TSTP Solution File: COM133+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM133+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 : n002.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 14.56s 2.69s
% Output : Proof 19.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 13:38:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.52/1.45 Prover 4: Preprocessing ...
% 5.52/1.46 Prover 1: Preprocessing ...
% 5.52/1.48 Prover 2: Preprocessing ...
% 5.52/1.48 Prover 5: Preprocessing ...
% 5.52/1.48 Prover 3: Preprocessing ...
% 5.52/1.48 Prover 0: Preprocessing ...
% 5.52/1.48 Prover 6: Preprocessing ...
% 11.97/2.32 Prover 1: Constructing countermodel ...
% 11.97/2.33 Prover 3: Constructing countermodel ...
% 12.57/2.39 Prover 6: Proving ...
% 12.81/2.43 Prover 4: Constructing countermodel ...
% 13.01/2.46 Prover 5: Proving ...
% 13.01/2.53 Prover 0: Proving ...
% 14.56/2.68 Prover 2: Proving ...
% 14.56/2.69 Prover 6: proved (2061ms)
% 14.56/2.69
% 14.56/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.56/2.69
% 14.56/2.69 Prover 3: stopped
% 14.56/2.70 Prover 0: stopped
% 14.56/2.71 Prover 5: stopped
% 14.56/2.72 Prover 2: stopped
% 15.12/2.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.12/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.12/2.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.12/2.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.12/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.23/2.92 Prover 10: Preprocessing ...
% 16.66/2.93 Prover 7: Preprocessing ...
% 16.66/2.94 Prover 13: Preprocessing ...
% 16.66/2.94 Prover 8: Preprocessing ...
% 16.90/2.96 Prover 11: Preprocessing ...
% 17.79/3.14 Prover 4: Found proof (size 61)
% 18.31/3.14 Prover 4: proved (2514ms)
% 18.31/3.14 Prover 1: stopped
% 18.31/3.15 Prover 13: stopped
% 18.31/3.21 Prover 7: Warning: ignoring some quantifiers
% 18.31/3.21 Prover 10: Warning: ignoring some quantifiers
% 18.31/3.23 Prover 10: Constructing countermodel ...
% 18.31/3.23 Prover 7: Constructing countermodel ...
% 18.93/3.25 Prover 10: stopped
% 18.93/3.25 Prover 7: stopped
% 18.93/3.27 Prover 8: Warning: ignoring some quantifiers
% 18.93/3.28 Prover 8: Constructing countermodel ...
% 18.93/3.29 Prover 8: stopped
% 19.33/3.30 Prover 11: Constructing countermodel ...
% 19.33/3.31 Prover 11: stopped
% 19.33/3.31
% 19.33/3.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.33/3.31
% 19.46/3.32 % SZS output start Proof for theBenchmark
% 19.49/3.33 Assumptions after simplification:
% 19.49/3.33 ---------------------------------
% 19.49/3.33
% 19.49/3.33 (T-subst-abs)
% 19.49/3.35 $i(veabs) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 19.49/3.35 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 19.49/3.35 ? [v10: int] : ( ~ (v10 = 0) & vsubst(v2, v3, v8) = v9 & vtcheck(v7, v8, v6) =
% 19.49/3.35 0 & vtcheck(v1, v9, v6) = v10 & vtcheck(v1, v3, v0) = 0 & vbind(v2, v0, v1)
% 19.49/3.35 = v7 & vabs(v4, v5, veabs) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 19.49/3.35 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 19.49/3.35
% 19.49/3.35 (T-subst-abs-1)
% 19.49/3.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.49/3.36 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: int]
% 19.49/3.36 : (v10 = 0 | ~ (vsubst(v2, v3, v8) = v9) | ~ (vtcheck(v7, v8, v6) = 0) | ~
% 19.49/3.36 (vtcheck(v1, v9, v6) = v10) | ~ (vbind(v2, v0, v1) = v7) | ~ (vabs(v2, v4,
% 19.49/3.36 v5) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 19.49/3.36 ~ $i(v1) | ~ $i(v0) | ? [v11: int] : ( ~ (v11 = 0) & vtcheck(v1, v3, v0) =
% 19.49/3.36 v11)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 19.49/3.36 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: int] :
% 19.49/3.36 (v9 = 0 | ~ (vsubst(v2, v3, v7) = v8) | ~ (vtcheck(v1, v8, v6) = v9) | ~
% 19.49/3.36 (vtcheck(v1, v3, v0) = 0) | ~ (vabs(v2, v4, v5) = v7) | ~ $i(v6) | ~
% 19.49/3.36 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 19.49/3.36 [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) & vtcheck(v10, v7, v6) = v11 &
% 19.49/3.36 vbind(v2, v0, v1) = v10 & $i(v10))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 19.49/3.36 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] :
% 19.49/3.36 ! [v8: $i] : ( ~ (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~
% 19.49/3.36 (vbind(v2, v0, v1) = v7) | ~ (vabs(v2, v4, v5) = v8) | ~ $i(v6) | ~
% 19.49/3.36 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 19.49/3.36 $i] : (vsubst(v2, v3, v8) = v9 & vtcheck(v1, v9, v6) = 0 & $i(v9)))
% 19.49/3.36
% 19.49/3.36 (T-subst-abs-2)
% 19.49/3.37 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 19.49/3.37 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 19.49/3.37 ! [v10: int] : (v10 = 0 | v4 = v2 | ~ (vsubst(v2, v3, v8) = v9) | ~
% 19.49/3.37 (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v9, v6) = v10) | ~ (vbind(v2,
% 19.49/3.37 v0, v1) = v7) | ~ (vabs(v4, v5, veabs) = v8) | ~ $i(v6) | ~ $i(v5) |
% 19.49/3.37 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v11: any] :
% 19.49/3.37 ? [v12: any] : (vtcheck(v1, v3, v0) = v12 & visFreeVar(v4, v3) = v11 & ( ~
% 19.49/3.37 (v12 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 19.49/3.37 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 19.49/3.37 : ! [v9: int] : (v9 = 0 | v4 = v2 | ~ (vsubst(v2, v3, v7) = v8) | ~
% 19.49/3.37 (vtcheck(v1, v8, v6) = v9) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vabs(v4, v5,
% 19.49/3.37 veabs) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 19.49/3.37 | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: $i] : ? [v12: any] :
% 19.49/3.37 (vtcheck(v11, v7, v6) = v12 & vbind(v2, v0, v1) = v11 & visFreeVar(v4, v3) =
% 19.49/3.37 v10 & $i(v11) & ( ~ (v12 = 0) | v10 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 19.49/3.37 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 19.49/3.37 int] : ! [v8: $i] : ! [v9: $i] : (v7 = 0 | v4 = v2 | ~ (vtcheck(v8, v9,
% 19.49/3.37 v6) = 0) | ~ (vbind(v2, v0, v1) = v8) | ~ (visFreeVar(v4, v3) = v7) |
% 19.49/3.37 ~ (vabs(v4, v5, veabs) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 19.49/3.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: $i] : ?
% 19.49/3.37 [v12: any] : (vsubst(v2, v3, v9) = v11 & vtcheck(v1, v11, v6) = v12 &
% 19.49/3.37 vtcheck(v1, v3, v0) = v10 & $i(v11) & ( ~ (v10 = 0) | v12 = 0))) & ! [v0:
% 19.49/3.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 19.49/3.37 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v2 | ~ (vtcheck(v7, v8, v6) =
% 19.49/3.37 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vbind(v2, v0, v1) = v7) | ~
% 19.49/3.37 (vabs(v4, v5, veabs) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 19.49/3.37 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11:
% 19.49/3.37 any] : (vsubst(v2, v3, v8) = v10 & vtcheck(v1, v10, v6) = v11 &
% 19.49/3.37 visFreeVar(v4, v3) = v9 & $i(v10) & (v11 = 0 | v9 = 0)))
% 19.49/3.37
% 19.49/3.37 (T-subst-abs-3)
% 19.49/3.37 $i(veabs) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 19.49/3.37 $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 19.49/3.37 ! [v10: int] : (v10 = 0 | v4 = v2 | ~ (vsubst(v2, v3, v8) = v9) | ~
% 19.49/3.37 (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v9, v6) = v10) | ~ (vbind(v2,
% 19.49/3.37 v0, v1) = v7) | ~ (vabs(v4, v5, veabs) = v8) | ~ $i(v6) | ~ $i(v5) |
% 19.49/3.37 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v11: any] :
% 19.49/3.37 ? [v12: any] : (vtcheck(v1, v3, v0) = v12 & visFreeVar(v4, v3) = v11 & ( ~
% 19.49/3.37 (v12 = 0) | ~ (v11 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.49/3.37 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 19.49/3.37 $i] : ! [v9: int] : (v9 = 0 | v4 = v2 | ~ (vsubst(v2, v3, v7) = v8) | ~
% 19.49/3.37 (vtcheck(v1, v8, v6) = v9) | ~ (vtcheck(v1, v3, v0) = 0) | ~ (vabs(v4, v5,
% 19.49/3.37 veabs) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 19.49/3.37 | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: $i] : ? [v12: any] :
% 19.49/3.37 (vtcheck(v11, v7, v6) = v12 & vbind(v2, v0, v1) = v11 & visFreeVar(v4, v3) =
% 19.49/3.37 v10 & $i(v11) & ( ~ (v12 = 0) | ~ (v10 = 0)))) & ! [v0: $i] : ! [v1:
% 19.49/3.37 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 19.49/3.37 ! [v7: $i] : ! [v8: $i] : (v4 = v2 | ~ (vtcheck(v7, v8, v6) = 0) | ~
% 19.49/3.37 (vtcheck(v1, v3, v0) = 0) | ~ (vbind(v2, v0, v1) = v7) | ~ (vabs(v4, v5,
% 19.49/3.37 veabs) = v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 19.49/3.37 | ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 19.49/3.37 (vsubst(v2, v3, v8) = v10 & vtcheck(v1, v10, v6) = v11 & visFreeVar(v4, v3)
% 19.49/3.37 = v9 & $i(v10) & ( ~ (v9 = 0) | v11 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 19.49/3.37 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 19.49/3.37 $i] : ! [v8: $i] : (v4 = v2 | ~ (vtcheck(v7, v8, v6) = 0) | ~ (vbind(v2,
% 19.49/3.37 v0, v1) = v7) | ~ (visFreeVar(v4, v3) = 0) | ~ (vabs(v4, v5, veabs) =
% 19.49/3.37 v8) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 19.49/3.37 $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 19.49/3.37 (vsubst(v2, v3, v8) = v10 & vtcheck(v1, v10, v6) = v11 & vtcheck(v1, v3, v0)
% 19.49/3.37 = v9 & $i(v10) & ( ~ (v9 = 0) | v11 = 0)))
% 19.49/3.37
% 19.49/3.37 (function-axioms)
% 19.49/3.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 19.49/3.38 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0)) & ! [v0:
% 19.49/3.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 19.49/3.38 : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) | ~ (vtcheck(v4, v3,
% 19.49/3.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 19.49/3.38 [v4: $i] : (v1 = v0 | ~ (vbind(v4, v3, v2) = v1) | ~ (vbind(v4, v3, v2) =
% 19.49/3.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 19.49/3.38 : (v1 = v0 | ~ (vabs(v4, v3, v2) = v1) | ~ (vabs(v4, v3, v2) = v0)) & !
% 19.49/3.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (varrow(v3,
% 19.49/3.38 v2) = v1) | ~ (varrow(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.49/3.38 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vlookup(v3, v2) = v1) | ~
% 19.49/3.38 (vlookup(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.49/3.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.49/3.38 (visFreeVar(v3, v2) = v1) | ~ (visFreeVar(v3, v2) = v0)) & ! [v0: $i] : !
% 19.49/3.38 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vapp(v3, v2) = v1) | ~
% 19.49/3.38 (vapp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 19.49/3.38 ~ (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 19.49/3.38 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeExp(v2) = v1) | ~ (vgetSomeExp(v2) = v0))
% 19.49/3.38 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 19.49/3.38 = v0 | ~ (visSomeExp(v2) = v1) | ~ (visSomeExp(v2) = v0)) & ! [v0: $i] :
% 19.49/3.38 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeExp(v2) = v1) | ~
% 19.49/3.38 (vsomeExp(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 19.49/3.38 ~ (vgensym(v2) = v1) | ~ (vgensym(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 19.49/3.38 ! [v2: $i] : (v1 = v0 | ~ (vgetSomeType(v2) = v1) | ~ (vgetSomeType(v2) =
% 19.49/3.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 19.49/3.38 $i] : (v1 = v0 | ~ (visSomeType(v2) = v1) | ~ (visSomeType(v2) = v0)) & !
% 19.49/3.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsomeType(v2) = v1) | ~
% 19.49/3.38 (vsomeType(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 19.49/3.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (visValue(v2) = v1) | ~
% 19.49/3.38 (visValue(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 19.49/3.38 ~ (vvar(v2) = v1) | ~ (vvar(v2) = v0))
% 19.49/3.38
% 19.49/3.38 Further assumptions not needed in the proof:
% 19.49/3.38 --------------------------------------------
% 19.49/3.38 DIFF-abs-app, DIFF-empty-bind, DIFF-noExp-someExp, DIFF-noType-someType,
% 19.49/3.38 DIFF-var-abs, DIFF-var-app, EQ-abs, EQ-app, EQ-arrow, EQ-bind, EQ-empty,
% 19.49/3.38 EQ-noExp, EQ-noType, EQ-someExp, EQ-someType, EQ-var, T-Context-Duplicate,
% 19.49/3.38 T-Context-Swap, T-Strong, T-Weak, T-Weak-FreeVar, T-abs, T-app, T-inv,
% 19.49/3.38 T-subst-IH-abs, T-var, gensym-is-fresh, getSomeExp0, getSomeType0, isFreeVar0,
% 19.49/3.38 isFreeVar1, isFreeVar2, isSomeExp0, isSomeExp1, isSomeType0, isSomeType1,
% 19.49/3.38 isValue0, isValue1, isValue2, lookup-INV, lookup0, lookup1, lookup2, reduce-INV,
% 19.49/3.38 reduce0, reduce1, reduce2, reduce3, reduce4, reduce5, reduce6, subst-INV,
% 19.49/3.38 subst0, subst1, subst2, subst3, subst4, subst5
% 19.49/3.38
% 19.49/3.38 Those formulas are unsatisfiable:
% 19.49/3.38 ---------------------------------
% 19.49/3.38
% 19.49/3.38 Begin of proof
% 19.49/3.38 |
% 19.49/3.38 | ALPHA: (T-subst-abs-1) implies:
% 19.49/3.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.49/3.38 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 19.49/3.38 | [v10: int] : (v10 = 0 | ~ (vsubst(v2, v3, v8) = v9) | ~ (vtcheck(v7,
% 19.49/3.38 | v8, v6) = 0) | ~ (vtcheck(v1, v9, v6) = v10) | ~ (vbind(v2, v0,
% 19.49/3.38 | v1) = v7) | ~ (vabs(v2, v4, v5) = v8) | ~ $i(v6) | ~ $i(v5) |
% 19.49/3.38 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v11:
% 19.49/3.38 | int] : ( ~ (v11 = 0) & vtcheck(v1, v3, v0) = v11))
% 19.49/3.38 |
% 19.49/3.38 | ALPHA: (T-subst-abs-2) implies:
% 19.49/3.39 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.49/3.39 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v2 | ~
% 19.49/3.39 | (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~
% 19.49/3.39 | (vbind(v2, v0, v1) = v7) | ~ (vabs(v4, v5, veabs) = v8) | ~ $i(v6)
% 19.49/3.39 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.49/3.39 | $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] : (vsubst(v2,
% 19.49/3.39 | v3, v8) = v10 & vtcheck(v1, v10, v6) = v11 & visFreeVar(v4, v3) =
% 19.49/3.39 | v9 & $i(v10) & (v11 = 0 | v9 = 0)))
% 19.49/3.39 |
% 19.49/3.39 | ALPHA: (T-subst-abs-3) implies:
% 19.49/3.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.49/3.39 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v4 = v2 | ~
% 19.49/3.39 | (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v3, v0) = 0) | ~
% 19.49/3.39 | (vbind(v2, v0, v1) = v7) | ~ (vabs(v4, v5, veabs) = v8) | ~ $i(v6)
% 19.49/3.39 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.49/3.39 | $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] : (vsubst(v2,
% 19.49/3.39 | v3, v8) = v10 & vtcheck(v1, v10, v6) = v11 & visFreeVar(v4, v3) =
% 19.49/3.39 | v9 & $i(v10) & ( ~ (v9 = 0) | v11 = 0)))
% 19.49/3.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.49/3.39 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 19.49/3.39 | [v10: int] : (v10 = 0 | v4 = v2 | ~ (vsubst(v2, v3, v8) = v9) | ~
% 19.49/3.39 | (vtcheck(v7, v8, v6) = 0) | ~ (vtcheck(v1, v9, v6) = v10) | ~
% 19.49/3.39 | (vbind(v2, v0, v1) = v7) | ~ (vabs(v4, v5, veabs) = v8) | ~ $i(v6)
% 19.49/3.39 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.49/3.39 | $i(v0) | ? [v11: any] : ? [v12: any] : (vtcheck(v1, v3, v0) = v12 &
% 19.49/3.39 | visFreeVar(v4, v3) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))
% 19.49/3.39 |
% 19.49/3.39 | ALPHA: (T-subst-abs) implies:
% 19.49/3.39 | (5) $i(veabs)
% 19.49/3.39 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 19.49/3.39 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 19.49/3.39 | [v10: int] : ( ~ (v10 = 0) & vsubst(v2, v3, v8) = v9 & vtcheck(v7, v8,
% 19.49/3.39 | v6) = 0 & vtcheck(v1, v9, v6) = v10 & vtcheck(v1, v3, v0) = 0 &
% 19.49/3.39 | vbind(v2, v0, v1) = v7 & vabs(v4, v5, veabs) = v8 & $i(v9) & $i(v8) &
% 19.49/3.39 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 19.49/3.39 | $i(v0))
% 19.49/3.39 |
% 19.49/3.39 | ALPHA: (function-axioms) implies:
% 19.49/3.39 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.49/3.39 | ! [v3: $i] : (v1 = v0 | ~ (visFreeVar(v3, v2) = v1) | ~
% 19.49/3.39 | (visFreeVar(v3, v2) = v0))
% 19.49/3.39 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.49/3.39 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vtcheck(v4, v3, v2) = v1) |
% 19.49/3.39 | ~ (vtcheck(v4, v3, v2) = v0))
% 19.49/3.40 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.49/3.40 | (v1 = v0 | ~ (vsubst(v4, v3, v2) = v1) | ~ (vsubst(v4, v3, v2) = v0))
% 19.49/3.40 |
% 19.49/3.40 | DELTA: instantiating (6) with fresh symbols all_60_0, all_60_1, all_60_2,
% 19.49/3.40 | all_60_3, all_60_4, all_60_5, all_60_6, all_60_7, all_60_8, all_60_9,
% 19.49/3.40 | all_60_10 gives:
% 19.49/3.40 | (10) ~ (all_60_0 = 0) & vsubst(all_60_8, all_60_7, all_60_2) = all_60_1 &
% 19.49/3.40 | vtcheck(all_60_3, all_60_2, all_60_4) = 0 & vtcheck(all_60_9,
% 19.49/3.40 | all_60_1, all_60_4) = all_60_0 & vtcheck(all_60_9, all_60_7,
% 19.49/3.40 | all_60_10) = 0 & vbind(all_60_8, all_60_10, all_60_9) = all_60_3 &
% 19.49/3.40 | vabs(all_60_6, all_60_5, veabs) = all_60_2 & $i(all_60_1) &
% 19.49/3.40 | $i(all_60_2) & $i(all_60_3) & $i(all_60_4) & $i(all_60_5) &
% 19.49/3.40 | $i(all_60_6) & $i(all_60_7) & $i(all_60_8) & $i(all_60_9) &
% 19.49/3.40 | $i(all_60_10)
% 19.49/3.40 |
% 19.49/3.40 | ALPHA: (10) implies:
% 19.49/3.40 | (11) ~ (all_60_0 = 0)
% 19.49/3.40 | (12) $i(all_60_10)
% 19.49/3.40 | (13) $i(all_60_9)
% 19.49/3.40 | (14) $i(all_60_8)
% 19.49/3.40 | (15) $i(all_60_7)
% 19.49/3.40 | (16) $i(all_60_6)
% 19.49/3.40 | (17) $i(all_60_5)
% 19.49/3.40 | (18) $i(all_60_4)
% 19.49/3.40 | (19) vabs(all_60_6, all_60_5, veabs) = all_60_2
% 19.49/3.40 | (20) vbind(all_60_8, all_60_10, all_60_9) = all_60_3
% 19.49/3.40 | (21) vtcheck(all_60_9, all_60_7, all_60_10) = 0
% 19.49/3.40 | (22) vtcheck(all_60_9, all_60_1, all_60_4) = all_60_0
% 19.49/3.40 | (23) vtcheck(all_60_3, all_60_2, all_60_4) = 0
% 19.49/3.40 | (24) vsubst(all_60_8, all_60_7, all_60_2) = all_60_1
% 19.49/3.40 |
% 19.84/3.40 | GROUND_INST: instantiating (3) with all_60_10, all_60_9, all_60_8, all_60_7,
% 19.84/3.40 | all_60_6, all_60_5, all_60_4, all_60_3, all_60_2, simplifying
% 19.84/3.40 | with (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 19.84/3.40 | (23) gives:
% 19.84/3.40 | (25) all_60_6 = all_60_8 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 19.84/3.40 | (vsubst(all_60_8, all_60_7, all_60_2) = v1 & vtcheck(all_60_9, v1,
% 19.84/3.40 | all_60_4) = v2 & visFreeVar(all_60_6, all_60_7) = v0 & $i(v1) & (
% 19.84/3.40 | ~ (v0 = 0) | v2 = 0))
% 19.84/3.40 |
% 19.84/3.40 | GROUND_INST: instantiating (2) with all_60_10, all_60_9, all_60_8, all_60_7,
% 19.84/3.40 | all_60_6, all_60_5, all_60_4, all_60_3, all_60_2, simplifying
% 19.84/3.40 | with (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 19.84/3.40 | (23) gives:
% 19.84/3.40 | (26) all_60_6 = all_60_8 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 19.84/3.40 | (vsubst(all_60_8, all_60_7, all_60_2) = v1 & vtcheck(all_60_9, v1,
% 19.84/3.40 | all_60_4) = v2 & visFreeVar(all_60_6, all_60_7) = v0 & $i(v1) &
% 19.84/3.40 | (v2 = 0 | v0 = 0))
% 19.84/3.40 |
% 19.84/3.41 | GROUND_INST: instantiating (4) with all_60_10, all_60_9, all_60_8, all_60_7,
% 19.84/3.41 | all_60_6, all_60_5, all_60_4, all_60_3, all_60_2, all_60_1,
% 19.84/3.41 | all_60_0, simplifying with (12), (13), (14), (15), (16), (17),
% 19.84/3.41 | (18), (19), (20), (22), (23), (24) gives:
% 19.84/3.41 | (27) all_60_0 = 0 | all_60_6 = all_60_8 | ? [v0: any] : ? [v1: any] :
% 19.84/3.41 | (vtcheck(all_60_9, all_60_7, all_60_10) = v1 & visFreeVar(all_60_6,
% 19.84/3.41 | all_60_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.84/3.41 |
% 19.84/3.41 | BETA: splitting (26) gives:
% 19.84/3.41 |
% 19.84/3.41 | Case 1:
% 19.84/3.41 | |
% 19.84/3.41 | | (28) all_60_6 = all_60_8
% 19.84/3.41 | |
% 19.84/3.41 | | REDUCE: (19), (28) imply:
% 19.84/3.41 | | (29) vabs(all_60_8, all_60_5, veabs) = all_60_2
% 19.84/3.41 | |
% 19.84/3.41 | | GROUND_INST: instantiating (1) with all_60_10, all_60_9, all_60_8, all_60_7,
% 19.84/3.41 | | all_60_5, veabs, all_60_4, all_60_3, all_60_2, all_60_1,
% 19.84/3.41 | | all_60_0, simplifying with (5), (12), (13), (14), (15), (17),
% 19.84/3.41 | | (18), (20), (22), (23), (24), (29) gives:
% 19.84/3.41 | | (30) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_60_9,
% 19.84/3.41 | | all_60_7, all_60_10) = v0)
% 19.84/3.41 | |
% 19.84/3.41 | | BETA: splitting (30) gives:
% 19.84/3.41 | |
% 19.84/3.41 | | Case 1:
% 19.84/3.41 | | |
% 19.84/3.41 | | | (31) all_60_0 = 0
% 19.84/3.41 | | |
% 19.84/3.41 | | | REDUCE: (11), (31) imply:
% 19.84/3.41 | | | (32) $false
% 19.84/3.41 | | |
% 19.84/3.41 | | | CLOSE: (32) is inconsistent.
% 19.84/3.41 | | |
% 19.84/3.41 | | Case 2:
% 19.84/3.41 | | |
% 19.84/3.41 | | | (33) ? [v0: int] : ( ~ (v0 = 0) & vtcheck(all_60_9, all_60_7,
% 19.84/3.41 | | | all_60_10) = v0)
% 19.84/3.41 | | |
% 19.84/3.41 | | | DELTA: instantiating (33) with fresh symbol all_118_0 gives:
% 19.84/3.41 | | | (34) ~ (all_118_0 = 0) & vtcheck(all_60_9, all_60_7, all_60_10) =
% 19.84/3.41 | | | all_118_0
% 19.84/3.41 | | |
% 19.84/3.41 | | | ALPHA: (34) implies:
% 19.84/3.41 | | | (35) ~ (all_118_0 = 0)
% 19.84/3.41 | | | (36) vtcheck(all_60_9, all_60_7, all_60_10) = all_118_0
% 19.84/3.41 | | |
% 19.84/3.41 | | | GROUND_INST: instantiating (8) with 0, all_118_0, all_60_10, all_60_7,
% 19.84/3.41 | | | all_60_9, simplifying with (21), (36) gives:
% 19.84/3.41 | | | (37) all_118_0 = 0
% 19.84/3.41 | | |
% 19.84/3.41 | | | REDUCE: (35), (37) imply:
% 19.84/3.41 | | | (38) $false
% 19.84/3.41 | | |
% 19.84/3.41 | | | CLOSE: (38) is inconsistent.
% 19.84/3.41 | | |
% 19.84/3.41 | | End of split
% 19.84/3.41 | |
% 19.84/3.41 | Case 2:
% 19.84/3.41 | |
% 19.84/3.41 | | (39) ~ (all_60_6 = all_60_8)
% 19.84/3.41 | | (40) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (vsubst(all_60_8,
% 19.84/3.41 | | all_60_7, all_60_2) = v1 & vtcheck(all_60_9, v1, all_60_4) = v2
% 19.84/3.41 | | & visFreeVar(all_60_6, all_60_7) = v0 & $i(v1) & (v2 = 0 | v0 =
% 19.84/3.41 | | 0))
% 19.84/3.41 | |
% 19.84/3.41 | | DELTA: instantiating (40) with fresh symbols all_100_0, all_100_1, all_100_2
% 19.84/3.41 | | gives:
% 19.84/3.41 | | (41) vsubst(all_60_8, all_60_7, all_60_2) = all_100_1 & vtcheck(all_60_9,
% 19.84/3.41 | | all_100_1, all_60_4) = all_100_0 & visFreeVar(all_60_6, all_60_7)
% 19.84/3.41 | | = all_100_2 & $i(all_100_1) & (all_100_0 = 0 | all_100_2 = 0)
% 19.84/3.41 | |
% 19.84/3.41 | | ALPHA: (41) implies:
% 19.84/3.41 | | (42) visFreeVar(all_60_6, all_60_7) = all_100_2
% 19.84/3.41 | | (43) vtcheck(all_60_9, all_100_1, all_60_4) = all_100_0
% 19.84/3.41 | | (44) vsubst(all_60_8, all_60_7, all_60_2) = all_100_1
% 19.84/3.41 | | (45) all_100_0 = 0 | all_100_2 = 0
% 19.84/3.41 | |
% 19.84/3.41 | | BETA: splitting (25) gives:
% 19.84/3.41 | |
% 19.84/3.41 | | Case 1:
% 19.84/3.41 | | |
% 19.84/3.42 | | | (46) all_60_6 = all_60_8
% 19.84/3.42 | | |
% 19.84/3.42 | | | REDUCE: (39), (46) imply:
% 19.84/3.42 | | | (47) $false
% 19.84/3.42 | | |
% 19.84/3.42 | | | CLOSE: (47) is inconsistent.
% 19.84/3.42 | | |
% 19.84/3.42 | | Case 2:
% 19.84/3.42 | | |
% 19.84/3.42 | | | (48) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (vsubst(all_60_8,
% 19.84/3.42 | | | all_60_7, all_60_2) = v1 & vtcheck(all_60_9, v1, all_60_4) =
% 19.84/3.42 | | | v2 & visFreeVar(all_60_6, all_60_7) = v0 & $i(v1) & ( ~ (v0 = 0)
% 19.84/3.42 | | | | v2 = 0))
% 19.84/3.42 | | |
% 19.84/3.42 | | | DELTA: instantiating (48) with fresh symbols all_106_0, all_106_1,
% 19.84/3.42 | | | all_106_2 gives:
% 19.84/3.42 | | | (49) vsubst(all_60_8, all_60_7, all_60_2) = all_106_1 &
% 19.84/3.42 | | | vtcheck(all_60_9, all_106_1, all_60_4) = all_106_0 &
% 19.84/3.42 | | | visFreeVar(all_60_6, all_60_7) = all_106_2 & $i(all_106_1) & ( ~
% 19.84/3.42 | | | (all_106_2 = 0) | all_106_0 = 0)
% 19.84/3.42 | | |
% 19.84/3.42 | | | ALPHA: (49) implies:
% 19.84/3.42 | | | (50) vtcheck(all_60_9, all_106_1, all_60_4) = all_106_0
% 19.84/3.42 | | | (51) vsubst(all_60_8, all_60_7, all_60_2) = all_106_1
% 19.84/3.42 | | |
% 19.84/3.42 | | | BETA: splitting (27) gives:
% 19.84/3.42 | | |
% 19.84/3.42 | | | Case 1:
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | (52) all_60_0 = 0
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | REDUCE: (11), (52) imply:
% 19.84/3.42 | | | | (53) $false
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | CLOSE: (53) is inconsistent.
% 19.84/3.42 | | | |
% 19.84/3.42 | | | Case 2:
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | (54) all_60_6 = all_60_8 | ? [v0: any] : ? [v1: any] :
% 19.84/3.42 | | | | (vtcheck(all_60_9, all_60_7, all_60_10) = v1 &
% 19.84/3.42 | | | | visFreeVar(all_60_6, all_60_7) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 19.84/3.42 | | | | 0)))
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | BETA: splitting (54) gives:
% 19.84/3.42 | | | |
% 19.84/3.42 | | | | Case 1:
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | (55) all_60_6 = all_60_8
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | REDUCE: (39), (55) imply:
% 19.84/3.42 | | | | | (56) $false
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | CLOSE: (56) is inconsistent.
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | Case 2:
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | (57) ? [v0: any] : ? [v1: any] : (vtcheck(all_60_9, all_60_7,
% 19.84/3.42 | | | | | all_60_10) = v1 & visFreeVar(all_60_6, all_60_7) = v0 & (
% 19.84/3.42 | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | DELTA: instantiating (57) with fresh symbols all_134_0, all_134_1
% 19.84/3.42 | | | | | gives:
% 19.84/3.42 | | | | | (58) vtcheck(all_60_9, all_60_7, all_60_10) = all_134_0 &
% 19.84/3.42 | | | | | visFreeVar(all_60_6, all_60_7) = all_134_1 & ( ~ (all_134_0 =
% 19.84/3.42 | | | | | 0) | ~ (all_134_1 = 0))
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | ALPHA: (58) implies:
% 19.84/3.42 | | | | | (59) visFreeVar(all_60_6, all_60_7) = all_134_1
% 19.84/3.42 | | | | | (60) vtcheck(all_60_9, all_60_7, all_60_10) = all_134_0
% 19.84/3.42 | | | | | (61) ~ (all_134_0 = 0) | ~ (all_134_1 = 0)
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | GROUND_INST: instantiating (7) with all_100_2, all_134_1, all_60_7,
% 19.84/3.42 | | | | | all_60_6, simplifying with (42), (59) gives:
% 19.84/3.42 | | | | | (62) all_134_1 = all_100_2
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | GROUND_INST: instantiating (8) with 0, all_134_0, all_60_10, all_60_7,
% 19.84/3.42 | | | | | all_60_9, simplifying with (21), (60) gives:
% 19.84/3.42 | | | | | (63) all_134_0 = 0
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | GROUND_INST: instantiating (9) with all_60_1, all_106_1, all_60_2,
% 19.84/3.42 | | | | | all_60_7, all_60_8, simplifying with (24), (51) gives:
% 19.84/3.42 | | | | | (64) all_106_1 = all_60_1
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | GROUND_INST: instantiating (9) with all_100_1, all_106_1, all_60_2,
% 19.84/3.42 | | | | | all_60_7, all_60_8, simplifying with (44), (51) gives:
% 19.84/3.42 | | | | | (65) all_106_1 = all_100_1
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | COMBINE_EQS: (64), (65) imply:
% 19.84/3.42 | | | | | (66) all_100_1 = all_60_1
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | REDUCE: (50), (64) imply:
% 19.84/3.42 | | | | | (67) vtcheck(all_60_9, all_60_1, all_60_4) = all_106_0
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | REDUCE: (43), (66) imply:
% 19.84/3.42 | | | | | (68) vtcheck(all_60_9, all_60_1, all_60_4) = all_100_0
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | BETA: splitting (61) gives:
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | | Case 1:
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | (69) ~ (all_134_0 = 0)
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | REDUCE: (63), (69) imply:
% 19.84/3.42 | | | | | | (70) $false
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | CLOSE: (70) is inconsistent.
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | Case 2:
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | (71) ~ (all_134_1 = 0)
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | REDUCE: (62), (71) imply:
% 19.84/3.42 | | | | | | (72) ~ (all_100_2 = 0)
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | BETA: splitting (45) gives:
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | | Case 1:
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | (73) all_100_0 = 0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | REDUCE: (68), (73) imply:
% 19.84/3.42 | | | | | | | (74) vtcheck(all_60_9, all_60_1, all_60_4) = 0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | GROUND_INST: instantiating (8) with all_60_0, all_106_0, all_60_4,
% 19.84/3.42 | | | | | | | all_60_1, all_60_9, simplifying with (22), (67)
% 19.84/3.42 | | | | | | | gives:
% 19.84/3.42 | | | | | | | (75) all_106_0 = all_60_0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | GROUND_INST: instantiating (8) with 0, all_106_0, all_60_4,
% 19.84/3.42 | | | | | | | all_60_1, all_60_9, simplifying with (67), (74)
% 19.84/3.42 | | | | | | | gives:
% 19.84/3.42 | | | | | | | (76) all_106_0 = 0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | COMBINE_EQS: (75), (76) imply:
% 19.84/3.42 | | | | | | | (77) all_60_0 = 0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | REDUCE: (11), (77) imply:
% 19.84/3.42 | | | | | | | (78) $false
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | CLOSE: (78) is inconsistent.
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | Case 2:
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | (79) all_100_2 = 0
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | REDUCE: (72), (79) imply:
% 19.84/3.42 | | | | | | | (80) $false
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | | CLOSE: (80) is inconsistent.
% 19.84/3.42 | | | | | | |
% 19.84/3.42 | | | | | | End of split
% 19.84/3.42 | | | | | |
% 19.84/3.42 | | | | | End of split
% 19.84/3.42 | | | | |
% 19.84/3.42 | | | | End of split
% 19.84/3.42 | | | |
% 19.84/3.42 | | | End of split
% 19.84/3.42 | | |
% 19.84/3.42 | | End of split
% 19.84/3.42 | |
% 19.84/3.42 | End of split
% 19.84/3.42 |
% 19.84/3.42 End of proof
% 19.84/3.43 % SZS output end Proof for theBenchmark
% 19.84/3.43
% 19.84/3.43 2820ms
%------------------------------------------------------------------------------