TSTP Solution File: SWV379+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV379+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 : n011.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 22:56:05 EDT 2023
% Result : Theorem 11.83s 2.34s
% Output : Proof 15.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV379+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.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 05:25:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.94/1.17 Prover 1: Preprocessing ...
% 2.94/1.17 Prover 4: Preprocessing ...
% 3.62/1.21 Prover 0: Preprocessing ...
% 3.62/1.21 Prover 3: Preprocessing ...
% 3.62/1.21 Prover 2: Preprocessing ...
% 3.62/1.21 Prover 5: Preprocessing ...
% 3.77/1.22 Prover 6: Preprocessing ...
% 7.83/1.79 Prover 1: Warning: ignoring some quantifiers
% 7.83/1.83 Prover 3: Warning: ignoring some quantifiers
% 8.42/1.87 Prover 6: Proving ...
% 8.42/1.87 Prover 1: Constructing countermodel ...
% 8.42/1.87 Prover 5: Proving ...
% 8.59/1.88 Prover 3: Constructing countermodel ...
% 8.59/1.89 Prover 4: Constructing countermodel ...
% 8.59/1.92 Prover 0: Proving ...
% 8.90/1.98 Prover 2: Proving ...
% 10.65/2.23 Prover 3: gave up
% 10.65/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.51/2.30 Prover 7: Preprocessing ...
% 11.83/2.34 Prover 0: proved (1699ms)
% 11.83/2.34
% 11.83/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.83/2.34
% 11.83/2.34 Prover 2: stopped
% 11.95/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.95/2.34 Prover 6: stopped
% 11.95/2.36 Prover 5: stopped
% 11.95/2.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.95/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.95/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.95/2.38 Prover 8: Preprocessing ...
% 12.51/2.42 Prover 10: Preprocessing ...
% 12.51/2.43 Prover 11: Preprocessing ...
% 12.51/2.43 Prover 13: Preprocessing ...
% 12.51/2.44 Prover 7: Warning: ignoring some quantifiers
% 12.97/2.48 Prover 7: Constructing countermodel ...
% 12.97/2.51 Prover 8: Warning: ignoring some quantifiers
% 12.97/2.55 Prover 8: Constructing countermodel ...
% 13.81/2.58 Prover 10: Warning: ignoring some quantifiers
% 13.81/2.62 Prover 10: Constructing countermodel ...
% 13.81/2.64 Prover 11: Constructing countermodel ...
% 13.81/2.66 Prover 4: Found proof (size 165)
% 13.81/2.67 Prover 4: proved (2008ms)
% 13.81/2.67 Prover 8: stopped
% 13.81/2.67 Prover 1: stopped
% 13.81/2.67 Prover 10: stopped
% 13.81/2.67 Prover 7: stopped
% 13.81/2.68 Prover 11: stopped
% 13.81/2.68 Prover 13: Warning: ignoring some quantifiers
% 13.81/2.72 Prover 13: Constructing countermodel ...
% 14.20/2.73 Prover 13: stopped
% 14.20/2.73
% 14.20/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.20/2.73
% 14.69/2.75 % SZS output start Proof for theBenchmark
% 14.69/2.76 Assumptions after simplification:
% 14.69/2.76 ---------------------------------
% 14.69/2.76
% 14.69/2.76 (ax40)
% 14.69/2.79 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) =
% 14.69/2.79 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3))
% 14.69/2.79
% 14.69/2.79 (ax41)
% 14.69/2.79 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad |
% 14.69/2.79 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) =
% 14.69/2.79 0)
% 14.69/2.79
% 14.69/2.79 (ax46)
% 14.69/2.79 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.69/2.79 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 14.69/2.79 (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3)))
% 14.69/2.79
% 14.69/2.79 (ax47)
% 14.69/2.79 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.69/2.79 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 14.69/2.79 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 14.69/2.79 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 &
% 14.69/2.79 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5)
% 14.69/2.79 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0)))
% 14.69/2.79
% 14.69/2.79 (ax48)
% 14.69/2.80 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.69/2.80 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 14.69/2.80 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 14.69/2.80 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 14.69/2.80 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) =
% 14.69/2.80 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 &
% 14.69/2.80 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~
% 14.69/2.80 (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 14.69/2.80
% 14.69/2.80 (ax49)
% 14.69/2.80 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 14.69/2.80 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~
% 14.69/2.80 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~
% 14.69/2.80 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i]
% 14.69/2.80 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 &
% 14.69/2.80 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) =
% 14.69/2.80 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5)))
% 14.69/2.80 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 14.69/2.80 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) |
% 14.69/2.80 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i]
% 14.69/2.80 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 &
% 14.69/2.80 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) =
% 14.69/2.80 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9)
% 14.69/2.80 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 14.69/2.80
% 14.69/2.80 (ax51)
% 14.69/2.81 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 14.69/2.81 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0,
% 14.69/2.81 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0)
% 14.69/2.81 = v4 & $i(v4)))
% 14.69/2.81
% 14.69/2.81 (ax52)
% 15.06/2.81 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ?
% 15.06/2.81 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) =
% 15.06/2.81 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1:
% 15.06/2.81 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 15.06/2.81 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 &
% 15.06/2.81 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 15.06/2.81 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 15.06/2.81 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 &
% 15.06/2.81 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2)))
% 15.06/2.81
% 15.06/2.81 (l15_co)
% 15.06/2.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 15.06/2.81 $i] : ( ~ (v4 = 0) & ok(v5) = 0 & ok(v3) = v4 & triple(v0, v1, v2) = v3 &
% 15.06/2.81 findmin_cpq_eff(v3) = v5 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 15.06/2.81
% 15.06/2.81 (stricly_smaller_definition)
% 15.06/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 15.06/2.81 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 15.06/2.81 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 15.06/2.81 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 15.06/2.81 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 15.06/2.81 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 15.06/2.81 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 15.06/2.81 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 15.06/2.81 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 15.06/2.81 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.06/2.81 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 15.06/2.81 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 15.06/2.81 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.06/2.81 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 15.06/2.81 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 15.06/2.81 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 15.06/2.81 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 15.06/2.81 v0) = v2 & (v3 = 0 | v2 = 0)))
% 15.06/2.81
% 15.06/2.81 (totality)
% 15.06/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 15.06/2.82 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 15.06/2.82 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 15.06/2.82 ~ $i(v0) | less_than(v1, v0) = 0)
% 15.06/2.82
% 15.06/2.82 (function-axioms)
% 15.06/2.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 15.06/2.82 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 15.06/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.06/2.82 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 15.06/2.82 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.06/2.82 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 15.06/2.82 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 15.06/2.82 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 15.06/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.06/2.82 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 15.06/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.82 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 15.06/2.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 15.06/2.82 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.06/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 15.06/2.82 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.06/2.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 15.06/2.82 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.06/2.82 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 15.06/2.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 15.06/2.82 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 15.06/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.06/2.82 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 15.06/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.82 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 15.06/2.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 15.06/2.82 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.06/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.82 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 15.06/2.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.06/2.82 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 15.06/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.06/2.82 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 15.06/2.82 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 15.06/2.82 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.06/2.82 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 15.06/2.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 15.06/2.82 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 15.06/2.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 15.06/2.82 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.06/2.82 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 15.06/2.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 15.06/2.82 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 15.06/2.82 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 15.06/2.82 v1) | ~ (isnonempty_slb(v2) = v0))
% 15.06/2.82
% 15.06/2.82 Further assumptions not needed in the proof:
% 15.06/2.82 --------------------------------------------
% 15.06/2.82 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 15.06/2.82 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax42, ax43, ax44, ax45,
% 15.06/2.82 ax50, ax53, bottom_smallest, reflexivity, transitivity
% 15.06/2.82
% 15.06/2.82 Those formulas are unsatisfiable:
% 15.06/2.82 ---------------------------------
% 15.06/2.82
% 15.06/2.82 Begin of proof
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (totality) implies:
% 15.06/2.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 15.06/2.83 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (stricly_smaller_definition) implies:
% 15.06/2.83 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 15.06/2.83 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 15.06/2.83 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 15.06/2.83 | 0) | (v2 = 0 & ~ (v4 = 0)))))
% 15.06/2.83 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 15.06/2.83 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 15.06/2.83 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 15.06/2.83 | 0) | (v4 = 0 & ~ (v2 = 0)))))
% 15.06/2.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 15.06/2.83 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 15.06/2.83 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) =
% 15.06/2.83 | v3 & ( ~ (v3 = 0) | v4 = 0)))
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (ax40) implies:
% 15.06/2.83 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) =
% 15.06/2.83 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2)
% 15.06/2.83 | = v3))
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (ax41) implies:
% 15.06/2.83 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~
% 15.06/2.83 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.06/2.83 | ok(v3) = 0)
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (ax46) implies:
% 15.06/2.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb,
% 15.06/2.83 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (triple(v0,
% 15.06/2.83 | create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3)))
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (ax47) implies:
% 15.06/2.83 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.06/2.83 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 15.06/2.83 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 15.06/2.83 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 15.06/2.83 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1,
% 15.06/2.83 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) &
% 15.06/2.83 | (v8 = v4 | v6 = 0)))
% 15.06/2.83 |
% 15.06/2.83 | ALPHA: (ax48) implies:
% 15.06/2.84 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.06/2.84 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 15.06/2.84 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 15.06/2.84 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] :
% 15.06/2.84 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 &
% 15.06/2.84 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 15.06/2.84 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 &
% 15.06/2.84 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) |
% 15.06/2.84 | v10 = v4)))
% 15.06/2.84 |
% 15.06/2.84 | ALPHA: (ax49) implies:
% 15.06/2.84 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.06/2.84 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 15.06/2.84 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 15.06/2.84 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] :
% 15.06/2.84 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10
% 15.06/2.84 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 15.06/2.84 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) &
% 15.06/2.84 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 =
% 15.06/2.84 | v4)))
% 15.06/2.84 |
% 15.06/2.84 | ALPHA: (ax51) implies:
% 15.06/2.84 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.06/2.84 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1,
% 15.06/2.84 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.06/2.84 | (findmin_pqp_res(v0) = v4 & $i(v4)))
% 15.06/2.84 |
% 15.06/2.84 | ALPHA: (ax52) implies:
% 15.06/2.84 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0)
% 15.06/2.84 | | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 &
% 15.06/2.84 | removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) &
% 15.06/2.84 | $i(v2)))
% 15.06/2.84 |
% 15.06/2.84 | ALPHA: (function-axioms) implies:
% 15.06/2.84 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.06/2.84 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 15.06/2.84 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.06/2.84 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 15.06/2.84 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.06/2.84 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 15.06/2.84 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.06/2.84 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 15.06/2.84 | (less_than(v3, v2) = v0))
% 15.06/2.84 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.06/2.84 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 15.06/2.84 | (contains_slb(v3, v2) = v0))
% 15.06/2.84 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.84 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 15.06/2.84 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.84 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0))
% 15.06/2.84 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 15.06/2.84 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) =
% 15.06/2.84 | v0))
% 15.06/2.84 |
% 15.06/2.84 | DELTA: instantiating (l15_co) with fresh symbols all_46_0, all_46_1, all_46_2,
% 15.06/2.84 | all_46_3, all_46_4, all_46_5 gives:
% 15.06/2.84 | (21) ~ (all_46_1 = 0) & ok(all_46_0) = 0 & ok(all_46_2) = all_46_1 &
% 15.06/2.84 | triple(all_46_5, all_46_4, all_46_3) = all_46_2 &
% 15.06/2.84 | findmin_cpq_eff(all_46_2) = all_46_0 & $i(all_46_0) & $i(all_46_2) &
% 15.06/2.84 | $i(all_46_3) & $i(all_46_4) & $i(all_46_5)
% 15.06/2.84 |
% 15.06/2.84 | ALPHA: (21) implies:
% 15.06/2.84 | (22) ~ (all_46_1 = 0)
% 15.06/2.84 | (23) $i(all_46_5)
% 15.06/2.85 | (24) $i(all_46_4)
% 15.06/2.85 | (25) $i(all_46_3)
% 15.06/2.85 | (26) $i(all_46_2)
% 15.06/2.85 | (27) findmin_cpq_eff(all_46_2) = all_46_0
% 15.06/2.85 | (28) triple(all_46_5, all_46_4, all_46_3) = all_46_2
% 15.06/2.85 | (29) ok(all_46_2) = all_46_1
% 15.06/2.85 | (30) ok(all_46_0) = 0
% 15.06/2.85 |
% 15.06/2.85 | GROUND_INST: instantiating (12) with all_46_2, all_46_0, simplifying with
% 15.06/2.85 | (26), (27) gives:
% 15.06/2.85 | (31) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_46_2) = v1 &
% 15.06/2.85 | removemin_cpq_eff(all_46_2) = v0 & remove_cpq(all_46_0, v1) = v0 &
% 15.06/2.85 | $i(v1) & $i(v0))
% 15.06/2.85 |
% 15.06/2.85 | GROUND_INST: instantiating (10) with all_46_5, all_46_4, all_46_3, all_46_2,
% 15.06/2.85 | all_46_0, simplifying with (23), (24), (25), (27), (28) gives:
% 15.06/2.85 | (32) all_46_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 15.06/2.85 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_5) =
% 15.06/2.85 | v0 & triple(all_46_5, v4, all_46_3) = v5 & update_slb(all_46_4, v0)
% 15.06/2.85 | = v4 & lookup_slb(all_46_4, v0) = v2 & contains_slb(all_46_4, v0) =
% 15.06/2.85 | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & (
% 15.06/2.85 | ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_0))
% 15.06/2.85 |
% 15.06/2.85 | GROUND_INST: instantiating (9) with all_46_5, all_46_4, all_46_3, all_46_2,
% 15.06/2.85 | all_46_0, simplifying with (23), (24), (25), (27), (28) gives:
% 15.06/2.85 | (33) all_46_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 15.06/2.85 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_5) =
% 15.06/2.85 | v0 & triple(all_46_5, v4, bad) = v5 & update_slb(all_46_4, v0) = v4
% 15.06/2.85 | & lookup_slb(all_46_4, v0) = v2 & contains_slb(all_46_4, v0) = v1 &
% 15.06/2.85 | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0)
% 15.06/2.85 | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_0))
% 15.06/2.85 |
% 15.06/2.85 | GROUND_INST: instantiating (8) with all_46_5, all_46_4, all_46_3, all_46_2,
% 15.06/2.85 | all_46_0, simplifying with (23), (24), (25), (27), (28) gives:
% 15.06/2.85 | (34) all_46_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 15.06/2.85 | [v3: $i] : (findmin_pqp_res(all_46_5) = v0 & triple(all_46_5, v2, bad)
% 15.06/2.85 | = v3 & update_slb(all_46_4, v0) = v2 & contains_slb(all_46_4, v0) =
% 15.06/2.85 | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_46_0 | v1 = 0))
% 15.06/2.85 |
% 15.06/2.85 | GROUND_INST: instantiating (6) with all_46_5, all_46_4, all_46_3, all_46_2,
% 15.06/2.85 | simplifying with (23), (24), (25), (28) gives:
% 15.06/2.85 | (35) all_46_3 = bad | ok(all_46_2) = 0
% 15.06/2.85 |
% 15.06/2.85 | DELTA: instantiating (31) with fresh symbols all_53_0, all_53_1 gives:
% 15.06/2.85 | (36) findmin_cpq_res(all_46_2) = all_53_0 & removemin_cpq_eff(all_46_2) =
% 15.06/2.85 | all_53_1 & remove_cpq(all_46_0, all_53_0) = all_53_1 & $i(all_53_0) &
% 15.06/2.85 | $i(all_53_1)
% 15.06/2.85 |
% 15.06/2.85 | ALPHA: (36) implies:
% 15.06/2.85 | (37) findmin_cpq_res(all_46_2) = all_53_0
% 15.06/2.85 |
% 15.06/2.85 | BETA: splitting (35) gives:
% 15.06/2.85 |
% 15.06/2.85 | Case 1:
% 15.06/2.85 | |
% 15.06/2.85 | | (38) ok(all_46_2) = 0
% 15.06/2.85 | |
% 15.06/2.85 | | GROUND_INST: instantiating (14) with all_46_1, 0, all_46_2, simplifying with
% 15.06/2.85 | | (29), (38) gives:
% 15.06/2.85 | | (39) all_46_1 = 0
% 15.06/2.85 | |
% 15.06/2.85 | | REDUCE: (22), (39) imply:
% 15.06/2.85 | | (40) $false
% 15.06/2.86 | |
% 15.06/2.86 | | CLOSE: (40) is inconsistent.
% 15.06/2.86 | |
% 15.06/2.86 | Case 2:
% 15.06/2.86 | |
% 15.06/2.86 | | (41) all_46_3 = bad
% 15.06/2.86 | | (42) ~ (ok(all_46_2) = 0)
% 15.06/2.86 | |
% 15.06/2.86 | | REDUCE: (28), (41) imply:
% 15.06/2.86 | | (43) triple(all_46_5, all_46_4, bad) = all_46_2
% 15.06/2.86 | |
% 15.06/2.86 | | REDUCE: (25), (41) imply:
% 15.06/2.86 | | (44) $i(bad)
% 15.06/2.86 | |
% 15.06/2.86 | | GROUND_INST: instantiating (11) with all_46_5, all_46_4, bad, all_46_2,
% 15.06/2.86 | | all_53_0, simplifying with (23), (24), (37), (43), (44) gives:
% 15.06/2.86 | | (45) all_46_4 = create_slb | (findmin_pqp_res(all_46_5) = all_53_0 &
% 15.06/2.86 | | $i(all_53_0))
% 15.06/2.86 | |
% 15.06/2.86 | | BETA: splitting (32) gives:
% 15.06/2.86 | |
% 15.06/2.86 | | Case 1:
% 15.06/2.86 | | |
% 15.06/2.86 | | | (46) all_46_4 = create_slb
% 15.06/2.86 | | |
% 15.06/2.86 | | | REDUCE: (43), (46) imply:
% 15.06/2.86 | | | (47) triple(all_46_5, create_slb, bad) = all_46_2
% 15.06/2.86 | | |
% 15.06/2.86 | | | GROUND_INST: instantiating (7) with all_46_5, bad, all_46_2, simplifying
% 15.06/2.86 | | | with (23), (44), (47) gives:
% 15.06/2.86 | | | (48) ? [v0: $i] : (triple(all_46_5, create_slb, bad) = v0 &
% 15.06/2.86 | | | findmin_cpq_eff(all_46_2) = v0 & $i(v0))
% 15.06/2.86 | | |
% 15.06/2.86 | | | DELTA: instantiating (48) with fresh symbol all_78_0 gives:
% 15.06/2.86 | | | (49) triple(all_46_5, create_slb, bad) = all_78_0 &
% 15.06/2.86 | | | findmin_cpq_eff(all_46_2) = all_78_0 & $i(all_78_0)
% 15.06/2.86 | | |
% 15.06/2.86 | | | ALPHA: (49) implies:
% 15.06/2.86 | | | (50) findmin_cpq_eff(all_46_2) = all_78_0
% 15.06/2.86 | | | (51) triple(all_46_5, create_slb, bad) = all_78_0
% 15.06/2.86 | | |
% 15.06/2.86 | | | GROUND_INST: instantiating (13) with all_46_0, all_78_0, all_46_2,
% 15.06/2.86 | | | simplifying with (27), (50) gives:
% 15.06/2.86 | | | (52) all_78_0 = all_46_0
% 15.06/2.86 | | |
% 15.06/2.86 | | | GROUND_INST: instantiating (20) with all_46_2, all_78_0, bad, create_slb,
% 15.06/2.86 | | | all_46_5, simplifying with (47), (51) gives:
% 15.06/2.86 | | | (53) all_78_0 = all_46_2
% 15.06/2.86 | | |
% 15.06/2.86 | | | COMBINE_EQS: (52), (53) imply:
% 15.06/2.86 | | | (54) all_46_0 = all_46_2
% 15.06/2.86 | | |
% 15.06/2.86 | | | REDUCE: (30), (54) imply:
% 15.06/2.86 | | | (55) ok(all_46_2) = 0
% 15.06/2.86 | | |
% 15.06/2.86 | | | PRED_UNIFY: (42), (55) imply:
% 15.06/2.86 | | | (56) $false
% 15.06/2.86 | | |
% 15.06/2.86 | | | CLOSE: (56) is inconsistent.
% 15.06/2.86 | | |
% 15.06/2.86 | | Case 2:
% 15.06/2.86 | | |
% 15.06/2.86 | | | (57) ~ (all_46_4 = create_slb)
% 15.06/2.86 | | | (58) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 15.06/2.86 | | | $i] : ? [v5: $i] : (findmin_pqp_res(all_46_5) = v0 &
% 15.06/2.86 | | | triple(all_46_5, v4, all_46_3) = v5 & update_slb(all_46_4, v0) =
% 15.06/2.86 | | | v4 & lookup_slb(all_46_4, v0) = v2 & contains_slb(all_46_4, v0)
% 15.06/2.86 | | | = v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) &
% 15.06/2.86 | | | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_0))
% 15.06/2.86 | | |
% 15.06/2.86 | | | DELTA: instantiating (58) with fresh symbols all_72_0, all_72_1, all_72_2,
% 15.06/2.86 | | | all_72_3, all_72_4, all_72_5 gives:
% 15.06/2.87 | | | (59) findmin_pqp_res(all_46_5) = all_72_5 & triple(all_46_5, all_72_1,
% 15.06/2.87 | | | all_46_3) = all_72_0 & update_slb(all_46_4, all_72_5) = all_72_1
% 15.06/2.87 | | | & lookup_slb(all_46_4, all_72_5) = all_72_3 &
% 15.06/2.87 | | | contains_slb(all_46_4, all_72_5) = all_72_4 & less_than(all_72_3,
% 15.06/2.87 | | | all_72_5) = all_72_2 & $i(all_72_0) & $i(all_72_1) &
% 15.06/2.87 | | | $i(all_72_3) & $i(all_72_5) & ( ~ (all_72_2 = 0) | ~ (all_72_4 =
% 15.06/2.87 | | | 0) | all_72_0 = all_46_0)
% 15.06/2.87 | | |
% 15.06/2.87 | | | ALPHA: (59) implies:
% 15.06/2.87 | | | (60) $i(all_72_5)
% 15.06/2.87 | | | (61) less_than(all_72_3, all_72_5) = all_72_2
% 15.06/2.87 | | | (62) contains_slb(all_46_4, all_72_5) = all_72_4
% 15.06/2.87 | | | (63) lookup_slb(all_46_4, all_72_5) = all_72_3
% 15.06/2.87 | | | (64) update_slb(all_46_4, all_72_5) = all_72_1
% 15.06/2.87 | | | (65) triple(all_46_5, all_72_1, all_46_3) = all_72_0
% 15.06/2.87 | | | (66) findmin_pqp_res(all_46_5) = all_72_5
% 15.06/2.87 | | | (67) ~ (all_72_2 = 0) | ~ (all_72_4 = 0) | all_72_0 = all_46_0
% 15.06/2.87 | | |
% 15.06/2.87 | | | REDUCE: (41), (65) imply:
% 15.06/2.87 | | | (68) triple(all_46_5, all_72_1, bad) = all_72_0
% 15.06/2.87 | | |
% 15.06/2.87 | | | BETA: splitting (45) gives:
% 15.06/2.87 | | |
% 15.06/2.87 | | | Case 1:
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | (69) all_46_4 = create_slb
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | REDUCE: (57), (69) imply:
% 15.06/2.87 | | | | (70) $false
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | CLOSE: (70) is inconsistent.
% 15.06/2.87 | | | |
% 15.06/2.87 | | | Case 2:
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | (71) findmin_pqp_res(all_46_5) = all_53_0 & $i(all_53_0)
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | ALPHA: (71) implies:
% 15.06/2.87 | | | | (72) findmin_pqp_res(all_46_5) = all_53_0
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | BETA: splitting (33) gives:
% 15.06/2.87 | | | |
% 15.06/2.87 | | | | Case 1:
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | | (73) all_46_4 = create_slb
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | | REDUCE: (57), (73) imply:
% 15.06/2.87 | | | | | (74) $false
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | | CLOSE: (74) is inconsistent.
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | Case 2:
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | | (75) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ?
% 15.06/2.87 | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_5) = v0 &
% 15.06/2.87 | | | | | triple(all_46_5, v4, bad) = v5 & update_slb(all_46_4, v0) =
% 15.06/2.87 | | | | | v4 & lookup_slb(all_46_4, v0) = v2 & contains_slb(all_46_4,
% 15.06/2.87 | | | | | v0) = v1 & strictly_less_than(v0, v2) = v3 & $i(v5) &
% 15.06/2.87 | | | | | $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 =
% 15.06/2.87 | | | | | all_46_0))
% 15.06/2.87 | | | | |
% 15.06/2.87 | | | | | DELTA: instantiating (75) with fresh symbols all_82_0, all_82_1,
% 15.06/2.87 | | | | | all_82_2, all_82_3, all_82_4, all_82_5 gives:
% 15.37/2.87 | | | | | (76) findmin_pqp_res(all_46_5) = all_82_5 & triple(all_46_5,
% 15.37/2.87 | | | | | all_82_1, bad) = all_82_0 & update_slb(all_46_4, all_82_5) =
% 15.37/2.87 | | | | | all_82_1 & lookup_slb(all_46_4, all_82_5) = all_82_3 &
% 15.37/2.87 | | | | | contains_slb(all_46_4, all_82_5) = all_82_4 &
% 15.37/2.87 | | | | | strictly_less_than(all_82_5, all_82_3) = all_82_2 &
% 15.37/2.87 | | | | | $i(all_82_0) & $i(all_82_1) & $i(all_82_3) & $i(all_82_5) & (
% 15.37/2.87 | | | | | ~ (all_82_2 = 0) | ~ (all_82_4 = 0) | all_82_0 = all_46_0)
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | ALPHA: (76) implies:
% 15.37/2.87 | | | | | (77) $i(all_82_3)
% 15.37/2.87 | | | | | (78) $i(all_82_1)
% 15.37/2.87 | | | | | (79) strictly_less_than(all_82_5, all_82_3) = all_82_2
% 15.37/2.87 | | | | | (80) contains_slb(all_46_4, all_82_5) = all_82_4
% 15.37/2.87 | | | | | (81) lookup_slb(all_46_4, all_82_5) = all_82_3
% 15.37/2.87 | | | | | (82) update_slb(all_46_4, all_82_5) = all_82_1
% 15.37/2.87 | | | | | (83) triple(all_46_5, all_82_1, bad) = all_82_0
% 15.37/2.87 | | | | | (84) findmin_pqp_res(all_46_5) = all_82_5
% 15.37/2.87 | | | | | (85) ~ (all_82_2 = 0) | ~ (all_82_4 = 0) | all_82_0 = all_46_0
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | GROUND_INST: instantiating (15) with all_72_5, all_82_5, all_46_5,
% 15.37/2.87 | | | | | simplifying with (66), (84) gives:
% 15.37/2.87 | | | | | (86) all_82_5 = all_72_5
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | GROUND_INST: instantiating (15) with all_53_0, all_82_5, all_46_5,
% 15.37/2.87 | | | | | simplifying with (72), (84) gives:
% 15.37/2.87 | | | | | (87) all_82_5 = all_53_0
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | COMBINE_EQS: (86), (87) imply:
% 15.37/2.87 | | | | | (88) all_72_5 = all_53_0
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | SIMP: (88) implies:
% 15.37/2.87 | | | | | (89) all_72_5 = all_53_0
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (82), (87) imply:
% 15.37/2.87 | | | | | (90) update_slb(all_46_4, all_53_0) = all_82_1
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (64), (89) imply:
% 15.37/2.87 | | | | | (91) update_slb(all_46_4, all_53_0) = all_72_1
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (81), (87) imply:
% 15.37/2.87 | | | | | (92) lookup_slb(all_46_4, all_53_0) = all_82_3
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (63), (89) imply:
% 15.37/2.87 | | | | | (93) lookup_slb(all_46_4, all_53_0) = all_72_3
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (80), (87) imply:
% 15.37/2.87 | | | | | (94) contains_slb(all_46_4, all_53_0) = all_82_4
% 15.37/2.87 | | | | |
% 15.37/2.87 | | | | | REDUCE: (62), (89) imply:
% 15.37/2.87 | | | | | (95) contains_slb(all_46_4, all_53_0) = all_72_4
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (79), (87) imply:
% 15.37/2.88 | | | | | (96) strictly_less_than(all_53_0, all_82_3) = all_82_2
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (61), (89) imply:
% 15.37/2.88 | | | | | (97) less_than(all_72_3, all_53_0) = all_72_2
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (60), (89) imply:
% 15.37/2.88 | | | | | (98) $i(all_53_0)
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (17) with all_72_4, all_82_4, all_53_0,
% 15.37/2.88 | | | | | all_46_4, simplifying with (94), (95) gives:
% 15.37/2.88 | | | | | (99) all_82_4 = all_72_4
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (18) with all_72_3, all_82_3, all_53_0,
% 15.37/2.88 | | | | | all_46_4, simplifying with (92), (93) gives:
% 15.37/2.88 | | | | | (100) all_82_3 = all_72_3
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (19) with all_72_1, all_82_1, all_53_0,
% 15.37/2.88 | | | | | all_46_4, simplifying with (90), (91) gives:
% 15.37/2.88 | | | | | (101) all_82_1 = all_72_1
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (83), (101) imply:
% 15.37/2.88 | | | | | (102) triple(all_46_5, all_72_1, bad) = all_82_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (96), (100) imply:
% 15.37/2.88 | | | | | (103) strictly_less_than(all_53_0, all_72_3) = all_82_2
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (78), (101) imply:
% 15.37/2.88 | | | | | (104) $i(all_72_1)
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | REDUCE: (77), (100) imply:
% 15.37/2.88 | | | | | (105) $i(all_72_3)
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (20) with all_72_0, all_82_0, bad,
% 15.37/2.88 | | | | | all_72_1, all_46_5, simplifying with (68), (102) gives:
% 15.37/2.88 | | | | | (106) all_82_0 = all_72_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (1) with all_53_0, all_72_3, all_72_2,
% 15.37/2.88 | | | | | simplifying with (97), (98), (105) gives:
% 15.37/2.88 | | | | | (107) all_72_2 = 0 | less_than(all_53_0, all_72_3) = 0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (3) with all_53_0, all_72_3, all_72_2,
% 15.37/2.88 | | | | | simplifying with (97), (98), (105) gives:
% 15.37/2.88 | | | | | (108) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_53_0,
% 15.37/2.88 | | | | | all_72_3) = v0 & less_than(all_53_0, all_72_3) = v1 & ( ~
% 15.37/2.88 | | | | | (v0 = 0) | (v1 = 0 & ~ (all_72_2 = 0))))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (2) with all_72_3, all_53_0, all_72_2,
% 15.37/2.88 | | | | | simplifying with (97), (98), (105) gives:
% 15.37/2.88 | | | | | (109) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_72_3,
% 15.37/2.88 | | | | | all_53_0) = v0 & less_than(all_53_0, all_72_3) = v1 & ( ~
% 15.37/2.88 | | | | | (v0 = 0) | (all_72_2 = 0 & ~ (v1 = 0))))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (4) with all_53_0, all_72_3, all_82_2,
% 15.37/2.88 | | | | | simplifying with (98), (103), (105) gives:
% 15.37/2.88 | | | | | (110) all_82_2 = 0 | ? [v0: any] : ? [v1: any] :
% 15.37/2.88 | | | | | (less_than(all_72_3, all_53_0) = v1 & less_than(all_53_0,
% 15.37/2.88 | | | | | all_72_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (5) with all_46_5, all_72_1, all_72_0,
% 15.37/2.88 | | | | | simplifying with (23), (68), (104) gives:
% 15.37/2.88 | | | | | (111) ? [v0: int] : ( ~ (v0 = 0) & ok(all_72_0) = v0)
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | DELTA: instantiating (111) with fresh symbol all_101_0 gives:
% 15.37/2.88 | | | | | (112) ~ (all_101_0 = 0) & ok(all_72_0) = all_101_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | ALPHA: (112) implies:
% 15.37/2.88 | | | | | (113) ~ (all_101_0 = 0)
% 15.37/2.88 | | | | | (114) ok(all_72_0) = all_101_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | DELTA: instantiating (109) with fresh symbols all_103_0, all_103_1
% 15.37/2.88 | | | | | gives:
% 15.37/2.88 | | | | | (115) strictly_less_than(all_72_3, all_53_0) = all_103_1 &
% 15.37/2.88 | | | | | less_than(all_53_0, all_72_3) = all_103_0 & ( ~ (all_103_1 =
% 15.37/2.88 | | | | | 0) | (all_72_2 = 0 & ~ (all_103_0 = 0)))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | ALPHA: (115) implies:
% 15.37/2.88 | | | | | (116) less_than(all_53_0, all_72_3) = all_103_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | DELTA: instantiating (108) with fresh symbols all_105_0, all_105_1
% 15.37/2.88 | | | | | gives:
% 15.37/2.88 | | | | | (117) strictly_less_than(all_53_0, all_72_3) = all_105_1 &
% 15.37/2.88 | | | | | less_than(all_53_0, all_72_3) = all_105_0 & ( ~ (all_105_1 =
% 15.37/2.88 | | | | | 0) | (all_105_0 = 0 & ~ (all_72_2 = 0)))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | ALPHA: (117) implies:
% 15.37/2.88 | | | | | (118) less_than(all_53_0, all_72_3) = all_105_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (16) with all_103_0, all_105_0, all_72_3,
% 15.37/2.88 | | | | | all_53_0, simplifying with (116), (118) gives:
% 15.37/2.88 | | | | | (119) all_105_0 = all_103_0
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (3) with all_72_3, all_53_0, all_103_0,
% 15.37/2.88 | | | | | simplifying with (98), (105), (116) gives:
% 15.37/2.88 | | | | | (120) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_72_3,
% 15.37/2.88 | | | | | all_53_0) = v0 & less_than(all_72_3, all_53_0) = v1 & ( ~
% 15.37/2.88 | | | | | (v0 = 0) | (v1 = 0 & ~ (all_103_0 = 0))))
% 15.37/2.88 | | | | |
% 15.37/2.88 | | | | | GROUND_INST: instantiating (2) with all_53_0, all_72_3, all_103_0,
% 15.37/2.88 | | | | | simplifying with (98), (105), (116) gives:
% 15.37/2.89 | | | | | (121) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_53_0,
% 15.37/2.89 | | | | | all_72_3) = v0 & less_than(all_72_3, all_53_0) = v1 & ( ~
% 15.37/2.89 | | | | | (v0 = 0) | (all_103_0 = 0 & ~ (v1 = 0))))
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | DELTA: instantiating (121) with fresh symbols all_116_0, all_116_1
% 15.37/2.89 | | | | | gives:
% 15.37/2.89 | | | | | (122) strictly_less_than(all_53_0, all_72_3) = all_116_1 &
% 15.37/2.89 | | | | | less_than(all_72_3, all_53_0) = all_116_0 & ( ~ (all_116_1 =
% 15.37/2.89 | | | | | 0) | (all_103_0 = 0 & ~ (all_116_0 = 0)))
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | ALPHA: (122) implies:
% 15.37/2.89 | | | | | (123) less_than(all_72_3, all_53_0) = all_116_0
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | DELTA: instantiating (120) with fresh symbols all_118_0, all_118_1
% 15.37/2.89 | | | | | gives:
% 15.37/2.89 | | | | | (124) strictly_less_than(all_72_3, all_53_0) = all_118_1 &
% 15.37/2.89 | | | | | less_than(all_72_3, all_53_0) = all_118_0 & ( ~ (all_118_1 =
% 15.37/2.89 | | | | | 0) | (all_118_0 = 0 & ~ (all_103_0 = 0)))
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | ALPHA: (124) implies:
% 15.37/2.89 | | | | | (125) less_than(all_72_3, all_53_0) = all_118_0
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | GROUND_INST: instantiating (16) with all_72_2, all_118_0, all_53_0,
% 15.37/2.89 | | | | | all_72_3, simplifying with (97), (125) gives:
% 15.37/2.89 | | | | | (126) all_118_0 = all_72_2
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | GROUND_INST: instantiating (16) with all_116_0, all_118_0, all_53_0,
% 15.37/2.89 | | | | | all_72_3, simplifying with (123), (125) gives:
% 15.37/2.89 | | | | | (127) all_118_0 = all_116_0
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | COMBINE_EQS: (126), (127) imply:
% 15.37/2.89 | | | | | (128) all_116_0 = all_72_2
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | BETA: splitting (34) gives:
% 15.37/2.89 | | | | |
% 15.37/2.89 | | | | | Case 1:
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | (129) all_46_4 = create_slb
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | REDUCE: (57), (129) imply:
% 15.37/2.89 | | | | | | (130) $false
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | CLOSE: (130) is inconsistent.
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | Case 2:
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | (131) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 15.37/2.89 | | | | | | (findmin_pqp_res(all_46_5) = v0 & triple(all_46_5, v2, bad)
% 15.37/2.89 | | | | | | = v3 & update_slb(all_46_4, v0) = v2 &
% 15.37/2.89 | | | | | | contains_slb(all_46_4, v0) = v1 & $i(v3) & $i(v2) &
% 15.37/2.89 | | | | | | $i(v0) & (v3 = all_46_0 | v1 = 0))
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | DELTA: instantiating (131) with fresh symbols all_131_0, all_131_1,
% 15.37/2.89 | | | | | | all_131_2, all_131_3 gives:
% 15.37/2.89 | | | | | | (132) findmin_pqp_res(all_46_5) = all_131_3 & triple(all_46_5,
% 15.37/2.89 | | | | | | all_131_1, bad) = all_131_0 & update_slb(all_46_4,
% 15.37/2.89 | | | | | | all_131_3) = all_131_1 & contains_slb(all_46_4,
% 15.37/2.89 | | | | | | all_131_3) = all_131_2 & $i(all_131_0) & $i(all_131_1) &
% 15.37/2.89 | | | | | | $i(all_131_3) & (all_131_0 = all_46_0 | all_131_2 = 0)
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | ALPHA: (132) implies:
% 15.37/2.89 | | | | | | (133) contains_slb(all_46_4, all_131_3) = all_131_2
% 15.37/2.89 | | | | | | (134) update_slb(all_46_4, all_131_3) = all_131_1
% 15.37/2.89 | | | | | | (135) triple(all_46_5, all_131_1, bad) = all_131_0
% 15.37/2.89 | | | | | | (136) findmin_pqp_res(all_46_5) = all_131_3
% 15.37/2.89 | | | | | | (137) all_131_0 = all_46_0 | all_131_2 = 0
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | GROUND_INST: instantiating (15) with all_53_0, all_131_3, all_46_5,
% 15.37/2.89 | | | | | | simplifying with (72), (136) gives:
% 15.37/2.89 | | | | | | (138) all_131_3 = all_53_0
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | REDUCE: (134), (138) imply:
% 15.37/2.89 | | | | | | (139) update_slb(all_46_4, all_53_0) = all_131_1
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | REDUCE: (133), (138) imply:
% 15.37/2.89 | | | | | | (140) contains_slb(all_46_4, all_53_0) = all_131_2
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | GROUND_INST: instantiating (17) with all_72_4, all_131_2, all_53_0,
% 15.37/2.89 | | | | | | all_46_4, simplifying with (95), (140) gives:
% 15.37/2.89 | | | | | | (141) all_131_2 = all_72_4
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | GROUND_INST: instantiating (19) with all_72_1, all_131_1, all_53_0,
% 15.37/2.89 | | | | | | all_46_4, simplifying with (91), (139) gives:
% 15.37/2.89 | | | | | | (142) all_131_1 = all_72_1
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | REDUCE: (135), (142) imply:
% 15.37/2.89 | | | | | | (143) triple(all_46_5, all_72_1, bad) = all_131_0
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | GROUND_INST: instantiating (20) with all_72_0, all_131_0, bad,
% 15.37/2.89 | | | | | | all_72_1, all_46_5, simplifying with (68), (143) gives:
% 15.37/2.89 | | | | | | (144) all_131_0 = all_72_0
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | BETA: splitting (67) gives:
% 15.37/2.89 | | | | | |
% 15.37/2.89 | | | | | | Case 1:
% 15.37/2.89 | | | | | | |
% 15.37/2.89 | | | | | | | (145) ~ (all_72_2 = 0)
% 15.37/2.89 | | | | | | |
% 15.37/2.89 | | | | | | | BETA: splitting (107) gives:
% 15.37/2.89 | | | | | | |
% 15.37/2.89 | | | | | | | Case 1:
% 15.37/2.89 | | | | | | | |
% 15.37/2.89 | | | | | | | | (146) less_than(all_53_0, all_72_3) = 0
% 15.37/2.89 | | | | | | | |
% 15.37/2.89 | | | | | | | | BETA: splitting (110) gives:
% 15.37/2.89 | | | | | | | |
% 15.37/2.89 | | | | | | | | Case 1:
% 15.37/2.89 | | | | | | | | |
% 15.37/2.89 | | | | | | | | | (147) all_82_2 = 0
% 15.37/2.89 | | | | | | | | |
% 15.37/2.89 | | | | | | | | | BETA: splitting (85) gives:
% 15.37/2.89 | | | | | | | | |
% 15.37/2.89 | | | | | | | | | Case 1:
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | (148) ~ (all_82_2 = 0)
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | REDUCE: (147), (148) imply:
% 15.37/2.89 | | | | | | | | | | (149) $false
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | CLOSE: (149) is inconsistent.
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | Case 2:
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | (150) ~ (all_82_4 = 0) | all_82_0 = all_46_0
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | BETA: splitting (137) gives:
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | Case 1:
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | (151) all_131_2 = 0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | COMBINE_EQS: (141), (151) imply:
% 15.37/2.89 | | | | | | | | | | | (152) all_72_4 = 0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | SIMP: (152) implies:
% 15.37/2.89 | | | | | | | | | | | (153) all_72_4 = 0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | COMBINE_EQS: (99), (153) imply:
% 15.37/2.89 | | | | | | | | | | | (154) all_82_4 = 0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | BETA: splitting (150) gives:
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | Case 1:
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | (155) ~ (all_82_4 = 0)
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | REDUCE: (154), (155) imply:
% 15.37/2.89 | | | | | | | | | | | | (156) $false
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | Case 2:
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | (157) all_82_0 = all_46_0
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | COMBINE_EQS: (106), (157) imply:
% 15.37/2.89 | | | | | | | | | | | | (158) all_72_0 = all_46_0
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | SIMP: (158) implies:
% 15.37/2.89 | | | | | | | | | | | | (159) all_72_0 = all_46_0
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | REDUCE: (114), (159) imply:
% 15.37/2.89 | | | | | | | | | | | | (160) ok(all_46_0) = all_101_0
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_101_0, all_46_0,
% 15.37/2.89 | | | | | | | | | | | | simplifying with (30), (160) gives:
% 15.37/2.89 | | | | | | | | | | | | (161) all_101_0 = 0
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | REDUCE: (113), (161) imply:
% 15.37/2.89 | | | | | | | | | | | | (162) $false
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 15.37/2.89 | | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | End of split
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | Case 2:
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | (163) all_131_0 = all_46_0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | COMBINE_EQS: (144), (163) imply:
% 15.37/2.89 | | | | | | | | | | | (164) all_72_0 = all_46_0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | REDUCE: (114), (164) imply:
% 15.37/2.89 | | | | | | | | | | | (165) ok(all_46_0) = all_101_0
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | | REF_CLOSE: (14), (30), (113), (165) are inconsistent by
% 15.37/2.89 | | | | | | | | | | | sub-proof #1.
% 15.37/2.89 | | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | | End of split
% 15.37/2.89 | | | | | | | | | |
% 15.37/2.89 | | | | | | | | | End of split
% 15.37/2.89 | | | | | | | | |
% 15.37/2.89 | | | | | | | | Case 2:
% 15.37/2.89 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | (166) ? [v0: any] : ? [v1: any] : (less_than(all_72_3,
% 15.37/2.90 | | | | | | | | | all_53_0) = v1 & less_than(all_53_0, all_72_3) =
% 15.37/2.90 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | DELTA: instantiating (166) with fresh symbols all_174_0,
% 15.37/2.90 | | | | | | | | | all_174_1 gives:
% 15.37/2.90 | | | | | | | | | (167) less_than(all_72_3, all_53_0) = all_174_0 &
% 15.37/2.90 | | | | | | | | | less_than(all_53_0, all_72_3) = all_174_1 & ( ~
% 15.37/2.90 | | | | | | | | | (all_174_1 = 0) | all_174_0 = 0)
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | ALPHA: (167) implies:
% 15.37/2.90 | | | | | | | | | (168) less_than(all_53_0, all_72_3) = all_174_1
% 15.37/2.90 | | | | | | | | | (169) less_than(all_72_3, all_53_0) = all_174_0
% 15.37/2.90 | | | | | | | | | (170) ~ (all_174_1 = 0) | all_174_0 = 0
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_174_1, all_72_3,
% 15.37/2.90 | | | | | | | | | all_53_0, simplifying with (146), (168) gives:
% 15.37/2.90 | | | | | | | | | (171) all_174_1 = 0
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | GROUND_INST: instantiating (16) with all_72_2, all_174_0,
% 15.37/2.90 | | | | | | | | | all_53_0, all_72_3, simplifying with (97), (169)
% 15.37/2.90 | | | | | | | | | gives:
% 15.37/2.90 | | | | | | | | | (172) all_174_0 = all_72_2
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | BETA: splitting (170) gives:
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | Case 1:
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | (173) ~ (all_174_1 = 0)
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | REDUCE: (171), (173) imply:
% 15.37/2.90 | | | | | | | | | | (174) $false
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | CLOSE: (174) is inconsistent.
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | Case 2:
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | (175) all_174_0 = 0
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | COMBINE_EQS: (172), (175) imply:
% 15.37/2.90 | | | | | | | | | | (176) all_72_2 = 0
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | REDUCE: (145), (176) imply:
% 15.37/2.90 | | | | | | | | | | (177) $false
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | | CLOSE: (177) is inconsistent.
% 15.37/2.90 | | | | | | | | | |
% 15.37/2.90 | | | | | | | | | End of split
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | End of split
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | Case 2:
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | (178) all_72_2 = 0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | REDUCE: (145), (178) imply:
% 15.37/2.90 | | | | | | | | (179) $false
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | CLOSE: (179) is inconsistent.
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | End of split
% 15.37/2.90 | | | | | | |
% 15.37/2.90 | | | | | | Case 2:
% 15.37/2.90 | | | | | | |
% 15.37/2.90 | | | | | | | (180) ~ (all_72_4 = 0) | all_72_0 = all_46_0
% 15.37/2.90 | | | | | | |
% 15.37/2.90 | | | | | | | BETA: splitting (137) gives:
% 15.37/2.90 | | | | | | |
% 15.37/2.90 | | | | | | | Case 1:
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | (181) all_131_2 = 0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | COMBINE_EQS: (141), (181) imply:
% 15.37/2.90 | | | | | | | | (182) all_72_4 = 0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | BETA: splitting (180) gives:
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | Case 1:
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | (183) ~ (all_72_4 = 0)
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | REDUCE: (182), (183) imply:
% 15.37/2.90 | | | | | | | | | (184) $false
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | CLOSE: (184) is inconsistent.
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | Case 2:
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | (185) all_72_0 = all_46_0
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | REDUCE: (114), (185) imply:
% 15.37/2.90 | | | | | | | | | (186) ok(all_46_0) = all_101_0
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | | REF_CLOSE: (14), (30), (113), (186) are inconsistent by
% 15.37/2.90 | | | | | | | | | sub-proof #1.
% 15.37/2.90 | | | | | | | | |
% 15.37/2.90 | | | | | | | | End of split
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | Case 2:
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | (187) all_131_0 = all_46_0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | COMBINE_EQS: (144), (187) imply:
% 15.37/2.90 | | | | | | | | (188) all_72_0 = all_46_0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | REDUCE: (114), (188) imply:
% 15.37/2.90 | | | | | | | | (189) ok(all_46_0) = all_101_0
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | | REF_CLOSE: (14), (30), (113), (189) are inconsistent by
% 15.37/2.90 | | | | | | | | sub-proof #1.
% 15.37/2.90 | | | | | | | |
% 15.37/2.90 | | | | | | | End of split
% 15.37/2.90 | | | | | | |
% 15.37/2.90 | | | | | | End of split
% 15.37/2.90 | | | | | |
% 15.37/2.90 | | | | | End of split
% 15.37/2.90 | | | | |
% 15.37/2.90 | | | | End of split
% 15.37/2.90 | | | |
% 15.37/2.90 | | | End of split
% 15.37/2.90 | | |
% 15.37/2.90 | | End of split
% 15.37/2.90 | |
% 15.37/2.90 | End of split
% 15.37/2.90 |
% 15.37/2.90 End of proof
% 15.37/2.90
% 15.37/2.90 Sub-proof #1 shows that the following formulas are inconsistent:
% 15.37/2.90 ----------------------------------------------------------------
% 15.37/2.90 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.37/2.90 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 15.37/2.90 (2) ok(all_46_0) = all_101_0
% 15.37/2.90 (3) ok(all_46_0) = 0
% 15.37/2.90 (4) ~ (all_101_0 = 0)
% 15.37/2.90
% 15.37/2.90 Begin of proof
% 15.37/2.90 |
% 15.37/2.90 | GROUND_INST: instantiating (1) with 0, all_101_0, all_46_0, simplifying with
% 15.37/2.90 | (2), (3) gives:
% 15.37/2.90 | (5) all_101_0 = 0
% 15.37/2.90 |
% 15.37/2.90 | REDUCE: (4), (5) imply:
% 15.37/2.90 | (6) $false
% 15.37/2.90 |
% 15.37/2.90 | CLOSE: (6) is inconsistent.
% 15.37/2.90 |
% 15.37/2.90 End of proof
% 15.37/2.90 % SZS output end Proof for theBenchmark
% 15.37/2.90
% 15.37/2.90 2284ms
%------------------------------------------------------------------------------