 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 49.75/7.14 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 49.75/7.14 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 49.75/7.14
% 49.75/7.14 Further assumptions not needed in the proof:
% 49.75/7.14 --------------------------------------------
% 49.75/7.14 DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType, EQ-bind, EQ-empty,
% 49.75/7.14 EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Context-Duplicate,
% 49.75/7.14 T-subst-abs-1, T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0,
% 49.75/7.14 isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1,
% 49.75/7.14 isValue0, isValue1, isValue2, lookup0, lookup1, lookup2, reduce-INV, reduce0,
% 49.75/7.14 reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst0, subst1, subst2,
% 49.75/7.14 subst3, subst4, subst5
% 49.75/7.14
% 49.75/7.14 Those formulas are unsatisfiable:
% 49.75/7.14 ---------------------------------
% 49.75/7.14
% 49.75/7.14 Begin of proof
% 49.75/7.14 |
% 49.75/7.15 | ALPHA: (EQ-abs) implies:
% 49.75/7.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | ! [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~
% 49.75/7.15 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.75/7.15 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | ! [v5: $i] : ! [v6: $i] : (v4 = v1 | ~ (vabs(v3, v4, v5) = v6) | ~
% 49.75/7.15 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.75/7.15 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | ! [v5: $i] : ! [v6: $i] : (v5 = v2 | ~ (vabs(v3, v4, v5) = v6) | ~
% 49.75/7.15 | (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 49.75/7.15 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.15 |
% 49.75/7.15 | ALPHA: (EQ-app) implies:
% 49.75/7.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | (v3 = v1 | ~ (vapp(v2, v3) = v4) | ~ (vapp(v0, v1) = v4) | ~ $i(v3)
% 49.75/7.15 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.15 |
% 49.75/7.15 | ALPHA: (lookup-INV) implies:
% 49.75/7.15 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vlookup(v0, v1) = v2) |
% 49.75/7.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ?
% 49.75/7.15 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 49.75/7.15 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i]
% 49.75/7.15 | : ? [v15: $i] : ($i(v15) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 49.75/7.15 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ((v15 = v0 & v2 = vnoType & v1
% 49.75/7.15 | = vempty) | (v14 = v2 & v13 = v1 & v11 = v0 & v10 = v0 &
% 49.75/7.15 | vsomeType(v12) = v2 & vbind(v0, v12, v9) = v1) | (v8 = v2 & v7
% 49.75/7.15 | = v1 & v5 = v0 & ~ (v4 = v0) & vlookup(v0, v6) = v2 &
% 49.75/7.15 | vbind(v4, v3, v6) = v1))))
% 49.75/7.15 |
% 49.75/7.15 | ALPHA: (T-Context-Swap) implies:
% 49.75/7.15 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v2 = v0 | ~
% 49.75/7.15 | (vtcheck(v8, v5, v6) = 0) | ~ (vbind(v2, v3, v7) = v8) | ~
% 49.75/7.15 | (vbind(v0, v1, v4) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 49.75/7.15 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: $i] : ? [v10:
% 49.75/7.15 | $i] : (vtcheck(v10, v5, v6) = 0 & vbind(v2, v3, v4) = v9 &
% 49.75/7.15 | vbind(v0, v1, v9) = v10 & $i(v10) & $i(v9)))
% 49.75/7.15 |
% 49.75/7.15 | ALPHA: (EQ-arrow) implies:
% 49.75/7.15 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.15 | (v2 = v0 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~
% 49.75/7.16 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.16 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | (v3 = v1 | ~ (varrow(v2, v3) = v4) | ~ (varrow(v0, v1) = v4) | ~
% 49.75/7.16 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (T-abs) implies:
% 49.75/7.16 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | ! [v5: $i] : ( ~ (vtcheck(v5, v2, v4) = 0) | ~ (vbind(v1, v3, v0) =
% 49.75/7.16 | v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 49.75/7.16 | ? [v6: $i] : ? [v7: $i] : (varrow(v3, v4) = v7 & vtcheck(v0, v6, v7)
% 49.75/7.16 | = 0 & vabs(v1, v3, v2) = v6 & $i(v7) & $i(v6)))
% 49.75/7.16 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (varrow(v3, v4)
% 49.75/7.16 | = v6) | ~ (vtcheck(v0, v5, v6) = v7) | ~ (vabs(v1, v3, v2) = v5)
% 49.75/7.16 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 49.75/7.16 | [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & vtcheck(v8, v2, v4) = v9 &
% 49.75/7.16 | vbind(v1, v3, v0) = v8 & $i(v8)))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (T-app) implies:
% 49.75/7.16 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | ! [v5: $i] : ( ~ (varrow(v0, v4) = v5) | ~ (vtcheck(v1, v3, v0) = 0)
% 49.75/7.16 | | ~ (vtcheck(v1, v2, v5) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 49.75/7.16 | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vtcheck(v1, v6, v4) = 0 &
% 49.75/7.16 | vapp(v2, v3) = v6 & $i(v6)))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (T-Weak) implies:
% 49.75/7.16 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) |
% 49.75/7.16 | ~ (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 49.75/7.16 | $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : (vtcheck(v2, v3,
% 49.75/7.16 | v4) = v8 & vlookup(v0, v2) = v7 & $i(v7) & ( ~ (v8 = 0) | ~ (v7
% 49.75/7.16 | = vnoType))))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (T-subst-IH-abs) implies:
% 49.75/7.16 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (vsubst(v2, v3,
% 49.75/7.16 | veabs) = v6) | ~ (vtcheck(v5, veabs, v4) = 0) | ~ (vtcheck(v1,
% 49.75/7.16 | v6, v4) = v7) | ~ (vbind(v2, v0, v1) = v5) | ~ $i(v4) | ~
% 49.75/7.16 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8
% 49.75/7.16 | = 0) & vtcheck(v1, v3, v0) = v8))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (T-subst-abs-2) implies:
% 49.75/7.16 | (14) $i(veabs)
% 49.75/7.16 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 49.75/7.16 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: $i] :
% 49.75/7.16 | ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) & ~ (v7 = 0) & ~ (v4 =
% 49.75/7.16 | v2) & vsubst(v2, v3, v9) = v10 & vtcheck(v8, v9, v6) = 0 &
% 49.75/7.16 | vtcheck(v1, v10, v6) = v11 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0,
% 49.75/7.16 | v1) = v8 & visFreeVar(v4, v3) = v7 & vabs(v4, v5, veabs) = v9 &
% 49.75/7.16 | $i(v10) & $i(v9) & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 49.75/7.16 | $i(v2) & $i(v1) & $i(v0))
% 49.75/7.16 |
% 49.75/7.16 | ALPHA: (function-axioms) implies:
% 49.75/7.16 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 49.75/7.16 | : ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~
% 49.75/7.16 | (visFreeVar(v3, v2) = v0))
% 49.75/7.16 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 49.75/7.16 | (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 49.75/7.16 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 49.75/7.16 | (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) = v0))
% 49.75/7.17 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 49.75/7.17 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1)
% 49.75/7.17 | | ~ (vtcheck(v4, v3, v2) = v0))
% 49.75/7.17 |
% 49.75/7.17 | DELTA: instantiating (15) with fresh symbols all_58_0, all_58_1, all_58_2,
% 49.75/7.17 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 49.75/7.17 | all_58_10, all_58_11 gives:
% 49.75/7.17 | (20) ~ (all_58_0 = 0) & ~ (all_58_4 = 0) & ~ (all_58_7 = all_58_9) &
% 49.75/7.17 | vsubst(all_58_9, all_58_8, all_58_2) = all_58_1 & vtcheck(all_58_3,
% 49.75/7.17 | all_58_2, all_58_5) = 0 & vtcheck(all_58_10, all_58_1, all_58_5) =
% 49.75/7.17 | all_58_0 & vtcheck(all_58_10, all_58_8, all_58_11) = 0 &
% 49.75/7.17 | vbind(all_58_9, all_58_11, all_58_10) = all_58_3 &
% 49.75/7.17 | visFreeVar(all_58_7, all_58_8) = all_58_4 & vabs(all_58_7, all_58_6,
% 49.75/7.17 | veabs) = all_58_2 & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) &
% 49.75/7.17 | $i(all_58_5) & $i(all_58_6) & $i(all_58_7) & $i(all_58_8) &
% 49.75/7.17 | $i(all_58_9) & $i(all_58_10) & $i(all_58_11)
% 49.75/7.17 |
% 49.75/7.17 | ALPHA: (20) implies:
% 49.75/7.17 | (21) ~ (all_58_7 = all_58_9)
% 49.75/7.17 | (22) ~ (all_58_4 = 0)
% 49.75/7.17 | (23) ~ (all_58_0 = 0)
% 49.75/7.17 | (24) $i(all_58_11)
% 49.75/7.17 | (25) $i(all_58_10)
% 49.75/7.17 | (26) $i(all_58_9)
% 49.75/7.17 | (27) $i(all_58_8)
% 49.75/7.17 | (28) $i(all_58_7)
% 49.75/7.17 | (29) $i(all_58_6)
% 49.75/7.17 | (30) $i(all_58_5)
% 49.75/7.17 | (31) $i(all_58_3)
% 49.75/7.17 | (32) $i(all_58_2)
% 49.75/7.17 | (33) $i(all_58_1)
% 49.75/7.17 | (34) vabs(all_58_7, all_58_6, veabs) = all_58_2
% 49.75/7.17 | (35) visFreeVar(all_58_7, all_58_8) = all_58_4
% 49.75/7.17 | (36) vbind(all_58_9, all_58_11, all_58_10) = all_58_3
% 49.75/7.17 | (37) vtcheck(all_58_10, all_58_8, all_58_11) = 0
% 49.75/7.17 | (38) vtcheck(all_58_10, all_58_1, all_58_5) = all_58_0
% 49.75/7.17 | (39) vtcheck(all_58_3, all_58_2, all_58_5) = 0
% 49.75/7.17 | (40) vsubst(all_58_9, all_58_8, all_58_2) = all_58_1
% 49.75/7.17 |
% 49.75/7.17 | GROUND_INST: instantiating (T-Strong) with all_58_9, all_58_11, all_58_10,
% 49.75/7.17 | all_58_2, all_58_5, all_58_3, simplifying with (24), (25), (26),
% 49.75/7.17 | (30), (32), (36), (39) gives:
% 49.75/7.17 | (41) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_10, all_58_2, all_58_5)
% 49.75/7.17 | = v1 & visFreeVar(all_58_9, all_58_2) = v0 & (v1 = 0 | v0 = 0))
% 49.75/7.17 |
% 49.75/7.17 | GROUND_INST: instantiating (9) with all_58_10, all_58_9, all_58_2, all_58_11,
% 49.75/7.17 | all_58_5, all_58_3, simplifying with (24), (25), (26), (30),
% 49.75/7.17 | (32), (36), (39) gives:
% 49.75/7.17 | (42) ? [v0: $i] : ? [v1: $i] : (varrow(all_58_11, all_58_5) = v1 &
% 49.75/7.17 | vtcheck(all_58_10, v0, v1) = 0 & vabs(all_58_9, all_58_11, all_58_2)
% 49.75/7.17 | = v0 & $i(v1) & $i(v0))
% 49.75/7.17 |
% 49.75/7.17 | GROUND_INST: instantiating (T-inv) with all_58_2, all_58_5, all_58_3,
% 49.75/7.17 | simplifying with (30), (31), (32), (39) gives:
% 49.75/7.17 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 49.75/7.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 49.75/7.17 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 49.75/7.17 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18:
% 49.75/7.17 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) &
% 49.75/7.17 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_58_5 & v15 = all_58_2 &
% 49.75/7.17 | varrow(v13, v14) = all_58_5 & vtcheck(v17, v12, v14) = 0 &
% 49.75/7.17 | vbind(v11, v13, all_58_3) = v17 & vabs(v11, v13, v12) = all_58_2
% 49.75/7.17 | & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_58_2 & varrow(v6,
% 49.75/7.17 | all_58_5) = v8 & vtcheck(all_58_3, v5, v6) = 0 &
% 49.75/7.17 | vtcheck(all_58_3, v4, v8) = 0 & vapp(v4, v5) = all_58_2 &
% 49.75/7.17 | $i(v8)) | (v3 = v0 & v2 = all_58_2 & vlookup(v1, all_58_3) = v0
% 49.75/7.17 | & vsomeType(all_58_5) = v0 & vvar(v1) = all_58_2 & $i(v0))))
% 49.75/7.17 |
% 49.75/7.17 | GROUND_INST: instantiating (subst-INV) with all_58_9, all_58_8, all_58_2,
% 49.75/7.17 | all_58_1, simplifying with (26), (27), (32), (33), (40) gives:
% 49.75/7.18 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 49.75/7.18 | ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i]
% 49.75/7.18 | : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 49.75/7.18 | $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18: $i] :
% 49.75/7.18 | ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23:
% 49.75/7.18 | $i] : ? [v24: int] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] :
% 49.75/7.18 | ? [v28: $i] : ? [v29: $i] : ? [v30: int] : ? [v31: $i] : ? [v32:
% 49.75/7.18 | $i] : ? [v33: $i] : ? [v34: $i] : ? [v35: int] : ? [v36: $i] :
% 49.75/7.18 | ? [v37: $i] : ? [v38: int] : ? [v39: $i] : ? [v40: $i] : ? [v41:
% 49.75/7.18 | $i] : ? [v42: int] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] :
% 49.75/7.18 | ? [v46: int] : ($i(v45) & $i(v44) & $i(v43) & $i(v41) & $i(v40) &
% 49.75/7.18 | $i(v39) & $i(v34) & $i(v33) & $i(v32) & $i(v31) & $i(v29) & $i(v28)
% 49.75/7.18 | & $i(v27) & $i(v26) & $i(v25) & $i(v14) & $i(v13) & $i(v12) &
% 49.75/7.18 | $i(v11) & $i(v10) & $i(v9) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 49.75/7.18 | $i(v0) & ((v46 = all_58_2 & v45 = all_58_8 & v44 = all_58_9 & v43 =
% 49.75/7.18 | all_58_9 & all_58_1 = all_58_8 & vvar(all_58_9) = all_58_2) |
% 49.75/7.18 | (v42 = all_58_2 & v40 = all_58_9 & v39 = all_58_8 & all_58_1 =
% 49.75/7.18 | all_58_2 & ~ (v41 = all_58_9) & vvar(v41) = all_58_2) | (v38 =
% 49.75/7.18 | all_58_1 & v35 = all_58_2 & v33 = all_58_8 & v32 = all_58_9 &
% 49.75/7.18 | vsubst(all_58_9, all_58_8, v34) = v37 & vsubst(all_58_9,
% 49.75/7.18 | all_58_8, v31) = v36 & vapp(v36, v37) = all_58_1 & vapp(v31,
% 49.75/7.18 | v34) = all_58_2 & $i(v37) & $i(v36)) | (v30 = all_58_2 & v27 =
% 49.75/7.18 | all_58_9 & v26 = all_58_9 & v25 = all_58_8 & all_58_1 = all_58_2
% 49.75/7.18 | & vabs(all_58_9, v28, v29) = all_58_2) | (v24 = all_58_1 & v20 =
% 49.75/7.18 | v13 & v16 = 0 & v15 = all_58_2 & v10 = all_58_8 & v9 = all_58_9
% 49.75/7.18 | & ~ (v12 = all_58_9) & vsubst(v12, v21, v14) = v22 &
% 49.75/7.18 | vsubst(all_58_9, all_58_8, v23) = all_58_1 & vgensym(v19) = v13
% 49.75/7.18 | & visFreeVar(v12, all_58_8) = 0 & vapp(v17, v18) = v19 &
% 49.75/7.18 | vapp(all_58_8, v14) = v17 & vabs(v13, v11, v22) = v23 &
% 49.75/7.18 | vabs(v12, v11, v14) = all_58_2 & vvar(v13) = v21 &
% 49.75/7.18 | vvar(all_58_9) = v18 & $i(v23) & $i(v22) & $i(v21) & $i(v19) &
% 49.75/7.18 | $i(v18) & $i(v17)) | (v8 = all_58_1 & v5 = all_58_2 & v3 =
% 49.75/7.18 | all_58_8 & v2 = all_58_9 & ~ (v6 = 0) & ~ (v0 = all_58_9) &
% 49.75/7.18 | vsubst(all_58_9, all_58_8, v4) = v7 & visFreeVar(v0, all_58_8) =
% 49.75/7.18 | v6 & vabs(v0, v1, v7) = all_58_1 & vabs(v0, v1, v4) = all_58_2 &
% 49.75/7.18 | $i(v7))))
% 49.75/7.18 |
% 49.75/7.18 | DELTA: instantiating (41) with fresh symbols all_65_0, all_65_1 gives:
% 49.75/7.18 | (45) vtcheck(all_58_10, all_58_2, all_58_5) = all_65_0 &
% 49.75/7.18 | visFreeVar(all_58_9, all_58_2) = all_65_1 & (all_65_0 = 0 | all_65_1 =
% 49.75/7.18 | 0)
% 49.75/7.18 |
% 49.75/7.18 | ALPHA: (45) implies:
% 49.75/7.18 | (46) vtcheck(all_58_10, all_58_2, all_58_5) = all_65_0
% 49.75/7.18 | (47) all_65_0 = 0 | all_65_1 = 0
% 49.75/7.18 |
% 49.75/7.18 | DELTA: instantiating (42) with fresh symbols all_67_0, all_67_1 gives:
% 49.75/7.18 | (48) varrow(all_58_11, all_58_5) = all_67_0 & vtcheck(all_58_10, all_67_1,
% 49.75/7.18 | all_67_0) = 0 & vabs(all_58_9, all_58_11, all_58_2) = all_67_1 &
% 49.75/7.18 | $i(all_67_0) & $i(all_67_1)
% 49.75/7.18 |
% 49.75/7.18 | ALPHA: (48) implies:
% 49.75/7.18 | (49) $i(all_67_1)
% 49.75/7.18 | (50) $i(all_67_0)
% 49.75/7.18 | (51) vabs(all_58_9, all_58_11, all_58_2) = all_67_1
% 49.75/7.18 | (52) vtcheck(all_58_10, all_67_1, all_67_0) = 0
% 49.75/7.18 | (53) varrow(all_58_11, all_58_5) = all_67_0
% 49.75/7.18 |
% 49.75/7.18 | DELTA: instantiating (43) with fresh symbols all_71_0, all_71_1, all_71_2,
% 49.75/7.18 | all_71_3, all_71_4, all_71_5, all_71_6, all_71_7, all_71_8, all_71_9,
% 49.75/7.18 | all_71_10, all_71_11, all_71_12, all_71_13, all_71_14, all_71_15,
% 49.75/7.18 | all_71_16, all_71_17, all_71_18 gives:
% 49.75/7.18 | (54) $i(all_71_4) & $i(all_71_5) & $i(all_71_6) & $i(all_71_7) &
% 49.75/7.18 | $i(all_71_12) & $i(all_71_13) & $i(all_71_14) & $i(all_71_17) &
% 49.75/7.18 | ((all_71_0 = 0 & all_71_2 = all_58_5 & all_71_3 = all_58_2 &
% 49.75/7.18 | varrow(all_71_5, all_71_4) = all_58_5 & vtcheck(all_71_1,
% 49.75/7.18 | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_3) =
% 49.75/7.18 | all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_58_2 &
% 49.75/7.18 | $i(all_71_1)) | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 =
% 49.75/7.18 | all_58_2 & varrow(all_71_12, all_58_5) = all_71_10 &
% 49.75/7.18 | vtcheck(all_58_3, all_71_13, all_71_12) = 0 & vtcheck(all_58_3,
% 49.75/7.18 | all_71_14, all_71_10) = 0 & vapp(all_71_14, all_71_13) =
% 49.75/7.18 | all_58_2 & $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 =
% 49.75/7.18 | all_58_2 & vlookup(all_71_17, all_58_3) = all_71_18 &
% 49.75/7.18 | vsomeType(all_58_5) = all_71_18 & vvar(all_71_17) = all_58_2 &
% 49.75/7.18 | $i(all_71_18)))
% 49.75/7.18 |
% 49.75/7.18 | ALPHA: (54) implies:
% 49.75/7.18 | (55) $i(all_71_17)
% 49.75/7.18 | (56) $i(all_71_14)
% 49.75/7.18 | (57) $i(all_71_13)
% 49.75/7.18 | (58) $i(all_71_7)
% 49.75/7.18 | (59) $i(all_71_6)
% 49.75/7.18 | (60) $i(all_71_5)
% 49.75/7.18 | (61) $i(all_71_4)
% 49.75/7.18 | (62) (all_71_0 = 0 & all_71_2 = all_58_5 & all_71_3 = all_58_2 &
% 49.75/7.18 | varrow(all_71_5, all_71_4) = all_58_5 & vtcheck(all_71_1, all_71_6,
% 49.75/7.18 | all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_3) = all_71_1 &
% 49.75/7.18 | vabs(all_71_7, all_71_5, all_71_6) = all_58_2 & $i(all_71_1)) |
% 49.75/7.18 | (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_2 &
% 49.75/7.18 | varrow(all_71_12, all_58_5) = all_71_10 & vtcheck(all_58_3,
% 49.75/7.18 | all_71_13, all_71_12) = 0 & vtcheck(all_58_3, all_71_14,
% 49.75/7.18 | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_2 &
% 49.75/7.18 | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_58_2 &
% 49.75/7.18 | vlookup(all_71_17, all_58_3) = all_71_18 & vsomeType(all_58_5) =
% 49.75/7.18 | all_71_18 & vvar(all_71_17) = all_58_2 & $i(all_71_18))
% 49.75/7.18 |
% 49.75/7.18 | DELTA: instantiating (44) with fresh symbols all_73_0, all_73_1, all_73_2,
% 49.75/7.18 | all_73_3, all_73_4, all_73_5, all_73_6, all_73_7, all_73_8, all_73_9,
% 49.75/7.18 | all_73_10, all_73_11, all_73_12, all_73_13, all_73_14, all_73_15,
% 49.75/7.18 | all_73_16, all_73_17, all_73_18, all_73_19, all_73_20, all_73_21,
% 49.75/7.18 | all_73_22, all_73_23, all_73_24, all_73_25, all_73_26, all_73_27,
% 49.75/7.18 | all_73_28, all_73_29, all_73_30, all_73_31, all_73_32, all_73_33,
% 49.75/7.18 | all_73_34, all_73_35, all_73_36, all_73_37, all_73_38, all_73_39,
% 49.75/7.18 | all_73_40, all_73_41, all_73_42, all_73_43, all_73_44, all_73_45,
% 49.75/7.18 | all_73_46 gives:
% 49.75/7.19 | (63) $i(all_73_1) & $i(all_73_2) & $i(all_73_3) & $i(all_73_5) &
% 49.75/7.19 | $i(all_73_6) & $i(all_73_7) & $i(all_73_12) & $i(all_73_13) &
% 49.75/7.19 | $i(all_73_14) & $i(all_73_15) & $i(all_73_17) & $i(all_73_18) &
% 49.75/7.19 | $i(all_73_19) & $i(all_73_20) & $i(all_73_21) & $i(all_73_32) &
% 49.75/7.19 | $i(all_73_33) & $i(all_73_34) & $i(all_73_35) & $i(all_73_36) &
% 49.75/7.19 | $i(all_73_37) & $i(all_73_42) & $i(all_73_43) & $i(all_73_44) &
% 49.75/7.19 | $i(all_73_45) & $i(all_73_46) & ((all_73_0 = all_58_2 & all_73_1 =
% 49.75/7.19 | all_58_8 & all_73_2 = all_58_9 & all_73_3 = all_58_9 & all_58_1 =
% 49.75/7.19 | all_58_8 & vvar(all_58_9) = all_58_2) | (all_73_4 = all_58_2 &
% 49.75/7.19 | all_73_6 = all_58_9 & all_73_7 = all_58_8 & all_58_1 = all_58_2 &
% 49.75/7.19 | ~ (all_73_5 = all_58_9) & vvar(all_73_5) = all_58_2) | (all_73_8 =
% 49.75/7.19 | all_58_1 & all_73_11 = all_58_2 & all_73_13 = all_58_8 & all_73_14
% 49.75/7.19 | = all_58_9 & vsubst(all_58_9, all_58_8, all_73_12) = all_73_9 &
% 49.75/7.19 | vsubst(all_58_9, all_58_8, all_73_15) = all_73_10 &
% 49.75/7.19 | vapp(all_73_10, all_73_9) = all_58_1 & vapp(all_73_15, all_73_12)
% 49.75/7.19 | = all_58_2 & $i(all_73_9) & $i(all_73_10)) | (all_73_16 = all_58_2
% 49.75/7.19 | & all_73_19 = all_58_9 & all_73_20 = all_58_9 & all_73_21 =
% 49.75/7.19 | all_58_8 & all_58_1 = all_58_2 & vabs(all_58_9, all_73_18,
% 49.75/7.19 | all_73_17) = all_58_2) | (all_73_22 = all_58_1 & all_73_26 =
% 49.75/7.19 | all_73_33 & all_73_30 = 0 & all_73_31 = all_58_2 & all_73_36 =
% 49.75/7.19 | all_58_8 & all_73_37 = all_58_9 & ~ (all_73_34 = all_58_9) &
% 49.75/7.19 | vsubst(all_73_34, all_73_25, all_73_32) = all_73_24 &
% 49.75/7.19 | vsubst(all_58_9, all_58_8, all_73_23) = all_58_1 &
% 49.75/7.19 | vgensym(all_73_27) = all_73_33 & visFreeVar(all_73_34, all_58_8) =
% 49.75/7.19 | 0 & vapp(all_73_29, all_73_28) = all_73_27 & vapp(all_58_8,
% 49.75/7.19 | all_73_32) = all_73_29 & vabs(all_73_33, all_73_35, all_73_24) =
% 49.75/7.19 | all_73_23 & vabs(all_73_34, all_73_35, all_73_32) = all_58_2 &
% 49.75/7.19 | vvar(all_73_33) = all_73_25 & vvar(all_58_9) = all_73_28 &
% 49.75/7.19 | $i(all_73_23) & $i(all_73_24) & $i(all_73_25) & $i(all_73_27) &
% 49.75/7.19 | $i(all_73_28) & $i(all_73_29)) | (all_73_38 = all_58_1 & all_73_41
% 49.75/7.19 | = all_58_2 & all_73_43 = all_58_8 & all_73_44 = all_58_9 & ~
% 49.75/7.19 | (all_73_40 = 0) & ~ (all_73_46 = all_58_9) & vsubst(all_58_9,
% 49.75/7.19 | all_58_8, all_73_42) = all_73_39 & visFreeVar(all_73_46,
% 49.75/7.19 | all_58_8) = all_73_40 & vabs(all_73_46, all_73_45, all_73_39) =
% 49.75/7.19 | all_58_1 & vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 49.75/7.19 | $i(all_73_39)))
% 49.75/7.19 |
% 49.75/7.19 | ALPHA: (63) implies:
% 49.75/7.19 | (64) $i(all_73_46)
% 49.75/7.19 | (65) $i(all_73_45)
% 49.75/7.19 | (66) $i(all_73_44)
% 49.75/7.19 | (67) $i(all_73_43)
% 49.75/7.19 | (68) $i(all_73_42)
% 49.75/7.19 | (69) $i(all_73_35)
% 49.75/7.19 | (70) $i(all_73_34)
% 49.75/7.19 | (71) $i(all_73_32)
% 49.75/7.19 | (72) $i(all_73_20)
% 49.75/7.19 | (73) $i(all_73_18)
% 49.75/7.19 | (74) $i(all_73_17)
% 49.75/7.19 | (75) $i(all_73_15)
% 49.75/7.19 | (76) $i(all_73_12)
% 49.75/7.19 | (77) $i(all_73_5)
% 49.75/7.19 | (78) $i(all_73_3)
% 49.75/7.19 | (79) (all_73_0 = all_58_2 & all_73_1 = all_58_8 & all_73_2 = all_58_9 &
% 49.75/7.19 | all_73_3 = all_58_9 & all_58_1 = all_58_8 & vvar(all_58_9) =
% 49.75/7.19 | all_58_2) | (all_73_4 = all_58_2 & all_73_6 = all_58_9 & all_73_7 =
% 49.75/7.19 | all_58_8 & all_58_1 = all_58_2 & ~ (all_73_5 = all_58_9) &
% 49.75/7.19 | vvar(all_73_5) = all_58_2) | (all_73_8 = all_58_1 & all_73_11 =
% 49.75/7.19 | all_58_2 & all_73_13 = all_58_8 & all_73_14 = all_58_9 &
% 49.75/7.19 | vsubst(all_58_9, all_58_8, all_73_12) = all_73_9 & vsubst(all_58_9,
% 49.75/7.19 | all_58_8, all_73_15) = all_73_10 & vapp(all_73_10, all_73_9) =
% 49.75/7.19 | all_58_1 & vapp(all_73_15, all_73_12) = all_58_2 & $i(all_73_9) &
% 49.75/7.19 | $i(all_73_10)) | (all_73_16 = all_58_2 & all_73_19 = all_58_9 &
% 49.75/7.19 | all_73_20 = all_58_9 & all_73_21 = all_58_8 & all_58_1 = all_58_2 &
% 49.75/7.19 | vabs(all_58_9, all_73_18, all_73_17) = all_58_2) | (all_73_22 =
% 49.75/7.19 | all_58_1 & all_73_26 = all_73_33 & all_73_30 = 0 & all_73_31 =
% 49.75/7.19 | all_58_2 & all_73_36 = all_58_8 & all_73_37 = all_58_9 & ~
% 49.75/7.19 | (all_73_34 = all_58_9) & vsubst(all_73_34, all_73_25, all_73_32) =
% 49.75/7.19 | all_73_24 & vsubst(all_58_9, all_58_8, all_73_23) = all_58_1 &
% 49.75/7.19 | vgensym(all_73_27) = all_73_33 & visFreeVar(all_73_34, all_58_8) = 0
% 49.75/7.19 | & vapp(all_73_29, all_73_28) = all_73_27 & vapp(all_58_8, all_73_32)
% 49.75/7.19 | = all_73_29 & vabs(all_73_33, all_73_35, all_73_24) = all_73_23 &
% 49.75/7.19 | vabs(all_73_34, all_73_35, all_73_32) = all_58_2 & vvar(all_73_33) =
% 49.75/7.19 | all_73_25 & vvar(all_58_9) = all_73_28 & $i(all_73_23) &
% 49.75/7.19 | $i(all_73_24) & $i(all_73_25) & $i(all_73_27) & $i(all_73_28) &
% 49.75/7.19 | $i(all_73_29)) | (all_73_38 = all_58_1 & all_73_41 = all_58_2 &
% 49.75/7.19 | all_73_43 = all_58_8 & all_73_44 = all_58_9 & ~ (all_73_40 = 0) &
% 49.75/7.19 | ~ (all_73_46 = all_58_9) & vsubst(all_58_9, all_58_8, all_73_42) =
% 49.75/7.19 | all_73_39 & visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 49.75/7.19 | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 & vabs(all_73_46,
% 49.75/7.19 | all_73_45, all_73_42) = all_58_2 & $i(all_73_39))
% 49.75/7.19 |
% 49.75/7.19 | GROUND_INST: instantiating (T-inv) with all_67_1, all_67_0, all_58_10,
% 49.75/7.19 | simplifying with (25), (49), (50), (52) gives:
% 49.75/7.19 | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 49.75/7.19 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 49.75/7.19 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 49.75/7.19 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18:
% 49.75/7.19 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) &
% 49.75/7.19 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_67_0 & v15 = all_67_1 &
% 49.75/7.19 | varrow(v13, v14) = all_67_0 & vtcheck(v17, v12, v14) = 0 &
% 49.75/7.19 | vbind(v11, v13, all_58_10) = v17 & vabs(v11, v13, v12) =
% 49.75/7.19 | all_67_1 & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_67_1 &
% 49.75/7.19 | varrow(v6, all_67_0) = v8 & vtcheck(all_58_10, v5, v6) = 0 &
% 49.75/7.19 | vtcheck(all_58_10, v4, v8) = 0 & vapp(v4, v5) = all_67_1 &
% 49.75/7.19 | $i(v8)) | (v3 = v0 & v2 = all_67_1 & vlookup(v1, all_58_10) = v0
% 49.75/7.19 | & vsomeType(all_67_0) = v0 & vvar(v1) = all_67_1 & $i(v0))))
% 49.75/7.19 |
% 49.75/7.19 | GROUND_INST: instantiating (11) with all_58_11, all_58_10, all_67_1, all_58_8,
% 49.75/7.19 | all_58_5, all_67_0, simplifying with (24), (25), (27), (30),
% 49.75/7.19 | (37), (49), (52), (53) gives:
% 49.75/7.19 | (81) ? [v0: $i] : (vtcheck(all_58_10, v0, all_58_5) = 0 & vapp(all_67_1,
% 49.75/7.19 | all_58_8) = v0 & $i(v0))
% 49.75/7.19 |
% 49.75/7.19 | DELTA: instantiating (81) with fresh symbol all_80_0 gives:
% 49.75/7.19 | (82) vtcheck(all_58_10, all_80_0, all_58_5) = 0 & vapp(all_67_1, all_58_8)
% 49.75/7.19 | = all_80_0 & $i(all_80_0)
% 49.75/7.19 |
% 49.75/7.19 | ALPHA: (82) implies:
% 49.75/7.19 | (83) $i(all_80_0)
% 49.75/7.19 | (84) vapp(all_67_1, all_58_8) = all_80_0
% 49.75/7.19 | (85) vtcheck(all_58_10, all_80_0, all_58_5) = 0
% 49.75/7.19 |
% 49.75/7.19 | DELTA: instantiating (80) with fresh symbols all_82_0, all_82_1, all_82_2,
% 49.75/7.19 | all_82_3, all_82_4, all_82_5, all_82_6, all_82_7, all_82_8, all_82_9,
% 49.75/7.19 | all_82_10, all_82_11, all_82_12, all_82_13, all_82_14, all_82_15,
% 49.75/7.19 | all_82_16, all_82_17, all_82_18 gives:
% 49.75/7.19 | (86) $i(all_82_4) & $i(all_82_5) & $i(all_82_6) & $i(all_82_7) &
% 49.75/7.19 | $i(all_82_12) & $i(all_82_13) & $i(all_82_14) & $i(all_82_17) &
% 49.75/7.19 | ((all_82_0 = 0 & all_82_2 = all_67_0 & all_82_3 = all_67_1 &
% 49.75/7.19 | varrow(all_82_5, all_82_4) = all_67_0 & vtcheck(all_82_1,
% 49.75/7.19 | all_82_6, all_82_4) = 0 & vbind(all_82_7, all_82_5, all_58_10) =
% 49.75/7.19 | all_82_1 & vabs(all_82_7, all_82_5, all_82_6) = all_67_1 &
% 49.75/7.19 | $i(all_82_1)) | (all_82_8 = 0 & all_82_9 = 0 & all_82_11 =
% 49.75/7.19 | all_67_1 & varrow(all_82_12, all_67_0) = all_82_10 &
% 49.75/7.19 | vtcheck(all_58_10, all_82_13, all_82_12) = 0 & vtcheck(all_58_10,
% 49.75/7.19 | all_82_14, all_82_10) = 0 & vapp(all_82_14, all_82_13) =
% 49.75/7.19 | all_67_1 & $i(all_82_10)) | (all_82_15 = all_82_18 & all_82_16 =
% 49.75/7.19 | all_67_1 & vlookup(all_82_17, all_58_10) = all_82_18 &
% 49.75/7.19 | vsomeType(all_67_0) = all_82_18 & vvar(all_82_17) = all_67_1 &
% 49.75/7.19 | $i(all_82_18)))
% 49.75/7.19 |
% 49.75/7.19 | ALPHA: (86) implies:
% 49.75/7.19 | (87) $i(all_82_17)
% 49.75/7.19 | (88) $i(all_82_14)
% 49.75/7.19 | (89) $i(all_82_13)
% 49.75/7.19 | (90) $i(all_82_7)
% 49.75/7.19 | (91) $i(all_82_6)
% 49.75/7.19 | (92) $i(all_82_5)
% 49.75/7.19 | (93) $i(all_82_4)
% 49.75/7.20 | (94) (all_82_0 = 0 & all_82_2 = all_67_0 & all_82_3 = all_67_1 &
% 49.75/7.20 | varrow(all_82_5, all_82_4) = all_67_0 & vtcheck(all_82_1, all_82_6,
% 49.75/7.20 | all_82_4) = 0 & vbind(all_82_7, all_82_5, all_58_10) = all_82_1 &
% 49.75/7.20 | vabs(all_82_7, all_82_5, all_82_6) = all_67_1 & $i(all_82_1)) |
% 49.75/7.20 | (all_82_8 = 0 & all_82_9 = 0 & all_82_11 = all_67_1 &
% 49.75/7.20 | varrow(all_82_12, all_67_0) = all_82_10 & vtcheck(all_58_10,
% 49.75/7.20 | all_82_13, all_82_12) = 0 & vtcheck(all_58_10, all_82_14,
% 49.75/7.20 | all_82_10) = 0 & vapp(all_82_14, all_82_13) = all_67_1 &
% 49.75/7.20 | $i(all_82_10)) | (all_82_15 = all_82_18 & all_82_16 = all_67_1 &
% 49.75/7.20 | vlookup(all_82_17, all_58_10) = all_82_18 & vsomeType(all_67_0) =
% 49.75/7.20 | all_82_18 & vvar(all_82_17) = all_67_1 & $i(all_82_18))
% 49.75/7.20 |
% 49.75/7.20 | GROUND_INST: instantiating (T-inv) with all_80_0, all_58_5, all_58_10,
% 49.75/7.20 | simplifying with (25), (30), (83), (85) gives:
% 49.75/7.20 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] :
% 49.75/7.20 | ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int]
% 49.75/7.20 | : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 49.75/7.20 | [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i] : ? [v18:
% 49.75/7.20 | int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) & $i(v5) &
% 49.75/7.20 | $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_58_5 & v15 = all_80_0 &
% 49.75/7.20 | varrow(v13, v14) = all_58_5 & vtcheck(v17, v12, v14) = 0 &
% 49.75/7.20 | vbind(v11, v13, all_58_10) = v17 & vabs(v11, v13, v12) =
% 49.75/7.20 | all_80_0 & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_80_0 &
% 49.75/7.20 | varrow(v6, all_58_5) = v8 & vtcheck(all_58_10, v5, v6) = 0 &
% 49.75/7.20 | vtcheck(all_58_10, v4, v8) = 0 & vapp(v4, v5) = all_80_0 &
% 49.75/7.20 | $i(v8)) | (v3 = v0 & v2 = all_80_0 & vlookup(v1, all_58_10) = v0
% 49.75/7.20 | & vsomeType(all_58_5) = v0 & vvar(v1) = all_80_0 & $i(v0))))
% 49.75/7.20 |
% 49.75/7.20 | DELTA: instantiating (95) with fresh symbols all_89_0, all_89_1, all_89_2,
% 49.75/7.20 | all_89_3, all_89_4, all_89_5, all_89_6, all_89_7, all_89_8, all_89_9,
% 49.75/7.20 | all_89_10, all_89_11, all_89_12, all_89_13, all_89_14, all_89_15,
% 49.75/7.20 | all_89_16, all_89_17, all_89_18 gives:
% 49.75/7.20 | (96) $i(all_89_4) & $i(all_89_5) & $i(all_89_6) & $i(all_89_7) &
% 49.75/7.20 | $i(all_89_12) & $i(all_89_13) & $i(all_89_14) & $i(all_89_17) &
% 49.75/7.20 | ((all_89_0 = 0 & all_89_2 = all_58_5 & all_89_3 = all_80_0 &
% 49.75/7.20 | varrow(all_89_5, all_89_4) = all_58_5 & vtcheck(all_89_1,
% 49.75/7.20 | all_89_6, all_89_4) = 0 & vbind(all_89_7, all_89_5, all_58_10) =
% 49.75/7.20 | all_89_1 & vabs(all_89_7, all_89_5, all_89_6) = all_80_0 &
% 49.75/7.20 | $i(all_89_1)) | (all_89_8 = 0 & all_89_9 = 0 & all_89_11 =
% 49.75/7.20 | all_80_0 & varrow(all_89_12, all_58_5) = all_89_10 &
% 49.75/7.20 | vtcheck(all_58_10, all_89_13, all_89_12) = 0 & vtcheck(all_58_10,
% 49.75/7.20 | all_89_14, all_89_10) = 0 & vapp(all_89_14, all_89_13) =
% 49.75/7.20 | all_80_0 & $i(all_89_10)) | (all_89_15 = all_89_18 & all_89_16 =
% 49.75/7.20 | all_80_0 & vlookup(all_89_17, all_58_10) = all_89_18 &
% 49.75/7.20 | vsomeType(all_58_5) = all_89_18 & vvar(all_89_17) = all_80_0 &
% 49.75/7.20 | $i(all_89_18)))
% 49.75/7.20 |
% 49.75/7.20 | ALPHA: (96) implies:
% 49.75/7.20 | (97) $i(all_89_17)
% 49.75/7.20 | (98) $i(all_89_14)
% 49.75/7.20 | (99) $i(all_89_13)
% 49.75/7.20 | (100) $i(all_89_7)
% 49.75/7.20 | (101) $i(all_89_6)
% 49.75/7.20 | (102) $i(all_89_5)
% 49.75/7.20 | (103) (all_89_0 = 0 & all_89_2 = all_58_5 & all_89_3 = all_80_0 &
% 49.75/7.20 | varrow(all_89_5, all_89_4) = all_58_5 & vtcheck(all_89_1, all_89_6,
% 49.75/7.20 | all_89_4) = 0 & vbind(all_89_7, all_89_5, all_58_10) = all_89_1 &
% 49.75/7.20 | vabs(all_89_7, all_89_5, all_89_6) = all_80_0 & $i(all_89_1)) |
% 49.75/7.20 | (all_89_8 = 0 & all_89_9 = 0 & all_89_11 = all_80_0 &
% 49.75/7.20 | varrow(all_89_12, all_58_5) = all_89_10 & vtcheck(all_58_10,
% 49.75/7.20 | all_89_13, all_89_12) = 0 & vtcheck(all_58_10, all_89_14,
% 49.75/7.20 | all_89_10) = 0 & vapp(all_89_14, all_89_13) = all_80_0 &
% 49.75/7.20 | $i(all_89_10)) | (all_89_15 = all_89_18 & all_89_16 = all_80_0 &
% 49.75/7.20 | vlookup(all_89_17, all_58_10) = all_89_18 & vsomeType(all_58_5) =
% 49.75/7.20 | all_89_18 & vvar(all_89_17) = all_80_0 & $i(all_89_18))
% 49.75/7.20 |
% 49.75/7.20 | BETA: splitting (47) gives:
% 49.75/7.20 |
% 49.75/7.20 | Case 1:
% 49.75/7.20 | |
% 49.75/7.20 | | (104) all_65_0 = 0
% 49.75/7.20 | |
% 49.75/7.20 | | REDUCE: (46), (104) imply:
% 49.75/7.20 | | (105) vtcheck(all_58_10, all_58_2, all_58_5) = 0
% 49.75/7.20 | |
% 49.75/7.20 | | GROUND_INST: instantiating (T-inv) with all_58_2, all_58_5, all_58_10,
% 49.75/7.20 | | simplifying with (25), (30), (32), (105) gives:
% 49.75/7.20 | | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4:
% 49.75/7.20 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ?
% 49.75/7.20 | | [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 49.75/7.20 | | $i] : ? [v14: $i] : ? [v15: int] : ? [v16: int] : ? [v17: $i]
% 49.75/7.20 | | : ? [v18: int] : ($i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v6) &
% 49.75/7.20 | | $i(v5) & $i(v4) & $i(v1) & ((v18 = 0 & v16 = all_58_5 & v15 =
% 49.75/7.20 | | all_58_2 & varrow(v13, v14) = all_58_5 & vtcheck(v17, v12,
% 49.75/7.20 | | v14) = 0 & vbind(v11, v13, all_58_10) = v17 & vabs(v11,
% 49.75/7.20 | | v13, v12) = all_58_2 & $i(v17)) | (v10 = 0 & v9 = 0 & v7 =
% 49.75/7.20 | | all_58_2 & varrow(v6, all_58_5) = v8 & vtcheck(all_58_10, v5,
% 49.75/7.20 | | v6) = 0 & vtcheck(all_58_10, v4, v8) = 0 & vapp(v4, v5) =
% 49.75/7.20 | | all_58_2 & $i(v8)) | (v3 = v0 & v2 = all_58_2 & vlookup(v1,
% 49.75/7.20 | | all_58_10) = v0 & vsomeType(all_58_5) = v0 & vvar(v1) =
% 49.75/7.20 | | all_58_2 & $i(v0))))
% 49.75/7.20 | |
% 49.75/7.20 | | DELTA: instantiating (106) with fresh symbols all_103_0, all_103_1,
% 49.75/7.20 | | all_103_2, all_103_3, all_103_4, all_103_5, all_103_6, all_103_7,
% 49.75/7.20 | | all_103_8, all_103_9, all_103_10, all_103_11, all_103_12, all_103_13,
% 49.75/7.20 | | all_103_14, all_103_15, all_103_16, all_103_17, all_103_18 gives:
% 49.75/7.20 | | (107) $i(all_103_4) & $i(all_103_5) & $i(all_103_6) & $i(all_103_7) &
% 49.75/7.20 | | $i(all_103_12) & $i(all_103_13) & $i(all_103_14) & $i(all_103_17) &
% 49.75/7.20 | | ((all_103_0 = 0 & all_103_2 = all_58_5 & all_103_3 = all_58_2 &
% 49.75/7.20 | | varrow(all_103_5, all_103_4) = all_58_5 & vtcheck(all_103_1,
% 49.75/7.20 | | all_103_6, all_103_4) = 0 & vbind(all_103_7, all_103_5,
% 49.75/7.20 | | all_58_10) = all_103_1 & vabs(all_103_7, all_103_5,
% 49.75/7.20 | | all_103_6) = all_58_2 & $i(all_103_1)) | (all_103_8 = 0 &
% 49.75/7.20 | | all_103_9 = 0 & all_103_11 = all_58_2 & varrow(all_103_12,
% 49.75/7.20 | | all_58_5) = all_103_10 & vtcheck(all_58_10, all_103_13,
% 49.75/7.20 | | all_103_12) = 0 & vtcheck(all_58_10, all_103_14, all_103_10)
% 49.75/7.20 | | = 0 & vapp(all_103_14, all_103_13) = all_58_2 & $i(all_103_10))
% 49.75/7.20 | | | (all_103_15 = all_103_18 & all_103_16 = all_58_2 &
% 49.75/7.20 | | vlookup(all_103_17, all_58_10) = all_103_18 &
% 49.75/7.20 | | vsomeType(all_58_5) = all_103_18 & vvar(all_103_17) = all_58_2
% 49.75/7.20 | | & $i(all_103_18)))
% 49.75/7.20 | |
% 49.75/7.20 | | ALPHA: (107) implies:
% 49.75/7.20 | | (108) $i(all_103_17)
% 49.75/7.20 | | (109) $i(all_103_14)
% 49.75/7.20 | | (110) $i(all_103_13)
% 49.75/7.20 | | (111) $i(all_103_7)
% 49.75/7.20 | | (112) $i(all_103_6)
% 49.75/7.20 | | (113) $i(all_103_5)
% 49.75/7.20 | | (114) $i(all_103_4)
% 49.75/7.21 | | (115) (all_103_0 = 0 & all_103_2 = all_58_5 & all_103_3 = all_58_2 &
% 49.75/7.21 | | varrow(all_103_5, all_103_4) = all_58_5 & vtcheck(all_103_1,
% 49.75/7.21 | | all_103_6, all_103_4) = 0 & vbind(all_103_7, all_103_5,
% 49.75/7.21 | | all_58_10) = all_103_1 & vabs(all_103_7, all_103_5, all_103_6)
% 49.75/7.21 | | = all_58_2 & $i(all_103_1)) | (all_103_8 = 0 & all_103_9 = 0 &
% 49.75/7.21 | | all_103_11 = all_58_2 & varrow(all_103_12, all_58_5) = all_103_10
% 49.75/7.21 | | & vtcheck(all_58_10, all_103_13, all_103_12) = 0 &
% 49.75/7.21 | | vtcheck(all_58_10, all_103_14, all_103_10) = 0 & vapp(all_103_14,
% 49.75/7.21 | | all_103_13) = all_58_2 & $i(all_103_10)) | (all_103_15 =
% 49.75/7.21 | | all_103_18 & all_103_16 = all_58_2 & vlookup(all_103_17,
% 49.75/7.21 | | all_58_10) = all_103_18 & vsomeType(all_58_5) = all_103_18 &
% 49.75/7.21 | | vvar(all_103_17) = all_58_2 & $i(all_103_18))
% 49.75/7.21 | |
% 49.75/7.21 | | BETA: splitting (62) gives:
% 49.75/7.21 | |
% 49.75/7.21 | | Case 1:
% 49.75/7.21 | | |
% 49.75/7.21 | | | (116) all_71_0 = 0 & all_71_2 = all_58_5 & all_71_3 = all_58_2 &
% 49.75/7.21 | | | varrow(all_71_5, all_71_4) = all_58_5 & vtcheck(all_71_1,
% 49.75/7.21 | | | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_3) =
% 49.75/7.21 | | | all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_58_2 &
% 49.75/7.21 | | | $i(all_71_1)
% 49.75/7.21 | | |
% 49.75/7.21 | | | ALPHA: (116) implies:
% 49.75/7.21 | | | (117) vabs(all_71_7, all_71_5, all_71_6) = all_58_2
% 49.75/7.21 | | | (118) vbind(all_71_7, all_71_5, all_58_3) = all_71_1
% 49.75/7.21 | | | (119) vtcheck(all_71_1, all_71_6, all_71_4) = 0
% 49.75/7.21 | | | (120) varrow(all_71_5, all_71_4) = all_58_5
% 49.75/7.21 | | |
% 49.75/7.21 | | | GROUND_INST: instantiating (3) with all_58_7, all_58_6, veabs, all_71_7,
% 49.75/7.21 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 49.75/7.21 | | | (29), (34), (58), (59), (60), (117) gives:
% 49.75/7.21 | | | (121) all_71_6 = veabs
% 49.75/7.21 | | |
% 49.75/7.21 | | | GROUND_INST: instantiating (2) with all_58_7, all_58_6, veabs, all_71_7,
% 49.75/7.21 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 49.75/7.21 | | | (29), (34), (58), (59), (60), (117) gives:
% 49.75/7.21 | | | (122) all_71_5 = all_58_6
% 49.75/7.21 | | |
% 49.75/7.21 | | | GROUND_INST: instantiating (1) with all_58_7, all_58_6, veabs, all_71_7,
% 49.75/7.21 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 49.75/7.21 | | | (29), (34), (58), (59), (60), (117) gives:
% 49.75/7.21 | | | (123) all_71_7 = all_58_7
% 49.75/7.21 | | |
% 49.75/7.21 | | | GROUND_INST: instantiating (6) with all_58_9, all_58_11, all_71_7,
% 49.75/7.21 | | | all_71_5, all_58_10, all_71_6, all_71_4, all_58_3, all_71_1,
% 49.75/7.21 | | | simplifying with (24), (25), (26), (36), (58), (59), (60),
% 49.75/7.21 | | | (61), (118), (119) gives:
% 49.75/7.21 | | | (124) all_71_7 = all_58_9 | ? [v0: $i] : ? [v1: $i] : (vtcheck(v1,
% 49.75/7.21 | | | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5,
% 49.75/7.21 | | | all_58_10) = v0 & vbind(all_58_9, all_58_11, v0) = v1 &
% 49.75/7.21 | | | $i(v1) & $i(v0))
% 49.75/7.21 | | |
% 49.75/7.21 | | | REDUCE: (120), (122) imply:
% 49.75/7.21 | | | (125) varrow(all_58_6, all_71_4) = all_58_5
% 49.75/7.21 | | |
% 49.75/7.21 | | | BETA: splitting (124) gives:
% 49.75/7.21 | | |
% 49.75/7.21 | | | Case 1:
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | (126) all_71_7 = all_58_9
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | COMBINE_EQS: (123), (126) imply:
% 49.75/7.21 | | | | (127) all_58_7 = all_58_9
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | REDUCE: (21), (127) imply:
% 49.75/7.21 | | | | (128) $false
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | CLOSE: (128) is inconsistent.
% 49.75/7.21 | | | |
% 49.75/7.21 | | | Case 2:
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | (129) ~ (all_71_7 = all_58_9)
% 49.75/7.21 | | | | (130) ? [v0: $i] : ? [v1: $i] : (vtcheck(v1, all_71_6, all_71_4) =
% 49.75/7.21 | | | | 0 & vbind(all_71_7, all_71_5, all_58_10) = v0 &
% 49.75/7.21 | | | | vbind(all_58_9, all_58_11, v0) = v1 & $i(v1) & $i(v0))
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | DELTA: instantiating (130) with fresh symbols all_140_0, all_140_1
% 49.75/7.21 | | | | gives:
% 49.75/7.21 | | | | (131) vtcheck(all_140_0, all_71_6, all_71_4) = 0 & vbind(all_71_7,
% 49.75/7.21 | | | | all_71_5, all_58_10) = all_140_1 & vbind(all_58_9, all_58_11,
% 49.75/7.21 | | | | all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1)
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | ALPHA: (131) implies:
% 49.75/7.21 | | | | (132) $i(all_140_1)
% 49.75/7.21 | | | | (133) vbind(all_58_9, all_58_11, all_140_1) = all_140_0
% 49.75/7.21 | | | | (134) vbind(all_71_7, all_71_5, all_58_10) = all_140_1
% 49.75/7.21 | | | | (135) vtcheck(all_140_0, all_71_6, all_71_4) = 0
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | REDUCE: (121), (135) imply:
% 49.75/7.21 | | | | (136) vtcheck(all_140_0, veabs, all_71_4) = 0
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | REDUCE: (122), (123), (134) imply:
% 49.75/7.21 | | | | (137) vbind(all_58_7, all_58_6, all_58_10) = all_140_1
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | GROUND_INST: instantiating (9) with all_140_1, all_58_9, veabs,
% 49.75/7.21 | | | | all_58_11, all_71_4, all_140_0, simplifying with (14),
% 49.75/7.21 | | | | (24), (26), (61), (132), (133), (136) gives:
% 49.75/7.21 | | | | (138) ? [v0: $i] : ? [v1: $i] : (varrow(all_58_11, all_71_4) = v1 &
% 49.75/7.21 | | | | vtcheck(all_140_1, v0, v1) = 0 & vabs(all_58_9, all_58_11,
% 49.75/7.21 | | | | veabs) = v0 & $i(v1) & $i(v0))
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | DELTA: instantiating (138) with fresh symbols all_151_0, all_151_1
% 49.75/7.21 | | | | gives:
% 49.75/7.21 | | | | (139) varrow(all_58_11, all_71_4) = all_151_0 & vtcheck(all_140_1,
% 49.75/7.21 | | | | all_151_1, all_151_0) = 0 & vabs(all_58_9, all_58_11, veabs)
% 49.75/7.21 | | | | = all_151_1 & $i(all_151_0) & $i(all_151_1)
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | ALPHA: (139) implies:
% 49.75/7.21 | | | | (140) $i(all_151_1)
% 49.75/7.21 | | | | (141) $i(all_151_0)
% 49.75/7.21 | | | | (142) vabs(all_58_9, all_58_11, veabs) = all_151_1
% 49.75/7.21 | | | | (143) vtcheck(all_140_1, all_151_1, all_151_0) = 0
% 49.75/7.21 | | | |
% 49.75/7.21 | | | | GROUND_INST: instantiating (T-inv) with all_151_1, all_151_0, all_140_1,
% 49.75/7.21 | | | | simplifying with (132), (140), (141), (143) gives:
% 49.75/7.22 | | | | (144) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ?
% 49.75/7.22 | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8:
% 49.75/7.22 | | | | $i] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12:
% 49.75/7.22 | | | | $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: int] : ? [v16:
% 49.75/7.22 | | | | int] : ? [v17: $i] : ? [v18: int] : ($i(v14) & $i(v13) &
% 49.75/7.22 | | | | $i(v12) & $i(v11) & $i(v6) & $i(v5) & $i(v4) & $i(v1) & ((v18
% 49.75/7.22 | | | | = 0 & v16 = all_151_0 & v15 = all_151_1 & varrow(v13,
% 49.75/7.22 | | | | v14) = all_151_0 & vtcheck(v17, v12, v14) = 0 &
% 49.75/7.22 | | | | vbind(v11, v13, all_140_1) = v17 & vabs(v11, v13, v12) =
% 49.75/7.22 | | | | all_151_1 & $i(v17)) | (v10 = 0 & v9 = 0 & v7 = all_151_1
% 49.75/7.22 | | | | & varrow(v6, all_151_0) = v8 & vtcheck(all_140_1, v5, v6)
% 49.75/7.22 | | | | = 0 & vtcheck(all_140_1, v4, v8) = 0 & vapp(v4, v5) =
% 49.75/7.22 | | | | all_151_1 & $i(v8)) | (v3 = v0 & v2 = all_151_1 &
% 49.75/7.22 | | | | vlookup(v1, all_140_1) = v0 & vsomeType(all_151_0) = v0 &
% 49.75/7.22 | | | | vvar(v1) = all_151_1 & $i(v0))))
% 49.75/7.22 | | | |
% 49.75/7.22 | | | | DELTA: instantiating (144) with fresh symbols all_168_0, all_168_1,
% 49.75/7.22 | | | | all_168_2, all_168_3, all_168_4, all_168_5, all_168_6, all_168_7,
% 49.75/7.22 | | | | all_168_8, all_168_9, all_168_10, all_168_11, all_168_12,
% 49.75/7.22 | | | | all_168_13, all_168_14, all_168_15, all_168_16, all_168_17,
% 49.75/7.22 | | | | all_168_18 gives:
% 49.75/7.22 | | | | (145) $i(all_168_4) & $i(all_168_5) & $i(all_168_6) & $i(all_168_7) &
% 49.75/7.22 | | | | $i(all_168_12) & $i(all_168_13) & $i(all_168_14) &
% 49.75/7.22 | | | | $i(all_168_17) & ((all_168_0 = 0 & all_168_2 = all_151_0 &
% 49.75/7.22 | | | | all_168_3 = all_151_1 & varrow(all_168_5, all_168_4) =
% 49.75/7.22 | | | | all_151_0 & vtcheck(all_168_1, all_168_6, all_168_4) = 0 &
% 49.75/7.22 | | | | vbind(all_168_7, all_168_5, all_140_1) = all_168_1 &
% 49.75/7.22 | | | | vabs(all_168_7, all_168_5, all_168_6) = all_151_1 &
% 49.75/7.22 | | | | $i(all_168_1)) | (all_168_8 = 0 & all_168_9 = 0 &
% 49.75/7.22 | | | | all_168_11 = all_151_1 & varrow(all_168_12, all_151_0) =
% 49.75/7.22 | | | | all_168_10 & vtcheck(all_140_1, all_168_13, all_168_12) = 0
% 49.75/7.22 | | | | & vtcheck(all_140_1, all_168_14, all_168_10) = 0 &
% 49.75/7.22 | | | | vapp(all_168_14, all_168_13) = all_151_1 & $i(all_168_10))
% 49.75/7.22 | | | | | (all_168_15 = all_168_18 & all_168_16 = all_151_1 &
% 49.75/7.22 | | | | vlookup(all_168_17, all_140_1) = all_168_18 &
% 49.75/7.22 | | | | vsomeType(all_151_0) = all_168_18 & vvar(all_168_17) =
% 49.75/7.22 | | | | all_151_1 & $i(all_168_18)))
% 49.75/7.22 | | | |
% 49.75/7.22 | | | | ALPHA: (145) implies:
% 49.75/7.22 | | | | (146) $i(all_168_17)
% 49.75/7.22 | | | | (147) $i(all_168_14)
% 49.75/7.22 | | | | (148) $i(all_168_13)
% 49.75/7.22 | | | | (149) (all_168_0 = 0 & all_168_2 = all_151_0 & all_168_3 = all_151_1
% 49.75/7.22 | | | | & varrow(all_168_5, all_168_4) = all_151_0 &
% 49.75/7.22 | | | | vtcheck(all_168_1, all_168_6, all_168_4) = 0 &
% 49.75/7.22 | | | | vbind(all_168_7, all_168_5, all_140_1) = all_168_1 &
% 49.75/7.22 | | | | vabs(all_168_7, all_168_5, all_168_6) = all_151_1 &
% 49.75/7.22 | | | | $i(all_168_1)) | (all_168_8 = 0 & all_168_9 = 0 & all_168_11
% 49.75/7.22 | | | | = all_151_1 & varrow(all_168_12, all_151_0) = all_168_10 &
% 49.75/7.22 | | | | vtcheck(all_140_1, all_168_13, all_168_12) = 0 &
% 49.75/7.22 | | | | vtcheck(all_140_1, all_168_14, all_168_10) = 0 &
% 49.75/7.22 | | | | vapp(all_168_14, all_168_13) = all_151_1 & $i(all_168_10)) |
% 49.75/7.22 | | | | (all_168_15 = all_168_18 & all_168_16 = all_151_1 &
% 49.75/7.22 | | | | vlookup(all_168_17, all_140_1) = all_168_18 &
% 49.75/7.22 | | | | vsomeType(all_151_0) = all_168_18 & vvar(all_168_17) =
% 49.75/7.22 | | | | all_151_1 & $i(all_168_18))
% 49.75/7.22 | | | |
% 49.75/7.22 | | | | BETA: splitting (94) gives:
% 49.75/7.22 | | | |
% 49.75/7.22 | | | | Case 1:
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | (150) all_82_0 = 0 & all_82_2 = all_67_0 & all_82_3 = all_67_1 &
% 49.75/7.22 | | | | | varrow(all_82_5, all_82_4) = all_67_0 & vtcheck(all_82_1,
% 49.75/7.22 | | | | | all_82_6, all_82_4) = 0 & vbind(all_82_7, all_82_5,
% 49.75/7.22 | | | | | all_58_10) = all_82_1 & vabs(all_82_7, all_82_5, all_82_6)
% 49.75/7.22 | | | | | = all_67_1 & $i(all_82_1)
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | ALPHA: (150) implies:
% 49.75/7.22 | | | | | (151) vabs(all_82_7, all_82_5, all_82_6) = all_67_1
% 49.75/7.22 | | | | | (152) varrow(all_82_5, all_82_4) = all_67_0
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | GROUND_INST: instantiating (1) with all_58_9, all_58_11, all_58_2,
% 49.75/7.22 | | | | | all_82_7, all_82_5, all_82_6, all_67_1, simplifying with
% 49.75/7.22 | | | | | (24), (26), (32), (51), (90), (91), (92), (151) gives:
% 49.75/7.22 | | | | | (153) all_82_7 = all_58_9
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | GROUND_INST: instantiating (7) with all_58_11, all_58_5, all_82_5,
% 49.75/7.22 | | | | | all_82_4, all_67_0, simplifying with (24), (30), (53),
% 49.75/7.22 | | | | | (92), (93), (152) gives:
% 49.75/7.22 | | | | | (154) all_82_5 = all_58_11
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | BETA: splitting (79) gives:
% 49.75/7.22 | | | | |
% 49.75/7.22 | | | | | Case 1:
% 49.75/7.22 | | | | | |
% 49.75/7.22 | | | | | | (155) (all_73_0 = all_58_2 & all_73_1 = all_58_8 & all_73_2 =
% 49.75/7.22 | | | | | | all_58_9 & all_73_3 = all_58_9 & all_58_1 = all_58_8 &
% 49.75/7.22 | | | | | | vvar(all_58_9) = all_58_2) | (all_73_4 = all_58_2 &
% 49.75/7.22 | | | | | | all_73_6 = all_58_9 & all_73_7 = all_58_8 & all_58_1 =
% 49.75/7.22 | | | | | | all_58_2 & ~ (all_73_5 = all_58_9) & vvar(all_73_5) =
% 49.75/7.22 | | | | | | all_58_2) | (all_73_8 = all_58_1 & all_73_11 = all_58_2 &
% 49.75/7.22 | | | | | | all_73_13 = all_58_8 & all_73_14 = all_58_9 &
% 49.75/7.22 | | | | | | vsubst(all_58_9, all_58_8, all_73_12) = all_73_9 &
% 49.75/7.22 | | | | | | vsubst(all_58_9, all_58_8, all_73_15) = all_73_10 &
% 49.75/7.22 | | | | | | vapp(all_73_10, all_73_9) = all_58_1 & vapp(all_73_15,
% 49.75/7.22 | | | | | | all_73_12) = all_58_2 & $i(all_73_9) & $i(all_73_10))
% 49.75/7.22 | | | | | |
% 49.75/7.22 | | | | | | BETA: splitting (155) gives:
% 49.75/7.22 | | | | | |
% 49.75/7.22 | | | | | | Case 1:
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | (156) all_73_0 = all_58_2 & all_73_1 = all_58_8 & all_73_2 =
% 49.75/7.22 | | | | | | | all_58_9 & all_73_3 = all_58_9 & all_58_1 = all_58_8 &
% 49.75/7.22 | | | | | | | vvar(all_58_9) = all_58_2
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | ALPHA: (156) implies:
% 49.75/7.22 | | | | | | | (157) vvar(all_58_9) = all_58_2
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_58_9, all_58_7,
% 49.75/7.22 | | | | | | | all_58_6, veabs, all_58_2, simplifying with (14),
% 49.75/7.22 | | | | | | | (26), (28), (29), (34), (157) gives:
% 49.75/7.22 | | | | | | | (158) $false
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | CLOSE: (158) is inconsistent.
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | Case 2:
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | (159) (all_73_4 = all_58_2 & all_73_6 = all_58_9 & all_73_7 =
% 49.75/7.22 | | | | | | | all_58_8 & all_58_1 = all_58_2 & ~ (all_73_5 =
% 49.75/7.22 | | | | | | | all_58_9) & vvar(all_73_5) = all_58_2) | (all_73_8 =
% 49.75/7.22 | | | | | | | all_58_1 & all_73_11 = all_58_2 & all_73_13 = all_58_8
% 49.75/7.22 | | | | | | | & all_73_14 = all_58_9 & vsubst(all_58_9, all_58_8,
% 49.75/7.22 | | | | | | | all_73_12) = all_73_9 & vsubst(all_58_9, all_58_8,
% 49.75/7.22 | | | | | | | all_73_15) = all_73_10 & vapp(all_73_10, all_73_9) =
% 49.75/7.22 | | | | | | | all_58_1 & vapp(all_73_15, all_73_12) = all_58_2 &
% 49.75/7.22 | | | | | | | $i(all_73_9) & $i(all_73_10))
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | BETA: splitting (159) gives:
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | | Case 1:
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | (160) all_73_4 = all_58_2 & all_73_6 = all_58_9 & all_73_7 =
% 49.75/7.22 | | | | | | | | all_58_8 & all_58_1 = all_58_2 & ~ (all_73_5 =
% 49.75/7.22 | | | | | | | | all_58_9) & vvar(all_73_5) = all_58_2
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | ALPHA: (160) implies:
% 49.75/7.22 | | | | | | | | (161) vvar(all_73_5) = all_58_2
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_73_5,
% 49.75/7.22 | | | | | | | | all_58_7, all_58_6, veabs, all_58_2, simplifying
% 49.75/7.22 | | | | | | | | with (14), (28), (29), (34), (77), (161) gives:
% 49.75/7.22 | | | | | | | | (162) $false
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | CLOSE: (162) is inconsistent.
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | Case 2:
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | (163) all_73_8 = all_58_1 & all_73_11 = all_58_2 & all_73_13
% 49.75/7.22 | | | | | | | | = all_58_8 & all_73_14 = all_58_9 & vsubst(all_58_9,
% 49.75/7.22 | | | | | | | | all_58_8, all_73_12) = all_73_9 & vsubst(all_58_9,
% 49.75/7.22 | | | | | | | | all_58_8, all_73_15) = all_73_10 & vapp(all_73_10,
% 49.75/7.22 | | | | | | | | all_73_9) = all_58_1 & vapp(all_73_15, all_73_12) =
% 49.75/7.22 | | | | | | | | all_58_2 & $i(all_73_9) & $i(all_73_10)
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | ALPHA: (163) implies:
% 49.75/7.22 | | | | | | | | (164) vapp(all_73_15, all_73_12) = all_58_2
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_7,
% 49.75/7.22 | | | | | | | | all_58_6, veabs, all_73_15, all_73_12, all_58_2,
% 49.75/7.22 | | | | | | | | simplifying with (14), (28), (29), (34), (75),
% 49.75/7.22 | | | | | | | | (76), (164) gives:
% 49.75/7.22 | | | | | | | | (165) $false
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | | CLOSE: (165) is inconsistent.
% 49.75/7.22 | | | | | | | |
% 49.75/7.22 | | | | | | | End of split
% 49.75/7.22 | | | | | | |
% 49.75/7.22 | | | | | | End of split
% 49.75/7.22 | | | | | |
% 49.75/7.22 | | | | | Case 2:
% 49.75/7.22 | | | | | |
% 49.75/7.23 | | | | | | (166) (all_73_16 = all_58_2 & all_73_19 = all_58_9 & all_73_20 =
% 49.75/7.23 | | | | | | all_58_9 & all_73_21 = all_58_8 & all_58_1 = all_58_2 &
% 49.75/7.23 | | | | | | vabs(all_58_9, all_73_18, all_73_17) = all_58_2) |
% 49.75/7.23 | | | | | | (all_73_22 = all_58_1 & all_73_26 = all_73_33 & all_73_30 =
% 49.75/7.23 | | | | | | 0 & all_73_31 = all_58_2 & all_73_36 = all_58_8 &
% 49.75/7.23 | | | | | | all_73_37 = all_58_9 & ~ (all_73_34 = all_58_9) &
% 49.75/7.23 | | | | | | vsubst(all_73_34, all_73_25, all_73_32) = all_73_24 &
% 49.75/7.23 | | | | | | vsubst(all_58_9, all_58_8, all_73_23) = all_58_1 &
% 49.75/7.23 | | | | | | vgensym(all_73_27) = all_73_33 & visFreeVar(all_73_34,
% 49.75/7.23 | | | | | | all_58_8) = 0 & vapp(all_73_29, all_73_28) = all_73_27
% 49.75/7.23 | | | | | | & vapp(all_58_8, all_73_32) = all_73_29 & vabs(all_73_33,
% 49.75/7.23 | | | | | | all_73_35, all_73_24) = all_73_23 & vabs(all_73_34,
% 49.75/7.23 | | | | | | all_73_35, all_73_32) = all_58_2 & vvar(all_73_33) =
% 49.75/7.23 | | | | | | all_73_25 & vvar(all_58_9) = all_73_28 & $i(all_73_23) &
% 49.75/7.23 | | | | | | $i(all_73_24) & $i(all_73_25) & $i(all_73_27) &
% 49.75/7.23 | | | | | | $i(all_73_28) & $i(all_73_29)) | (all_73_38 = all_58_1 &
% 49.75/7.23 | | | | | | all_73_41 = all_58_2 & all_73_43 = all_58_8 & all_73_44 =
% 49.75/7.23 | | | | | | all_58_9 & ~ (all_73_40 = 0) & ~ (all_73_46 = all_58_9)
% 49.75/7.23 | | | | | | & vsubst(all_58_9, all_58_8, all_73_42) = all_73_39 &
% 49.75/7.23 | | | | | | visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 49.75/7.23 | | | | | | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 &
% 49.75/7.23 | | | | | | vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 49.75/7.23 | | | | | | $i(all_73_39))
% 49.75/7.23 | | | | | |
% 49.75/7.23 | | | | | | BETA: splitting (166) gives:
% 49.75/7.23 | | | | | |
% 49.75/7.23 | | | | | | Case 1:
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | (167) all_73_16 = all_58_2 & all_73_19 = all_58_9 & all_73_20 =
% 49.75/7.23 | | | | | | | all_58_9 & all_73_21 = all_58_8 & all_58_1 = all_58_2 &
% 49.75/7.23 | | | | | | | vabs(all_58_9, all_73_18, all_73_17) = all_58_2
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | ALPHA: (167) implies:
% 49.75/7.23 | | | | | | | (168) vabs(all_58_9, all_73_18, all_73_17) = all_58_2
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | REF_CLOSE: (1), (14), (21), (26), (28), (29), (34), (73), (74),
% 49.75/7.23 | | | | | | | (168) are inconsistent by sub-proof #5.
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | Case 2:
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | (169) (all_73_22 = all_58_1 & all_73_26 = all_73_33 & all_73_30
% 49.75/7.23 | | | | | | | = 0 & all_73_31 = all_58_2 & all_73_36 = all_58_8 &
% 49.75/7.23 | | | | | | | all_73_37 = all_58_9 & ~ (all_73_34 = all_58_9) &
% 49.75/7.23 | | | | | | | vsubst(all_73_34, all_73_25, all_73_32) = all_73_24 &
% 49.75/7.23 | | | | | | | vsubst(all_58_9, all_58_8, all_73_23) = all_58_1 &
% 49.75/7.23 | | | | | | | vgensym(all_73_27) = all_73_33 & visFreeVar(all_73_34,
% 49.75/7.23 | | | | | | | all_58_8) = 0 & vapp(all_73_29, all_73_28) =
% 49.75/7.23 | | | | | | | all_73_27 & vapp(all_58_8, all_73_32) = all_73_29 &
% 49.75/7.23 | | | | | | | vabs(all_73_33, all_73_35, all_73_24) = all_73_23 &
% 49.75/7.23 | | | | | | | vabs(all_73_34, all_73_35, all_73_32) = all_58_2 &
% 49.75/7.23 | | | | | | | vvar(all_73_33) = all_73_25 & vvar(all_58_9) =
% 49.75/7.23 | | | | | | | all_73_28 & $i(all_73_23) & $i(all_73_24) &
% 49.75/7.23 | | | | | | | $i(all_73_25) & $i(all_73_27) & $i(all_73_28) &
% 49.75/7.23 | | | | | | | $i(all_73_29)) | (all_73_38 = all_58_1 & all_73_41 =
% 49.75/7.23 | | | | | | | all_58_2 & all_73_43 = all_58_8 & all_73_44 = all_58_9
% 49.75/7.23 | | | | | | | & ~ (all_73_40 = 0) & ~ (all_73_46 = all_58_9) &
% 49.75/7.23 | | | | | | | vsubst(all_58_9, all_58_8, all_73_42) = all_73_39 &
% 49.75/7.23 | | | | | | | visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 49.75/7.23 | | | | | | | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 &
% 49.75/7.23 | | | | | | | vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 49.75/7.23 | | | | | | | $i(all_73_39))
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | BETA: splitting (169) gives:
% 49.75/7.23 | | | | | | |
% 49.75/7.23 | | | | | | | Case 1:
% 49.75/7.23 | | | | | | | |
% 49.75/7.23 | | | | | | | | (170) all_73_22 = all_58_1 & all_73_26 = all_73_33 &
% 49.75/7.23 | | | | | | | | all_73_30 = 0 & all_73_31 = all_58_2 & all_73_36 =
% 49.75/7.23 | | | | | | | | all_58_8 & all_73_37 = all_58_9 & ~ (all_73_34 =
% 49.75/7.23 | | | | | | | | all_58_9) & vsubst(all_73_34, all_73_25, all_73_32) =
% 49.75/7.23 | | | | | | | | all_73_24 & vsubst(all_58_9, all_58_8, all_73_23) =
% 49.75/7.23 | | | | | | | | all_58_1 & vgensym(all_73_27) = all_73_33 &
% 49.75/7.23 | | | | | | | | visFreeVar(all_73_34, all_58_8) = 0 & vapp(all_73_29,
% 49.75/7.23 | | | | | | | | all_73_28) = all_73_27 & vapp(all_58_8, all_73_32) =
% 49.75/7.23 | | | | | | | | all_73_29 & vabs(all_73_33, all_73_35, all_73_24) =
% 49.75/7.23 | | | | | | | | all_73_23 & vabs(all_73_34, all_73_35, all_73_32) =
% 49.75/7.23 | | | | | | | | all_58_2 & vvar(all_73_33) = all_73_25 & vvar(all_58_9)
% 49.75/7.23 | | | | | | | | = all_73_28 & $i(all_73_23) & $i(all_73_24) &
% 49.75/7.23 | | | | | | | | $i(all_73_25) & $i(all_73_27) & $i(all_73_28) &
% 49.75/7.23 | | | | | | | | $i(all_73_29)
% 49.75/7.23 | | | | | | | |
% 49.75/7.23 | | | | | | | | ALPHA: (170) implies:
% 49.75/7.23 | | | | | | | | (171) vabs(all_73_34, all_73_35, all_73_32) = all_58_2
% 50.17/7.23 | | | | | | | | (172) visFreeVar(all_73_34, all_58_8) = 0
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | | REF_CLOSE: (1), (14), (16), (22), (28), (29), (34), (35), (69),
% 50.17/7.23 | | | | | | | | (70), (71), (171), (172) are inconsistent by
% 50.17/7.23 | | | | | | | | sub-proof #4.
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | Case 2:
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | | (173) all_73_38 = all_58_1 & all_73_41 = all_58_2 & all_73_43
% 50.17/7.23 | | | | | | | | = all_58_8 & all_73_44 = all_58_9 & ~ (all_73_40 = 0)
% 50.17/7.23 | | | | | | | | & ~ (all_73_46 = all_58_9) & vsubst(all_58_9,
% 50.17/7.23 | | | | | | | | all_58_8, all_73_42) = all_73_39 &
% 50.17/7.23 | | | | | | | | visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 50.17/7.23 | | | | | | | | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 &
% 50.17/7.23 | | | | | | | | vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 50.17/7.23 | | | | | | | | $i(all_73_39)
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | | ALPHA: (173) implies:
% 50.17/7.23 | | | | | | | | (174) all_73_44 = all_58_9
% 50.17/7.23 | | | | | | | | (175) all_73_43 = all_58_8
% 50.17/7.23 | | | | | | | | (176) ~ (all_73_40 = 0)
% 50.17/7.23 | | | | | | | | (177) $i(all_73_39)
% 50.17/7.23 | | | | | | | | (178) vabs(all_73_46, all_73_45, all_73_42) = all_58_2
% 50.17/7.23 | | | | | | | | (179) vabs(all_73_46, all_73_45, all_73_39) = all_58_1
% 50.17/7.23 | | | | | | | | (180) visFreeVar(all_73_46, all_58_8) = all_73_40
% 50.17/7.23 | | | | | | | | (181) vsubst(all_58_9, all_58_8, all_73_42) = all_73_39
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | | BETA: splitting (103) gives:
% 50.17/7.23 | | | | | | | |
% 50.17/7.23 | | | | | | | | Case 1:
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | (182) all_89_0 = 0 & all_89_2 = all_58_5 & all_89_3 =
% 50.17/7.23 | | | | | | | | | all_80_0 & varrow(all_89_5, all_89_4) = all_58_5 &
% 50.17/7.23 | | | | | | | | | vtcheck(all_89_1, all_89_6, all_89_4) = 0 &
% 50.17/7.23 | | | | | | | | | vbind(all_89_7, all_89_5, all_58_10) = all_89_1 &
% 50.17/7.23 | | | | | | | | | vabs(all_89_7, all_89_5, all_89_6) = all_80_0 &
% 50.17/7.23 | | | | | | | | | $i(all_89_1)
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | ALPHA: (182) implies:
% 50.17/7.23 | | | | | | | | | (183) vabs(all_89_7, all_89_5, all_89_6) = all_80_0
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_89_7,
% 50.17/7.23 | | | | | | | | | all_89_5, all_89_6, all_67_1, all_58_8, all_80_0,
% 50.17/7.23 | | | | | | | | | simplifying with (27), (49), (84), (100), (101),
% 50.17/7.23 | | | | | | | | | (102), (183) gives:
% 50.17/7.23 | | | | | | | | | (184) $false
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | CLOSE: (184) is inconsistent.
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | Case 2:
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | (185) (all_89_8 = 0 & all_89_9 = 0 & all_89_11 = all_80_0 &
% 50.17/7.23 | | | | | | | | | varrow(all_89_12, all_58_5) = all_89_10 &
% 50.17/7.23 | | | | | | | | | vtcheck(all_58_10, all_89_13, all_89_12) = 0 &
% 50.17/7.23 | | | | | | | | | vtcheck(all_58_10, all_89_14, all_89_10) = 0 &
% 50.17/7.23 | | | | | | | | | vapp(all_89_14, all_89_13) = all_80_0 &
% 50.17/7.23 | | | | | | | | | $i(all_89_10)) | (all_89_15 = all_89_18 & all_89_16
% 50.17/7.23 | | | | | | | | | = all_80_0 & vlookup(all_89_17, all_58_10) =
% 50.17/7.23 | | | | | | | | | all_89_18 & vsomeType(all_58_5) = all_89_18 &
% 50.17/7.23 | | | | | | | | | vvar(all_89_17) = all_80_0 & $i(all_89_18))
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | BETA: splitting (185) gives:
% 50.17/7.23 | | | | | | | | |
% 50.17/7.23 | | | | | | | | | Case 1:
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | (186) all_89_8 = 0 & all_89_9 = 0 & all_89_11 = all_80_0
% 50.17/7.23 | | | | | | | | | | & varrow(all_89_12, all_58_5) = all_89_10 &
% 50.17/7.23 | | | | | | | | | | vtcheck(all_58_10, all_89_13, all_89_12) = 0 &
% 50.17/7.23 | | | | | | | | | | vtcheck(all_58_10, all_89_14, all_89_10) = 0 &
% 50.17/7.23 | | | | | | | | | | vapp(all_89_14, all_89_13) = all_80_0 &
% 50.17/7.23 | | | | | | | | | | $i(all_89_10)
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | ALPHA: (186) implies:
% 50.17/7.23 | | | | | | | | | | (187) vapp(all_89_14, all_89_13) = all_80_0
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | GROUND_INST: instantiating (3) with all_58_7, all_58_6, veabs,
% 50.17/7.23 | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.23 | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.23 | | | | | | | | | | (65), (68), (178) gives:
% 50.17/7.23 | | | | | | | | | | (188) all_73_42 = veabs
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | GROUND_INST: instantiating (2) with all_58_7, all_58_6, veabs,
% 50.17/7.23 | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.23 | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.23 | | | | | | | | | | (65), (68), (178) gives:
% 50.17/7.23 | | | | | | | | | | (189) all_73_45 = all_58_6
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | GROUND_INST: instantiating (1) with all_58_7, all_58_6, veabs,
% 50.17/7.23 | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.23 | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.23 | | | | | | | | | | (65), (68), (178) gives:
% 50.17/7.23 | | | | | | | | | | (190) all_73_46 = all_58_7
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | GROUND_INST: instantiating (4) with all_67_1, all_58_8,
% 50.17/7.23 | | | | | | | | | | all_89_14, all_89_13, all_80_0, simplifying with
% 50.17/7.23 | | | | | | | | | | (27), (49), (84), (98), (99), (187) gives:
% 50.17/7.23 | | | | | | | | | | (191) all_89_13 = all_58_8
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | REDUCE: (181), (188) imply:
% 50.17/7.23 | | | | | | | | | | (192) vsubst(all_58_9, all_58_8, veabs) = all_73_39
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | REDUCE: (180), (190) imply:
% 50.17/7.23 | | | | | | | | | | (193) visFreeVar(all_58_7, all_58_8) = all_73_40
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | REDUCE: (179), (189), (190) imply:
% 50.17/7.23 | | | | | | | | | | (194) vabs(all_58_7, all_58_6, all_73_39) = all_58_1
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | GROUND_INST: instantiating (16) with all_58_4, all_73_40,
% 50.17/7.23 | | | | | | | | | | all_58_8, all_58_7, simplifying with (35), (193)
% 50.17/7.23 | | | | | | | | | | gives:
% 50.17/7.23 | | | | | | | | | | (195) all_73_40 = all_58_4
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | BETA: splitting (115) gives:
% 50.17/7.23 | | | | | | | | | |
% 50.17/7.23 | | | | | | | | | | Case 1:
% 50.17/7.23 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | (196) all_103_0 = 0 & all_103_2 = all_58_5 & all_103_3 =
% 50.17/7.24 | | | | | | | | | | | all_58_2 & varrow(all_103_5, all_103_4) = all_58_5
% 50.17/7.24 | | | | | | | | | | | & vtcheck(all_103_1, all_103_6, all_103_4) = 0 &
% 50.17/7.24 | | | | | | | | | | | vbind(all_103_7, all_103_5, all_58_10) = all_103_1
% 50.17/7.24 | | | | | | | | | | | & vabs(all_103_7, all_103_5, all_103_6) = all_58_2
% 50.17/7.24 | | | | | | | | | | | & $i(all_103_1)
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | ALPHA: (196) implies:
% 50.17/7.24 | | | | | | | | | | | (197) vabs(all_103_7, all_103_5, all_103_6) = all_58_2
% 50.17/7.24 | | | | | | | | | | | (198) vbind(all_103_7, all_103_5, all_58_10) = all_103_1
% 50.17/7.24 | | | | | | | | | | | (199) varrow(all_103_5, all_103_4) = all_58_5
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | GROUND_INST: instantiating (10) with all_58_10, all_58_7,
% 50.17/7.24 | | | | | | | | | | | all_73_39, all_58_6, all_71_4, all_58_1, all_58_5,
% 50.17/7.24 | | | | | | | | | | | all_58_0, simplifying with (25), (28), (29), (38),
% 50.17/7.24 | | | | | | | | | | | (61), (125), (177), (194) gives:
% 50.17/7.24 | | | | | | | | | | | (200) all_58_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 50.17/7.24 | | | | | | | | | | | (v1 = 0) & vtcheck(v0, all_73_39, all_71_4) = v1
% 50.17/7.24 | | | | | | | | | | | & vbind(all_58_7, all_58_6, all_58_10) = v0 &
% 50.17/7.24 | | | | | | | | | | | $i(v0))
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_58_7, all_58_6, veabs,
% 50.17/7.24 | | | | | | | | | | | all_103_7, all_103_5, all_103_6, all_58_2,
% 50.17/7.24 | | | | | | | | | | | simplifying with (14), (28), (29), (34), (111),
% 50.17/7.24 | | | | | | | | | | | (112), (113), (197) gives:
% 50.17/7.24 | | | | | | | | | | | (201) all_103_6 = veabs
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_58_7, all_58_6, veabs,
% 50.17/7.24 | | | | | | | | | | | all_103_7, all_103_5, all_103_6, all_58_2,
% 50.17/7.24 | | | | | | | | | | | simplifying with (14), (28), (29), (34), (111),
% 50.17/7.24 | | | | | | | | | | | (112), (113), (197) gives:
% 50.17/7.24 | | | | | | | | | | | (202) all_103_7 = all_58_7
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_58_6, all_71_4,
% 50.17/7.24 | | | | | | | | | | | all_103_5, all_103_4, all_58_5, simplifying with
% 50.17/7.24 | | | | | | | | | | | (29), (61), (113), (114), (125), (199) gives:
% 50.17/7.24 | | | | | | | | | | | (203) all_103_4 = all_71_4
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_58_6, all_71_4,
% 50.17/7.24 | | | | | | | | | | | all_103_5, all_103_4, all_58_5, simplifying with
% 50.17/7.24 | | | | | | | | | | | (29), (61), (113), (114), (125), (199) gives:
% 50.17/7.24 | | | | | | | | | | | (204) all_103_5 = all_58_6
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | REDUCE: (198), (202), (204) imply:
% 50.17/7.24 | | | | | | | | | | | (205) vbind(all_58_7, all_58_6, all_58_10) = all_103_1
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | BETA: splitting (200) gives:
% 50.17/7.24 | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | Case 1:
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | (206) all_58_0 = 0
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | REDUCE: (23), (206) imply:
% 50.17/7.24 | | | | | | | | | | | | (207) $false
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | Case 2:
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | (208) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 50.17/7.24 | | | | | | | | | | | | vtcheck(v0, all_73_39, all_71_4) = v1 &
% 50.17/7.24 | | | | | | | | | | | | vbind(all_58_7, all_58_6, all_58_10) = v0 &
% 50.17/7.24 | | | | | | | | | | | | $i(v0))
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | DELTA: instantiating (208) with fresh symbols all_247_0,
% 50.17/7.24 | | | | | | | | | | | | all_247_1 gives:
% 50.17/7.24 | | | | | | | | | | | | (209) ~ (all_247_0 = 0) & vtcheck(all_247_1, all_73_39,
% 50.17/7.24 | | | | | | | | | | | | all_71_4) = all_247_0 & vbind(all_58_7,
% 50.17/7.24 | | | | | | | | | | | | all_58_6, all_58_10) = all_247_1 & $i(all_247_1)
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | ALPHA: (209) implies:
% 50.17/7.24 | | | | | | | | | | | | (210) ~ (all_247_0 = 0)
% 50.17/7.24 | | | | | | | | | | | | (211) vbind(all_58_7, all_58_6, all_58_10) = all_247_1
% 50.17/7.24 | | | | | | | | | | | | (212) vtcheck(all_247_1, all_73_39, all_71_4) =
% 50.17/7.24 | | | | | | | | | | | | all_247_0
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_140_1, all_247_1,
% 50.17/7.24 | | | | | | | | | | | | all_58_10, all_58_6, all_58_7, simplifying with
% 50.17/7.24 | | | | | | | | | | | | (137), (211) gives:
% 50.17/7.24 | | | | | | | | | | | | (213) all_247_1 = all_140_1
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_103_1, all_247_1,
% 50.17/7.24 | | | | | | | | | | | | all_58_10, all_58_6, all_58_7, simplifying with
% 50.17/7.24 | | | | | | | | | | | | (205), (211) gives:
% 50.17/7.24 | | | | | | | | | | | | (214) all_247_1 = all_103_1
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | COMBINE_EQS: (213), (214) imply:
% 50.17/7.24 | | | | | | | | | | | | (215) all_140_1 = all_103_1
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | SIMP: (215) implies:
% 50.17/7.24 | | | | | | | | | | | | (216) all_140_1 = all_103_1
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | REDUCE: (212), (214) imply:
% 50.17/7.24 | | | | | | | | | | | | (217) vtcheck(all_103_1, all_73_39, all_71_4) =
% 50.17/7.24 | | | | | | | | | | | | all_247_0
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | REDUCE: (133), (216) imply:
% 50.17/7.24 | | | | | | | | | | | | (218) vbind(all_58_9, all_58_11, all_103_1) = all_140_0
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | REDUCE: (132), (216) imply:
% 50.17/7.24 | | | | | | | | | | | | (219) $i(all_103_1)
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_58_11, all_103_1,
% 50.17/7.24 | | | | | | | | | | | | all_58_9, all_58_8, all_71_4, all_140_0,
% 50.17/7.24 | | | | | | | | | | | | all_73_39, all_247_0, simplifying with (24), (26),
% 50.17/7.24 | | | | | | | | | | | | (27), (61), (136), (192), (217), (218), (219)
% 50.17/7.24 | | | | | | | | | | | | gives:
% 50.17/7.24 | | | | | | | | | | | | (220) all_247_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 50.17/7.24 | | | | | | | | | | | | vtcheck(all_103_1, all_58_8, all_58_11) = v0)
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | BETA: splitting (220) gives:
% 50.17/7.24 | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | Case 1:
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | (221) all_247_0 = 0
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | REDUCE: (210), (221) imply:
% 50.17/7.24 | | | | | | | | | | | | | (222) $false
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | Case 2:
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | (223) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_103_1,
% 50.17/7.24 | | | | | | | | | | | | | all_58_8, all_58_11) = v0)
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_366_0
% 50.17/7.24 | | | | | | | | | | | | | gives:
% 50.17/7.24 | | | | | | | | | | | | | (224) ~ (all_366_0 = 0) & vtcheck(all_103_1, all_58_8,
% 50.17/7.24 | | | | | | | | | | | | | all_58_11) = all_366_0
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | ALPHA: (224) implies:
% 50.17/7.24 | | | | | | | | | | | | | (225) ~ (all_366_0 = 0)
% 50.17/7.24 | | | | | | | | | | | | | (226) vtcheck(all_103_1, all_58_8, all_58_11) =
% 50.17/7.24 | | | | | | | | | | | | | all_366_0
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 50.17/7.24 | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | Case 1:
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | GROUND_INST: instantiating (T-Weak-FreeVar) with all_58_7,
% 50.17/7.24 | | | | | | | | | | | | | | all_58_6, all_58_10, all_58_8, all_58_11,
% 50.17/7.24 | | | | | | | | | | | | | | all_103_1, all_366_0, simplifying with (24), (25),
% 50.17/7.24 | | | | | | | | | | | | | | (27), (28), (29), (205), (226) gives:
% 50.17/7.24 | | | | | | | | | | | | | | (227) all_366_0 = 0 | ? [v0: any] : ? [v1: any] :
% 50.17/7.24 | | | | | | | | | | | | | | (vtcheck(all_58_10, all_58_8, all_58_11) = v1 &
% 50.17/7.24 | | | | | | | | | | | | | | visFreeVar(all_58_7, all_58_8) = v0 & ( ~ (v1 =
% 50.17/7.24 | | | | | | | | | | | | | | 0) | v0 = 0))
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | Case 1:
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | (228) all_366_0 = 0
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | REDUCE: (225), (228) imply:
% 50.17/7.24 | | | | | | | | | | | | | | | (229) $false
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | Case 2:
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | (230) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_10,
% 50.17/7.24 | | | | | | | | | | | | | | | all_58_8, all_58_11) = v1 &
% 50.17/7.24 | | | | | | | | | | | | | | | visFreeVar(all_58_7, all_58_8) = v0 & ( ~ (v1 =
% 50.17/7.24 | | | | | | | | | | | | | | | 0) | v0 = 0))
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_603_0,
% 50.17/7.24 | | | | | | | | | | | | | | | all_603_1 gives:
% 50.17/7.24 | | | | | | | | | | | | | | | (231) vtcheck(all_58_10, all_58_8, all_58_11) =
% 50.17/7.24 | | | | | | | | | | | | | | | all_603_0 & visFreeVar(all_58_7, all_58_8) =
% 50.17/7.24 | | | | | | | | | | | | | | | all_603_1 & ( ~ (all_603_0 = 0) | all_603_1 = 0)
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (22), (35), (37), (231) are
% 50.17/7.24 | | | | | | | | | | | | | | | inconsistent by sub-proof #3.
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | End of split
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | Case 2:
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | (232) (all_168_8 = 0 & all_168_9 = 0 & all_168_11 =
% 50.17/7.24 | | | | | | | | | | | | | | all_151_1 & varrow(all_168_12, all_151_0) =
% 50.17/7.24 | | | | | | | | | | | | | | all_168_10 & vtcheck(all_140_1, all_168_13,
% 50.17/7.24 | | | | | | | | | | | | | | all_168_12) = 0 & vtcheck(all_140_1,
% 50.17/7.24 | | | | | | | | | | | | | | all_168_14, all_168_10) = 0 & vapp(all_168_14,
% 50.17/7.24 | | | | | | | | | | | | | | all_168_13) = all_151_1 & $i(all_168_10)) |
% 50.17/7.24 | | | | | | | | | | | | | | (all_168_15 = all_168_18 & all_168_16 = all_151_1
% 50.17/7.24 | | | | | | | | | | | | | | & vlookup(all_168_17, all_140_1) = all_168_18 &
% 50.17/7.24 | | | | | | | | | | | | | | vsomeType(all_151_0) = all_168_18 &
% 50.17/7.24 | | | | | | | | | | | | | | vvar(all_168_17) = all_151_1 & $i(all_168_18))
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 50.17/7.24 | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | Case 1:
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | (233) all_168_8 = 0 & all_168_9 = 0 & all_168_11 =
% 50.17/7.24 | | | | | | | | | | | | | | | all_151_1 & varrow(all_168_12, all_151_0) =
% 50.17/7.24 | | | | | | | | | | | | | | | all_168_10 & vtcheck(all_140_1, all_168_13,
% 50.17/7.24 | | | | | | | | | | | | | | | all_168_12) = 0 & vtcheck(all_140_1, all_168_14,
% 50.17/7.24 | | | | | | | | | | | | | | | all_168_10) = 0 & vapp(all_168_14, all_168_13) =
% 50.17/7.24 | | | | | | | | | | | | | | | all_151_1 & $i(all_168_10)
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 50.17/7.24 | | | | | | | | | | | | | | | (234) vapp(all_168_14, all_168_13) = all_151_1
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_9,
% 50.17/7.24 | | | | | | | | | | | | | | | all_58_11, veabs, all_168_14, all_168_13,
% 50.17/7.24 | | | | | | | | | | | | | | | all_151_1, simplifying with (14), (24), (26),
% 50.17/7.24 | | | | | | | | | | | | | | | (142), (147), (148), (234) gives:
% 50.17/7.24 | | | | | | | | | | | | | | | (235) $false
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.24 | | | | | | | | | | | | | | Case 2:
% 50.17/7.24 | | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | | | (236) all_168_15 = all_168_18 & all_168_16 = all_151_1 &
% 50.17/7.25 | | | | | | | | | | | | | | | vlookup(all_168_17, all_140_1) = all_168_18 &
% 50.17/7.25 | | | | | | | | | | | | | | | vsomeType(all_151_0) = all_168_18 &
% 50.17/7.25 | | | | | | | | | | | | | | | vvar(all_168_17) = all_151_1 & $i(all_168_18)
% 50.17/7.25 | | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 50.17/7.25 | | | | | | | | | | | | | | | (237) vvar(all_168_17) = all_151_1
% 50.17/7.25 | | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_168_17,
% 50.17/7.25 | | | | | | | | | | | | | | | all_58_9, all_58_11, veabs, all_151_1, simplifying
% 50.17/7.25 | | | | | | | | | | | | | | | with (14), (24), (26), (142), (146), (237) gives:
% 50.17/7.25 | | | | | | | | | | | | | | | (238) $false
% 50.17/7.25 | | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 50.17/7.25 | | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | Case 2:
% 50.17/7.25 | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | (239) (all_103_8 = 0 & all_103_9 = 0 & all_103_11 =
% 50.17/7.25 | | | | | | | | | | | all_58_2 & varrow(all_103_12, all_58_5) =
% 50.17/7.25 | | | | | | | | | | | all_103_10 & vtcheck(all_58_10, all_103_13,
% 50.17/7.25 | | | | | | | | | | | all_103_12) = 0 & vtcheck(all_58_10,
% 50.17/7.25 | | | | | | | | | | | all_103_14, all_103_10) = 0 & vapp(all_103_14,
% 50.17/7.25 | | | | | | | | | | | all_103_13) = all_58_2 & $i(all_103_10)) |
% 50.17/7.25 | | | | | | | | | | | (all_103_15 = all_103_18 & all_103_16 = all_58_2 &
% 50.17/7.25 | | | | | | | | | | | vlookup(all_103_17, all_58_10) = all_103_18 &
% 50.17/7.25 | | | | | | | | | | | vsomeType(all_58_5) = all_103_18 &
% 50.17/7.25 | | | | | | | | | | | vvar(all_103_17) = all_58_2 & $i(all_103_18))
% 50.17/7.25 | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | BETA: splitting (239) gives:
% 50.17/7.25 | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | Case 1:
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | (240) all_103_8 = 0 & all_103_9 = 0 & all_103_11 =
% 50.17/7.25 | | | | | | | | | | | | all_58_2 & varrow(all_103_12, all_58_5) =
% 50.17/7.25 | | | | | | | | | | | | all_103_10 & vtcheck(all_58_10, all_103_13,
% 50.17/7.25 | | | | | | | | | | | | all_103_12) = 0 & vtcheck(all_58_10, all_103_14,
% 50.17/7.25 | | | | | | | | | | | | all_103_10) = 0 & vapp(all_103_14, all_103_13) =
% 50.17/7.25 | | | | | | | | | | | | all_58_2 & $i(all_103_10)
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | ALPHA: (240) implies:
% 50.17/7.25 | | | | | | | | | | | | (241) vapp(all_103_14, all_103_13) = all_58_2
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_7,
% 50.17/7.25 | | | | | | | | | | | | all_58_6, veabs, all_103_14, all_103_13, all_58_2,
% 50.17/7.25 | | | | | | | | | | | | simplifying with (14), (28), (29), (34), (109),
% 50.17/7.25 | | | | | | | | | | | | (110), (241) gives:
% 50.17/7.25 | | | | | | | | | | | | (242) $false
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | Case 2:
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | (243) all_103_15 = all_103_18 & all_103_16 = all_58_2 &
% 50.17/7.25 | | | | | | | | | | | | vlookup(all_103_17, all_58_10) = all_103_18 &
% 50.17/7.25 | | | | | | | | | | | | vsomeType(all_58_5) = all_103_18 &
% 50.17/7.25 | | | | | | | | | | | | vvar(all_103_17) = all_58_2 & $i(all_103_18)
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | ALPHA: (243) implies:
% 50.17/7.25 | | | | | | | | | | | | (244) vvar(all_103_17) = all_58_2
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_103_17,
% 50.17/7.25 | | | | | | | | | | | | all_58_7, all_58_6, veabs, all_58_2, simplifying
% 50.17/7.25 | | | | | | | | | | | | with (14), (28), (29), (34), (108), (244) gives:
% 50.17/7.25 | | | | | | | | | | | | (245) $false
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 50.17/7.25 | | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | Case 2:
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | (246) all_89_15 = all_89_18 & all_89_16 = all_80_0 &
% 50.17/7.25 | | | | | | | | | | vlookup(all_89_17, all_58_10) = all_89_18 &
% 50.17/7.25 | | | | | | | | | | vsomeType(all_58_5) = all_89_18 & vvar(all_89_17) =
% 50.17/7.25 | | | | | | | | | | all_80_0 & $i(all_89_18)
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | ALPHA: (246) implies:
% 50.17/7.25 | | | | | | | | | | (247) vvar(all_89_17) = all_80_0
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-app) with all_89_17,
% 50.17/7.25 | | | | | | | | | | all_67_1, all_58_8, all_80_0, simplifying with
% 50.17/7.25 | | | | | | | | | | (27), (49), (84), (97), (247) gives:
% 50.17/7.25 | | | | | | | | | | (248) $false
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | | CLOSE: (248) is inconsistent.
% 50.17/7.25 | | | | | | | | | |
% 50.17/7.25 | | | | | | | | | End of split
% 50.17/7.25 | | | | | | | | |
% 50.17/7.25 | | | | | | | | End of split
% 50.17/7.25 | | | | | | | |
% 50.17/7.25 | | | | | | | End of split
% 50.17/7.25 | | | | | | |
% 50.17/7.25 | | | | | | End of split
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | End of split
% 50.17/7.25 | | | | |
% 50.17/7.25 | | | | Case 2:
% 50.17/7.25 | | | | |
% 50.17/7.25 | | | | | (249) (all_82_8 = 0 & all_82_9 = 0 & all_82_11 = all_67_1 &
% 50.17/7.25 | | | | | varrow(all_82_12, all_67_0) = all_82_10 &
% 50.17/7.25 | | | | | vtcheck(all_58_10, all_82_13, all_82_12) = 0 &
% 50.17/7.25 | | | | | vtcheck(all_58_10, all_82_14, all_82_10) = 0 &
% 50.17/7.25 | | | | | vapp(all_82_14, all_82_13) = all_67_1 & $i(all_82_10)) |
% 50.17/7.25 | | | | | (all_82_15 = all_82_18 & all_82_16 = all_67_1 &
% 50.17/7.25 | | | | | vlookup(all_82_17, all_58_10) = all_82_18 &
% 50.17/7.25 | | | | | vsomeType(all_67_0) = all_82_18 & vvar(all_82_17) =
% 50.17/7.25 | | | | | all_67_1 & $i(all_82_18))
% 50.17/7.25 | | | | |
% 50.17/7.25 | | | | | BETA: splitting (249) gives:
% 50.17/7.25 | | | | |
% 50.17/7.25 | | | | | Case 1:
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | (250) all_82_8 = 0 & all_82_9 = 0 & all_82_11 = all_67_1 &
% 50.17/7.25 | | | | | | varrow(all_82_12, all_67_0) = all_82_10 &
% 50.17/7.25 | | | | | | vtcheck(all_58_10, all_82_13, all_82_12) = 0 &
% 50.17/7.25 | | | | | | vtcheck(all_58_10, all_82_14, all_82_10) = 0 &
% 50.17/7.25 | | | | | | vapp(all_82_14, all_82_13) = all_67_1 & $i(all_82_10)
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | ALPHA: (250) implies:
% 50.17/7.25 | | | | | | (251) vapp(all_82_14, all_82_13) = all_67_1
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_9, all_58_11,
% 50.17/7.25 | | | | | | all_58_2, all_82_14, all_82_13, all_67_1, simplifying
% 50.17/7.25 | | | | | | with (24), (26), (32), (51), (88), (89), (251) gives:
% 50.17/7.25 | | | | | | (252) $false
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | CLOSE: (252) is inconsistent.
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | Case 2:
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | (253) all_82_15 = all_82_18 & all_82_16 = all_67_1 &
% 50.17/7.25 | | | | | | vlookup(all_82_17, all_58_10) = all_82_18 &
% 50.17/7.25 | | | | | | vsomeType(all_67_0) = all_82_18 & vvar(all_82_17) =
% 50.17/7.25 | | | | | | all_67_1 & $i(all_82_18)
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | ALPHA: (253) implies:
% 50.17/7.25 | | | | | | (254) vvar(all_82_17) = all_67_1
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_82_17, all_58_9,
% 50.17/7.25 | | | | | | all_58_11, all_58_2, all_67_1, simplifying with (24),
% 50.17/7.25 | | | | | | (26), (32), (51), (87), (254) gives:
% 50.17/7.25 | | | | | | (255) $false
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | | CLOSE: (255) is inconsistent.
% 50.17/7.25 | | | | | |
% 50.17/7.25 | | | | | End of split
% 50.17/7.25 | | | | |
% 50.17/7.25 | | | | End of split
% 50.17/7.25 | | | |
% 50.17/7.25 | | | End of split
% 50.17/7.25 | | |
% 50.17/7.25 | | Case 2:
% 50.17/7.25 | | |
% 50.17/7.25 | | | (256) (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_2 &
% 50.17/7.25 | | | varrow(all_71_12, all_58_5) = all_71_10 & vtcheck(all_58_3,
% 50.17/7.25 | | | all_71_13, all_71_12) = 0 & vtcheck(all_58_3, all_71_14,
% 50.17/7.25 | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_2 &
% 50.17/7.25 | | | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_58_2
% 50.17/7.25 | | | & vlookup(all_71_17, all_58_3) = all_71_18 &
% 50.17/7.25 | | | vsomeType(all_58_5) = all_71_18 & vvar(all_71_17) = all_58_2 &
% 50.17/7.25 | | | $i(all_71_18))
% 50.17/7.25 | | |
% 50.17/7.25 | | | BETA: splitting (256) gives:
% 50.17/7.25 | | |
% 50.17/7.25 | | | Case 1:
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | (257) all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_2 &
% 50.17/7.25 | | | | varrow(all_71_12, all_58_5) = all_71_10 & vtcheck(all_58_3,
% 50.17/7.25 | | | | all_71_13, all_71_12) = 0 & vtcheck(all_58_3, all_71_14,
% 50.17/7.25 | | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_2 &
% 50.17/7.25 | | | | $i(all_71_10)
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | ALPHA: (257) implies:
% 50.17/7.25 | | | | (258) vapp(all_71_14, all_71_13) = all_58_2
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_7, all_58_6,
% 50.17/7.25 | | | | veabs, all_71_14, all_71_13, all_58_2, simplifying with
% 50.17/7.25 | | | | (14), (28), (29), (34), (56), (57), (258) gives:
% 50.17/7.25 | | | | (259) $false
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | CLOSE: (259) is inconsistent.
% 50.17/7.25 | | | |
% 50.17/7.25 | | | Case 2:
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | (260) all_71_15 = all_71_18 & all_71_16 = all_58_2 &
% 50.17/7.25 | | | | vlookup(all_71_17, all_58_3) = all_71_18 & vsomeType(all_58_5)
% 50.17/7.25 | | | | = all_71_18 & vvar(all_71_17) = all_58_2 & $i(all_71_18)
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | ALPHA: (260) implies:
% 50.17/7.25 | | | | (261) vvar(all_71_17) = all_58_2
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_71_17, all_58_7,
% 50.17/7.25 | | | | all_58_6, veabs, all_58_2, simplifying with (14), (28),
% 50.17/7.25 | | | | (29), (34), (55), (261) gives:
% 50.17/7.25 | | | | (262) $false
% 50.17/7.25 | | | |
% 50.17/7.25 | | | | CLOSE: (262) is inconsistent.
% 50.17/7.25 | | | |
% 50.17/7.25 | | | End of split
% 50.17/7.25 | | |
% 50.17/7.25 | | End of split
% 50.17/7.25 | |
% 50.17/7.25 | Case 2:
% 50.17/7.25 | |
% 50.17/7.25 | | (263) ~ (all_65_0 = 0)
% 50.17/7.25 | |
% 50.17/7.25 | | BETA: splitting (62) gives:
% 50.17/7.25 | |
% 50.17/7.25 | | Case 1:
% 50.17/7.25 | | |
% 50.17/7.25 | | | (264) all_71_0 = 0 & all_71_2 = all_58_5 & all_71_3 = all_58_2 &
% 50.17/7.25 | | | varrow(all_71_5, all_71_4) = all_58_5 & vtcheck(all_71_1,
% 50.17/7.25 | | | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5, all_58_3) =
% 50.17/7.25 | | | all_71_1 & vabs(all_71_7, all_71_5, all_71_6) = all_58_2 &
% 50.17/7.25 | | | $i(all_71_1)
% 50.17/7.25 | | |
% 50.17/7.25 | | | ALPHA: (264) implies:
% 50.17/7.25 | | | (265) vabs(all_71_7, all_71_5, all_71_6) = all_58_2
% 50.17/7.25 | | | (266) vbind(all_71_7, all_71_5, all_58_3) = all_71_1
% 50.17/7.25 | | | (267) vtcheck(all_71_1, all_71_6, all_71_4) = 0
% 50.17/7.25 | | | (268) varrow(all_71_5, all_71_4) = all_58_5
% 50.17/7.25 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (3) with all_58_7, all_58_6, veabs, all_71_7,
% 50.17/7.26 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 50.17/7.26 | | | (29), (34), (58), (59), (60), (265) gives:
% 50.17/7.26 | | | (269) all_71_6 = veabs
% 50.17/7.26 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (2) with all_58_7, all_58_6, veabs, all_71_7,
% 50.17/7.26 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 50.17/7.26 | | | (29), (34), (58), (59), (60), (265) gives:
% 50.17/7.26 | | | (270) all_71_5 = all_58_6
% 50.17/7.26 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (1) with all_58_7, all_58_6, veabs, all_71_7,
% 50.17/7.26 | | | all_71_5, all_71_6, all_58_2, simplifying with (14), (28),
% 50.17/7.26 | | | (29), (34), (58), (59), (60), (265) gives:
% 50.17/7.26 | | | (271) all_71_7 = all_58_7
% 50.17/7.26 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (6) with all_58_9, all_58_11, all_71_7,
% 50.17/7.26 | | | all_71_5, all_58_10, all_71_6, all_71_4, all_58_3, all_71_1,
% 50.17/7.26 | | | simplifying with (24), (25), (26), (36), (58), (59), (60),
% 50.17/7.26 | | | (61), (266), (267) gives:
% 50.17/7.26 | | | (272) all_71_7 = all_58_9 | ? [v0: $i] : ? [v1: $i] : (vtcheck(v1,
% 50.17/7.26 | | | all_71_6, all_71_4) = 0 & vbind(all_71_7, all_71_5,
% 50.17/7.26 | | | all_58_10) = v0 & vbind(all_58_9, all_58_11, v0) = v1 &
% 50.17/7.26 | | | $i(v1) & $i(v0))
% 50.17/7.26 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (T-Strong) with all_71_7, all_71_5, all_58_3,
% 50.17/7.26 | | | all_71_6, all_71_4, all_71_1, simplifying with (31), (58),
% 50.17/7.26 | | | (59), (60), (61), (266), (267) gives:
% 50.17/7.26 | | | (273) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_3, all_71_6,
% 50.17/7.26 | | | all_71_4) = v1 & visFreeVar(all_71_7, all_71_6) = v0 & (v1 =
% 50.17/7.26 | | | 0 | v0 = 0))
% 50.17/7.26 | | |
% 50.17/7.26 | | | GROUND_INST: instantiating (10) with all_58_10, all_71_7, all_71_6,
% 50.17/7.26 | | | all_71_5, all_71_4, all_58_2, all_58_5, all_65_0, simplifying
% 50.17/7.26 | | | with (25), (46), (58), (59), (60), (61), (265), (268) gives:
% 50.17/7.26 | | | (274) all_65_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 50.17/7.26 | | | vtcheck(v0, all_71_6, all_71_4) = v1 & vbind(all_71_7,
% 50.17/7.26 | | | all_71_5, all_58_10) = v0 & $i(v0))
% 50.17/7.26 | | |
% 50.17/7.26 | | | DELTA: instantiating (273) with fresh symbols all_134_0, all_134_1 gives:
% 50.17/7.26 | | | (275) vtcheck(all_58_3, all_71_6, all_71_4) = all_134_0 &
% 50.17/7.26 | | | visFreeVar(all_71_7, all_71_6) = all_134_1 & (all_134_0 = 0 |
% 50.17/7.26 | | | all_134_1 = 0)
% 50.17/7.26 | | |
% 50.17/7.26 | | | ALPHA: (275) implies:
% 50.17/7.26 | | | (276) vtcheck(all_58_3, all_71_6, all_71_4) = all_134_0
% 50.17/7.26 | | | (277) all_134_0 = 0 | all_134_1 = 0
% 50.17/7.26 | | |
% 50.17/7.26 | | | REDUCE: (268), (270) imply:
% 50.17/7.26 | | | (278) varrow(all_58_6, all_71_4) = all_58_5
% 50.17/7.26 | | |
% 50.17/7.26 | | | REDUCE: (269), (276) imply:
% 50.17/7.26 | | | (279) vtcheck(all_58_3, veabs, all_71_4) = all_134_0
% 50.17/7.26 | | |
% 50.17/7.26 | | | BETA: splitting (272) gives:
% 50.17/7.26 | | |
% 50.17/7.26 | | | Case 1:
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | (280) all_71_7 = all_58_9
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | COMBINE_EQS: (271), (280) imply:
% 50.17/7.26 | | | | (281) all_58_7 = all_58_9
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | REDUCE: (21), (281) imply:
% 50.17/7.26 | | | | (282) $false
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | CLOSE: (282) is inconsistent.
% 50.17/7.26 | | | |
% 50.17/7.26 | | | Case 2:
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | (283) ~ (all_71_7 = all_58_9)
% 50.17/7.26 | | | | (284) ? [v0: $i] : ? [v1: $i] : (vtcheck(v1, all_71_6, all_71_4) =
% 50.17/7.26 | | | | 0 & vbind(all_71_7, all_71_5, all_58_10) = v0 &
% 50.17/7.26 | | | | vbind(all_58_9, all_58_11, v0) = v1 & $i(v1) & $i(v0))
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | DELTA: instantiating (284) with fresh symbols all_142_0, all_142_1
% 50.17/7.26 | | | | gives:
% 50.17/7.26 | | | | (285) vtcheck(all_142_0, all_71_6, all_71_4) = 0 & vbind(all_71_7,
% 50.17/7.26 | | | | all_71_5, all_58_10) = all_142_1 & vbind(all_58_9, all_58_11,
% 50.17/7.26 | | | | all_142_1) = all_142_0 & $i(all_142_0) & $i(all_142_1)
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | ALPHA: (285) implies:
% 50.17/7.26 | | | | (286) vbind(all_58_9, all_58_11, all_142_1) = all_142_0
% 50.17/7.26 | | | | (287) vbind(all_71_7, all_71_5, all_58_10) = all_142_1
% 50.17/7.26 | | | | (288) vtcheck(all_142_0, all_71_6, all_71_4) = 0
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | REDUCE: (269), (288) imply:
% 50.17/7.26 | | | | (289) vtcheck(all_142_0, veabs, all_71_4) = 0
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | REDUCE: (270), (271), (287) imply:
% 50.17/7.26 | | | | (290) vbind(all_58_7, all_58_6, all_58_10) = all_142_1
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | BETA: splitting (274) gives:
% 50.17/7.26 | | | |
% 50.17/7.26 | | | | Case 1:
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | (291) all_65_0 = 0
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | REDUCE: (263), (291) imply:
% 50.17/7.26 | | | | | (292) $false
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | CLOSE: (292) is inconsistent.
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | Case 2:
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | (293) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & vtcheck(v0,
% 50.17/7.26 | | | | | all_71_6, all_71_4) = v1 & vbind(all_71_7, all_71_5,
% 50.17/7.26 | | | | | all_58_10) = v0 & $i(v0))
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | DELTA: instantiating (293) with fresh symbols all_147_0, all_147_1
% 50.17/7.26 | | | | | gives:
% 50.17/7.26 | | | | | (294) ~ (all_147_0 = 0) & vtcheck(all_147_1, all_71_6, all_71_4) =
% 50.17/7.26 | | | | | all_147_0 & vbind(all_71_7, all_71_5, all_58_10) = all_147_1
% 50.17/7.26 | | | | | & $i(all_147_1)
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | ALPHA: (294) implies:
% 50.17/7.26 | | | | | (295) ~ (all_147_0 = 0)
% 50.17/7.26 | | | | | (296) vbind(all_71_7, all_71_5, all_58_10) = all_147_1
% 50.17/7.26 | | | | | (297) vtcheck(all_147_1, all_71_6, all_71_4) = all_147_0
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | REDUCE: (269), (297) imply:
% 50.17/7.26 | | | | | (298) vtcheck(all_147_1, veabs, all_71_4) = all_147_0
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | REDUCE: (270), (271), (296) imply:
% 50.17/7.26 | | | | | (299) vbind(all_58_7, all_58_6, all_58_10) = all_147_1
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | GROUND_INST: instantiating (18) with all_142_1, all_147_1, all_58_10,
% 50.17/7.26 | | | | | all_58_6, all_58_7, simplifying with (290), (299) gives:
% 50.17/7.26 | | | | | (300) all_147_1 = all_142_1
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | REDUCE: (298), (300) imply:
% 50.17/7.26 | | | | | (301) vtcheck(all_142_1, veabs, all_71_4) = all_147_0
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | GROUND_INST: instantiating (12) with all_58_9, all_58_11, all_58_10,
% 50.17/7.26 | | | | | veabs, all_71_4, all_58_3, all_134_0, simplifying with
% 50.17/7.26 | | | | | (14), (24), (25), (26), (36), (61), (279) gives:
% 50.17/7.26 | | | | | (302) all_134_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 50.17/7.26 | | | | | (vtcheck(all_58_10, veabs, all_71_4) = v1 & vlookup(all_58_9,
% 50.17/7.26 | | | | | all_58_10) = v0 & $i(v0) & ( ~ (v1 = 0) | ~ (v0 =
% 50.17/7.26 | | | | | vnoType)))
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | GROUND_INST: instantiating (12) with all_58_7, all_58_6, all_58_10,
% 50.17/7.26 | | | | | veabs, all_71_4, all_142_1, all_147_0, simplifying with
% 50.17/7.26 | | | | | (14), (25), (28), (29), (61), (290), (301) gives:
% 50.17/7.26 | | | | | (303) all_147_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 50.17/7.26 | | | | | (vtcheck(all_58_10, veabs, all_71_4) = v1 & vlookup(all_58_7,
% 50.17/7.26 | | | | | all_58_10) = v0 & $i(v0) & ( ~ (v1 = 0) | ~ (v0 =
% 50.17/7.26 | | | | | vnoType)))
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | BETA: splitting (303) gives:
% 50.17/7.26 | | | | |
% 50.17/7.26 | | | | | Case 1:
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | (304) all_147_0 = 0
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | REDUCE: (295), (304) imply:
% 50.17/7.26 | | | | | | (305) $false
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | CLOSE: (305) is inconsistent.
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | Case 2:
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | (306) ? [v0: $i] : ? [v1: any] : (vtcheck(all_58_10, veabs,
% 50.17/7.26 | | | | | | all_71_4) = v1 & vlookup(all_58_7, all_58_10) = v0 &
% 50.17/7.26 | | | | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | DELTA: instantiating (306) with fresh symbols all_170_0, all_170_1
% 50.17/7.26 | | | | | | gives:
% 50.17/7.26 | | | | | | (307) vtcheck(all_58_10, veabs, all_71_4) = all_170_0 &
% 50.17/7.26 | | | | | | vlookup(all_58_7, all_58_10) = all_170_1 & $i(all_170_1) &
% 50.17/7.26 | | | | | | ( ~ (all_170_0 = 0) | ~ (all_170_1 = vnoType))
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | ALPHA: (307) implies:
% 50.17/7.26 | | | | | | (308) $i(all_170_1)
% 50.17/7.26 | | | | | | (309) vlookup(all_58_7, all_58_10) = all_170_1
% 50.17/7.26 | | | | | |
% 50.17/7.26 | | | | | | GROUND_INST: instantiating (5) with all_58_7, all_58_10, all_170_1,
% 50.17/7.26 | | | | | | simplifying with (25), (28), (308), (309) gives:
% 50.17/7.27 | | | | | | (310) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 50.17/7.27 | | | | | | [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ?
% 50.17/7.27 | | | | | | [v8: $i] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ?
% 50.17/7.27 | | | | | | [v12: $i] : ($i(v12) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 50.17/7.27 | | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v12 = all_58_7 &
% 50.17/7.27 | | | | | | all_170_1 = vnoType & all_58_10 = vempty) | (v11 =
% 50.17/7.27 | | | | | | all_170_1 & v10 = all_58_10 & v8 = all_58_7 & v7 =
% 50.17/7.27 | | | | | | all_58_7 & vsomeType(v9) = all_170_1 &
% 50.17/7.27 | | | | | | vbind(all_58_7, v9, v6) = all_58_10) | (v5 =
% 50.17/7.27 | | | | | | all_170_1 & v4 = all_58_10 & v2 = all_58_7 & ~ (v1 =
% 50.17/7.27 | | | | | | all_58_7) & vlookup(all_58_7, v3) = all_170_1 &
% 50.17/7.27 | | | | | | vbind(v1, v0, v3) = all_58_10)))
% 50.17/7.27 | | | | | |
% 50.17/7.27 | | | | | | DELTA: instantiating (310) with fresh symbols all_196_0, all_196_1,
% 50.17/7.27 | | | | | | all_196_2, all_196_3, all_196_4, all_196_5, all_196_6,
% 50.17/7.27 | | | | | | all_196_7, all_196_8, all_196_9, all_196_10, all_196_11,
% 50.17/7.27 | | | | | | all_196_12 gives:
% 50.17/7.27 | | | | | | (311) $i(all_196_0) & $i(all_196_3) & $i(all_196_4) &
% 50.17/7.27 | | | | | | $i(all_196_5) & $i(all_196_6) & $i(all_196_9) &
% 50.17/7.27 | | | | | | $i(all_196_10) & $i(all_196_11) & $i(all_196_12) &
% 50.17/7.27 | | | | | | ((all_196_0 = all_58_7 & all_170_1 = vnoType & all_58_10 =
% 50.17/7.27 | | | | | | vempty) | (all_196_1 = all_170_1 & all_196_2 =
% 50.17/7.27 | | | | | | all_58_10 & all_196_4 = all_58_7 & all_196_5 = all_58_7
% 50.17/7.27 | | | | | | & vsomeType(all_196_3) = all_170_1 & vbind(all_58_7,
% 50.17/7.27 | | | | | | all_196_3, all_196_6) = all_58_10) | (all_196_7 =
% 50.17/7.27 | | | | | | all_170_1 & all_196_8 = all_58_10 & all_196_10 =
% 50.17/7.27 | | | | | | all_58_7 & ~ (all_196_11 = all_58_7) &
% 50.17/7.27 | | | | | | vlookup(all_58_7, all_196_9) = all_170_1 &
% 50.17/7.27 | | | | | | vbind(all_196_11, all_196_12, all_196_9) = all_58_10))
% 50.17/7.27 | | | | | |
% 50.17/7.27 | | | | | | ALPHA: (311) implies:
% 50.17/7.27 | | | | | | (312) $i(all_196_10)
% 50.17/7.27 | | | | | | (313) $i(all_196_5)
% 50.17/7.27 | | | | | | (314) $i(all_196_0)
% 50.17/7.27 | | | | | | (315) (all_196_0 = all_58_7 & all_170_1 = vnoType & all_58_10 =
% 50.17/7.27 | | | | | | vempty) | (all_196_1 = all_170_1 & all_196_2 = all_58_10
% 50.17/7.27 | | | | | | & all_196_4 = all_58_7 & all_196_5 = all_58_7 &
% 50.17/7.27 | | | | | | vsomeType(all_196_3) = all_170_1 & vbind(all_58_7,
% 50.17/7.27 | | | | | | all_196_3, all_196_6) = all_58_10) | (all_196_7 =
% 50.17/7.27 | | | | | | all_170_1 & all_196_8 = all_58_10 & all_196_10 = all_58_7
% 50.17/7.27 | | | | | | & ~ (all_196_11 = all_58_7) & vlookup(all_58_7,
% 50.17/7.27 | | | | | | all_196_9) = all_170_1 & vbind(all_196_11, all_196_12,
% 50.17/7.27 | | | | | | all_196_9) = all_58_10)
% 50.17/7.27 | | | | | |
% 50.17/7.27 | | | | | | BETA: splitting (94) gives:
% 50.17/7.27 | | | | | |
% 50.17/7.27 | | | | | | Case 1:
% 50.17/7.27 | | | | | | |
% 50.17/7.27 | | | | | | | (316) all_82_0 = 0 & all_82_2 = all_67_0 & all_82_3 = all_67_1
% 50.17/7.27 | | | | | | | & varrow(all_82_5, all_82_4) = all_67_0 &
% 50.17/7.27 | | | | | | | vtcheck(all_82_1, all_82_6, all_82_4) = 0 &
% 50.17/7.27 | | | | | | | vbind(all_82_7, all_82_5, all_58_10) = all_82_1 &
% 50.17/7.27 | | | | | | | vabs(all_82_7, all_82_5, all_82_6) = all_67_1 &
% 50.17/7.27 | | | | | | | $i(all_82_1)
% 50.17/7.27 | | | | | | |
% 50.17/7.27 | | | | | | | ALPHA: (316) implies:
% 50.17/7.27 | | | | | | | (317) varrow(all_82_5, all_82_4) = all_67_0
% 50.17/7.27 | | | | | | |
% 50.17/7.27 | | | | | | | GROUND_INST: instantiating (7) with all_58_11, all_58_5, all_82_5,
% 50.17/7.27 | | | | | | | all_82_4, all_67_0, simplifying with (24), (30),
% 50.17/7.27 | | | | | | | (53), (92), (93), (317) gives:
% 50.17/7.27 | | | | | | | (318) all_82_5 = all_58_11
% 50.17/7.27 | | | | | | |
% 50.17/7.27 | | | | | | | BETA: splitting (79) gives:
% 50.17/7.27 | | | | | | |
% 50.17/7.27 | | | | | | | Case 1:
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | (319) (all_73_0 = all_58_2 & all_73_1 = all_58_8 & all_73_2 =
% 50.17/7.27 | | | | | | | | all_58_9 & all_73_3 = all_58_9 & all_58_1 = all_58_8
% 50.17/7.27 | | | | | | | | & vvar(all_58_9) = all_58_2) | (all_73_4 = all_58_2 &
% 50.17/7.27 | | | | | | | | all_73_6 = all_58_9 & all_73_7 = all_58_8 & all_58_1
% 50.17/7.27 | | | | | | | | = all_58_2 & ~ (all_73_5 = all_58_9) &
% 50.17/7.27 | | | | | | | | vvar(all_73_5) = all_58_2) | (all_73_8 = all_58_1 &
% 50.17/7.27 | | | | | | | | all_73_11 = all_58_2 & all_73_13 = all_58_8 &
% 50.17/7.27 | | | | | | | | all_73_14 = all_58_9 & vsubst(all_58_9, all_58_8,
% 50.17/7.27 | | | | | | | | all_73_12) = all_73_9 & vsubst(all_58_9, all_58_8,
% 50.17/7.27 | | | | | | | | all_73_15) = all_73_10 & vapp(all_73_10, all_73_9)
% 50.17/7.27 | | | | | | | | = all_58_1 & vapp(all_73_15, all_73_12) = all_58_2 &
% 50.17/7.27 | | | | | | | | $i(all_73_9) & $i(all_73_10))
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | BETA: splitting (319) gives:
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | Case 1:
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | (320) all_73_0 = all_58_2 & all_73_1 = all_58_8 & all_73_2
% 50.17/7.27 | | | | | | | | | = all_58_9 & all_73_3 = all_58_9 & all_58_1 =
% 50.17/7.27 | | | | | | | | | all_58_8 & vvar(all_58_9) = all_58_2
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | ALPHA: (320) implies:
% 50.17/7.27 | | | | | | | | | (321) all_73_3 = all_58_9
% 50.17/7.27 | | | | | | | | | (322) vvar(all_58_9) = all_58_2
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_58_9,
% 50.17/7.27 | | | | | | | | | all_58_7, all_58_6, veabs, all_58_2, simplifying
% 50.17/7.27 | | | | | | | | | with (14), (26), (28), (29), (34), (322) gives:
% 50.17/7.27 | | | | | | | | | (323) $false
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | CLOSE: (323) is inconsistent.
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | Case 2:
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | (324) (all_73_4 = all_58_2 & all_73_6 = all_58_9 & all_73_7
% 50.17/7.27 | | | | | | | | | = all_58_8 & all_58_1 = all_58_2 & ~ (all_73_5 =
% 50.17/7.27 | | | | | | | | | all_58_9) & vvar(all_73_5) = all_58_2) |
% 50.17/7.27 | | | | | | | | | (all_73_8 = all_58_1 & all_73_11 = all_58_2 &
% 50.17/7.27 | | | | | | | | | all_73_13 = all_58_8 & all_73_14 = all_58_9 &
% 50.17/7.27 | | | | | | | | | vsubst(all_58_9, all_58_8, all_73_12) = all_73_9 &
% 50.17/7.27 | | | | | | | | | vsubst(all_58_9, all_58_8, all_73_15) = all_73_10 &
% 50.17/7.27 | | | | | | | | | vapp(all_73_10, all_73_9) = all_58_1 &
% 50.17/7.27 | | | | | | | | | vapp(all_73_15, all_73_12) = all_58_2 &
% 50.17/7.27 | | | | | | | | | $i(all_73_9) & $i(all_73_10))
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | BETA: splitting (324) gives:
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | Case 1:
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | (325) all_73_4 = all_58_2 & all_73_6 = all_58_9 &
% 50.17/7.27 | | | | | | | | | | all_73_7 = all_58_8 & all_58_1 = all_58_2 & ~
% 50.17/7.27 | | | | | | | | | | (all_73_5 = all_58_9) & vvar(all_73_5) = all_58_2
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | ALPHA: (325) implies:
% 50.17/7.27 | | | | | | | | | | (326) vvar(all_73_5) = all_58_2
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_73_5,
% 50.17/7.27 | | | | | | | | | | all_58_7, all_58_6, veabs, all_58_2, simplifying
% 50.17/7.27 | | | | | | | | | | with (14), (28), (29), (34), (77), (326) gives:
% 50.17/7.27 | | | | | | | | | | (327) $false
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | CLOSE: (327) is inconsistent.
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | Case 2:
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | (328) all_73_8 = all_58_1 & all_73_11 = all_58_2 &
% 50.17/7.27 | | | | | | | | | | all_73_13 = all_58_8 & all_73_14 = all_58_9 &
% 50.17/7.27 | | | | | | | | | | vsubst(all_58_9, all_58_8, all_73_12) = all_73_9 &
% 50.17/7.27 | | | | | | | | | | vsubst(all_58_9, all_58_8, all_73_15) = all_73_10 &
% 50.17/7.27 | | | | | | | | | | vapp(all_73_10, all_73_9) = all_58_1 &
% 50.17/7.27 | | | | | | | | | | vapp(all_73_15, all_73_12) = all_58_2 &
% 50.17/7.27 | | | | | | | | | | $i(all_73_9) & $i(all_73_10)
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | ALPHA: (328) implies:
% 50.17/7.27 | | | | | | | | | | (329) vapp(all_73_15, all_73_12) = all_58_2
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_7,
% 50.17/7.27 | | | | | | | | | | all_58_6, veabs, all_73_15, all_73_12, all_58_2,
% 50.17/7.27 | | | | | | | | | | simplifying with (14), (28), (29), (34), (75),
% 50.17/7.27 | | | | | | | | | | (76), (329) gives:
% 50.17/7.27 | | | | | | | | | | (330) $false
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | | CLOSE: (330) is inconsistent.
% 50.17/7.27 | | | | | | | | | |
% 50.17/7.27 | | | | | | | | | End of split
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | End of split
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | Case 2:
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | (331) (all_73_16 = all_58_2 & all_73_19 = all_58_9 &
% 50.17/7.27 | | | | | | | | all_73_20 = all_58_9 & all_73_21 = all_58_8 &
% 50.17/7.27 | | | | | | | | all_58_1 = all_58_2 & vabs(all_58_9, all_73_18,
% 50.17/7.27 | | | | | | | | all_73_17) = all_58_2) | (all_73_22 = all_58_1 &
% 50.17/7.27 | | | | | | | | all_73_26 = all_73_33 & all_73_30 = 0 & all_73_31 =
% 50.17/7.27 | | | | | | | | all_58_2 & all_73_36 = all_58_8 & all_73_37 =
% 50.17/7.27 | | | | | | | | all_58_9 & ~ (all_73_34 = all_58_9) &
% 50.17/7.27 | | | | | | | | vsubst(all_73_34, all_73_25, all_73_32) = all_73_24 &
% 50.17/7.27 | | | | | | | | vsubst(all_58_9, all_58_8, all_73_23) = all_58_1 &
% 50.17/7.27 | | | | | | | | vgensym(all_73_27) = all_73_33 &
% 50.17/7.27 | | | | | | | | visFreeVar(all_73_34, all_58_8) = 0 & vapp(all_73_29,
% 50.17/7.27 | | | | | | | | all_73_28) = all_73_27 & vapp(all_58_8, all_73_32)
% 50.17/7.27 | | | | | | | | = all_73_29 & vabs(all_73_33, all_73_35, all_73_24) =
% 50.17/7.27 | | | | | | | | all_73_23 & vabs(all_73_34, all_73_35, all_73_32) =
% 50.17/7.27 | | | | | | | | all_58_2 & vvar(all_73_33) = all_73_25 &
% 50.17/7.27 | | | | | | | | vvar(all_58_9) = all_73_28 & $i(all_73_23) &
% 50.17/7.27 | | | | | | | | $i(all_73_24) & $i(all_73_25) & $i(all_73_27) &
% 50.17/7.27 | | | | | | | | $i(all_73_28) & $i(all_73_29)) | (all_73_38 =
% 50.17/7.27 | | | | | | | | all_58_1 & all_73_41 = all_58_2 & all_73_43 =
% 50.17/7.27 | | | | | | | | all_58_8 & all_73_44 = all_58_9 & ~ (all_73_40 = 0)
% 50.17/7.27 | | | | | | | | & ~ (all_73_46 = all_58_9) & vsubst(all_58_9,
% 50.17/7.27 | | | | | | | | all_58_8, all_73_42) = all_73_39 &
% 50.17/7.27 | | | | | | | | visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 50.17/7.27 | | | | | | | | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 &
% 50.17/7.27 | | | | | | | | vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 50.17/7.27 | | | | | | | | $i(all_73_39))
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | BETA: splitting (331) gives:
% 50.17/7.27 | | | | | | | |
% 50.17/7.27 | | | | | | | | Case 1:
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | (332) all_73_16 = all_58_2 & all_73_19 = all_58_9 &
% 50.17/7.27 | | | | | | | | | all_73_20 = all_58_9 & all_73_21 = all_58_8 &
% 50.17/7.27 | | | | | | | | | all_58_1 = all_58_2 & vabs(all_58_9, all_73_18,
% 50.17/7.27 | | | | | | | | | all_73_17) = all_58_2
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | ALPHA: (332) implies:
% 50.17/7.27 | | | | | | | | | (333) all_73_20 = all_58_9
% 50.17/7.27 | | | | | | | | | (334) vabs(all_58_9, all_73_18, all_73_17) = all_58_2
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | REF_CLOSE: (1), (14), (21), (26), (28), (29), (34), (73),
% 50.17/7.27 | | | | | | | | | (74), (334) are inconsistent by sub-proof #5.
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | Case 2:
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | (335) (all_73_22 = all_58_1 & all_73_26 = all_73_33 &
% 50.17/7.27 | | | | | | | | | all_73_30 = 0 & all_73_31 = all_58_2 & all_73_36 =
% 50.17/7.27 | | | | | | | | | all_58_8 & all_73_37 = all_58_9 & ~ (all_73_34 =
% 50.17/7.27 | | | | | | | | | all_58_9) & vsubst(all_73_34, all_73_25,
% 50.17/7.27 | | | | | | | | | all_73_32) = all_73_24 & vsubst(all_58_9,
% 50.17/7.27 | | | | | | | | | all_58_8, all_73_23) = all_58_1 &
% 50.17/7.27 | | | | | | | | | vgensym(all_73_27) = all_73_33 &
% 50.17/7.27 | | | | | | | | | visFreeVar(all_73_34, all_58_8) = 0 &
% 50.17/7.27 | | | | | | | | | vapp(all_73_29, all_73_28) = all_73_27 &
% 50.17/7.27 | | | | | | | | | vapp(all_58_8, all_73_32) = all_73_29 &
% 50.17/7.27 | | | | | | | | | vabs(all_73_33, all_73_35, all_73_24) = all_73_23 &
% 50.17/7.27 | | | | | | | | | vabs(all_73_34, all_73_35, all_73_32) = all_58_2 &
% 50.17/7.27 | | | | | | | | | vvar(all_73_33) = all_73_25 & vvar(all_58_9) =
% 50.17/7.27 | | | | | | | | | all_73_28 & $i(all_73_23) & $i(all_73_24) &
% 50.17/7.27 | | | | | | | | | $i(all_73_25) & $i(all_73_27) & $i(all_73_28) &
% 50.17/7.27 | | | | | | | | | $i(all_73_29)) | (all_73_38 = all_58_1 & all_73_41
% 50.17/7.27 | | | | | | | | | = all_58_2 & all_73_43 = all_58_8 & all_73_44 =
% 50.17/7.27 | | | | | | | | | all_58_9 & ~ (all_73_40 = 0) & ~ (all_73_46 =
% 50.17/7.27 | | | | | | | | | all_58_9) & vsubst(all_58_9, all_58_8, all_73_42)
% 50.17/7.27 | | | | | | | | | = all_73_39 & visFreeVar(all_73_46, all_58_8) =
% 50.17/7.27 | | | | | | | | | all_73_40 & vabs(all_73_46, all_73_45, all_73_39) =
% 50.17/7.27 | | | | | | | | | all_58_1 & vabs(all_73_46, all_73_45, all_73_42) =
% 50.17/7.27 | | | | | | | | | all_58_2 & $i(all_73_39))
% 50.17/7.27 | | | | | | | | |
% 50.17/7.27 | | | | | | | | | BETA: splitting (335) gives:
% 50.17/7.28 | | | | | | | | |
% 50.17/7.28 | | | | | | | | | Case 1:
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | (336) all_73_22 = all_58_1 & all_73_26 = all_73_33 &
% 50.17/7.28 | | | | | | | | | | all_73_30 = 0 & all_73_31 = all_58_2 & all_73_36 =
% 50.17/7.28 | | | | | | | | | | all_58_8 & all_73_37 = all_58_9 & ~ (all_73_34 =
% 50.17/7.28 | | | | | | | | | | all_58_9) & vsubst(all_73_34, all_73_25,
% 50.17/7.28 | | | | | | | | | | all_73_32) = all_73_24 & vsubst(all_58_9,
% 50.17/7.28 | | | | | | | | | | all_58_8, all_73_23) = all_58_1 &
% 50.17/7.28 | | | | | | | | | | vgensym(all_73_27) = all_73_33 &
% 50.17/7.28 | | | | | | | | | | visFreeVar(all_73_34, all_58_8) = 0 &
% 50.17/7.28 | | | | | | | | | | vapp(all_73_29, all_73_28) = all_73_27 &
% 50.17/7.28 | | | | | | | | | | vapp(all_58_8, all_73_32) = all_73_29 &
% 50.17/7.28 | | | | | | | | | | vabs(all_73_33, all_73_35, all_73_24) = all_73_23 &
% 50.17/7.28 | | | | | | | | | | vabs(all_73_34, all_73_35, all_73_32) = all_58_2 &
% 50.17/7.28 | | | | | | | | | | vvar(all_73_33) = all_73_25 & vvar(all_58_9) =
% 50.17/7.28 | | | | | | | | | | all_73_28 & $i(all_73_23) & $i(all_73_24) &
% 50.17/7.28 | | | | | | | | | | $i(all_73_25) & $i(all_73_27) & $i(all_73_28) &
% 50.17/7.28 | | | | | | | | | | $i(all_73_29)
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | ALPHA: (336) implies:
% 50.17/7.28 | | | | | | | | | | (337) vabs(all_73_34, all_73_35, all_73_32) = all_58_2
% 50.17/7.28 | | | | | | | | | | (338) visFreeVar(all_73_34, all_58_8) = 0
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | REF_CLOSE: (1), (14), (16), (22), (28), (29), (34), (35),
% 50.17/7.28 | | | | | | | | | | (69), (70), (71), (337), (338) are inconsistent by
% 50.17/7.28 | | | | | | | | | | sub-proof #4.
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | Case 2:
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | (339) all_73_38 = all_58_1 & all_73_41 = all_58_2 &
% 50.17/7.28 | | | | | | | | | | all_73_43 = all_58_8 & all_73_44 = all_58_9 & ~
% 50.17/7.28 | | | | | | | | | | (all_73_40 = 0) & ~ (all_73_46 = all_58_9) &
% 50.17/7.28 | | | | | | | | | | vsubst(all_58_9, all_58_8, all_73_42) = all_73_39 &
% 50.17/7.28 | | | | | | | | | | visFreeVar(all_73_46, all_58_8) = all_73_40 &
% 50.17/7.28 | | | | | | | | | | vabs(all_73_46, all_73_45, all_73_39) = all_58_1 &
% 50.17/7.28 | | | | | | | | | | vabs(all_73_46, all_73_45, all_73_42) = all_58_2 &
% 50.17/7.28 | | | | | | | | | | $i(all_73_39)
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | ALPHA: (339) implies:
% 50.17/7.28 | | | | | | | | | | (340) all_73_44 = all_58_9
% 50.17/7.28 | | | | | | | | | | (341) all_73_43 = all_58_8
% 50.17/7.28 | | | | | | | | | | (342) ~ (all_73_40 = 0)
% 50.17/7.28 | | | | | | | | | | (343) $i(all_73_39)
% 50.17/7.28 | | | | | | | | | | (344) vabs(all_73_46, all_73_45, all_73_42) = all_58_2
% 50.17/7.28 | | | | | | | | | | (345) vabs(all_73_46, all_73_45, all_73_39) = all_58_1
% 50.17/7.28 | | | | | | | | | | (346) visFreeVar(all_73_46, all_58_8) = all_73_40
% 50.17/7.28 | | | | | | | | | | (347) vsubst(all_58_9, all_58_8, all_73_42) = all_73_39
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | BETA: splitting (103) gives:
% 50.17/7.28 | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | Case 1:
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | (348) all_89_0 = 0 & all_89_2 = all_58_5 & all_89_3 =
% 50.17/7.28 | | | | | | | | | | | all_80_0 & varrow(all_89_5, all_89_4) = all_58_5 &
% 50.17/7.28 | | | | | | | | | | | vtcheck(all_89_1, all_89_6, all_89_4) = 0 &
% 50.17/7.28 | | | | | | | | | | | vbind(all_89_7, all_89_5, all_58_10) = all_89_1 &
% 50.17/7.28 | | | | | | | | | | | vabs(all_89_7, all_89_5, all_89_6) = all_80_0 &
% 50.17/7.28 | | | | | | | | | | | $i(all_89_1)
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | ALPHA: (348) implies:
% 50.17/7.28 | | | | | | | | | | | (349) vabs(all_89_7, all_89_5, all_89_6) = all_80_0
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_89_7,
% 50.17/7.28 | | | | | | | | | | | all_89_5, all_89_6, all_67_1, all_58_8, all_80_0,
% 50.17/7.28 | | | | | | | | | | | simplifying with (27), (49), (84), (100), (101),
% 50.17/7.28 | | | | | | | | | | | (102), (349) gives:
% 50.17/7.28 | | | | | | | | | | | (350) $false
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | Case 2:
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | (351) (all_89_8 = 0 & all_89_9 = 0 & all_89_11 =
% 50.17/7.28 | | | | | | | | | | | all_80_0 & varrow(all_89_12, all_58_5) =
% 50.17/7.28 | | | | | | | | | | | all_89_10 & vtcheck(all_58_10, all_89_13,
% 50.17/7.28 | | | | | | | | | | | all_89_12) = 0 & vtcheck(all_58_10, all_89_14,
% 50.17/7.28 | | | | | | | | | | | all_89_10) = 0 & vapp(all_89_14, all_89_13) =
% 50.17/7.28 | | | | | | | | | | | all_80_0 & $i(all_89_10)) | (all_89_15 =
% 50.17/7.28 | | | | | | | | | | | all_89_18 & all_89_16 = all_80_0 &
% 50.17/7.28 | | | | | | | | | | | vlookup(all_89_17, all_58_10) = all_89_18 &
% 50.17/7.28 | | | | | | | | | | | vsomeType(all_58_5) = all_89_18 &
% 50.17/7.28 | | | | | | | | | | | vvar(all_89_17) = all_80_0 & $i(all_89_18))
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | BETA: splitting (351) gives:
% 50.17/7.28 | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | Case 1:
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | (352) all_89_8 = 0 & all_89_9 = 0 & all_89_11 = all_80_0
% 50.17/7.28 | | | | | | | | | | | | & varrow(all_89_12, all_58_5) = all_89_10 &
% 50.17/7.28 | | | | | | | | | | | | vtcheck(all_58_10, all_89_13, all_89_12) = 0 &
% 50.17/7.28 | | | | | | | | | | | | vtcheck(all_58_10, all_89_14, all_89_10) = 0 &
% 50.17/7.28 | | | | | | | | | | | | vapp(all_89_14, all_89_13) = all_80_0 &
% 50.17/7.28 | | | | | | | | | | | | $i(all_89_10)
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | ALPHA: (352) implies:
% 50.17/7.28 | | | | | | | | | | | | (353) vapp(all_89_14, all_89_13) = all_80_0
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_58_7, all_58_6, veabs,
% 50.17/7.28 | | | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.28 | | | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.28 | | | | | | | | | | | | (65), (68), (344) gives:
% 50.17/7.28 | | | | | | | | | | | | (354) all_73_42 = veabs
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_58_7, all_58_6, veabs,
% 50.17/7.28 | | | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.28 | | | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.28 | | | | | | | | | | | | (65), (68), (344) gives:
% 50.17/7.28 | | | | | | | | | | | | (355) all_73_45 = all_58_6
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_58_7, all_58_6, veabs,
% 50.17/7.28 | | | | | | | | | | | | all_73_46, all_73_45, all_73_42, all_58_2,
% 50.17/7.28 | | | | | | | | | | | | simplifying with (14), (28), (29), (34), (64),
% 50.17/7.28 | | | | | | | | | | | | (65), (68), (344) gives:
% 50.17/7.28 | | | | | | | | | | | | (356) all_73_46 = all_58_7
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_67_1, all_58_8,
% 50.17/7.28 | | | | | | | | | | | | all_89_14, all_89_13, all_80_0, simplifying with
% 50.17/7.28 | | | | | | | | | | | | (27), (49), (84), (98), (99), (353) gives:
% 50.17/7.28 | | | | | | | | | | | | (357) all_89_13 = all_58_8
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | REDUCE: (347), (354) imply:
% 50.17/7.28 | | | | | | | | | | | | (358) vsubst(all_58_9, all_58_8, veabs) = all_73_39
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | REDUCE: (346), (356) imply:
% 50.17/7.28 | | | | | | | | | | | | (359) visFreeVar(all_58_7, all_58_8) = all_73_40
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | REDUCE: (345), (355), (356) imply:
% 50.17/7.28 | | | | | | | | | | | | (360) vabs(all_58_7, all_58_6, all_73_39) = all_58_1
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_58_4, all_73_40,
% 50.17/7.28 | | | | | | | | | | | | all_58_8, all_58_7, simplifying with (35), (359)
% 50.17/7.28 | | | | | | | | | | | | gives:
% 50.17/7.28 | | | | | | | | | | | | (361) all_73_40 = all_58_4
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_58_10, all_58_7,
% 50.17/7.28 | | | | | | | | | | | | all_73_39, all_58_6, all_71_4, all_58_1, all_58_5,
% 50.17/7.28 | | | | | | | | | | | | all_58_0, simplifying with (25), (28), (29), (38),
% 50.17/7.28 | | | | | | | | | | | | (61), (278), (343), (360) gives:
% 50.17/7.28 | | | | | | | | | | | | (362) all_58_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 50.17/7.28 | | | | | | | | | | | | (v1 = 0) & vtcheck(v0, all_73_39, all_71_4) = v1
% 50.17/7.28 | | | | | | | | | | | | & vbind(all_58_7, all_58_6, all_58_10) = v0 &
% 50.17/7.28 | | | | | | | | | | | | $i(v0))
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | BETA: splitting (362) gives:
% 50.17/7.28 | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | Case 1:
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | (363) all_58_0 = 0
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | REDUCE: (23), (363) imply:
% 50.17/7.28 | | | | | | | | | | | | | (364) $false
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | CLOSE: (364) is inconsistent.
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | Case 2:
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | (365) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 50.17/7.28 | | | | | | | | | | | | | vtcheck(v0, all_73_39, all_71_4) = v1 &
% 50.17/7.28 | | | | | | | | | | | | | vbind(all_58_7, all_58_6, all_58_10) = v0 &
% 50.17/7.28 | | | | | | | | | | | | | $i(v0))
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | DELTA: instantiating (365) with fresh symbols all_280_0,
% 50.17/7.28 | | | | | | | | | | | | | all_280_1 gives:
% 50.17/7.28 | | | | | | | | | | | | | (366) ~ (all_280_0 = 0) & vtcheck(all_280_1, all_73_39,
% 50.17/7.28 | | | | | | | | | | | | | all_71_4) = all_280_0 & vbind(all_58_7,
% 50.17/7.28 | | | | | | | | | | | | | all_58_6, all_58_10) = all_280_1 & $i(all_280_1)
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | ALPHA: (366) implies:
% 50.17/7.28 | | | | | | | | | | | | | (367) ~ (all_280_0 = 0)
% 50.17/7.28 | | | | | | | | | | | | | (368) $i(all_280_1)
% 50.17/7.28 | | | | | | | | | | | | | (369) vbind(all_58_7, all_58_6, all_58_10) = all_280_1
% 50.17/7.28 | | | | | | | | | | | | | (370) vtcheck(all_280_1, all_73_39, all_71_4) =
% 50.17/7.28 | | | | | | | | | | | | | all_280_0
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_142_1, all_280_1,
% 50.17/7.28 | | | | | | | | | | | | | all_58_10, all_58_6, all_58_7, simplifying with
% 50.17/7.28 | | | | | | | | | | | | | (290), (369) gives:
% 50.17/7.28 | | | | | | | | | | | | | (371) all_280_1 = all_142_1
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | REDUCE: (370), (371) imply:
% 50.17/7.28 | | | | | | | | | | | | | (372) vtcheck(all_142_1, all_73_39, all_71_4) =
% 50.17/7.28 | | | | | | | | | | | | | all_280_0
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | REDUCE: (368), (371) imply:
% 50.17/7.28 | | | | | | | | | | | | | (373) $i(all_142_1)
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | BETA: splitting (277) gives:
% 50.17/7.28 | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | Case 1:
% 50.17/7.28 | | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_58_11, all_142_1,
% 50.17/7.28 | | | | | | | | | | | | | | all_58_9, all_58_8, all_71_4, all_142_0,
% 50.17/7.28 | | | | | | | | | | | | | | all_73_39, all_280_0, simplifying with (24), (26),
% 50.17/7.28 | | | | | | | | | | | | | | (27), (61), (286), (289), (358), (372), (373)
% 50.17/7.28 | | | | | | | | | | | | | | gives:
% 50.17/7.28 | | | | | | | | | | | | | | (374) all_280_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 50.17/7.28 | | | | | | | | | | | | | | vtcheck(all_142_1, all_58_8, all_58_11) = v0)
% 50.17/7.28 | | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_58_7, all_58_6,
% 50.17/7.28 | | | | | | | | | | | | | | all_58_10, all_73_39, all_71_4, all_142_1,
% 50.17/7.28 | | | | | | | | | | | | | | all_280_0, simplifying with (25), (28), (29),
% 50.17/7.28 | | | | | | | | | | | | | | (61), (290), (343), (372) gives:
% 50.17/7.28 | | | | | | | | | | | | | | (375) all_280_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 50.17/7.28 | | | | | | | | | | | | | | (vtcheck(all_58_10, all_73_39, all_71_4) = v1 &
% 50.17/7.28 | | | | | | | | | | | | | | vlookup(all_58_7, all_58_10) = v0 & $i(v0) & ( ~
% 50.17/7.28 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = vnoType)))
% 50.17/7.28 | | | | | | | | | | | | | |
% 50.17/7.28 | | | | | | | | | | | | | | GROUND_INST: instantiating (T-Weak-FreeVar) with all_58_7,
% 50.17/7.28 | | | | | | | | | | | | | | all_58_6, all_58_10, all_73_39, all_71_4,
% 50.17/7.28 | | | | | | | | | | | | | | all_142_1, all_280_0, simplifying with (25), (28),
% 50.17/7.28 | | | | | | | | | | | | | | (29), (61), (290), (343), (372) gives:
% 50.17/7.29 | | | | | | | | | | | | | | (376) all_280_0 = 0 | ? [v0: any] : ? [v1: any] :
% 50.17/7.29 | | | | | | | | | | | | | | (vtcheck(all_58_10, all_73_39, all_71_4) = v1 &
% 50.17/7.29 | | | | | | | | | | | | | | visFreeVar(all_58_7, all_73_39) = v0 & ( ~ (v1 =
% 50.17/7.29 | | | | | | | | | | | | | | 0) | v0 = 0))
% 50.17/7.29 | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (17), (19), (22), (24), (25), (27),
% 50.17/7.29 | | | | | | | | | | | | | | (29), (35), (37), (290), (309), (312), (313),
% 50.17/7.29 | | | | | | | | | | | | | | (314), (315), (367), (374), (375), (376),
% 50.17/7.29 | | | | | | | | | | | | | | (T-Weak-FreeVar) are inconsistent by sub-proof #1.
% 50.17/7.29 | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | Case 2:
% 50.17/7.29 | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | (377) ~ (all_134_0 = 0)
% 50.17/7.29 | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 50.17/7.29 | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | Case 1:
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | | (378) all_134_0 = 0
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | | REDUCE: (377), (378) imply:
% 50.17/7.29 | | | | | | | | | | | | | | | (379) $false
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | | CLOSE: (379) is inconsistent.
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | Case 2:
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.17/7.29 | | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_58_11, all_142_1,
% 50.43/7.29 | | | | | | | | | | | | | | | all_58_9, all_58_8, all_71_4, all_142_0,
% 50.43/7.29 | | | | | | | | | | | | | | | all_73_39, all_280_0, simplifying with (24), (26),
% 50.43/7.29 | | | | | | | | | | | | | | | (27), (61), (286), (289), (358), (372), (373)
% 50.43/7.29 | | | | | | | | | | | | | | | gives:
% 50.43/7.29 | | | | | | | | | | | | | | | (380) all_280_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 50.43/7.29 | | | | | | | | | | | | | | | vtcheck(all_142_1, all_58_8, all_58_11) = v0)
% 50.43/7.29 | | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_58_7, all_58_6,
% 50.43/7.29 | | | | | | | | | | | | | | | all_58_10, all_73_39, all_71_4, all_142_1,
% 50.43/7.29 | | | | | | | | | | | | | | | all_280_0, simplifying with (25), (28), (29),
% 50.43/7.29 | | | | | | | | | | | | | | | (61), (290), (343), (372) gives:
% 50.43/7.29 | | | | | | | | | | | | | | | (381) all_280_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 50.43/7.29 | | | | | | | | | | | | | | | (vtcheck(all_58_10, all_73_39, all_71_4) = v1 &
% 50.43/7.29 | | | | | | | | | | | | | | | vlookup(all_58_7, all_58_10) = v0 & $i(v0) & ( ~
% 50.43/7.29 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = vnoType)))
% 50.43/7.29 | | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (T-Weak-FreeVar) with all_58_7,
% 50.43/7.29 | | | | | | | | | | | | | | | all_58_6, all_58_10, all_73_39, all_71_4,
% 50.43/7.29 | | | | | | | | | | | | | | | all_142_1, all_280_0, simplifying with (25), (28),
% 50.43/7.29 | | | | | | | | | | | | | | | (29), (61), (290), (343), (372) gives:
% 50.43/7.29 | | | | | | | | | | | | | | | (382) all_280_0 = 0 | ? [v0: any] : ? [v1: any] :
% 50.43/7.29 | | | | | | | | | | | | | | | (vtcheck(all_58_10, all_73_39, all_71_4) = v1 &
% 50.43/7.29 | | | | | | | | | | | | | | | visFreeVar(all_58_7, all_73_39) = v0 & ( ~ (v1 =
% 50.43/7.29 | | | | | | | | | | | | | | | 0) | v0 = 0))
% 50.43/7.29 | | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (17), (19), (22), (24), (25), (27),
% 50.43/7.29 | | | | | | | | | | | | | | | (29), (35), (37), (290), (309), (312), (313),
% 50.43/7.29 | | | | | | | | | | | | | | | (314), (315), (367), (380), (381), (382),
% 50.43/7.29 | | | | | | | | | | | | | | | (T-Weak-FreeVar) are inconsistent by sub-proof #1.
% 50.43/7.29 | | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | Case 2:
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | (383) all_89_15 = all_89_18 & all_89_16 = all_80_0 &
% 50.43/7.29 | | | | | | | | | | | | vlookup(all_89_17, all_58_10) = all_89_18 &
% 50.43/7.29 | | | | | | | | | | | | vsomeType(all_58_5) = all_89_18 & vvar(all_89_17)
% 50.43/7.29 | | | | | | | | | | | | = all_80_0 & $i(all_89_18)
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | ALPHA: (383) implies:
% 50.43/7.29 | | | | | | | | | | | | (384) vvar(all_89_17) = all_80_0
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | GROUND_INST: instantiating (DIFF-var-app) with all_89_17,
% 50.43/7.29 | | | | | | | | | | | | all_67_1, all_58_8, all_80_0, simplifying with
% 50.43/7.29 | | | | | | | | | | | | (27), (49), (84), (97), (384) gives:
% 50.43/7.29 | | | | | | | | | | | | (385) $false
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | | CLOSE: (385) is inconsistent.
% 50.43/7.29 | | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | | |
% 50.43/7.29 | | | | | | | | | End of split
% 50.43/7.29 | | | | | | | | |
% 50.43/7.29 | | | | | | | | End of split
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | End of split
% 50.43/7.29 | | | | | | |
% 50.43/7.29 | | | | | | Case 2:
% 50.43/7.29 | | | | | | |
% 50.43/7.29 | | | | | | | (386) (all_82_8 = 0 & all_82_9 = 0 & all_82_11 = all_67_1 &
% 50.43/7.29 | | | | | | | varrow(all_82_12, all_67_0) = all_82_10 &
% 50.43/7.29 | | | | | | | vtcheck(all_58_10, all_82_13, all_82_12) = 0 &
% 50.43/7.29 | | | | | | | vtcheck(all_58_10, all_82_14, all_82_10) = 0 &
% 50.43/7.29 | | | | | | | vapp(all_82_14, all_82_13) = all_67_1 & $i(all_82_10))
% 50.43/7.29 | | | | | | | | (all_82_15 = all_82_18 & all_82_16 = all_67_1 &
% 50.43/7.29 | | | | | | | vlookup(all_82_17, all_58_10) = all_82_18 &
% 50.43/7.29 | | | | | | | vsomeType(all_67_0) = all_82_18 & vvar(all_82_17) =
% 50.43/7.29 | | | | | | | all_67_1 & $i(all_82_18))
% 50.43/7.29 | | | | | | |
% 50.43/7.29 | | | | | | | BETA: splitting (386) gives:
% 50.43/7.29 | | | | | | |
% 50.43/7.29 | | | | | | | Case 1:
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | (387) all_82_8 = 0 & all_82_9 = 0 & all_82_11 = all_67_1 &
% 50.43/7.29 | | | | | | | | varrow(all_82_12, all_67_0) = all_82_10 &
% 50.43/7.29 | | | | | | | | vtcheck(all_58_10, all_82_13, all_82_12) = 0 &
% 50.43/7.29 | | | | | | | | vtcheck(all_58_10, all_82_14, all_82_10) = 0 &
% 50.43/7.29 | | | | | | | | vapp(all_82_14, all_82_13) = all_67_1 & $i(all_82_10)
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | ALPHA: (387) implies:
% 50.43/7.29 | | | | | | | | (388) vapp(all_82_14, all_82_13) = all_67_1
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_9,
% 50.43/7.29 | | | | | | | | all_58_11, all_58_2, all_82_14, all_82_13,
% 50.43/7.29 | | | | | | | | all_67_1, simplifying with (24), (26), (32), (51),
% 50.43/7.29 | | | | | | | | (88), (89), (388) gives:
% 50.43/7.29 | | | | | | | | (389) $false
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | CLOSE: (389) is inconsistent.
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | Case 2:
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | (390) all_82_15 = all_82_18 & all_82_16 = all_67_1 &
% 50.43/7.29 | | | | | | | | vlookup(all_82_17, all_58_10) = all_82_18 &
% 50.43/7.29 | | | | | | | | vsomeType(all_67_0) = all_82_18 & vvar(all_82_17) =
% 50.43/7.29 | | | | | | | | all_67_1 & $i(all_82_18)
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | ALPHA: (390) implies:
% 50.43/7.29 | | | | | | | | (391) vvar(all_82_17) = all_67_1
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_82_17,
% 50.43/7.29 | | | | | | | | all_58_9, all_58_11, all_58_2, all_67_1,
% 50.43/7.29 | | | | | | | | simplifying with (24), (26), (32), (51), (87),
% 50.43/7.29 | | | | | | | | (391) gives:
% 50.43/7.29 | | | | | | | | (392) $false
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | | CLOSE: (392) is inconsistent.
% 50.43/7.29 | | | | | | | |
% 50.43/7.29 | | | | | | | End of split
% 50.43/7.29 | | | | | | |
% 50.43/7.29 | | | | | | End of split
% 50.43/7.29 | | | | | |
% 50.43/7.29 | | | | | End of split
% 50.43/7.29 | | | | |
% 50.43/7.29 | | | | End of split
% 50.43/7.29 | | | |
% 50.43/7.29 | | | End of split
% 50.43/7.29 | | |
% 50.43/7.29 | | Case 2:
% 50.43/7.29 | | |
% 50.43/7.29 | | | (393) (all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_2 &
% 50.43/7.29 | | | varrow(all_71_12, all_58_5) = all_71_10 & vtcheck(all_58_3,
% 50.43/7.29 | | | all_71_13, all_71_12) = 0 & vtcheck(all_58_3, all_71_14,
% 50.43/7.29 | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_2 &
% 50.43/7.29 | | | $i(all_71_10)) | (all_71_15 = all_71_18 & all_71_16 = all_58_2
% 50.43/7.29 | | | & vlookup(all_71_17, all_58_3) = all_71_18 &
% 50.43/7.29 | | | vsomeType(all_58_5) = all_71_18 & vvar(all_71_17) = all_58_2 &
% 50.43/7.29 | | | $i(all_71_18))
% 50.43/7.29 | | |
% 50.43/7.29 | | | BETA: splitting (393) gives:
% 50.43/7.29 | | |
% 50.43/7.29 | | | Case 1:
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | (394) all_71_8 = 0 & all_71_9 = 0 & all_71_11 = all_58_2 &
% 50.43/7.29 | | | | varrow(all_71_12, all_58_5) = all_71_10 & vtcheck(all_58_3,
% 50.43/7.29 | | | | all_71_13, all_71_12) = 0 & vtcheck(all_58_3, all_71_14,
% 50.43/7.29 | | | | all_71_10) = 0 & vapp(all_71_14, all_71_13) = all_58_2 &
% 50.43/7.29 | | | | $i(all_71_10)
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | ALPHA: (394) implies:
% 50.43/7.29 | | | | (395) vapp(all_71_14, all_71_13) = all_58_2
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | GROUND_INST: instantiating (DIFF-abs-app) with all_58_7, all_58_6,
% 50.43/7.29 | | | | veabs, all_71_14, all_71_13, all_58_2, simplifying with
% 50.43/7.29 | | | | (14), (28), (29), (34), (56), (57), (395) gives:
% 50.43/7.29 | | | | (396) $false
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | CLOSE: (396) is inconsistent.
% 50.43/7.29 | | | |
% 50.43/7.29 | | | Case 2:
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | (397) all_71_15 = all_71_18 & all_71_16 = all_58_2 &
% 50.43/7.29 | | | | vlookup(all_71_17, all_58_3) = all_71_18 & vsomeType(all_58_5)
% 50.43/7.29 | | | | = all_71_18 & vvar(all_71_17) = all_58_2 & $i(all_71_18)
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | ALPHA: (397) implies:
% 50.43/7.29 | | | | (398) vvar(all_71_17) = all_58_2
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | GROUND_INST: instantiating (DIFF-var-abs) with all_71_17, all_58_7,
% 50.43/7.29 | | | | all_58_6, veabs, all_58_2, simplifying with (14), (28),
% 50.43/7.29 | | | | (29), (34), (55), (398) gives:
% 50.43/7.29 | | | | (399) $false
% 50.43/7.29 | | | |
% 50.43/7.29 | | | | CLOSE: (399) is inconsistent.
% 50.43/7.29 | | | |
% 50.43/7.29 | | | End of split
% 50.43/7.29 | | |
% 50.43/7.29 | | End of split
% 50.43/7.29 | |
% 50.43/7.29 | End of split
% 50.43/7.29 |
% 50.43/7.29 End of proof
% 50.43/7.29
% 50.43/7.29 Sub-proof #1 shows that the following formulas are inconsistent:
% 50.43/7.29 ----------------------------------------------------------------
% 50.43/7.29 (1) vtcheck(all_58_10, all_58_8, all_58_11) = 0
% 50.43/7.29 (2) $i(all_58_8)
% 50.43/7.29 (3) vlookup(all_58_7, all_58_10) = all_170_1
% 50.43/7.30 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.30 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~
% 50.43/7.30 (vtcheck(v4, v3, v2) = v0))
% 50.43/7.30 (5) $i(all_196_0)
% 50.43/7.30 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.43/7.30 [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~
% 50.43/7.30 (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 50.43/7.30 $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: any] : (vtcheck(v2, v3, v4)
% 50.43/7.30 = v8 & vlookup(v0, v2) = v7 & $i(v7) & ( ~ (v8 = 0) | ~ (v7 =
% 50.43/7.30 vnoType))))
% 50.43/7.30 (7) vbind(all_58_7, all_58_6, all_58_10) = all_142_1
% 50.43/7.30 (8) ~ (all_58_4 = 0)
% 50.43/7.30 (9) all_280_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_142_1,
% 50.43/7.30 all_58_8, all_58_11) = v0)
% 50.43/7.30 (10) $i(all_196_5)
% 50.43/7.30 (11) visFreeVar(all_58_7, all_58_8) = all_58_4
% 50.43/7.30 (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.30 ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~
% 50.43/7.30 (visFreeVar(v3, v2) = v0))
% 50.43/7.30 (13) $i(all_58_11)
% 50.43/7.30 (14) ~ (all_280_0 = 0)
% 50.43/7.30 (15) all_280_0 = 0 | ? [v0: $i] : ? [v1: any] : (vtcheck(all_58_10,
% 50.43/7.30 all_73_39, all_71_4) = v1 & vlookup(all_58_7, all_58_10) = v0 &
% 50.43/7.30 $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 50.43/7.30 (16) $i(all_58_10)
% 50.43/7.30 (17) $i(all_58_6)
% 50.43/7.30 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.43/7.30 [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~
% 50.43/7.30 (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 50.43/7.30 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (vtcheck(v2, v3,
% 50.43/7.30 v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0)))
% 50.43/7.30 (19) (all_196_0 = all_58_7 & all_170_1 = vnoType & all_58_10 = vempty) |
% 50.43/7.30 (all_196_1 = all_170_1 & all_196_2 = all_58_10 & all_196_4 = all_58_7 &
% 50.43/7.30 all_196_5 = all_58_7 & vsomeType(all_196_3) = all_170_1 &
% 50.43/7.30 vbind(all_58_7, all_196_3, all_196_6) = all_58_10) | (all_196_7 =
% 50.43/7.30 all_170_1 & all_196_8 = all_58_10 & all_196_10 = all_58_7 & ~
% 50.43/7.30 (all_196_11 = all_58_7) & vlookup(all_58_7, all_196_9) = all_170_1 &
% 50.43/7.30 vbind(all_196_11, all_196_12, all_196_9) = all_58_10)
% 50.43/7.30 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.43/7.30 (vlookup(v3, v2) = v1) | ~ (vlookup(v3, v2) = v0))
% 50.43/7.30 (21) $i(all_196_10)
% 50.43/7.30 (22) all_280_0 = 0 | ? [v0: any] : ? [v1: any] : (vtcheck(all_58_10,
% 50.43/7.30 all_73_39, all_71_4) = v1 & visFreeVar(all_58_7, all_73_39) = v0 & (
% 50.43/7.30 ~ (v1 = 0) | v0 = 0))
% 50.43/7.30
% 50.43/7.30 Begin of proof
% 50.43/7.30 |
% 50.43/7.30 | BETA: splitting (9) gives:
% 50.43/7.30 |
% 50.43/7.30 | Case 1:
% 50.43/7.30 | |
% 50.43/7.30 | | (23) all_280_0 = 0
% 50.43/7.30 | |
% 50.43/7.30 | | REDUCE: (14), (23) imply:
% 50.43/7.30 | | (24) $false
% 50.43/7.30 | |
% 50.43/7.30 | | CLOSE: (24) is inconsistent.
% 50.43/7.30 | |
% 50.43/7.30 | Case 2:
% 50.43/7.30 | |
% 50.43/7.30 | | (25) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_142_1, all_58_8,
% 50.43/7.30 | | all_58_11) = v0)
% 50.43/7.30 | |
% 50.43/7.30 | | DELTA: instantiating (25) with fresh symbol all_335_0 gives:
% 50.43/7.30 | | (26) ~ (all_335_0 = 0) & vtcheck(all_142_1, all_58_8, all_58_11) =
% 50.43/7.30 | | all_335_0
% 50.43/7.30 | |
% 50.43/7.30 | | ALPHA: (26) implies:
% 50.43/7.30 | | (27) ~ (all_335_0 = 0)
% 50.43/7.30 | | (28) vtcheck(all_142_1, all_58_8, all_58_11) = all_335_0
% 50.43/7.30 | |
% 50.43/7.30 | | BETA: splitting (15) gives:
% 50.43/7.30 | |
% 50.43/7.30 | | Case 1:
% 50.43/7.30 | | |
% 50.43/7.30 | | | (29) all_280_0 = 0
% 50.43/7.30 | | |
% 50.43/7.30 | | | REDUCE: (14), (29) imply:
% 50.43/7.30 | | | (30) $false
% 50.43/7.30 | | |
% 50.43/7.30 | | | CLOSE: (30) is inconsistent.
% 50.43/7.30 | | |
% 50.43/7.30 | | Case 2:
% 50.43/7.30 | | |
% 50.43/7.30 | | | (31) ? [v0: $i] : ? [v1: any] : (vtcheck(all_58_10, all_73_39,
% 50.43/7.30 | | | all_71_4) = v1 & vlookup(all_58_7, all_58_10) = v0 & $i(v0) &
% 50.43/7.30 | | | ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 50.43/7.30 | | |
% 50.43/7.30 | | | DELTA: instantiating (31) with fresh symbols all_341_0, all_341_1 gives:
% 50.43/7.30 | | | (32) vtcheck(all_58_10, all_73_39, all_71_4) = all_341_0 &
% 50.43/7.30 | | | vlookup(all_58_7, all_58_10) = all_341_1 & $i(all_341_1) & ( ~
% 50.43/7.30 | | | (all_341_0 = 0) | ~ (all_341_1 = vnoType))
% 50.43/7.30 | | |
% 50.43/7.30 | | | ALPHA: (32) implies:
% 50.43/7.30 | | | (33) vlookup(all_58_7, all_58_10) = all_341_1
% 50.43/7.30 | | | (34) ~ (all_341_0 = 0) | ~ (all_341_1 = vnoType)
% 50.43/7.30 | | |
% 50.43/7.30 | | | BETA: splitting (22) gives:
% 50.43/7.30 | | |
% 50.43/7.30 | | | Case 1:
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | (35) all_280_0 = 0
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | REDUCE: (14), (35) imply:
% 50.43/7.30 | | | | (36) $false
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | CLOSE: (36) is inconsistent.
% 50.43/7.30 | | | |
% 50.43/7.30 | | | Case 2:
% 50.43/7.30 | | | |
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | GROUND_INST: instantiating (20) with all_170_1, all_341_1, all_58_10,
% 50.43/7.30 | | | | all_58_7, simplifying with (3), (33) gives:
% 50.43/7.30 | | | | (37) all_341_1 = all_170_1
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | BETA: splitting (19) gives:
% 50.43/7.30 | | | |
% 50.43/7.30 | | | | Case 1:
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | (38) all_196_0 = all_58_7 & all_170_1 = vnoType & all_58_10 =
% 50.43/7.30 | | | | | vempty
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | ALPHA: (38) implies:
% 50.43/7.30 | | | | | (39) all_58_10 = vempty
% 50.43/7.30 | | | | | (40) all_170_1 = vnoType
% 50.43/7.30 | | | | | (41) all_196_0 = all_58_7
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | COMBINE_EQS: (37), (40) imply:
% 50.43/7.30 | | | | | (42) all_341_1 = vnoType
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | REDUCE: (1), (39) imply:
% 50.43/7.30 | | | | | (43) vtcheck(vempty, all_58_8, all_58_11) = 0
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | REDUCE: (3), (39), (40) imply:
% 50.43/7.30 | | | | | (44) vlookup(all_58_7, vempty) = vnoType
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | REDUCE: (7), (39) imply:
% 50.43/7.30 | | | | | (45) vbind(all_58_7, all_58_6, vempty) = all_142_1
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | REDUCE: (5), (41) imply:
% 50.43/7.30 | | | | | (46) $i(all_58_7)
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | REDUCE: (16), (39) imply:
% 50.43/7.30 | | | | | (47) $i(vempty)
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | BETA: splitting (34) gives:
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | Case 1:
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | GROUND_INST: instantiating (6) with all_58_7, all_58_6, vempty,
% 50.43/7.30 | | | | | | all_58_8, all_58_11, all_142_1, all_335_0, simplifying
% 50.43/7.30 | | | | | | with (2), (13), (17), (28), (45), (46), (47) gives:
% 50.43/7.30 | | | | | | (48) all_335_0 = 0 | ? [v0: $i] : ? [v1: any] :
% 50.43/7.30 | | | | | | (vtcheck(vempty, all_58_8, all_58_11) = v1 &
% 50.43/7.30 | | | | | | vlookup(all_58_7, vempty) = v0 & $i(v0) & ( ~ (v1 = 0) |
% 50.43/7.30 | | | | | | ~ (v0 = vnoType)))
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | BETA: splitting (48) gives:
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | Case 1:
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | (49) all_335_0 = 0
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | REDUCE: (27), (49) imply:
% 50.43/7.30 | | | | | | | (50) $false
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | CLOSE: (50) is inconsistent.
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | Case 2:
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | (51) ? [v0: $i] : ? [v1: any] : (vtcheck(vempty, all_58_8,
% 50.43/7.30 | | | | | | | all_58_11) = v1 & vlookup(all_58_7, vempty) = v0 &
% 50.43/7.30 | | | | | | | $i(v0) & ( ~ (v1 = 0) | ~ (v0 = vnoType)))
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | DELTA: instantiating (51) with fresh symbols all_449_0, all_449_1
% 50.43/7.30 | | | | | | | gives:
% 50.43/7.30 | | | | | | | (52) vtcheck(vempty, all_58_8, all_58_11) = all_449_0 &
% 50.43/7.30 | | | | | | | vlookup(all_58_7, vempty) = all_449_1 & $i(all_449_1) & (
% 50.43/7.30 | | | | | | | ~ (all_449_0 = 0) | ~ (all_449_1 = vnoType))
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | ALPHA: (52) implies:
% 50.43/7.30 | | | | | | | (53) vlookup(all_58_7, vempty) = all_449_1
% 50.43/7.30 | | | | | | | (54) vtcheck(vempty, all_58_8, all_58_11) = all_449_0
% 50.43/7.30 | | | | | | | (55) ~ (all_449_0 = 0) | ~ (all_449_1 = vnoType)
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | GROUND_INST: instantiating (20) with vnoType, all_449_1, vempty,
% 50.43/7.30 | | | | | | | all_58_7, simplifying with (44), (53) gives:
% 50.43/7.30 | | | | | | | (56) all_449_1 = vnoType
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | GROUND_INST: instantiating (4) with 0, all_449_0, all_58_11,
% 50.43/7.30 | | | | | | | all_58_8, vempty, simplifying with (43), (54) gives:
% 50.43/7.30 | | | | | | | (57) all_449_0 = 0
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | BETA: splitting (55) gives:
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | | Case 1:
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | (58) ~ (all_449_0 = 0)
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | REDUCE: (57), (58) imply:
% 50.43/7.30 | | | | | | | | (59) $false
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | CLOSE: (59) is inconsistent.
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | Case 2:
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | (60) ~ (all_449_1 = vnoType)
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | REDUCE: (56), (60) imply:
% 50.43/7.30 | | | | | | | | (61) $false
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | | CLOSE: (61) is inconsistent.
% 50.43/7.30 | | | | | | | |
% 50.43/7.30 | | | | | | | End of split
% 50.43/7.30 | | | | | | |
% 50.43/7.30 | | | | | | End of split
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | Case 2:
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | (62) ~ (all_341_1 = vnoType)
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | REDUCE: (42), (62) imply:
% 50.43/7.30 | | | | | | (63) $false
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | | CLOSE: (63) is inconsistent.
% 50.43/7.30 | | | | | |
% 50.43/7.30 | | | | | End of split
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | Case 2:
% 50.43/7.30 | | | | |
% 50.43/7.30 | | | | | (64) (all_196_1 = all_170_1 & all_196_2 = all_58_10 & all_196_4 =
% 50.43/7.30 | | | | | all_58_7 & all_196_5 = all_58_7 & vsomeType(all_196_3) =
% 50.43/7.30 | | | | | all_170_1 & vbind(all_58_7, all_196_3, all_196_6) =
% 50.43/7.30 | | | | | all_58_10) | (all_196_7 = all_170_1 & all_196_8 = all_58_10
% 50.43/7.31 | | | | | & all_196_10 = all_58_7 & ~ (all_196_11 = all_58_7) &
% 50.43/7.31 | | | | | vlookup(all_58_7, all_196_9) = all_170_1 & vbind(all_196_11,
% 50.43/7.31 | | | | | all_196_12, all_196_9) = all_58_10)
% 50.43/7.31 | | | | |
% 50.43/7.31 | | | | | BETA: splitting (64) gives:
% 50.43/7.31 | | | | |
% 50.43/7.31 | | | | | Case 1:
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | (65) all_196_1 = all_170_1 & all_196_2 = all_58_10 & all_196_4 =
% 50.43/7.31 | | | | | | all_58_7 & all_196_5 = all_58_7 & vsomeType(all_196_3) =
% 50.43/7.31 | | | | | | all_170_1 & vbind(all_58_7, all_196_3, all_196_6) =
% 50.43/7.31 | | | | | | all_58_10
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | ALPHA: (65) implies:
% 50.43/7.31 | | | | | | (66) all_196_5 = all_58_7
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | REDUCE: (10), (66) imply:
% 50.43/7.31 | | | | | | (67) $i(all_58_7)
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (11), (12), (13), (16), (17),
% 50.43/7.31 | | | | | | (18), (27), (28), (67) are inconsistent by sub-proof #2.
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | Case 2:
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | (68) all_196_7 = all_170_1 & all_196_8 = all_58_10 & all_196_10 =
% 50.43/7.31 | | | | | | all_58_7 & ~ (all_196_11 = all_58_7) & vlookup(all_58_7,
% 50.43/7.31 | | | | | | all_196_9) = all_170_1 & vbind(all_196_11, all_196_12,
% 50.43/7.31 | | | | | | all_196_9) = all_58_10
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | ALPHA: (68) implies:
% 50.43/7.31 | | | | | | (69) all_196_10 = all_58_7
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | REDUCE: (21), (69) imply:
% 50.43/7.31 | | | | | | (70) $i(all_58_7)
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (11), (12), (13), (16), (17),
% 50.43/7.31 | | | | | | (18), (27), (28), (70) are inconsistent by sub-proof #2.
% 50.43/7.31 | | | | | |
% 50.43/7.31 | | | | | End of split
% 50.43/7.31 | | | | |
% 50.43/7.31 | | | | End of split
% 50.43/7.31 | | | |
% 50.43/7.31 | | | End of split
% 50.43/7.31 | | |
% 50.43/7.31 | | End of split
% 50.43/7.31 | |
% 50.43/7.31 | End of split
% 50.43/7.31 |
% 50.43/7.31 End of proof
% 50.43/7.31
% 50.43/7.31 Sub-proof #2 shows that the following formulas are inconsistent:
% 50.43/7.31 ----------------------------------------------------------------
% 50.43/7.31 (1) $i(all_58_7)
% 50.43/7.31 (2) vtcheck(all_58_10, all_58_8, all_58_11) = 0
% 50.43/7.31 (3) $i(all_58_8)
% 50.43/7.31 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~
% 50.43/7.31 (vtcheck(v4, v3, v2) = v0))
% 50.43/7.31 (5) vbind(all_58_7, all_58_6, all_58_10) = all_142_1
% 50.43/7.31 (6) ~ (all_58_4 = 0)
% 50.43/7.31 (7) ~ (all_335_0 = 0)
% 50.43/7.31 (8) visFreeVar(all_58_7, all_58_8) = all_58_4
% 50.43/7.31 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.31 ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3,
% 50.43/7.31 v2) = v0))
% 50.43/7.31 (10) $i(all_58_11)
% 50.43/7.31 (11) $i(all_58_10)
% 50.43/7.31 (12) $i(all_58_6)
% 50.43/7.31 (13) vtcheck(all_142_1, all_58_8, all_58_11) = all_335_0
% 50.43/7.31 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.43/7.31 [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (vtcheck(v5, v3, v4) = v6) | ~
% 50.43/7.31 (vbind(v0, v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 50.43/7.31 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (vtcheck(v2, v3,
% 50.43/7.31 v4) = v8 & visFreeVar(v0, v3) = v7 & ( ~ (v8 = 0) | v7 = 0)))
% 50.43/7.31
% 50.43/7.31 Begin of proof
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (14) with all_58_7, all_58_6, all_58_10, all_58_8,
% 50.43/7.31 | all_58_11, all_142_1, all_335_0, simplifying with (1), (3), (5),
% 50.43/7.31 | (10), (11), (12), (13) gives:
% 50.43/7.31 | (15) all_335_0 = 0 | ? [v0: any] : ? [v1: any] : (vtcheck(all_58_10,
% 50.43/7.31 | all_58_8, all_58_11) = v1 & visFreeVar(all_58_7, all_58_8) = v0 &
% 50.43/7.31 | ( ~ (v1 = 0) | v0 = 0))
% 50.43/7.31 |
% 50.43/7.31 | BETA: splitting (15) gives:
% 50.43/7.31 |
% 50.43/7.31 | Case 1:
% 50.43/7.31 | |
% 50.43/7.31 | | (16) all_335_0 = 0
% 50.43/7.31 | |
% 50.43/7.31 | | REDUCE: (7), (16) imply:
% 50.43/7.31 | | (17) $false
% 50.43/7.31 | |
% 50.43/7.31 | | CLOSE: (17) is inconsistent.
% 50.43/7.31 | |
% 50.43/7.31 | Case 2:
% 50.43/7.31 | |
% 50.43/7.31 | | (18) ? [v0: any] : ? [v1: any] : (vtcheck(all_58_10, all_58_8,
% 50.43/7.31 | | all_58_11) = v1 & visFreeVar(all_58_7, all_58_8) = v0 & ( ~ (v1
% 50.43/7.31 | | = 0) | v0 = 0))
% 50.43/7.31 | |
% 50.43/7.31 | | DELTA: instantiating (18) with fresh symbols all_603_0, all_603_1 gives:
% 50.43/7.31 | | (19) vtcheck(all_58_10, all_58_8, all_58_11) = all_603_0 &
% 50.43/7.31 | | visFreeVar(all_58_7, all_58_8) = all_603_1 & ( ~ (all_603_0 = 0) |
% 50.43/7.31 | | all_603_1 = 0)
% 50.43/7.31 | |
% 50.43/7.31 | | REF_CLOSE: (2), (4), (6), (8), (9), (19) are inconsistent by sub-proof #3.
% 50.43/7.31 | |
% 50.43/7.31 | End of split
% 50.43/7.31 |
% 50.43/7.31 End of proof
% 50.43/7.31
% 50.43/7.31 Sub-proof #3 shows that the following formulas are inconsistent:
% 50.43/7.31 ----------------------------------------------------------------
% 50.43/7.31 (1) vtcheck(all_58_10, all_58_8, all_58_11) = 0
% 50.43/7.31 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~
% 50.43/7.31 (vtcheck(v4, v3, v2) = v0))
% 50.43/7.31 (3) ~ (all_58_4 = 0)
% 50.43/7.31 (4) visFreeVar(all_58_7, all_58_8) = all_58_4
% 50.43/7.31 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.31 ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3,
% 50.43/7.31 v2) = v0))
% 50.43/7.31 (6) vtcheck(all_58_10, all_58_8, all_58_11) = all_603_0 &
% 50.43/7.31 visFreeVar(all_58_7, all_58_8) = all_603_1 & ( ~ (all_603_0 = 0) |
% 50.43/7.31 all_603_1 = 0)
% 50.43/7.31
% 50.43/7.31 Begin of proof
% 50.43/7.31 |
% 50.43/7.31 | ALPHA: (6) implies:
% 50.43/7.31 | (7) visFreeVar(all_58_7, all_58_8) = all_603_1
% 50.43/7.31 | (8) vtcheck(all_58_10, all_58_8, all_58_11) = all_603_0
% 50.43/7.31 | (9) ~ (all_603_0 = 0) | all_603_1 = 0
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (5) with all_58_4, all_603_1, all_58_8, all_58_7,
% 50.43/7.31 | simplifying with (4), (7) gives:
% 50.43/7.31 | (10) all_603_1 = all_58_4
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (2) with 0, all_603_0, all_58_11, all_58_8,
% 50.43/7.31 | all_58_10, simplifying with (1), (8) gives:
% 50.43/7.31 | (11) all_603_0 = 0
% 50.43/7.31 |
% 50.43/7.31 | BETA: splitting (9) gives:
% 50.43/7.31 |
% 50.43/7.31 | Case 1:
% 50.43/7.31 | |
% 50.43/7.31 | | (12) ~ (all_603_0 = 0)
% 50.43/7.31 | |
% 50.43/7.31 | | REDUCE: (11), (12) imply:
% 50.43/7.31 | | (13) $false
% 50.43/7.31 | |
% 50.43/7.31 | | CLOSE: (13) is inconsistent.
% 50.43/7.31 | |
% 50.43/7.31 | Case 2:
% 50.43/7.31 | |
% 50.43/7.31 | | (14) all_603_1 = 0
% 50.43/7.31 | |
% 50.43/7.31 | | COMBINE_EQS: (10), (14) imply:
% 50.43/7.31 | | (15) all_58_4 = 0
% 50.43/7.31 | |
% 50.43/7.31 | | REDUCE: (3), (15) imply:
% 50.43/7.31 | | (16) $false
% 50.43/7.31 | |
% 50.43/7.31 | | CLOSE: (16) is inconsistent.
% 50.43/7.31 | |
% 50.43/7.31 | End of split
% 50.43/7.31 |
% 50.43/7.31 End of proof
% 50.43/7.31
% 50.43/7.31 Sub-proof #4 shows that the following formulas are inconsistent:
% 50.43/7.31 ----------------------------------------------------------------
% 50.43/7.31 (1) $i(all_73_35)
% 50.43/7.31 (2) $i(all_58_7)
% 50.43/7.31 (3) $i(all_73_32)
% 50.43/7.31 (4) ~ (all_58_4 = 0)
% 50.43/7.31 (5) visFreeVar(all_58_7, all_58_8) = all_58_4
% 50.43/7.31 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.43/7.31 ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3,
% 50.43/7.31 v2) = v0))
% 50.43/7.31 (7) $i(all_73_34)
% 50.43/7.31 (8) visFreeVar(all_73_34, all_58_8) = 0
% 50.43/7.31 (9) $i(all_58_6)
% 50.43/7.31 (10) vabs(all_73_34, all_73_35, all_73_32) = all_58_2
% 50.43/7.31 (11) vabs(all_58_7, all_58_6, veabs) = all_58_2
% 50.43/7.31 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.43/7.31 [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~
% 50.43/7.31 (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 50.43/7.31 $i(v2) | ~ $i(v1) | ~ $i(v0))
% 50.43/7.31 (13) $i(veabs)
% 50.43/7.31
% 50.43/7.31 Begin of proof
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (12) with all_58_7, all_58_6, veabs, all_73_34,
% 50.43/7.31 | all_73_35, all_73_32, all_58_2, simplifying with (1), (2), (3),
% 50.43/7.31 | (7), (9), (10), (11), (13) gives:
% 50.43/7.31 | (14) all_73_34 = all_58_7
% 50.43/7.31 |
% 50.43/7.31 | REDUCE: (8), (14) imply:
% 50.43/7.31 | (15) visFreeVar(all_58_7, all_58_8) = 0
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (6) with all_58_4, 0, all_58_8, all_58_7,
% 50.43/7.31 | simplifying with (5), (15) gives:
% 50.43/7.31 | (16) all_58_4 = 0
% 50.43/7.31 |
% 50.43/7.31 | REDUCE: (4), (16) imply:
% 50.43/7.31 | (17) $false
% 50.43/7.31 |
% 50.43/7.31 | CLOSE: (17) is inconsistent.
% 50.43/7.31 |
% 50.43/7.31 End of proof
% 50.43/7.31
% 50.43/7.31 Sub-proof #5 shows that the following formulas are inconsistent:
% 50.43/7.31 ----------------------------------------------------------------
% 50.43/7.31 (1) $i(all_58_7)
% 50.43/7.31 (2) $i(all_58_9)
% 50.43/7.31 (3) $i(all_73_18)
% 50.43/7.31 (4) $i(all_58_6)
% 50.43/7.31 (5) vabs(all_58_7, all_58_6, veabs) = all_58_2
% 50.43/7.31 (6) $i(all_73_17)
% 50.43/7.31 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.43/7.31 [v5: $i] : ! [v6: $i] : (v3 = v0 | ~ (vabs(v3, v4, v5) = v6) | ~
% 50.43/7.31 (vabs(v0, v1, v2) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 50.43/7.31 | ~ $i(v1) | ~ $i(v0))
% 50.43/7.31 (8) vabs(all_58_9, all_73_18, all_73_17) = all_58_2
% 50.43/7.31 (9) ~ (all_58_7 = all_58_9)
% 50.43/7.31 (10) $i(veabs)
% 50.43/7.31
% 50.43/7.31 Begin of proof
% 50.43/7.31 |
% 50.43/7.31 | GROUND_INST: instantiating (7) with all_58_7, all_58_6, veabs, all_58_9,
% 50.43/7.31 | all_73_18, all_73_17, all_58_2, simplifying with (1), (2), (3),
% 50.43/7.31 | (4), (5), (6), (8), (10) gives:
% 50.43/7.31 | (11) all_58_7 = all_58_9
% 50.43/7.31 |
% 50.43/7.31 | REDUCE: (9), (11) imply:
% 50.43/7.31 | (12) $false
% 50.43/7.31 |
% 50.43/7.31 | CLOSE: (12) is inconsistent.
% 50.43/7.31 |
% 50.43/7.31 End of proof
% 50.43/7.31 % SZS output end Proof for theBenchmark
% 50.43/7.32
% 50.43/7.32 6716ms
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