TSTP Solution File: SWV373+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV373+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 : n031.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 22:56:04 EDT 2023
% Result : Theorem 10.24s 2.13s
% Output : Proof 13.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV373+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 07:13:11 EDT 2023
% 0.14/0.35 % 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 3.19/1.18 Prover 1: Preprocessing ...
% 3.41/1.19 Prover 4: Preprocessing ...
% 3.71/1.23 Prover 5: Preprocessing ...
% 3.71/1.23 Prover 2: Preprocessing ...
% 3.71/1.23 Prover 0: Preprocessing ...
% 3.71/1.23 Prover 3: Preprocessing ...
% 3.71/1.24 Prover 6: Preprocessing ...
% 7.53/1.77 Prover 1: Warning: ignoring some quantifiers
% 7.89/1.84 Prover 3: Warning: ignoring some quantifiers
% 8.29/1.86 Prover 1: Constructing countermodel ...
% 8.29/1.87 Prover 3: Constructing countermodel ...
% 8.29/1.88 Prover 6: Proving ...
% 8.29/1.89 Prover 4: Constructing countermodel ...
% 8.29/1.94 Prover 5: Proving ...
% 9.36/2.00 Prover 0: Proving ...
% 9.36/2.10 Prover 2: Proving ...
% 10.24/2.13 Prover 0: proved (1490ms)
% 10.24/2.13
% 10.24/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.24/2.13
% 10.24/2.13 Prover 2: stopped
% 10.24/2.13 Prover 6: stopped
% 10.24/2.13 Prover 3: stopped
% 10.24/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.24/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.24/2.13 Prover 5: stopped
% 10.24/2.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.24/2.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.24/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.24/2.18 Prover 10: Preprocessing ...
% 10.24/2.19 Prover 13: Preprocessing ...
% 10.24/2.19 Prover 11: Preprocessing ...
% 10.24/2.19 Prover 7: Preprocessing ...
% 10.24/2.20 Prover 8: Preprocessing ...
% 11.37/2.32 Prover 4: Found proof (size 83)
% 11.37/2.32 Prover 4: proved (1677ms)
% 11.37/2.32 Prover 1: stopped
% 11.91/2.35 Prover 7: Warning: ignoring some quantifiers
% 11.91/2.37 Prover 10: Warning: ignoring some quantifiers
% 12.07/2.37 Prover 7: Constructing countermodel ...
% 12.07/2.39 Prover 10: Constructing countermodel ...
% 12.07/2.39 Prover 7: stopped
% 12.07/2.40 Prover 10: stopped
% 12.07/2.40 Prover 8: Warning: ignoring some quantifiers
% 12.40/2.42 Prover 8: Constructing countermodel ...
% 12.40/2.44 Prover 8: stopped
% 12.57/2.45 Prover 11: Constructing countermodel ...
% 12.57/2.45 Prover 13: Warning: ignoring some quantifiers
% 12.57/2.47 Prover 11: stopped
% 12.57/2.47 Prover 13: Constructing countermodel ...
% 12.57/2.48 Prover 13: stopped
% 12.57/2.48
% 12.57/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.57/2.49
% 12.57/2.50 % SZS output start Proof for theBenchmark
% 12.57/2.50 Assumptions after simplification:
% 12.57/2.50 ---------------------------------
% 12.57/2.50
% 12.57/2.50 (ax39)
% 12.96/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.96/2.53 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) =
% 12.96/2.53 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 12.96/2.53 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : !
% 12.96/2.53 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~
% 12.96/2.53 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.96/2.53 contains_slb(v1, v3) = 0)
% 12.96/2.53
% 12.96/2.53 (ax47)
% 12.96/2.53 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.96/2.53 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 12.96/2.53 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 12.96/2.53 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 &
% 12.96/2.53 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5)
% 12.96/2.53 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0)))
% 12.96/2.53
% 12.96/2.54 (ax48)
% 12.96/2.54 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.96/2.54 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 12.96/2.54 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 12.96/2.54 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 12.96/2.54 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) =
% 12.96/2.54 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 &
% 12.96/2.54 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~
% 12.96/2.54 (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 12.96/2.54
% 12.96/2.54 (ax49)
% 12.96/2.54 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 12.96/2.54 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~
% 12.96/2.54 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~
% 12.96/2.54 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i]
% 12.96/2.54 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 &
% 12.96/2.54 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) =
% 12.96/2.54 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5)))
% 12.96/2.54 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 12.96/2.54 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) |
% 12.96/2.54 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i]
% 12.96/2.54 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 &
% 12.96/2.54 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) =
% 12.96/2.54 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9)
% 12.96/2.54 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 12.96/2.54
% 12.96/2.54 (ax51)
% 12.96/2.55 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 12.96/2.55 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0,
% 12.96/2.55 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0)
% 12.96/2.55 = v4 & $i(v4)))
% 12.96/2.55
% 12.96/2.55 (ax52)
% 12.96/2.55 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ?
% 12.96/2.55 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) =
% 12.96/2.55 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1:
% 12.96/2.55 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 12.96/2.55 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 &
% 12.96/2.55 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 12.96/2.55 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 12.96/2.55 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 &
% 12.96/2.55 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2)))
% 12.96/2.55
% 12.96/2.55 (l9_co)
% 12.96/2.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 12.96/2.55 int] : ? [v6: $i] : ( ~ (v5 = 0) & findmin_cpq_res(v3) = v4 & ok(v6) = 0 &
% 12.96/2.55 contains_cpq(v3, v4) = v5 & triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) =
% 12.96/2.55 v6 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.96/2.55
% 12.96/2.55 (l9_l10)
% 12.96/2.55 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.96/2.55 (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i]
% 12.96/2.55 : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 12.96/2.55 (findmin_pqp_res(v0) = v6 & ok(v4) = v5 & findmin_cpq_eff(v3) = v4 &
% 12.96/2.55 lookup_slb(v1, v6) = v8 & contains_slb(v1, v6) = v7 & less_than(v8, v6) =
% 12.96/2.55 v9 & $i(v8) & $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & ~ (v1 =
% 12.96/2.55 create_slb)))))
% 12.96/2.55
% 12.96/2.55 (function-axioms)
% 12.96/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 12.96/2.56 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.96/2.56 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 12.96/2.56 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.96/2.56 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 12.96/2.56 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 12.96/2.56 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.96/2.56 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.96/2.56 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 12.96/2.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 12.96/2.56 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.96/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 12.96/2.56 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.96/2.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 12.96/2.56 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 12.96/2.56 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 12.96/2.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 12.96/2.56 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.96/2.56 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.96/2.56 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 12.96/2.56 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 12.96/2.56 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.96/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.96/2.56 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 12.96/2.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.96/2.56 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.96/2.56 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 12.96/2.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 12.96/2.56 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.96/2.56 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 12.96/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 12.96/2.56 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.96/2.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 12.96/2.56 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 12.96/2.56 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 12.96/2.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 12.96/2.56 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.96/2.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 12.96/2.56 v1) | ~ (isnonempty_slb(v2) = v0))
% 12.96/2.56
% 12.96/2.56 Further assumptions not needed in the proof:
% 12.96/2.56 --------------------------------------------
% 12.96/2.56 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 12.96/2.56 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40, ax41, ax42, ax43, ax44,
% 12.96/2.56 ax45, ax46, ax50, ax53, bottom_smallest, reflexivity,
% 12.96/2.56 stricly_smaller_definition, totality, transitivity
% 12.96/2.56
% 12.96/2.56 Those formulas are unsatisfiable:
% 12.96/2.56 ---------------------------------
% 12.96/2.56
% 12.96/2.56 Begin of proof
% 12.96/2.56 |
% 12.96/2.56 | ALPHA: (ax39) implies:
% 12.96/2.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.96/2.56 | ! [v5: int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0,
% 12.96/2.56 | v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.96/2.56 | ? [v6: int] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))
% 12.96/2.56 |
% 12.96/2.56 | ALPHA: (ax47) implies:
% 12.96/2.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.96/2.56 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 12.96/2.56 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.96/2.56 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 12.96/2.56 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1,
% 12.96/2.56 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) &
% 12.96/2.56 | (v8 = v4 | v6 = 0)))
% 12.96/2.56 |
% 12.96/2.56 | ALPHA: (ax48) implies:
% 12.96/2.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.96/2.57 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 12.96/2.57 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.96/2.57 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] :
% 12.96/2.57 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 &
% 12.96/2.57 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 12.96/2.57 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 &
% 12.96/2.57 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) |
% 12.96/2.57 | v10 = v4)))
% 12.96/2.57 |
% 12.96/2.57 | ALPHA: (ax49) implies:
% 12.96/2.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.96/2.57 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 12.96/2.57 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.96/2.57 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] :
% 12.96/2.57 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 &
% 12.96/2.57 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 12.96/2.57 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) &
% 12.96/2.57 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 12.96/2.57 |
% 12.96/2.57 | ALPHA: (ax51) implies:
% 12.96/2.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 12.96/2.57 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1,
% 12.96/2.57 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.96/2.57 | (findmin_pqp_res(v0) = v4 & $i(v4)))
% 12.96/2.57 |
% 12.96/2.57 | ALPHA: (ax52) implies:
% 12.96/2.57 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0)
% 12.96/2.57 | | ? [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 &
% 12.96/2.57 | findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2 & $i(v3) &
% 12.96/2.57 | $i(v2)))
% 12.96/2.57 |
% 12.96/2.57 | ALPHA: (l9_l10) implies:
% 12.96/2.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0,
% 12.96/2.57 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 12.96/2.57 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 12.96/2.57 | any] : (findmin_pqp_res(v0) = v6 & ok(v4) = v5 &
% 12.96/2.57 | findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v6) = v8 &
% 12.96/2.57 | contains_slb(v1, v6) = v7 & less_than(v8, v6) = v9 & $i(v8) &
% 12.96/2.57 | $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & ~ (v1 =
% 12.96/2.57 | create_slb)))))
% 12.96/2.57 |
% 12.96/2.57 | ALPHA: (function-axioms) implies:
% 12.96/2.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.96/2.57 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 12.96/2.57 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.96/2.57 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 13.21/2.57 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.21/2.57 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0))
% 13.21/2.57 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 13.21/2.57 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 13.21/2.57 | (contains_slb(v3, v2) = v0))
% 13.21/2.57 |
% 13.21/2.57 | DELTA: instantiating (l9_co) with fresh symbols all_47_0, all_47_1, all_47_2,
% 13.21/2.57 | all_47_3, all_47_4, all_47_5, all_47_6 gives:
% 13.21/2.57 | (12) ~ (all_47_1 = 0) & findmin_cpq_res(all_47_3) = all_47_2 &
% 13.21/2.58 | ok(all_47_0) = 0 & contains_cpq(all_47_3, all_47_2) = all_47_1 &
% 13.21/2.58 | triple(all_47_6, all_47_5, all_47_4) = all_47_3 &
% 13.21/2.58 | findmin_cpq_eff(all_47_3) = all_47_0 & $i(all_47_0) & $i(all_47_2) &
% 13.21/2.58 | $i(all_47_3) & $i(all_47_4) & $i(all_47_5) & $i(all_47_6)
% 13.21/2.58 |
% 13.21/2.58 | ALPHA: (12) implies:
% 13.21/2.58 | (13) ~ (all_47_1 = 0)
% 13.21/2.58 | (14) $i(all_47_6)
% 13.21/2.58 | (15) $i(all_47_5)
% 13.21/2.58 | (16) $i(all_47_4)
% 13.21/2.58 | (17) $i(all_47_3)
% 13.21/2.58 | (18) $i(all_47_2)
% 13.21/2.58 | (19) findmin_cpq_eff(all_47_3) = all_47_0
% 13.21/2.58 | (20) triple(all_47_6, all_47_5, all_47_4) = all_47_3
% 13.21/2.58 | (21) contains_cpq(all_47_3, all_47_2) = all_47_1
% 13.21/2.58 | (22) ok(all_47_0) = 0
% 13.21/2.58 | (23) findmin_cpq_res(all_47_3) = all_47_2
% 13.21/2.58 |
% 13.21/2.58 | GROUND_INST: instantiating (4) with all_47_6, all_47_5, all_47_4, all_47_3,
% 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives:
% 13.21/2.58 | (24) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 13.21/2.58 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) =
% 13.21/2.58 | v0 & triple(all_47_6, v4, all_47_4) = v5 & update_slb(all_47_5, v0)
% 13.21/2.58 | = v4 & lookup_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) =
% 13.21/2.58 | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & (
% 13.21/2.58 | ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_47_0))
% 13.21/2.58 |
% 13.21/2.58 | GROUND_INST: instantiating (3) with all_47_6, all_47_5, all_47_4, all_47_3,
% 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives:
% 13.21/2.58 | (25) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 13.21/2.58 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) =
% 13.21/2.58 | v0 & triple(all_47_6, v4, bad) = v5 & update_slb(all_47_5, v0) = v4
% 13.21/2.58 | & lookup_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) = v1 &
% 13.21/2.58 | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0)
% 13.21/2.58 | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_47_0))
% 13.21/2.58 |
% 13.21/2.58 | GROUND_INST: instantiating (2) with all_47_6, all_47_5, all_47_4, all_47_3,
% 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives:
% 13.21/2.58 | (26) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ?
% 13.21/2.58 | [v3: $i] : (findmin_pqp_res(all_47_6) = v0 & triple(all_47_6, v2, bad)
% 13.21/2.58 | = v3 & update_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) =
% 13.21/2.58 | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_47_0 | v1 = 0))
% 13.21/2.58 |
% 13.21/2.58 | GROUND_INST: instantiating (7) with all_47_6, all_47_5, all_47_4, all_47_3,
% 13.21/2.58 | simplifying with (14), (15), (16), (20) gives:
% 13.21/2.58 | (27) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 13.21/2.58 | : ? [v5: any] : (findmin_pqp_res(all_47_6) = v2 & ok(v0) = v1 &
% 13.21/2.58 | findmin_cpq_eff(all_47_3) = v0 & lookup_slb(all_47_5, v2) = v4 &
% 13.21/2.58 | contains_slb(all_47_5, v2) = v3 & less_than(v4, v2) = v5 & $i(v4) &
% 13.21/2.58 | $i(v2) & $i(v0) & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & ~ (all_47_5 =
% 13.21/2.58 | create_slb))))
% 13.21/2.58 |
% 13.21/2.59 | GROUND_INST: instantiating (1) with all_47_6, all_47_5, all_47_4, all_47_2,
% 13.21/2.59 | all_47_3, all_47_1, simplifying with (14), (15), (16), (18),
% 13.21/2.59 | (20), (21) gives:
% 13.21/2.59 | (28) all_47_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_47_5,
% 13.21/2.59 | all_47_2) = v0)
% 13.21/2.59 |
% 13.21/2.59 | GROUND_INST: instantiating (5) with all_47_6, all_47_5, all_47_4, all_47_3,
% 13.21/2.59 | all_47_2, simplifying with (14), (15), (16), (20), (23) gives:
% 13.21/2.59 | (29) all_47_5 = create_slb | (findmin_pqp_res(all_47_6) = all_47_2 &
% 13.21/2.59 | $i(all_47_2))
% 13.21/2.59 |
% 13.21/2.59 | GROUND_INST: instantiating (6) with all_47_3, all_47_2, simplifying with (17),
% 13.21/2.59 | (23) gives:
% 13.21/2.59 | (30) ? [v0: $i] : ? [v1: $i] : (removemin_cpq_eff(all_47_3) = v0 &
% 13.21/2.59 | findmin_cpq_eff(all_47_3) = v1 & remove_cpq(v1, all_47_2) = v0 &
% 13.21/2.59 | $i(v1) & $i(v0))
% 13.21/2.59 |
% 13.21/2.59 | DELTA: instantiating (30) with fresh symbols all_57_0, all_57_1 gives:
% 13.21/2.59 | (31) removemin_cpq_eff(all_47_3) = all_57_1 & findmin_cpq_eff(all_47_3) =
% 13.21/2.59 | all_57_0 & remove_cpq(all_57_0, all_47_2) = all_57_1 & $i(all_57_0) &
% 13.21/2.59 | $i(all_57_1)
% 13.21/2.59 |
% 13.21/2.59 | ALPHA: (31) implies:
% 13.21/2.59 | (32) findmin_cpq_eff(all_47_3) = all_57_0
% 13.21/2.59 |
% 13.21/2.59 | DELTA: instantiating (27) with fresh symbols all_59_0, all_59_1, all_59_2,
% 13.21/2.59 | all_59_3, all_59_4, all_59_5 gives:
% 13.21/2.59 | (33) findmin_pqp_res(all_47_6) = all_59_3 & ok(all_59_5) = all_59_4 &
% 13.21/2.59 | findmin_cpq_eff(all_47_3) = all_59_5 & lookup_slb(all_47_5, all_59_3)
% 13.21/2.59 | = all_59_1 & contains_slb(all_47_5, all_59_3) = all_59_2 &
% 13.21/2.59 | less_than(all_59_1, all_59_3) = all_59_0 & $i(all_59_1) & $i(all_59_3)
% 13.21/2.59 | & $i(all_59_5) & ( ~ (all_59_4 = 0) | (all_59_0 = 0 & all_59_2 = 0 &
% 13.21/2.59 | ~ (all_47_5 = create_slb)))
% 13.21/2.59 |
% 13.21/2.59 | ALPHA: (33) implies:
% 13.21/2.59 | (34) contains_slb(all_47_5, all_59_3) = all_59_2
% 13.21/2.59 | (35) findmin_cpq_eff(all_47_3) = all_59_5
% 13.21/2.59 | (36) ok(all_59_5) = all_59_4
% 13.21/2.59 | (37) findmin_pqp_res(all_47_6) = all_59_3
% 13.21/2.59 | (38) ~ (all_59_4 = 0) | (all_59_0 = 0 & all_59_2 = 0 & ~ (all_47_5 =
% 13.21/2.59 | create_slb))
% 13.21/2.59 |
% 13.21/2.59 | BETA: splitting (28) gives:
% 13.21/2.59 |
% 13.21/2.59 | Case 1:
% 13.21/2.59 | |
% 13.21/2.59 | | (39) all_47_1 = 0
% 13.21/2.59 | |
% 13.21/2.59 | | REDUCE: (13), (39) imply:
% 13.21/2.59 | | (40) $false
% 13.21/2.59 | |
% 13.21/2.59 | | CLOSE: (40) is inconsistent.
% 13.21/2.59 | |
% 13.21/2.59 | Case 2:
% 13.21/2.59 | |
% 13.21/2.59 | | (41) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_47_5, all_47_2) = v0)
% 13.21/2.59 | |
% 13.21/2.59 | | DELTA: instantiating (41) with fresh symbol all_65_0 gives:
% 13.21/2.59 | | (42) ~ (all_65_0 = 0) & contains_slb(all_47_5, all_47_2) = all_65_0
% 13.21/2.59 | |
% 13.21/2.59 | | ALPHA: (42) implies:
% 13.21/2.59 | | (43) ~ (all_65_0 = 0)
% 13.21/2.59 | | (44) contains_slb(all_47_5, all_47_2) = all_65_0
% 13.21/2.59 | |
% 13.21/2.59 | | GROUND_INST: instantiating (8) with all_47_0, all_59_5, all_47_3,
% 13.21/2.59 | | simplifying with (19), (35) gives:
% 13.21/2.59 | | (45) all_59_5 = all_47_0
% 13.21/2.59 | |
% 13.21/2.59 | | GROUND_INST: instantiating (8) with all_57_0, all_59_5, all_47_3,
% 13.21/2.59 | | simplifying with (32), (35) gives:
% 13.21/2.59 | | (46) all_59_5 = all_57_0
% 13.21/2.59 | |
% 13.21/2.59 | | COMBINE_EQS: (45), (46) imply:
% 13.21/2.60 | | (47) all_57_0 = all_47_0
% 13.21/2.60 | |
% 13.21/2.60 | | REDUCE: (36), (45) imply:
% 13.21/2.60 | | (48) ok(all_47_0) = all_59_4
% 13.21/2.60 | |
% 13.21/2.60 | | GROUND_INST: instantiating (9) with 0, all_59_4, all_47_0, simplifying with
% 13.21/2.60 | | (22), (48) gives:
% 13.21/2.60 | | (49) all_59_4 = 0
% 13.21/2.60 | |
% 13.21/2.60 | | BETA: splitting (38) gives:
% 13.21/2.60 | |
% 13.21/2.60 | | Case 1:
% 13.21/2.60 | | |
% 13.21/2.60 | | | (50) ~ (all_59_4 = 0)
% 13.21/2.60 | | |
% 13.21/2.60 | | | REDUCE: (49), (50) imply:
% 13.21/2.60 | | | (51) $false
% 13.21/2.60 | | |
% 13.21/2.60 | | | CLOSE: (51) is inconsistent.
% 13.21/2.60 | | |
% 13.21/2.60 | | Case 2:
% 13.21/2.60 | | |
% 13.21/2.60 | | | (52) all_59_0 = 0 & all_59_2 = 0 & ~ (all_47_5 = create_slb)
% 13.21/2.60 | | |
% 13.21/2.60 | | | ALPHA: (52) implies:
% 13.21/2.60 | | | (53) all_59_2 = 0
% 13.21/2.60 | | | (54) ~ (all_47_5 = create_slb)
% 13.21/2.60 | | |
% 13.21/2.60 | | | REDUCE: (34), (53) imply:
% 13.21/2.60 | | | (55) contains_slb(all_47_5, all_59_3) = 0
% 13.21/2.60 | | |
% 13.21/2.60 | | | BETA: splitting (29) gives:
% 13.21/2.60 | | |
% 13.21/2.60 | | | Case 1:
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | (56) all_47_5 = create_slb
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | REDUCE: (54), (56) imply:
% 13.21/2.60 | | | | (57) $false
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | CLOSE: (57) is inconsistent.
% 13.21/2.60 | | | |
% 13.21/2.60 | | | Case 2:
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | (58) findmin_pqp_res(all_47_6) = all_47_2 & $i(all_47_2)
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | ALPHA: (58) implies:
% 13.21/2.60 | | | | (59) findmin_pqp_res(all_47_6) = all_47_2
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | BETA: splitting (26) gives:
% 13.21/2.60 | | | |
% 13.21/2.60 | | | | Case 1:
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | (60) all_47_5 = create_slb
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | REDUCE: (54), (60) imply:
% 13.21/2.60 | | | | | (61) $false
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | CLOSE: (61) is inconsistent.
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | Case 2:
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | (62) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 13.21/2.60 | | | | | (findmin_pqp_res(all_47_6) = v0 & triple(all_47_6, v2, bad) =
% 13.21/2.60 | | | | | v3 & update_slb(all_47_5, v0) = v2 & contains_slb(all_47_5,
% 13.21/2.60 | | | | | v0) = v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_47_0 | v1
% 13.21/2.60 | | | | | = 0))
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | DELTA: instantiating (62) with fresh symbols all_86_0, all_86_1,
% 13.21/2.60 | | | | | all_86_2, all_86_3 gives:
% 13.21/2.60 | | | | | (63) findmin_pqp_res(all_47_6) = all_86_3 & triple(all_47_6,
% 13.21/2.60 | | | | | all_86_1, bad) = all_86_0 & update_slb(all_47_5, all_86_3) =
% 13.21/2.60 | | | | | all_86_1 & contains_slb(all_47_5, all_86_3) = all_86_2 &
% 13.21/2.60 | | | | | $i(all_86_0) & $i(all_86_1) & $i(all_86_3) & (all_86_0 =
% 13.21/2.60 | | | | | all_47_0 | all_86_2 = 0)
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | ALPHA: (63) implies:
% 13.21/2.60 | | | | | (64) contains_slb(all_47_5, all_86_3) = all_86_2
% 13.21/2.60 | | | | | (65) findmin_pqp_res(all_47_6) = all_86_3
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | BETA: splitting (25) gives:
% 13.21/2.60 | | | | |
% 13.21/2.60 | | | | | Case 1:
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | (66) all_47_5 = create_slb
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | REDUCE: (54), (66) imply:
% 13.21/2.60 | | | | | | (67) $false
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | CLOSE: (67) is inconsistent.
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | Case 2:
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | (68) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ?
% 13.21/2.60 | | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = v0 &
% 13.21/2.60 | | | | | | triple(all_47_6, v4, bad) = v5 & update_slb(all_47_5, v0)
% 13.21/2.60 | | | | | | = v4 & lookup_slb(all_47_5, v0) = v2 &
% 13.21/2.60 | | | | | | contains_slb(all_47_5, v0) = v1 & strictly_less_than(v0,
% 13.21/2.60 | | | | | | v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 =
% 13.21/2.60 | | | | | | 0) | ~ (v1 = 0) | v5 = all_47_0))
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | DELTA: instantiating (68) with fresh symbols all_91_0, all_91_1,
% 13.21/2.60 | | | | | | all_91_2, all_91_3, all_91_4, all_91_5 gives:
% 13.21/2.60 | | | | | | (69) findmin_pqp_res(all_47_6) = all_91_5 & triple(all_47_6,
% 13.21/2.60 | | | | | | all_91_1, bad) = all_91_0 & update_slb(all_47_5, all_91_5)
% 13.21/2.60 | | | | | | = all_91_1 & lookup_slb(all_47_5, all_91_5) = all_91_3 &
% 13.21/2.60 | | | | | | contains_slb(all_47_5, all_91_5) = all_91_4 &
% 13.21/2.60 | | | | | | strictly_less_than(all_91_5, all_91_3) = all_91_2 &
% 13.21/2.60 | | | | | | $i(all_91_0) & $i(all_91_1) & $i(all_91_3) & $i(all_91_5) &
% 13.21/2.60 | | | | | | ( ~ (all_91_2 = 0) | ~ (all_91_4 = 0) | all_91_0 =
% 13.21/2.60 | | | | | | all_47_0)
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | ALPHA: (69) implies:
% 13.21/2.60 | | | | | | (70) contains_slb(all_47_5, all_91_5) = all_91_4
% 13.21/2.60 | | | | | | (71) findmin_pqp_res(all_47_6) = all_91_5
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | BETA: splitting (24) gives:
% 13.21/2.60 | | | | | |
% 13.21/2.60 | | | | | | Case 1:
% 13.21/2.60 | | | | | | |
% 13.21/2.60 | | | | | | | (72) all_47_5 = create_slb
% 13.21/2.60 | | | | | | |
% 13.21/2.60 | | | | | | | REDUCE: (54), (72) imply:
% 13.21/2.60 | | | | | | | (73) $false
% 13.21/2.60 | | | | | | |
% 13.21/2.60 | | | | | | | CLOSE: (73) is inconsistent.
% 13.21/2.60 | | | | | | |
% 13.21/2.60 | | | | | | Case 2:
% 13.21/2.60 | | | | | | |
% 13.21/2.61 | | | | | | | (74) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 13.21/2.61 | | | | | | | ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = v0
% 13.21/2.61 | | | | | | | & triple(all_47_6, v4, all_47_4) = v5 &
% 13.21/2.61 | | | | | | | update_slb(all_47_5, v0) = v4 & lookup_slb(all_47_5, v0)
% 13.21/2.61 | | | | | | | = v2 & contains_slb(all_47_5, v0) = v1 & less_than(v2,
% 13.21/2.61 | | | | | | | v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3
% 13.21/2.61 | | | | | | | = 0) | ~ (v1 = 0) | v5 = all_47_0))
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | DELTA: instantiating (74) with fresh symbols all_97_0, all_97_1,
% 13.21/2.61 | | | | | | | all_97_2, all_97_3, all_97_4, all_97_5 gives:
% 13.21/2.61 | | | | | | | (75) findmin_pqp_res(all_47_6) = all_97_5 & triple(all_47_6,
% 13.21/2.61 | | | | | | | all_97_1, all_47_4) = all_97_0 & update_slb(all_47_5,
% 13.21/2.61 | | | | | | | all_97_5) = all_97_1 & lookup_slb(all_47_5, all_97_5) =
% 13.21/2.61 | | | | | | | all_97_3 & contains_slb(all_47_5, all_97_5) = all_97_4 &
% 13.21/2.61 | | | | | | | less_than(all_97_3, all_97_5) = all_97_2 & $i(all_97_0) &
% 13.21/2.61 | | | | | | | $i(all_97_1) & $i(all_97_3) & $i(all_97_5) & ( ~ (all_97_2
% 13.21/2.61 | | | | | | | = 0) | ~ (all_97_4 = 0) | all_97_0 = all_47_0)
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | ALPHA: (75) implies:
% 13.21/2.61 | | | | | | | (76) contains_slb(all_47_5, all_97_5) = all_97_4
% 13.21/2.61 | | | | | | | (77) findmin_pqp_res(all_47_6) = all_97_5
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_59_3, all_91_5, all_47_6,
% 13.21/2.61 | | | | | | | simplifying with (37), (71) gives:
% 13.21/2.61 | | | | | | | (78) all_91_5 = all_59_3
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_86_3, all_91_5, all_47_6,
% 13.21/2.61 | | | | | | | simplifying with (65), (71) gives:
% 13.21/2.61 | | | | | | | (79) all_91_5 = all_86_3
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_91_5, all_97_5, all_47_6,
% 13.21/2.61 | | | | | | | simplifying with (71), (77) gives:
% 13.21/2.61 | | | | | | | (80) all_97_5 = all_91_5
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_47_2, all_97_5, all_47_6,
% 13.21/2.61 | | | | | | | simplifying with (59), (77) gives:
% 13.21/2.61 | | | | | | | (81) all_97_5 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (80), (81) imply:
% 13.21/2.61 | | | | | | | (82) all_91_5 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | SIMP: (82) implies:
% 13.21/2.61 | | | | | | | (83) all_91_5 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (78), (79) imply:
% 13.21/2.61 | | | | | | | (84) all_86_3 = all_59_3
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (79), (83) imply:
% 13.21/2.61 | | | | | | | (85) all_86_3 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (84), (85) imply:
% 13.21/2.61 | | | | | | | (86) all_59_3 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | SIMP: (86) implies:
% 13.21/2.61 | | | | | | | (87) all_59_3 = all_47_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | REDUCE: (76), (81) imply:
% 13.21/2.61 | | | | | | | (88) contains_slb(all_47_5, all_47_2) = all_97_4
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | REDUCE: (70), (83) imply:
% 13.21/2.61 | | | | | | | (89) contains_slb(all_47_5, all_47_2) = all_91_4
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | REDUCE: (64), (85) imply:
% 13.21/2.61 | | | | | | | (90) contains_slb(all_47_5, all_47_2) = all_86_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | REDUCE: (55), (87) imply:
% 13.21/2.61 | | | | | | | (91) contains_slb(all_47_5, all_47_2) = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_65_0, all_86_2, all_47_2,
% 13.21/2.61 | | | | | | | all_47_5, simplifying with (44), (90) gives:
% 13.21/2.61 | | | | | | | (92) all_86_2 = all_65_0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_86_2, all_91_4, all_47_2,
% 13.21/2.61 | | | | | | | all_47_5, simplifying with (89), (90) gives:
% 13.21/2.61 | | | | | | | (93) all_91_4 = all_86_2
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_91_4, all_97_4, all_47_2,
% 13.21/2.61 | | | | | | | all_47_5, simplifying with (88), (89) gives:
% 13.21/2.61 | | | | | | | (94) all_97_4 = all_91_4
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with 0, all_97_4, all_47_2,
% 13.21/2.61 | | | | | | | all_47_5, simplifying with (88), (91) gives:
% 13.21/2.61 | | | | | | | (95) all_97_4 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (94), (95) imply:
% 13.21/2.61 | | | | | | | (96) all_91_4 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | SIMP: (96) implies:
% 13.21/2.61 | | | | | | | (97) all_91_4 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (93), (97) imply:
% 13.21/2.61 | | | | | | | (98) all_86_2 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | SIMP: (98) implies:
% 13.21/2.61 | | | | | | | (99) all_86_2 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | COMBINE_EQS: (92), (99) imply:
% 13.21/2.61 | | | | | | | (100) all_65_0 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | SIMP: (100) implies:
% 13.21/2.61 | | | | | | | (101) all_65_0 = 0
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | REDUCE: (43), (101) imply:
% 13.21/2.61 | | | | | | | (102) $false
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | | CLOSE: (102) is inconsistent.
% 13.21/2.61 | | | | | | |
% 13.21/2.61 | | | | | | End of split
% 13.21/2.61 | | | | | |
% 13.21/2.61 | | | | | End of split
% 13.21/2.61 | | | | |
% 13.21/2.61 | | | | End of split
% 13.21/2.61 | | | |
% 13.21/2.61 | | | End of split
% 13.21/2.61 | | |
% 13.21/2.61 | | End of split
% 13.21/2.61 | |
% 13.21/2.61 | End of split
% 13.21/2.61 |
% 13.21/2.61 End of proof
% 13.21/2.61 % SZS output end Proof for theBenchmark
% 13.21/2.61
% 13.21/2.61 1994ms
%------------------------------------------------------------------------------