TSTP Solution File: SWV404+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV404+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 : Thu Aug 31 22:56:12 EDT 2023
% Result : Theorem 14.30s 2.85s
% Output : Proof 21.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV404+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 08:05:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.45/1.21 Prover 1: Preprocessing ...
% 3.45/1.21 Prover 4: Preprocessing ...
% 3.45/1.24 Prover 6: Preprocessing ...
% 3.45/1.24 Prover 2: Preprocessing ...
% 3.45/1.24 Prover 0: Preprocessing ...
% 3.45/1.24 Prover 5: Preprocessing ...
% 3.45/1.25 Prover 3: Preprocessing ...
% 7.76/1.80 Prover 1: Warning: ignoring some quantifiers
% 8.30/1.86 Prover 3: Warning: ignoring some quantifiers
% 8.42/1.90 Prover 6: Proving ...
% 8.42/1.90 Prover 1: Constructing countermodel ...
% 8.42/1.90 Prover 5: Proving ...
% 8.79/1.92 Prover 3: Constructing countermodel ...
% 8.79/1.96 Prover 4: Constructing countermodel ...
% 8.79/2.01 Prover 2: Proving ...
% 8.79/2.02 Prover 0: Proving ...
% 11.90/2.42 Prover 3: gave up
% 11.90/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.65/2.48 Prover 7: Preprocessing ...
% 13.78/2.73 Prover 7: Warning: ignoring some quantifiers
% 13.78/2.76 Prover 7: Constructing countermodel ...
% 14.30/2.85 Prover 0: proved (2206ms)
% 14.30/2.85
% 14.30/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.30/2.85
% 14.30/2.87 Prover 2: stopped
% 14.30/2.87 Prover 6: stopped
% 14.30/2.87 Prover 5: stopped
% 14.30/2.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.30/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.30/2.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.30/2.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.89/2.95 Prover 8: Preprocessing ...
% 15.89/2.97 Prover 10: Preprocessing ...
% 15.89/2.97 Prover 11: Preprocessing ...
% 15.89/2.98 Prover 13: Preprocessing ...
% 17.12/3.11 Prover 8: Warning: ignoring some quantifiers
% 17.12/3.12 Prover 10: Warning: ignoring some quantifiers
% 17.12/3.13 Prover 8: Constructing countermodel ...
% 17.12/3.14 Prover 10: Constructing countermodel ...
% 17.77/3.18 Prover 7: gave up
% 17.77/3.18 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.98/3.21 Prover 13: Warning: ignoring some quantifiers
% 17.98/3.22 Prover 11: Constructing countermodel ...
% 18.18/3.23 Prover 13: Constructing countermodel ...
% 18.18/3.24 Prover 16: Preprocessing ...
% 19.39/3.40 Prover 8: gave up
% 19.39/3.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 19.39/3.46 Prover 16: Warning: ignoring some quantifiers
% 19.39/3.46 Prover 19: Preprocessing ...
% 19.39/3.48 Prover 16: Constructing countermodel ...
% 19.39/3.63 Prover 11: Found proof (size 166)
% 19.39/3.63 Prover 11: proved (747ms)
% 19.39/3.63 Prover 4: stopped
% 19.39/3.63 Prover 10: stopped
% 19.39/3.63 Prover 1: stopped
% 19.39/3.63 Prover 13: stopped
% 19.39/3.64 Prover 16: stopped
% 20.24/3.66 Prover 19: Warning: ignoring some quantifiers
% 21.33/3.67 Prover 19: Constructing countermodel ...
% 21.33/3.68 Prover 19: stopped
% 21.33/3.68
% 21.33/3.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.33/3.68
% 21.48/3.70 % SZS output start Proof for theBenchmark
% 21.48/3.71 Assumptions after simplification:
% 21.48/3.71 ---------------------------------
% 21.48/3.71
% 21.48/3.71 (ax36)
% 21.64/3.73 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0,
% 21.64/3.73 create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2) = 0)
% 21.64/3.73
% 21.64/3.73 (ax47)
% 21.64/3.74 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 21.64/3.74 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.74 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 21.64/3.74 : ? [v6: int] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 &
% 21.64/3.74 $i(v5) & ((v8 = v4 & triple(v0, v7, bad) = v4 & update_slb(v1, v5) = v7 &
% 21.64/3.74 $i(v7) & $i(v4)) | (v6 = 0 & contains_slb(v1, v5) = 0))))
% 21.64/3.74
% 21.64/3.74 (ax48)
% 21.64/3.74 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 21.64/3.74 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.74 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 21.64/3.74 : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: $i] :
% 21.64/3.74 (findmin_pqp_res(v0) = v5 & $i(v5) & ((v10 = v4 & triple(v0, v9, bad) = v4 &
% 21.64/3.74 update_slb(v1, v5) = v9 & $i(v9) & $i(v4)) | ( ~ (v8 = 0) &
% 21.64/3.74 lookup_slb(v1, v5) = v7 & strictly_less_than(v5, v7) = v8 & $i(v7)) |
% 21.64/3.74 ( ~ (v6 = 0) & contains_slb(v1, v5) = v6))))
% 21.64/3.74
% 21.64/3.74 (ax49)
% 21.64/3.74 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 21.64/3.74 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~
% 21.64/3.74 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~
% 21.64/3.74 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i]
% 21.64/3.74 : ? [v10: $i] : ((v10 = v5 & triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9)
% 21.64/3.74 = v5 & $i(v9) & $i(v5)) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = v7 &
% 21.64/3.74 less_than(v7, v3) = v8 & $i(v7)) | ( ~ (v6 = 0) & contains_slb(v1, v3) =
% 21.64/3.74 v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 21.64/3.74 $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.74 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 21.64/3.74 : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: $i] :
% 21.64/3.74 (findmin_pqp_res(v0) = v5 & $i(v5) & ((v10 = v4 & triple(v0, v9, v2) = v4 &
% 21.64/3.74 update_slb(v1, v5) = v9 & $i(v9) & $i(v4)) | ( ~ (v8 = 0) &
% 21.64/3.74 lookup_slb(v1, v5) = v7 & less_than(v7, v5) = v8 & $i(v7)) | ( ~ (v6 =
% 21.64/3.74 0) & contains_slb(v1, v5) = v6))))
% 21.64/3.74
% 21.64/3.74 (ax51)
% 21.64/3.74 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 21.64/3.74 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0,
% 21.64/3.74 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0)
% 21.64/3.74 = v4 & $i(v4)))
% 21.64/3.74
% 21.64/3.75 (ax52)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ?
% 21.64/3.75 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) =
% 21.64/3.75 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1:
% 21.64/3.75 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 21.64/3.75 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 &
% 21.64/3.75 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 21.64/3.75 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 21.64/3.75 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 &
% 21.64/3.75 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2)))
% 21.64/3.75
% 21.64/3.75 (l40_co)
% 21.64/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 21.64/3.75 int] : ( ~ (v5 = 0) & ok(v4) = 0 & triple(v0, v1, v2) = v3 & check_cpq(v4) =
% 21.64/3.75 0 & check_cpq(v3) = v5 & removemin_cpq_eff(v3) = v4 & $i(v4) & $i(v3) &
% 21.64/3.75 $i(v2) & $i(v1) & $i(v0))
% 21.64/3.75
% 21.64/3.75 (l40_l27)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.64/3.75 $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~
% 21.64/3.75 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 21.64/3.75 ? [v8: int] : ((v8 = 0 & check_cpq(v4) = 0) | ( ~ (v7 = 0) & ok(v5) = v7) |
% 21.64/3.75 ( ~ (v6 = 0) & check_cpq(v5) = v6)))
% 21.64/3.75
% 21.64/3.75 (l40_l34)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 21.64/3.75 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 21.64/3.75 $i] : ? [v6: int] : ((v4 = 0 & check_cpq(v3) = 0) | ( ~ (v6 = 0) &
% 21.64/3.75 check_cpq(v5) = v6 & findmin_cpq_eff(v3) = v5 & $i(v5))))
% 21.64/3.75
% 21.64/3.75 (stricly_smaller_definition)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 21.64/3.75 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 21.64/3.75 ? [v4: int] : ((v4 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) &
% 21.64/3.75 less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 21.64/3.75 (v2 = 0 | ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 21.64/3.75 ? [v4: int] : ((v4 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) &
% 21.64/3.75 less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : (
% 21.64/3.75 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 21.64/3.75 int] : ((v4 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) &
% 21.64/3.75 strictly_less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.64/3.75 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 21.64/3.75 ? [v4: int] : ((v2 = 0 & ~ (v4 = 0) & less_than(v1, v0) = v4) | ( ~ (v3 =
% 21.64/3.75 0) & strictly_less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] :
% 21.64/3.75 ( ~ (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] :
% 21.64/3.75 ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 21.64/3.75 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 21.64/3.75 [v2: int] : ? [v3: int] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | (v2
% 21.64/3.75 = 0 & less_than(v1, v0) = 0)))
% 21.64/3.75
% 21.64/3.75 (totality)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 21.64/3.75 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 21.64/3.75 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 21.64/3.75 ~ $i(v0) | less_than(v1, v0) = 0)
% 21.64/3.75
% 21.64/3.76 (function-axioms)
% 21.64/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 21.64/3.76 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 21.64/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.64/3.76 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 21.64/3.76 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 21.64/3.76 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 21.64/3.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 21.64/3.76 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 21.64/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.64/3.76 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 21.64/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.64/3.76 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 21.64/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 21.64/3.76 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.64/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 21.64/3.76 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.64/3.76 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 21.64/3.76 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 21.64/3.76 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 21.64/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 21.64/3.76 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 21.64/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.64/3.76 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 21.64/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.64/3.76 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 21.64/3.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 21.64/3.76 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.64/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.64/3.76 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 21.64/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.64/3.76 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 21.64/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.64/3.76 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 21.64/3.76 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 21.64/3.76 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 21.64/3.76 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 21.64/3.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 21.64/3.76 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 21.64/3.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 21.64/3.76 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 21.64/3.76 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 21.64/3.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 21.64/3.76 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 21.64/3.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 21.64/3.76 v1) | ~ (isnonempty_slb(v2) = v0))
% 21.64/3.76
% 21.64/3.76 Further assumptions not needed in the proof:
% 21.64/3.76 --------------------------------------------
% 21.64/3.76 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 21.64/3.76 ax31, ax32, ax33, ax34, ax35, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44,
% 21.64/3.76 ax45, ax46, ax50, ax53, bottom_smallest, reflexivity, transitivity
% 21.64/3.76
% 21.64/3.76 Those formulas are unsatisfiable:
% 21.64/3.76 ---------------------------------
% 21.64/3.76
% 21.64/3.76 Begin of proof
% 21.64/3.76 |
% 21.64/3.76 | ALPHA: (totality) implies:
% 21.64/3.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 21.64/3.76 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 21.64/3.76 |
% 21.64/3.76 | ALPHA: (stricly_smaller_definition) implies:
% 21.64/3.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 21.64/3.76 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 21.64/3.76 | ((v4 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) &
% 21.64/3.76 | less_than(v0, v1) = v3)))
% 21.64/3.76 |
% 21.64/3.76 | ALPHA: (ax36) implies:
% 21.64/3.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb,
% 21.64/3.77 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2) = 0)
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (ax47) implies:
% 21.64/3.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.64/3.77 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.77 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 21.64/3.77 | [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: $i] :
% 21.64/3.77 | (findmin_pqp_res(v0) = v5 & $i(v5) & ((v8 = v4 & triple(v0, v7, bad)
% 21.64/3.77 | = v4 & update_slb(v1, v5) = v7 & $i(v7) & $i(v4)) | (v6 = 0 &
% 21.64/3.77 | contains_slb(v1, v5) = 0))))
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (ax48) implies:
% 21.64/3.77 | (5) $i(bad)
% 21.64/3.77 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.64/3.77 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.77 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 21.64/3.77 | [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 21.64/3.77 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & $i(v5) & ((v10 = v4 &
% 21.64/3.77 | triple(v0, v9, bad) = v4 & update_slb(v1, v5) = v9 & $i(v9) &
% 21.64/3.77 | $i(v4)) | ( ~ (v8 = 0) & lookup_slb(v1, v5) = v7 &
% 21.64/3.77 | strictly_less_than(v5, v7) = v8 & $i(v7)) | ( ~ (v6 = 0) &
% 21.64/3.77 | contains_slb(v1, v5) = v6))))
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (ax49) implies:
% 21.64/3.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.64/3.77 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 21.64/3.77 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 21.64/3.77 | [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 21.64/3.77 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & $i(v5) & ((v10 = v4 &
% 21.64/3.77 | triple(v0, v9, v2) = v4 & update_slb(v1, v5) = v9 & $i(v9) &
% 21.64/3.77 | $i(v4)) | ( ~ (v8 = 0) & lookup_slb(v1, v5) = v7 &
% 21.64/3.77 | less_than(v7, v5) = v8 & $i(v7)) | ( ~ (v6 = 0) &
% 21.64/3.77 | contains_slb(v1, v5) = v6))))
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (ax51) implies:
% 21.64/3.77 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 21.64/3.77 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1,
% 21.64/3.77 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 21.64/3.77 | (findmin_pqp_res(v0) = v4 & $i(v4)))
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (ax52) implies:
% 21.64/3.77 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~
% 21.64/3.77 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 &
% 21.64/3.77 | findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1 & $i(v3) &
% 21.64/3.77 | $i(v2) & $i(v1)))
% 21.64/3.77 |
% 21.64/3.77 | ALPHA: (function-axioms) implies:
% 21.64/3.77 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.64/3.77 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 21.64/3.77 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.64/3.77 | : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 21.64/3.77 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.64/3.77 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 21.64/3.77 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.64/3.77 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 21.64/3.77 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.64/3.77 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 21.64/3.77 | (less_than(v3, v2) = v0))
% 21.64/3.77 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.64/3.77 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 21.64/3.77 | (strictly_less_than(v3, v2) = v0))
% 21.64/3.78 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 21.64/3.78 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 21.64/3.78 | (contains_slb(v3, v2) = v0))
% 21.64/3.78 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.64/3.78 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 21.64/3.78 |
% 21.64/3.78 | DELTA: instantiating (l40_co) with fresh symbols all_48_0, all_48_1, all_48_2,
% 21.64/3.78 | all_48_3, all_48_4, all_48_5 gives:
% 21.64/3.78 | (18) ~ (all_48_0 = 0) & ok(all_48_1) = 0 & triple(all_48_5, all_48_4,
% 21.64/3.78 | all_48_3) = all_48_2 & check_cpq(all_48_1) = 0 & check_cpq(all_48_2)
% 21.64/3.78 | = all_48_0 & removemin_cpq_eff(all_48_2) = all_48_1 & $i(all_48_1) &
% 21.64/3.78 | $i(all_48_2) & $i(all_48_3) & $i(all_48_4) & $i(all_48_5)
% 21.64/3.78 |
% 21.64/3.78 | ALPHA: (18) implies:
% 21.64/3.78 | (19) ~ (all_48_0 = 0)
% 21.64/3.78 | (20) $i(all_48_5)
% 21.64/3.78 | (21) $i(all_48_4)
% 21.64/3.78 | (22) $i(all_48_3)
% 21.64/3.78 | (23) $i(all_48_2)
% 21.64/3.78 | (24) removemin_cpq_eff(all_48_2) = all_48_1
% 21.64/3.78 | (25) check_cpq(all_48_2) = all_48_0
% 21.64/3.78 | (26) check_cpq(all_48_1) = 0
% 21.64/3.78 | (27) triple(all_48_5, all_48_4, all_48_3) = all_48_2
% 21.64/3.78 | (28) ok(all_48_1) = 0
% 21.64/3.78 |
% 21.64/3.78 | GROUND_INST: instantiating (9) with all_48_2, all_48_1, simplifying with (23),
% 21.64/3.78 | (24) gives:
% 21.64/3.78 | (29) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_48_2) = v1 &
% 21.64/3.78 | findmin_cpq_eff(all_48_2) = v0 & remove_cpq(v0, v1) = all_48_1 &
% 21.64/3.78 | $i(v1) & $i(v0) & $i(all_48_1))
% 21.64/3.78 |
% 21.64/3.78 | GROUND_INST: instantiating (l40_l34) with all_48_5, all_48_4, all_48_3,
% 21.64/3.78 | all_48_2, simplifying with (20), (21), (22), (27) gives:
% 21.64/3.78 | (30) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 &
% 21.64/3.78 | check_cpq(all_48_2) = 0) | ( ~ (v2 = 0) & check_cpq(v1) = v2 &
% 21.64/3.78 | findmin_cpq_eff(all_48_2) = v1 & $i(v1)))
% 21.64/3.78 |
% 21.64/3.78 | DELTA: instantiating (30) with fresh symbols all_55_0, all_55_1, all_55_2
% 21.64/3.78 | gives:
% 21.64/3.78 | (31) (all_55_2 = 0 & check_cpq(all_48_2) = 0) | ( ~ (all_55_0 = 0) &
% 21.64/3.78 | check_cpq(all_55_1) = all_55_0 & findmin_cpq_eff(all_48_2) =
% 21.64/3.78 | all_55_1 & $i(all_55_1))
% 21.64/3.78 |
% 21.64/3.78 | DELTA: instantiating (29) with fresh symbols all_56_0, all_56_1 gives:
% 21.64/3.78 | (32) findmin_cpq_res(all_48_2) = all_56_0 & findmin_cpq_eff(all_48_2) =
% 21.64/3.78 | all_56_1 & remove_cpq(all_56_1, all_56_0) = all_48_1 & $i(all_56_0) &
% 21.64/3.78 | $i(all_56_1) & $i(all_48_1)
% 21.64/3.78 |
% 21.64/3.78 | ALPHA: (32) implies:
% 21.64/3.78 | (33) remove_cpq(all_56_1, all_56_0) = all_48_1
% 21.64/3.78 | (34) findmin_cpq_eff(all_48_2) = all_56_1
% 21.64/3.78 | (35) findmin_cpq_res(all_48_2) = all_56_0
% 21.64/3.78 |
% 21.64/3.78 | BETA: splitting (31) gives:
% 21.64/3.78 |
% 21.64/3.78 | Case 1:
% 21.64/3.78 | |
% 21.64/3.78 | | (36) all_55_2 = 0 & check_cpq(all_48_2) = 0
% 21.64/3.78 | |
% 21.64/3.78 | | ALPHA: (36) implies:
% 21.64/3.78 | | (37) check_cpq(all_48_2) = 0
% 21.64/3.78 | |
% 21.64/3.78 | | GROUND_INST: instantiating (11) with all_48_0, 0, all_48_2, simplifying with
% 21.64/3.78 | | (25), (37) gives:
% 21.64/3.78 | | (38) all_48_0 = 0
% 21.64/3.78 | |
% 21.64/3.78 | | REDUCE: (19), (38) imply:
% 21.64/3.78 | | (39) $false
% 21.64/3.78 | |
% 21.64/3.79 | | CLOSE: (39) is inconsistent.
% 21.64/3.79 | |
% 21.64/3.79 | Case 2:
% 21.64/3.79 | |
% 21.64/3.79 | | (40) ~ (all_55_0 = 0) & check_cpq(all_55_1) = all_55_0 &
% 21.64/3.79 | | findmin_cpq_eff(all_48_2) = all_55_1 & $i(all_55_1)
% 21.64/3.79 | |
% 21.64/3.79 | | ALPHA: (40) implies:
% 21.64/3.79 | | (41) ~ (all_55_0 = 0)
% 21.64/3.79 | | (42) findmin_cpq_eff(all_48_2) = all_55_1
% 21.64/3.79 | | (43) check_cpq(all_55_1) = all_55_0
% 21.64/3.79 | |
% 21.64/3.79 | | GROUND_INST: instantiating (10) with all_55_1, all_56_1, all_48_2,
% 21.64/3.79 | | simplifying with (34), (42) gives:
% 21.64/3.79 | | (44) all_56_1 = all_55_1
% 21.64/3.79 | |
% 21.64/3.79 | | REDUCE: (33), (44) imply:
% 21.64/3.79 | | (45) remove_cpq(all_55_1, all_56_0) = all_48_1
% 21.64/3.79 | |
% 21.64/3.79 | | GROUND_INST: instantiating (7) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.64/3.79 | | all_55_1, simplifying with (20), (21), (22), (27), (42) gives:
% 21.64/3.79 | | (46) all_48_4 = create_slb | ? [v0: $i] : ? [v1: int] : ? [v2: $i] :
% 21.64/3.79 | | ? [v3: int] : ? [v4: $i] : ? [v5: int] :
% 21.64/3.79 | | (findmin_pqp_res(all_48_5) = v0 & $i(v0) & ((v5 = all_55_1 &
% 21.64/3.79 | | triple(all_48_5, v4, all_48_3) = all_55_1 &
% 21.64/3.79 | | update_slb(all_48_4, v0) = v4 & $i(v4) & $i(all_55_1)) | ( ~
% 21.64/3.79 | | (v3 = 0) & lookup_slb(all_48_4, v0) = v2 & less_than(v2, v0) =
% 21.64/3.79 | | v3 & $i(v2)) | ( ~ (v1 = 0) & contains_slb(all_48_4, v0) =
% 21.64/3.79 | | v1)))
% 21.64/3.79 | |
% 21.64/3.79 | | GROUND_INST: instantiating (6) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.64/3.79 | | all_55_1, simplifying with (20), (21), (22), (27), (42) gives:
% 21.64/3.79 | | (47) all_48_4 = create_slb | ? [v0: $i] : ? [v1: int] : ? [v2: $i] :
% 21.64/3.79 | | ? [v3: int] : ? [v4: $i] : ? [v5: int] :
% 21.64/3.79 | | (findmin_pqp_res(all_48_5) = v0 & $i(v0) & ((v5 = all_55_1 &
% 21.64/3.79 | | triple(all_48_5, v4, bad) = all_55_1 & update_slb(all_48_4,
% 21.64/3.79 | | v0) = v4 & $i(v4) & $i(all_55_1)) | ( ~ (v3 = 0) &
% 21.64/3.79 | | lookup_slb(all_48_4, v0) = v2 & strictly_less_than(v0, v2) =
% 21.64/3.79 | | v3 & $i(v2)) | ( ~ (v1 = 0) & contains_slb(all_48_4, v0) =
% 21.64/3.79 | | v1)))
% 21.64/3.79 | |
% 21.64/3.79 | | GROUND_INST: instantiating (4) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.64/3.79 | | all_55_1, simplifying with (20), (21), (22), (27), (42) gives:
% 21.64/3.79 | | (48) all_48_4 = create_slb | ? [v0: $i] : ? [v1: int] : ? [v2: $i] :
% 21.64/3.79 | | ? [v3: int] : (findmin_pqp_res(all_48_5) = v0 & $i(v0) & ((v3 =
% 21.64/3.79 | | all_55_1 & triple(all_48_5, v2, bad) = all_55_1 &
% 21.64/3.79 | | update_slb(all_48_4, v0) = v2 & $i(v2) & $i(all_55_1)) | (v1 =
% 21.64/3.79 | | 0 & contains_slb(all_48_4, v0) = 0)))
% 21.64/3.79 | |
% 21.64/3.79 | | GROUND_INST: instantiating (8) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.64/3.79 | | all_56_0, simplifying with (20), (21), (22), (27), (35) gives:
% 21.64/3.79 | | (49) all_48_4 = create_slb | (findmin_pqp_res(all_48_5) = all_56_0 &
% 21.64/3.79 | | $i(all_56_0))
% 21.64/3.79 | |
% 21.64/3.79 | | BETA: splitting (49) gives:
% 21.64/3.79 | |
% 21.64/3.79 | | Case 1:
% 21.64/3.79 | | |
% 21.64/3.79 | | | (50) all_48_4 = create_slb
% 21.64/3.79 | | |
% 21.64/3.79 | | | REDUCE: (27), (50) imply:
% 21.64/3.79 | | | (51) triple(all_48_5, create_slb, all_48_3) = all_48_2
% 21.64/3.79 | | |
% 21.64/3.79 | | | GROUND_INST: instantiating (3) with all_48_5, all_48_3, all_48_2,
% 21.64/3.79 | | | simplifying with (20), (22), (51) gives:
% 21.64/3.79 | | | (52) check_cpq(all_48_2) = 0
% 21.64/3.79 | | |
% 21.64/3.79 | | | GROUND_INST: instantiating (11) with all_48_0, 0, all_48_2, simplifying
% 21.64/3.79 | | | with (25), (52) gives:
% 21.64/3.79 | | | (53) all_48_0 = 0
% 21.64/3.79 | | |
% 21.64/3.79 | | | REDUCE: (19), (53) imply:
% 21.64/3.79 | | | (54) $false
% 21.64/3.79 | | |
% 21.64/3.79 | | | CLOSE: (54) is inconsistent.
% 21.64/3.79 | | |
% 21.64/3.79 | | Case 2:
% 21.64/3.79 | | |
% 21.64/3.80 | | | (55) ~ (all_48_4 = create_slb)
% 21.64/3.80 | | | (56) findmin_pqp_res(all_48_5) = all_56_0 & $i(all_56_0)
% 21.64/3.80 | | |
% 21.64/3.80 | | | ALPHA: (56) implies:
% 21.64/3.80 | | | (57) findmin_pqp_res(all_48_5) = all_56_0
% 21.64/3.80 | | |
% 21.64/3.80 | | | BETA: splitting (48) gives:
% 21.64/3.80 | | |
% 21.64/3.80 | | | Case 1:
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | (58) all_48_4 = create_slb
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | REDUCE: (55), (58) imply:
% 21.64/3.80 | | | | (59) $false
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | CLOSE: (59) is inconsistent.
% 21.64/3.80 | | | |
% 21.64/3.80 | | | Case 2:
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | (60) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] :
% 21.64/3.80 | | | | (findmin_pqp_res(all_48_5) = v0 & $i(v0) & ((v3 = all_55_1 &
% 21.64/3.80 | | | | triple(all_48_5, v2, bad) = all_55_1 &
% 21.64/3.80 | | | | update_slb(all_48_4, v0) = v2 & $i(v2) & $i(all_55_1)) |
% 21.64/3.80 | | | | (v1 = 0 & contains_slb(all_48_4, v0) = 0)))
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | DELTA: instantiating (60) with fresh symbols all_90_0, all_90_1,
% 21.64/3.80 | | | | all_90_2, all_90_3 gives:
% 21.64/3.80 | | | | (61) findmin_pqp_res(all_48_5) = all_90_3 & $i(all_90_3) & ((all_90_0
% 21.64/3.80 | | | | = all_55_1 & triple(all_48_5, all_90_1, bad) = all_55_1 &
% 21.64/3.80 | | | | update_slb(all_48_4, all_90_3) = all_90_1 & $i(all_90_1) &
% 21.64/3.80 | | | | $i(all_55_1)) | (all_90_2 = 0 & contains_slb(all_48_4,
% 21.64/3.80 | | | | all_90_3) = 0))
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | ALPHA: (61) implies:
% 21.64/3.80 | | | | (62) $i(all_90_3)
% 21.64/3.80 | | | | (63) findmin_pqp_res(all_48_5) = all_90_3
% 21.64/3.80 | | | | (64) (all_90_0 = all_55_1 & triple(all_48_5, all_90_1, bad) =
% 21.64/3.80 | | | | all_55_1 & update_slb(all_48_4, all_90_3) = all_90_1 &
% 21.64/3.80 | | | | $i(all_90_1) & $i(all_55_1)) | (all_90_2 = 0 &
% 21.64/3.80 | | | | contains_slb(all_48_4, all_90_3) = 0)
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | BETA: splitting (46) gives:
% 21.64/3.80 | | | |
% 21.64/3.80 | | | | Case 1:
% 21.64/3.80 | | | | |
% 21.64/3.80 | | | | | (65) all_48_4 = create_slb
% 21.64/3.80 | | | | |
% 21.64/3.80 | | | | | REDUCE: (55), (65) imply:
% 21.64/3.80 | | | | | (66) $false
% 21.64/3.80 | | | | |
% 21.64/3.80 | | | | | CLOSE: (66) is inconsistent.
% 21.64/3.80 | | | | |
% 21.64/3.80 | | | | Case 2:
% 21.64/3.80 | | | | |
% 21.64/3.80 | | | | | (67) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ?
% 21.64/3.80 | | | | | [v4: $i] : ? [v5: int] : (findmin_pqp_res(all_48_5) = v0 &
% 21.64/3.80 | | | | | $i(v0) & ((v5 = all_55_1 & triple(all_48_5, v4, all_48_3) =
% 21.98/3.80 | | | | | all_55_1 & update_slb(all_48_4, v0) = v4 & $i(v4) &
% 21.98/3.80 | | | | | $i(all_55_1)) | ( ~ (v3 = 0) & lookup_slb(all_48_4, v0)
% 21.98/3.80 | | | | | = v2 & less_than(v2, v0) = v3 & $i(v2)) | ( ~ (v1 = 0) &
% 21.98/3.80 | | | | | contains_slb(all_48_4, v0) = v1)))
% 21.98/3.80 | | | | |
% 21.98/3.80 | | | | | DELTA: instantiating (67) with fresh symbols all_95_0, all_95_1,
% 21.98/3.80 | | | | | all_95_2, all_95_3, all_95_4, all_95_5 gives:
% 21.98/3.80 | | | | | (68) findmin_pqp_res(all_48_5) = all_95_5 & $i(all_95_5) &
% 21.98/3.80 | | | | | ((all_95_0 = all_55_1 & triple(all_48_5, all_95_1, all_48_3) =
% 21.98/3.80 | | | | | all_55_1 & update_slb(all_48_4, all_95_5) = all_95_1 &
% 21.98/3.80 | | | | | $i(all_95_1) & $i(all_55_1)) | ( ~ (all_95_2 = 0) &
% 21.98/3.80 | | | | | lookup_slb(all_48_4, all_95_5) = all_95_3 &
% 21.98/3.80 | | | | | less_than(all_95_3, all_95_5) = all_95_2 & $i(all_95_3)) |
% 21.98/3.80 | | | | | ( ~ (all_95_4 = 0) & contains_slb(all_48_4, all_95_5) =
% 21.98/3.80 | | | | | all_95_4))
% 21.98/3.80 | | | | |
% 21.98/3.80 | | | | | ALPHA: (68) implies:
% 21.98/3.80 | | | | | (69) findmin_pqp_res(all_48_5) = all_95_5
% 21.98/3.80 | | | | | (70) (all_95_0 = all_55_1 & triple(all_48_5, all_95_1, all_48_3) =
% 21.98/3.80 | | | | | all_55_1 & update_slb(all_48_4, all_95_5) = all_95_1 &
% 21.98/3.80 | | | | | $i(all_95_1) & $i(all_55_1)) | ( ~ (all_95_2 = 0) &
% 21.98/3.80 | | | | | lookup_slb(all_48_4, all_95_5) = all_95_3 &
% 21.98/3.80 | | | | | less_than(all_95_3, all_95_5) = all_95_2 & $i(all_95_3)) | (
% 21.98/3.80 | | | | | ~ (all_95_4 = 0) & contains_slb(all_48_4, all_95_5) =
% 21.98/3.80 | | | | | all_95_4)
% 21.98/3.80 | | | | |
% 21.98/3.80 | | | | | BETA: splitting (47) gives:
% 21.98/3.80 | | | | |
% 21.98/3.80 | | | | | Case 1:
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | (71) all_48_4 = create_slb
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | REDUCE: (55), (71) imply:
% 21.98/3.80 | | | | | | (72) $false
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | CLOSE: (72) is inconsistent.
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | Case 2:
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | (73) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ?
% 21.98/3.80 | | | | | | [v4: $i] : ? [v5: int] : (findmin_pqp_res(all_48_5) = v0 &
% 21.98/3.80 | | | | | | $i(v0) & ((v5 = all_55_1 & triple(all_48_5, v4, bad) =
% 21.98/3.80 | | | | | | all_55_1 & update_slb(all_48_4, v0) = v4 & $i(v4) &
% 21.98/3.80 | | | | | | $i(all_55_1)) | ( ~ (v3 = 0) & lookup_slb(all_48_4,
% 21.98/3.80 | | | | | | v0) = v2 & strictly_less_than(v0, v2) = v3 & $i(v2))
% 21.98/3.80 | | | | | | | ( ~ (v1 = 0) & contains_slb(all_48_4, v0) = v1)))
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | DELTA: instantiating (73) with fresh symbols all_100_0, all_100_1,
% 21.98/3.80 | | | | | | all_100_2, all_100_3, all_100_4, all_100_5 gives:
% 21.98/3.80 | | | | | | (74) findmin_pqp_res(all_48_5) = all_100_5 & $i(all_100_5) &
% 21.98/3.80 | | | | | | ((all_100_0 = all_55_1 & triple(all_48_5, all_100_1, bad) =
% 21.98/3.80 | | | | | | all_55_1 & update_slb(all_48_4, all_100_5) = all_100_1 &
% 21.98/3.80 | | | | | | $i(all_100_1) & $i(all_55_1)) | ( ~ (all_100_2 = 0) &
% 21.98/3.80 | | | | | | lookup_slb(all_48_4, all_100_5) = all_100_3 &
% 21.98/3.80 | | | | | | strictly_less_than(all_100_5, all_100_3) = all_100_2 &
% 21.98/3.80 | | | | | | $i(all_100_3)) | ( ~ (all_100_4 = 0) &
% 21.98/3.80 | | | | | | contains_slb(all_48_4, all_100_5) = all_100_4))
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | ALPHA: (74) implies:
% 21.98/3.80 | | | | | | (75) findmin_pqp_res(all_48_5) = all_100_5
% 21.98/3.80 | | | | | | (76) (all_100_0 = all_55_1 & triple(all_48_5, all_100_1, bad) =
% 21.98/3.80 | | | | | | all_55_1 & update_slb(all_48_4, all_100_5) = all_100_1 &
% 21.98/3.80 | | | | | | $i(all_100_1) & $i(all_55_1)) | ( ~ (all_100_2 = 0) &
% 21.98/3.80 | | | | | | lookup_slb(all_48_4, all_100_5) = all_100_3 &
% 21.98/3.80 | | | | | | strictly_less_than(all_100_5, all_100_3) = all_100_2 &
% 21.98/3.80 | | | | | | $i(all_100_3)) | ( ~ (all_100_4 = 0) &
% 21.98/3.80 | | | | | | contains_slb(all_48_4, all_100_5) = all_100_4)
% 21.98/3.80 | | | | | |
% 21.98/3.80 | | | | | | GROUND_INST: instantiating (13) with all_90_3, all_95_5, all_48_5,
% 21.98/3.80 | | | | | | simplifying with (63), (69) gives:
% 21.98/3.80 | | | | | | (77) all_95_5 = all_90_3
% 21.98/3.80 | | | | | |
% 21.98/3.81 | | | | | | GROUND_INST: instantiating (13) with all_95_5, all_100_5, all_48_5,
% 21.98/3.81 | | | | | | simplifying with (69), (75) gives:
% 21.98/3.81 | | | | | | (78) all_100_5 = all_95_5
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | GROUND_INST: instantiating (13) with all_56_0, all_100_5, all_48_5,
% 21.98/3.81 | | | | | | simplifying with (57), (75) gives:
% 21.98/3.81 | | | | | | (79) all_100_5 = all_56_0
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | COMBINE_EQS: (78), (79) imply:
% 21.98/3.81 | | | | | | (80) all_95_5 = all_56_0
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | SIMP: (80) implies:
% 21.98/3.81 | | | | | | (81) all_95_5 = all_56_0
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | COMBINE_EQS: (77), (81) imply:
% 21.98/3.81 | | | | | | (82) all_90_3 = all_56_0
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | SIMP: (82) implies:
% 21.98/3.81 | | | | | | (83) all_90_3 = all_56_0
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | REDUCE: (62), (83) imply:
% 21.98/3.81 | | | | | | (84) $i(all_56_0)
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | BETA: splitting (64) gives:
% 21.98/3.81 | | | | | |
% 21.98/3.81 | | | | | | Case 1:
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | (85) all_90_0 = all_55_1 & triple(all_48_5, all_90_1, bad) =
% 21.98/3.81 | | | | | | | all_55_1 & update_slb(all_48_4, all_90_3) = all_90_1 &
% 21.98/3.81 | | | | | | | $i(all_90_1) & $i(all_55_1)
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | ALPHA: (85) implies:
% 21.98/3.81 | | | | | | | (86) $i(all_90_1)
% 21.98/3.81 | | | | | | | (87) triple(all_48_5, all_90_1, bad) = all_55_1
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | GROUND_INST: instantiating (l40_l27) with all_48_5, all_90_1, bad,
% 21.98/3.81 | | | | | | | all_56_0, all_55_1, all_48_1, simplifying with (5),
% 21.98/3.81 | | | | | | | (20), (45), (84), (86), (87) gives:
% 21.98/3.81 | | | | | | | (88) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 21.98/3.81 | | | | | | | check_cpq(all_55_1) = 0) | ( ~ (v1 = 0) & ok(all_48_1)
% 21.98/3.81 | | | | | | | = v1) | ( ~ (v0 = 0) & check_cpq(all_48_1) = v0))
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | DELTA: instantiating (88) with fresh symbols all_122_0, all_122_1,
% 21.98/3.81 | | | | | | | all_122_2 gives:
% 21.98/3.81 | | | | | | | (89) (all_122_0 = 0 & check_cpq(all_55_1) = 0) | ( ~ (all_122_1
% 21.98/3.81 | | | | | | | = 0) & ok(all_48_1) = all_122_1) | ( ~ (all_122_2 = 0)
% 21.98/3.81 | | | | | | | & check_cpq(all_48_1) = all_122_2)
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | BETA: splitting (89) gives:
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | Case 1:
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | (90) all_122_0 = 0 & check_cpq(all_55_1) = 0
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | ALPHA: (90) implies:
% 21.98/3.81 | | | | | | | | (91) check_cpq(all_55_1) = 0
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | REF_CLOSE: (11), (41), (43), (91) are inconsistent by sub-proof
% 21.98/3.81 | | | | | | | | #1.
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | Case 2:
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | (92) ( ~ (all_122_1 = 0) & ok(all_48_1) = all_122_1) | ( ~
% 21.98/3.81 | | | | | | | | (all_122_2 = 0) & check_cpq(all_48_1) = all_122_2)
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | BETA: splitting (92) gives:
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | Case 1:
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | (93) ~ (all_122_1 = 0) & ok(all_48_1) = all_122_1
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | ALPHA: (93) implies:
% 21.98/3.81 | | | | | | | | | (94) ~ (all_122_1 = 0)
% 21.98/3.81 | | | | | | | | | (95) ok(all_48_1) = all_122_1
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_122_1, all_48_1,
% 21.98/3.81 | | | | | | | | | simplifying with (28), (95) gives:
% 21.98/3.81 | | | | | | | | | (96) all_122_1 = 0
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | REDUCE: (94), (96) imply:
% 21.98/3.81 | | | | | | | | | (97) $false
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | CLOSE: (97) is inconsistent.
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | Case 2:
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | (98) ~ (all_122_2 = 0) & check_cpq(all_48_1) = all_122_2
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | ALPHA: (98) implies:
% 21.98/3.81 | | | | | | | | | (99) ~ (all_122_2 = 0)
% 21.98/3.81 | | | | | | | | | (100) check_cpq(all_48_1) = all_122_2
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_122_2, all_48_1,
% 21.98/3.81 | | | | | | | | | simplifying with (26), (100) gives:
% 21.98/3.81 | | | | | | | | | (101) all_122_2 = 0
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | REDUCE: (99), (101) imply:
% 21.98/3.81 | | | | | | | | | (102) $false
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | CLOSE: (102) is inconsistent.
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | End of split
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | End of split
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | Case 2:
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | (103) all_90_2 = 0 & contains_slb(all_48_4, all_90_3) = 0
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | ALPHA: (103) implies:
% 21.98/3.81 | | | | | | | (104) contains_slb(all_48_4, all_90_3) = 0
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | REDUCE: (83), (104) imply:
% 21.98/3.81 | | | | | | | (105) contains_slb(all_48_4, all_56_0) = 0
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | BETA: splitting (70) gives:
% 21.98/3.81 | | | | | | |
% 21.98/3.81 | | | | | | | Case 1:
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | (106) all_95_0 = all_55_1 & triple(all_48_5, all_95_1,
% 21.98/3.81 | | | | | | | | all_48_3) = all_55_1 & update_slb(all_48_4, all_95_5)
% 21.98/3.81 | | | | | | | | = all_95_1 & $i(all_95_1) & $i(all_55_1)
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | ALPHA: (106) implies:
% 21.98/3.81 | | | | | | | | (107) $i(all_95_1)
% 21.98/3.81 | | | | | | | | (108) triple(all_48_5, all_95_1, all_48_3) = all_55_1
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | GROUND_INST: instantiating (l40_l27) with all_48_5, all_95_1,
% 21.98/3.81 | | | | | | | | all_48_3, all_56_0, all_55_1, all_48_1, simplifying
% 21.98/3.81 | | | | | | | | with (20), (22), (45), (84), (107), (108) gives:
% 21.98/3.81 | | | | | | | | (109) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 21.98/3.81 | | | | | | | | check_cpq(all_55_1) = 0) | ( ~ (v1 = 0) &
% 21.98/3.81 | | | | | | | | ok(all_48_1) = v1) | ( ~ (v0 = 0) &
% 21.98/3.81 | | | | | | | | check_cpq(all_48_1) = v0))
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | DELTA: instantiating (109) with fresh symbols all_126_0,
% 21.98/3.81 | | | | | | | | all_126_1, all_126_2 gives:
% 21.98/3.81 | | | | | | | | (110) (all_126_0 = 0 & check_cpq(all_55_1) = 0) | ( ~
% 21.98/3.81 | | | | | | | | (all_126_1 = 0) & ok(all_48_1) = all_126_1) | ( ~
% 21.98/3.81 | | | | | | | | (all_126_2 = 0) & check_cpq(all_48_1) = all_126_2)
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | BETA: splitting (110) gives:
% 21.98/3.81 | | | | | | | |
% 21.98/3.81 | | | | | | | | Case 1:
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | (111) all_126_0 = 0 & check_cpq(all_55_1) = 0
% 21.98/3.81 | | | | | | | | |
% 21.98/3.81 | | | | | | | | | ALPHA: (111) implies:
% 21.98/3.82 | | | | | | | | | (112) check_cpq(all_55_1) = 0
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | REF_CLOSE: (11), (41), (43), (112) are inconsistent by
% 21.98/3.82 | | | | | | | | | sub-proof #1.
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | (113) ( ~ (all_126_1 = 0) & ok(all_48_1) = all_126_1) | ( ~
% 21.98/3.82 | | | | | | | | | (all_126_2 = 0) & check_cpq(all_48_1) = all_126_2)
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | BETA: splitting (113) gives:
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | (114) ~ (all_126_1 = 0) & ok(all_48_1) = all_126_1
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | ALPHA: (114) implies:
% 21.98/3.82 | | | | | | | | | | (115) ~ (all_126_1 = 0)
% 21.98/3.82 | | | | | | | | | | (116) ok(all_48_1) = all_126_1
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_126_1, all_48_1,
% 21.98/3.82 | | | | | | | | | | simplifying with (28), (116) gives:
% 21.98/3.82 | | | | | | | | | | (117) all_126_1 = 0
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | REDUCE: (115), (117) imply:
% 21.98/3.82 | | | | | | | | | | (118) $false
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | CLOSE: (118) is inconsistent.
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | (119) ~ (all_126_2 = 0) & check_cpq(all_48_1) =
% 21.98/3.82 | | | | | | | | | | all_126_2
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | ALPHA: (119) implies:
% 21.98/3.82 | | | | | | | | | | (120) ~ (all_126_2 = 0)
% 21.98/3.82 | | | | | | | | | | (121) check_cpq(all_48_1) = all_126_2
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_126_2, all_48_1,
% 21.98/3.82 | | | | | | | | | | simplifying with (26), (121) gives:
% 21.98/3.82 | | | | | | | | | | (122) all_126_2 = 0
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | REDUCE: (120), (122) imply:
% 21.98/3.82 | | | | | | | | | | (123) $false
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | CLOSE: (123) is inconsistent.
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | End of split
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | End of split
% 21.98/3.82 | | | | | | | |
% 21.98/3.82 | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | |
% 21.98/3.82 | | | | | | | | (124) ( ~ (all_95_2 = 0) & lookup_slb(all_48_4, all_95_5) =
% 21.98/3.82 | | | | | | | | all_95_3 & less_than(all_95_3, all_95_5) = all_95_2 &
% 21.98/3.82 | | | | | | | | $i(all_95_3)) | ( ~ (all_95_4 = 0) &
% 21.98/3.82 | | | | | | | | contains_slb(all_48_4, all_95_5) = all_95_4)
% 21.98/3.82 | | | | | | | |
% 21.98/3.82 | | | | | | | | BETA: splitting (124) gives:
% 21.98/3.82 | | | | | | | |
% 21.98/3.82 | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | (125) ~ (all_95_2 = 0) & lookup_slb(all_48_4, all_95_5) =
% 21.98/3.82 | | | | | | | | | all_95_3 & less_than(all_95_3, all_95_5) = all_95_2 &
% 21.98/3.82 | | | | | | | | | $i(all_95_3)
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | ALPHA: (125) implies:
% 21.98/3.82 | | | | | | | | | (126) ~ (all_95_2 = 0)
% 21.98/3.82 | | | | | | | | | (127) $i(all_95_3)
% 21.98/3.82 | | | | | | | | | (128) less_than(all_95_3, all_95_5) = all_95_2
% 21.98/3.82 | | | | | | | | | (129) lookup_slb(all_48_4, all_95_5) = all_95_3
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | REDUCE: (81), (129) imply:
% 21.98/3.82 | | | | | | | | | (130) lookup_slb(all_48_4, all_56_0) = all_95_3
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | REDUCE: (81), (128) imply:
% 21.98/3.82 | | | | | | | | | (131) less_than(all_95_3, all_56_0) = all_95_2
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | GROUND_INST: instantiating (1) with all_56_0, all_95_3,
% 21.98/3.82 | | | | | | | | | all_95_2, simplifying with (84), (127), (131)
% 21.98/3.82 | | | | | | | | | gives:
% 21.98/3.82 | | | | | | | | | (132) all_95_2 = 0 | less_than(all_56_0, all_95_3) = 0
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | GROUND_INST: instantiating (2) with all_56_0, all_95_3,
% 21.98/3.82 | | | | | | | | | all_95_2, simplifying with (84), (127), (131)
% 21.98/3.82 | | | | | | | | | gives:
% 21.98/3.82 | | | | | | | | | (133) all_95_2 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0
% 21.98/3.82 | | | | | | | | | & strictly_less_than(all_56_0, all_95_3) = 0) | (
% 21.98/3.82 | | | | | | | | | ~ (v0 = 0) & less_than(all_56_0, all_95_3) = v0))
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | BETA: splitting (76) gives:
% 21.98/3.82 | | | | | | | | |
% 21.98/3.82 | | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | (134) all_100_0 = all_55_1 & triple(all_48_5, all_100_1,
% 21.98/3.82 | | | | | | | | | | bad) = all_55_1 & update_slb(all_48_4, all_100_5)
% 21.98/3.82 | | | | | | | | | | = all_100_1 & $i(all_100_1) & $i(all_55_1)
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | ALPHA: (134) implies:
% 21.98/3.82 | | | | | | | | | | (135) $i(all_100_1)
% 21.98/3.82 | | | | | | | | | | (136) triple(all_48_5, all_100_1, bad) = all_55_1
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | GROUND_INST: instantiating (l40_l27) with all_48_5, all_100_1,
% 21.98/3.82 | | | | | | | | | | bad, all_56_0, all_55_1, all_48_1, simplifying
% 21.98/3.82 | | | | | | | | | | with (5), (20), (45), (84), (135), (136) gives:
% 21.98/3.82 | | | | | | | | | | (137) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 =
% 21.98/3.82 | | | | | | | | | | 0 & check_cpq(all_55_1) = 0) | ( ~ (v1 = 0) &
% 21.98/3.82 | | | | | | | | | | ok(all_48_1) = v1) | ( ~ (v0 = 0) &
% 21.98/3.82 | | | | | | | | | | check_cpq(all_48_1) = v0))
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | DELTA: instantiating (137) with fresh symbols all_158_0,
% 21.98/3.82 | | | | | | | | | | all_158_1, all_158_2 gives:
% 21.98/3.82 | | | | | | | | | | (138) (all_158_0 = 0 & check_cpq(all_55_1) = 0) | ( ~
% 21.98/3.82 | | | | | | | | | | (all_158_1 = 0) & ok(all_48_1) = all_158_1) | ( ~
% 21.98/3.82 | | | | | | | | | | (all_158_2 = 0) & check_cpq(all_48_1) =
% 21.98/3.82 | | | | | | | | | | all_158_2)
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | BETA: splitting (138) gives:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | (139) all_158_0 = 0 & check_cpq(all_55_1) = 0
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | ALPHA: (139) implies:
% 21.98/3.82 | | | | | | | | | | | (140) check_cpq(all_55_1) = 0
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | REF_CLOSE: (11), (41), (43), (140) are inconsistent by
% 21.98/3.82 | | | | | | | | | | | sub-proof #1.
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | (141) ( ~ (all_158_1 = 0) & ok(all_48_1) = all_158_1) |
% 21.98/3.82 | | | | | | | | | | | ( ~ (all_158_2 = 0) & check_cpq(all_48_1) =
% 21.98/3.82 | | | | | | | | | | | all_158_2)
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | BETA: splitting (141) gives:
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | (142) ~ (all_158_1 = 0) & ok(all_48_1) = all_158_1
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | ALPHA: (142) implies:
% 21.98/3.82 | | | | | | | | | | | | (143) ~ (all_158_1 = 0)
% 21.98/3.82 | | | | | | | | | | | | (144) ok(all_48_1) = all_158_1
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_158_1, all_48_1,
% 21.98/3.82 | | | | | | | | | | | | simplifying with (28), (144) gives:
% 21.98/3.82 | | | | | | | | | | | | (145) all_158_1 = 0
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | REDUCE: (143), (145) imply:
% 21.98/3.82 | | | | | | | | | | | | (146) $false
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | (147) ~ (all_158_2 = 0) & check_cpq(all_48_1) =
% 21.98/3.82 | | | | | | | | | | | | all_158_2
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | ALPHA: (147) implies:
% 21.98/3.82 | | | | | | | | | | | | (148) ~ (all_158_2 = 0)
% 21.98/3.82 | | | | | | | | | | | | (149) check_cpq(all_48_1) = all_158_2
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_158_2, all_48_1,
% 21.98/3.82 | | | | | | | | | | | | simplifying with (26), (149) gives:
% 21.98/3.82 | | | | | | | | | | | | (150) all_158_2 = 0
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | REDUCE: (148), (150) imply:
% 21.98/3.82 | | | | | | | | | | | | (151) $false
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 21.98/3.82 | | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | End of split
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | End of split
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | Case 2:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | (152) ( ~ (all_100_2 = 0) & lookup_slb(all_48_4,
% 21.98/3.82 | | | | | | | | | | all_100_5) = all_100_3 &
% 21.98/3.82 | | | | | | | | | | strictly_less_than(all_100_5, all_100_3) =
% 21.98/3.82 | | | | | | | | | | all_100_2 & $i(all_100_3)) | ( ~ (all_100_4 = 0)
% 21.98/3.82 | | | | | | | | | | & contains_slb(all_48_4, all_100_5) = all_100_4)
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | BETA: splitting (152) gives:
% 21.98/3.82 | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | Case 1:
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | (153) ~ (all_100_2 = 0) & lookup_slb(all_48_4,
% 21.98/3.82 | | | | | | | | | | | all_100_5) = all_100_3 &
% 21.98/3.82 | | | | | | | | | | | strictly_less_than(all_100_5, all_100_3) =
% 21.98/3.82 | | | | | | | | | | | all_100_2 & $i(all_100_3)
% 21.98/3.82 | | | | | | | | | | |
% 21.98/3.82 | | | | | | | | | | | ALPHA: (153) implies:
% 21.98/3.82 | | | | | | | | | | | (154) ~ (all_100_2 = 0)
% 21.98/3.83 | | | | | | | | | | | (155) strictly_less_than(all_100_5, all_100_3) =
% 21.98/3.83 | | | | | | | | | | | all_100_2
% 21.98/3.83 | | | | | | | | | | | (156) lookup_slb(all_48_4, all_100_5) = all_100_3
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | REDUCE: (79), (156) imply:
% 21.98/3.83 | | | | | | | | | | | (157) lookup_slb(all_48_4, all_56_0) = all_100_3
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | REDUCE: (79), (155) imply:
% 21.98/3.83 | | | | | | | | | | | (158) strictly_less_than(all_56_0, all_100_3) =
% 21.98/3.83 | | | | | | | | | | | all_100_2
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | BETA: splitting (132) gives:
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | Case 1:
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | (159) less_than(all_56_0, all_95_3) = 0
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | BETA: splitting (133) gives:
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | Case 1:
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | (160) all_95_2 = 0
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | REDUCE: (126), (160) imply:
% 21.98/3.83 | | | | | | | | | | | | | (161) $false
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | Case 2:
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | (162) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 21.98/3.83 | | | | | | | | | | | | | strictly_less_than(all_56_0, all_95_3) = 0) |
% 21.98/3.83 | | | | | | | | | | | | | ( ~ (v0 = 0) & less_than(all_56_0, all_95_3) =
% 21.98/3.83 | | | | | | | | | | | | | v0))
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_137_0,
% 21.98/3.83 | | | | | | | | | | | | | all_137_1 gives:
% 21.98/3.83 | | | | | | | | | | | | | (163) (all_137_0 = 0 & strictly_less_than(all_56_0,
% 21.98/3.83 | | | | | | | | | | | | | all_95_3) = 0) | ( ~ (all_137_1 = 0) &
% 21.98/3.83 | | | | | | | | | | | | | less_than(all_56_0, all_95_3) = all_137_1)
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | BETA: splitting (163) gives:
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | Case 1:
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | (164) all_137_0 = 0 & strictly_less_than(all_56_0,
% 21.98/3.83 | | | | | | | | | | | | | | all_95_3) = 0
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | ALPHA: (164) implies:
% 21.98/3.83 | | | | | | | | | | | | | | (165) strictly_less_than(all_56_0, all_95_3) = 0
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_95_3, all_100_3,
% 21.98/3.83 | | | | | | | | | | | | | | all_56_0, all_48_4, simplifying with (130), (157)
% 21.98/3.83 | | | | | | | | | | | | | | gives:
% 21.98/3.83 | | | | | | | | | | | | | | (166) all_100_3 = all_95_3
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | REDUCE: (158), (166) imply:
% 21.98/3.83 | | | | | | | | | | | | | | (167) strictly_less_than(all_56_0, all_95_3) = all_100_2
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_100_2, all_95_3,
% 21.98/3.83 | | | | | | | | | | | | | | all_56_0, simplifying with (165), (167) gives:
% 21.98/3.83 | | | | | | | | | | | | | | (168) all_100_2 = 0
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | REDUCE: (154), (168) imply:
% 21.98/3.83 | | | | | | | | | | | | | | (169) $false
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | Case 2:
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | (170) ~ (all_137_1 = 0) & less_than(all_56_0, all_95_3)
% 21.98/3.83 | | | | | | | | | | | | | | = all_137_1
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | ALPHA: (170) implies:
% 21.98/3.83 | | | | | | | | | | | | | | (171) ~ (all_137_1 = 0)
% 21.98/3.83 | | | | | | | | | | | | | | (172) less_than(all_56_0, all_95_3) = all_137_1
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_137_1, all_95_3,
% 21.98/3.83 | | | | | | | | | | | | | | all_56_0, simplifying with (159), (172) gives:
% 21.98/3.83 | | | | | | | | | | | | | | (173) all_137_1 = 0
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | REDUCE: (171), (173) imply:
% 21.98/3.83 | | | | | | | | | | | | | | (174) $false
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 21.98/3.83 | | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | | End of split
% 21.98/3.83 | | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | End of split
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | Case 2:
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | (175) all_95_2 = 0
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | REDUCE: (126), (175) imply:
% 21.98/3.83 | | | | | | | | | | | | (176) $false
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 21.98/3.83 | | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | End of split
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | Case 2:
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | (177) ~ (all_100_4 = 0) & contains_slb(all_48_4,
% 21.98/3.83 | | | | | | | | | | | all_100_5) = all_100_4
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | ALPHA: (177) implies:
% 21.98/3.83 | | | | | | | | | | | (178) ~ (all_100_4 = 0)
% 21.98/3.83 | | | | | | | | | | | (179) contains_slb(all_48_4, all_100_5) = all_100_4
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | REDUCE: (79), (179) imply:
% 21.98/3.83 | | | | | | | | | | | (180) contains_slb(all_48_4, all_56_0) = all_100_4
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_100_4, all_56_0,
% 21.98/3.83 | | | | | | | | | | | all_48_4, simplifying with (105), (180) gives:
% 21.98/3.83 | | | | | | | | | | | (181) all_100_4 = 0
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | REDUCE: (178), (181) imply:
% 21.98/3.83 | | | | | | | | | | | (182) $false
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 21.98/3.83 | | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | | End of split
% 21.98/3.83 | | | | | | | | | |
% 21.98/3.83 | | | | | | | | | End of split
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | Case 2:
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | (183) ~ (all_95_4 = 0) & contains_slb(all_48_4, all_95_5)
% 21.98/3.83 | | | | | | | | | = all_95_4
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | ALPHA: (183) implies:
% 21.98/3.83 | | | | | | | | | (184) ~ (all_95_4 = 0)
% 21.98/3.83 | | | | | | | | | (185) contains_slb(all_48_4, all_95_5) = all_95_4
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | REDUCE: (81), (185) imply:
% 21.98/3.83 | | | | | | | | | (186) contains_slb(all_48_4, all_56_0) = all_95_4
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_95_4, all_56_0,
% 21.98/3.83 | | | | | | | | | all_48_4, simplifying with (105), (186) gives:
% 21.98/3.83 | | | | | | | | | (187) all_95_4 = 0
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | REDUCE: (184), (187) imply:
% 21.98/3.83 | | | | | | | | | (188) $false
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | | CLOSE: (188) is inconsistent.
% 21.98/3.83 | | | | | | | | |
% 21.98/3.83 | | | | | | | | End of split
% 21.98/3.83 | | | | | | | |
% 21.98/3.83 | | | | | | | End of split
% 21.98/3.83 | | | | | | |
% 21.98/3.83 | | | | | | End of split
% 21.98/3.83 | | | | | |
% 21.98/3.83 | | | | | End of split
% 21.98/3.83 | | | | |
% 21.98/3.83 | | | | End of split
% 21.98/3.83 | | | |
% 21.98/3.83 | | | End of split
% 21.98/3.83 | | |
% 21.98/3.83 | | End of split
% 21.98/3.83 | |
% 21.98/3.83 | End of split
% 21.98/3.83 |
% 21.98/3.83 End of proof
% 21.98/3.83
% 21.98/3.83 Sub-proof #1 shows that the following formulas are inconsistent:
% 21.98/3.83 ----------------------------------------------------------------
% 21.98/3.83 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.98/3.83 (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 21.98/3.83 (2) check_cpq(all_55_1) = all_55_0
% 21.98/3.83 (3) check_cpq(all_55_1) = 0
% 21.98/3.83 (4) ~ (all_55_0 = 0)
% 21.98/3.83
% 21.98/3.83 Begin of proof
% 21.98/3.83 |
% 21.98/3.83 | GROUND_INST: instantiating (1) with all_55_0, 0, all_55_1, simplifying with
% 21.98/3.83 | (2), (3) gives:
% 21.98/3.83 | (5) all_55_0 = 0
% 21.98/3.83 |
% 21.98/3.83 | REDUCE: (4), (5) imply:
% 21.98/3.83 | (6) $false
% 21.98/3.83 |
% 21.98/3.83 | CLOSE: (6) is inconsistent.
% 21.98/3.83 |
% 21.98/3.83 End of proof
% 21.98/3.83 % SZS output end Proof for theBenchmark
% 21.98/3.83
% 21.98/3.83 3213ms
%------------------------------------------------------------------------------