TSTP Solution File: SWV396+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV396+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 : n023.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 22:56:09 EDT 2023
% Result : Theorem 26.42s 4.21s
% Output : Proof 27.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV396+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 08:07:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.49/0.60 ________ _____
% 0.49/0.60 ___ __ \_________(_)________________________________
% 0.49/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.49/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.49/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.49/0.60
% 0.49/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.49/0.60 (2023-06-19)
% 0.49/0.60
% 0.49/0.60 (c) Philipp Rümmer, 2009-2023
% 0.49/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.49/0.60 Amanda Stjerna.
% 0.49/0.60 Free software under BSD-3-Clause.
% 0.49/0.60
% 0.49/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.49/0.60
% 0.49/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.49/0.61 Running up to 7 provers in parallel.
% 0.49/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.49/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.49/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.49/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.49/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.49/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.49/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.55/1.16 Prover 1: Preprocessing ...
% 3.55/1.16 Prover 4: Preprocessing ...
% 3.55/1.20 Prover 6: Preprocessing ...
% 3.55/1.20 Prover 0: Preprocessing ...
% 3.55/1.20 Prover 5: Preprocessing ...
% 3.55/1.20 Prover 2: Preprocessing ...
% 3.55/1.20 Prover 3: Preprocessing ...
% 8.74/1.87 Prover 1: Warning: ignoring some quantifiers
% 8.74/1.90 Prover 6: Proving ...
% 8.74/1.92 Prover 5: Proving ...
% 9.08/1.93 Prover 3: Warning: ignoring some quantifiers
% 9.28/1.94 Prover 1: Constructing countermodel ...
% 9.28/1.95 Prover 3: Constructing countermodel ...
% 9.28/1.98 Prover 4: Constructing countermodel ...
% 9.28/2.02 Prover 0: Proving ...
% 9.81/2.04 Prover 2: Proving ...
% 17.82/3.07 Prover 3: gave up
% 17.89/3.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.29/3.15 Prover 7: Preprocessing ...
% 18.98/3.28 Prover 7: Warning: ignoring some quantifiers
% 19.49/3.32 Prover 7: Constructing countermodel ...
% 24.99/4.03 Prover 7: gave up
% 24.99/4.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.50/4.10 Prover 8: Preprocessing ...
% 25.50/4.14 Prover 4: Found proof (size 519)
% 25.50/4.14 Prover 4: proved (3514ms)
% 25.50/4.14 Prover 5: stopped
% 25.50/4.14 Prover 6: stopped
% 25.50/4.14 Prover 0: stopped
% 25.50/4.14 Prover 2: stopped
% 25.50/4.14 Prover 1: stopped
% 26.19/4.20 Prover 8: Warning: ignoring some quantifiers
% 26.42/4.21 Prover 8: Constructing countermodel ...
% 26.42/4.21 Prover 8: stopped
% 26.42/4.21
% 26.42/4.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.42/4.21
% 26.80/4.33 % SZS output start Proof for theBenchmark
% 26.80/4.34 Assumptions after simplification:
% 26.80/4.34 ---------------------------------
% 26.80/4.34
% 26.80/4.34 (ax21)
% 27.03/4.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.36 $i] : ! [v6: int] : (v6 = 0 | ~ (contains_slb(v5, v2) = v6) | ~ (pair(v1,
% 27.03/4.36 v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 27.03/4.36 $i(v1) | ~ $i(v0) | ? [v7: int] : ( ~ (v7 = 0) & contains_slb(v0, v2) =
% 27.03/4.36 v7)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 27.03/4.36 : ! [v5: int] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1, v2) =
% 27.03/4.36 v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) &
% 27.03/4.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.36 $i] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1, v3) = v4) | ~
% 27.03/4.36 (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.36 contains_slb(v0, v2) = 0)
% 27.03/4.36
% 27.03/4.36 (ax23)
% 27.03/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.37 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (pair_in_list(v6, v2, v4) =
% 27.03/4.37 v7) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~ $i(v4) |
% 27.03/4.37 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) &
% 27.03/4.37 pair_in_list(v0, v2, v4) = v8)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 27.03/4.37 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v3 | ~
% 27.03/4.37 (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0,
% 27.03/4.37 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.37 pair_in_list(v0, v2, v4) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.03/4.37 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v2 = v1 | ~
% 27.03/4.37 (pair_in_list(v6, v2, v4) = 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0,
% 27.03/4.37 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.37 pair_in_list(v0, v2, v4) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.03/4.37 [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (pair_in_list(v4, v1, v2)
% 27.03/4.37 = v5) | ~ (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2)
% 27.03/4.37 | ~ $i(v1) | ~ $i(v0))
% 27.03/4.37
% 27.03/4.37 (ax24)
% 27.03/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 27.03/4.37 (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) |
% 27.03/4.37 ~ $i(v0) | remove_slb(v4, v1) = v0)
% 27.03/4.37
% 27.03/4.37 (ax25)
% 27.03/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.37 $i] : ! [v6: $i] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) | ~ (pair(v1,
% 27.03/4.37 v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 27.03/4.37 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 27.03/4.37 (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 & insert_slb(v8, v4) =
% 27.03/4.37 v9 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | v9 = v6))) & ! [v0: $i] : ! [v1:
% 27.03/4.37 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 27.03/4.37 (v2 = v1 | ~ (remove_slb(v0, v2) = v5) | ~ (pair(v1, v3) = v4) | ~
% 27.03/4.37 (insert_slb(v5, v4) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.37 ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (remove_slb(v8, v2) = v9 &
% 27.03/4.37 contains_slb(v0, v2) = v7 & insert_slb(v0, v4) = v8 & $i(v9) & $i(v8) & (
% 27.03/4.37 ~ (v7 = 0) | v9 = v6)))
% 27.03/4.37
% 27.03/4.38 (ax26)
% 27.03/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 27.03/4.38 (pair(v1, v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) |
% 27.03/4.38 ~ $i(v0) | lookup_slb(v4, v1) = v2)
% 27.03/4.38
% 27.03/4.38 (ax27)
% 27.03/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.38 $i] : ! [v6: $i] : (v2 = v1 | ~ (lookup_slb(v5, v2) = v6) | ~ (pair(v1,
% 27.03/4.38 v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 27.03/4.38 $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] : (lookup_slb(v0, v2) = v8 &
% 27.03/4.38 contains_slb(v0, v2) = v7 & $i(v8) & ( ~ (v7 = 0) | v8 = v6)))
% 27.03/4.38
% 27.03/4.38 (ax37)
% 27.03/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.38 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 27.03/4.38 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 27.03/4.38 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10:
% 27.03/4.38 $i] : ? [v11: any] : (triple(v0, v1, v2) = v10 & check_cpq(v10) = v11 &
% 27.03/4.38 check_cpq(v7) = v9 & less_than(v4, v3) = v8 & $i(v10) & ( ~ (v8 = 0) | ((
% 27.03/4.38 ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0)))))
% 27.03/4.38
% 27.03/4.38 (ax38)
% 27.03/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.38 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v0, v6, v2) = v7) | ~
% 27.03/4.38 (pair(v3, v4) = v5) | ~ (insert_slb(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 27.03/4.38 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: any] :
% 27.03/4.38 (check_cpq(v7) = v9 & strictly_less_than(v3, v4) = v8 & ( ~ (v9 = 0) | ~
% 27.03/4.38 (v8 = 0))))
% 27.03/4.38
% 27.03/4.38 (ax40)
% 27.03/4.38 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) =
% 27.03/4.38 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3))
% 27.03/4.38
% 27.03/4.38 (ax41)
% 27.03/4.38 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad |
% 27.03/4.38 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) =
% 27.03/4.38 0)
% 27.03/4.38
% 27.03/4.38 (ax43)
% 27.03/4.38 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 27.03/4.38 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) |
% 27.03/4.38 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] :
% 27.03/4.38 (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) = v6 & $i(v7) & (v7 = v5 |
% 27.03/4.38 v6 = 0)))
% 27.03/4.38
% 27.03/4.38 (ax44)
% 27.03/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.03/4.38 $i] : ! [v6: $i] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) =
% 27.03/4.38 v6) | ~ (remove_slb(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 27.03/4.38 ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ? [v9: any] : ? [v10: $i] : ?
% 27.03/4.38 [v11: $i] : (triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v11 &
% 27.03/4.38 lookup_slb(v1, v3) = v8 & contains_slb(v1, v3) = v7 & less_than(v8, v3) =
% 27.03/4.38 v9 & $i(v11) & $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6)))
% 27.03/4.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 27.03/4.38 [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~
% 27.03/4.38 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ?
% 27.03/4.38 [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (remove_pqp(v0, v3)
% 27.03/4.38 = v9 & triple(v9, v10, v2) = v11 & lookup_slb(v1, v3) = v7 &
% 27.03/4.39 remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 & less_than(v7, v3) =
% 27.03/4.39 v8 & $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) |
% 27.03/4.39 v11 = v5)))
% 27.03/4.39
% 27.03/4.39 (ax45)
% 27.03/4.39 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 27.03/4.39 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) |
% 27.03/4.39 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] :
% 27.03/4.39 ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (remove_pqp(v0,
% 27.03/4.39 v3) = v9 & triple(v9, v10, bad) = v11 & lookup_slb(v1, v3) = v7 &
% 27.03/4.39 remove_slb(v1, v3) = v10 & contains_slb(v1, v3) = v6 &
% 27.03/4.39 strictly_less_than(v3, v7) = v8 & $i(v11) & $i(v10) & $i(v9) & $i(v7) & (
% 27.03/4.39 ~ (v8 = 0) | ~ (v6 = 0) | v11 = v5)))
% 27.03/4.39
% 27.03/4.39 (ax48)
% 27.03/4.39 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 27.03/4.39 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~
% 27.03/4.39 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i]
% 27.03/4.39 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 27.03/4.39 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) =
% 27.03/4.39 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 &
% 27.03/4.39 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~
% 27.03/4.39 (v8 = 0) | ~ (v6 = 0) | v10 = v4)))
% 27.03/4.39
% 27.03/4.39 (l32_co)
% 27.03/4.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 27.03/4.39 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 27.03/4.39 ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & ok(v10) = 0 & triple(v1, v8,
% 27.03/4.39 v2) = v9 & remove_cpq(v9, v3) = v10 & remove_slb(v8, v3) = v11 &
% 27.03/4.39 pair_in_list(v11, v3, v4) = v12 & pair_in_list(v8, v3, v4) = 0 & pair(v5,
% 27.03/4.39 v6) = v7 & insert_slb(v0, v7) = v8 & strictly_less_than(v3, v4) = 0 &
% 27.03/4.39 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 27.03/4.39 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v13: $i] : ! [v14: $i] : ! [v15:
% 27.03/4.39 $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20:
% 27.03/4.39 int] : (v20 = 0 | ~ (ok(v18) = 0) | ~ (triple(v13, v0, v14) = v17) | ~
% 27.03/4.39 (remove_cpq(v17, v15) = v18) | ~ (remove_slb(v0, v15) = v19) | ~
% 27.03/4.39 (pair_in_list(v19, v15, v16) = v20) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14)
% 27.03/4.39 | ~ $i(v13) | ? [v21: any] : ? [v22: any] : (pair_in_list(v0, v15, v16)
% 27.03/4.39 = v21 & strictly_less_than(v15, v16) = v22 & ( ~ (v22 = 0) | ~ (v21 =
% 27.03/4.39 0)))) & ! [v13: $i] : ! [v14: $i] : ! [v15: $i] : ! [v16: $i] :
% 27.03/4.39 ! [v17: $i] : ! [v18: $i] : ( ~ (ok(v18) = 0) | ~ (triple(v13, v0, v14) =
% 27.03/4.39 v17) | ~ (remove_cpq(v17, v15) = v18) | ~ (pair_in_list(v0, v15, v16)
% 27.03/4.39 = 0) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14) | ~ $i(v13) | ? [v19: any]
% 27.03/4.39 : ? [v20: $i] : ? [v21: any] : (remove_slb(v0, v15) = v20 &
% 27.03/4.39 pair_in_list(v20, v15, v16) = v21 & strictly_less_than(v15, v16) = v19 &
% 27.03/4.39 $i(v20) & ( ~ (v19 = 0) | v21 = 0))) & ! [v13: $i] : ! [v14: $i] : !
% 27.03/4.39 [v15: $i] : ! [v16: $i] : ! [v17: $i] : ! [v18: $i] : ( ~ (ok(v18) = 0) |
% 27.03/4.39 ~ (triple(v13, v0, v14) = v17) | ~ (remove_cpq(v17, v15) = v18) | ~
% 27.03/4.39 (strictly_less_than(v15, v16) = 0) | ~ $i(v16) | ~ $i(v15) | ~ $i(v14)
% 27.03/4.39 | ~ $i(v13) | ? [v19: any] : ? [v20: $i] : ? [v21: any] :
% 27.03/4.39 (remove_slb(v0, v15) = v20 & pair_in_list(v20, v15, v16) = v21 &
% 27.03/4.39 pair_in_list(v0, v15, v16) = v19 & $i(v20) & ( ~ (v19 = 0) | v21 = 0))))
% 27.03/4.39
% 27.03/4.39 (stricly_smaller_definition)
% 27.03/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 27.03/4.40 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 27.03/4.40 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 27.03/4.40 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 27.03/4.40 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 27.03/4.40 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 27.03/4.40 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 27.03/4.40 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 27.03/4.40 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 27.03/4.40 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.03/4.40 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 27.03/4.40 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 27.03/4.40 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 27.03/4.40 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : (
% 27.03/4.40 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0:
% 27.03/4.40 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 27.03/4.40 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 27.03/4.40 v0) = v2 & (v3 = 0 | v2 = 0)))
% 27.03/4.40
% 27.03/4.40 (totality)
% 27.03/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) =
% 27.03/4.40 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : !
% 27.03/4.40 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) |
% 27.03/4.40 ~ $i(v0) | less_than(v1, v0) = 0)
% 27.03/4.40
% 27.03/4.40 (transitivity)
% 27.03/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 27.03/4.40 (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ~ $i(v2) | ~
% 27.03/4.40 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v0, v1) = v4))
% 27.03/4.40 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 27.03/4.40 (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | ~
% 27.03/4.40 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v1, v2) = v4))
% 27.03/4.40 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (less_than(v1, v2) = 0) | ~
% 27.03/4.40 (less_than(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0,
% 27.03/4.40 v2) = 0)
% 27.03/4.40
% 27.03/4.40 (function-axioms)
% 27.03/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 27.03/4.40 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 27.03/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.03/4.40 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 27.03/4.40 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 27.03/4.40 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 27.03/4.40 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 27.03/4.40 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 27.03/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.03/4.40 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 27.03/4.40 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.40 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 27.03/4.40 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 27.03/4.40 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.03/4.40 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 27.03/4.40 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 27.03/4.40 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 27.03/4.40 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.03/4.40 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 27.03/4.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 27.03/4.40 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 27.03/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.03/4.40 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 27.03/4.40 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.40 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 27.03/4.40 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 27.03/4.40 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.03/4.40 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.40 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 27.03/4.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.03/4.41 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 27.03/4.41 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.03/4.41 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 27.03/4.41 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 27.03/4.41 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 27.03/4.41 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 27.03/4.41 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 27.03/4.41 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 27.03/4.41 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 27.03/4.41 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 27.03/4.41 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 27.03/4.41 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 27.03/4.41 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 27.03/4.41 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 27.03/4.41 v1) | ~ (isnonempty_slb(v2) = v0))
% 27.03/4.41
% 27.03/4.41 Further assumptions not needed in the proof:
% 27.03/4.41 --------------------------------------------
% 27.03/4.41 ax18, ax19, ax20, ax22, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 27.03/4.41 ax39, ax42, ax46, ax47, ax49, ax50, ax51, ax52, ax53, bottom_smallest,
% 27.03/4.41 reflexivity
% 27.03/4.41
% 27.03/4.41 Those formulas are unsatisfiable:
% 27.03/4.41 ---------------------------------
% 27.03/4.41
% 27.03/4.41 Begin of proof
% 27.03/4.41 |
% 27.03/4.41 | ALPHA: (transitivity) implies:
% 27.03/4.41 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (less_than(v1, v2) = 0) |
% 27.03/4.41 | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.41 | less_than(v0, v2) = 0)
% 27.03/4.41 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 27.03/4.41 | (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ~ $i(v2) |
% 27.03/4.41 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v1,
% 27.03/4.41 | v2) = v4))
% 27.03/4.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 27.03/4.41 | (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ~ $i(v2) |
% 27.03/4.41 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v0,
% 27.03/4.41 | v1) = v4))
% 27.03/4.41 |
% 27.03/4.41 | ALPHA: (totality) implies:
% 27.03/4.41 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 27.03/4.41 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0)
% 27.03/4.41 |
% 27.03/4.41 | ALPHA: (stricly_smaller_definition) implies:
% 27.03/4.41 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) |
% 27.03/4.41 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1)
% 27.03/4.41 | = v3 & less_than(v1, v0) = v2 & (v3 = 0 | v2 = 0)))
% 27.03/4.41 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (strictly_less_than(v0, v1) = 0) | ~
% 27.03/4.41 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_than(v1, v0)
% 27.03/4.41 | = v2 & less_than(v0, v1) = 0))
% 27.03/4.41 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 27.03/4.41 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 27.03/4.41 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 27.03/4.41 | 0) | (v2 = 0 & ~ (v4 = 0)))))
% 27.03/4.41 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 27.03/4.41 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 27.03/4.42 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 27.03/4.42 | 0) | (v4 = 0 & ~ (v2 = 0)))))
% 27.03/4.42 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1,
% 27.03/4.42 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 27.03/4.42 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 27.03/4.42 | 0) | v4 = 0)))
% 27.03/4.42 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 27.03/4.42 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 27.03/4.42 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1)
% 27.03/4.42 | = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax21) implies:
% 27.03/4.42 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : (v2 = v1 | ~ (contains_slb(v5, v2) = 0) | ~ (pair(v1,
% 27.03/4.42 | v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2)
% 27.03/4.42 | | ~ $i(v1) | ~ $i(v0) | contains_slb(v0, v2) = 0)
% 27.03/4.42 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: int] : (v5 = 0 | ~ (contains_slb(v4, v1) = v5) | ~ (pair(v1,
% 27.03/4.42 | v2) = v3) | ~ (insert_slb(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 27.03/4.42 | | ~ $i(v0))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax23) implies:
% 27.03/4.42 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : ! [v6: $i] : (v2 = v1 | ~ (pair_in_list(v6, v2, v4) =
% 27.03/4.42 | 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~
% 27.03/4.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.42 | pair_in_list(v0, v2, v4) = 0)
% 27.03/4.42 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : ! [v6: $i] : (v4 = v3 | ~ (pair_in_list(v6, v2, v4) =
% 27.03/4.42 | 0) | ~ (pair(v1, v3) = v5) | ~ (insert_slb(v0, v5) = v6) | ~
% 27.03/4.42 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.42 | pair_in_list(v0, v2, v4) = 0)
% 27.03/4.42 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~
% 27.03/4.42 | (pair_in_list(v6, v2, v4) = v7) | ~ (pair(v1, v3) = v5) | ~
% 27.03/4.42 | (insert_slb(v0, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 27.03/4.42 | $i(v1) | ~ $i(v0) | ? [v8: int] : ( ~ (v8 = 0) & pair_in_list(v0,
% 27.03/4.42 | v2, v4) = v8))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax25) implies:
% 27.03/4.42 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : ! [v6: $i] : (v2 = v1 | ~ (remove_slb(v5, v2) = v6) |
% 27.03/4.42 | ~ (pair(v1, v3) = v4) | ~ (insert_slb(v0, v4) = v5) | ~ $i(v3) |
% 27.03/4.42 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] : ?
% 27.03/4.42 | [v9: $i] : (remove_slb(v0, v2) = v8 & contains_slb(v0, v2) = v7 &
% 27.03/4.42 | insert_slb(v8, v4) = v9 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | v9 =
% 27.03/4.42 | v6)))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax40) implies:
% 27.03/4.42 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) =
% 27.03/4.42 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2)
% 27.03/4.42 | = v3))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax41) implies:
% 27.03/4.42 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~
% 27.03/4.42 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.03/4.42 | ok(v3) = 0)
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax43) implies:
% 27.03/4.42 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.42 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) =
% 27.03/4.42 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 27.03/4.42 | : ? [v7: $i] : (triple(v0, v1, bad) = v7 & contains_slb(v1, v3) =
% 27.03/4.42 | v6 & $i(v7) & (v7 = v5 | v6 = 0)))
% 27.03/4.42 |
% 27.03/4.42 | ALPHA: (ax44) implies:
% 27.03/4.43 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.43 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) =
% 27.03/4.43 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 27.03/4.43 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 27.03/4.43 | $i] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, v2) = v11 &
% 27.03/4.43 | lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 &
% 27.03/4.43 | contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & $i(v11) &
% 27.03/4.43 | $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v11 =
% 27.03/4.43 | v5)))
% 27.03/4.43 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.43 | ! [v5: $i] : ! [v6: $i] : ( ~ (remove_pqp(v0, v3) = v4) | ~
% 27.03/4.43 | (triple(v4, v5, v2) = v6) | ~ (remove_slb(v1, v3) = v5) | ~ $i(v3)
% 27.03/4.43 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: $i] :
% 27.03/4.43 | ? [v9: any] : ? [v10: $i] : ? [v11: $i] : (triple(v0, v1, v2) =
% 27.03/4.43 | v10 & remove_cpq(v10, v3) = v11 & lookup_slb(v1, v3) = v8 &
% 27.03/4.43 | contains_slb(v1, v3) = v7 & less_than(v8, v3) = v9 & $i(v11) &
% 27.03/4.43 | $i(v10) & $i(v8) & ( ~ (v9 = 0) | ~ (v7 = 0) | v11 = v6)))
% 27.03/4.43 |
% 27.03/4.43 | ALPHA: (ax45) implies:
% 27.03/4.43 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.43 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) =
% 27.03/4.43 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 27.03/4.43 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11:
% 27.03/4.43 | $i] : (remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v11 &
% 27.03/4.43 | lookup_slb(v1, v3) = v7 & remove_slb(v1, v3) = v10 &
% 27.03/4.43 | contains_slb(v1, v3) = v6 & strictly_less_than(v3, v7) = v8 &
% 27.03/4.43 | $i(v11) & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) |
% 27.03/4.43 | v11 = v5)))
% 27.03/4.43 |
% 27.03/4.43 | ALPHA: (ax48) implies:
% 27.03/4.43 | (23) $i(bad)
% 27.03/4.43 |
% 27.03/4.43 | ALPHA: (function-axioms) implies:
% 27.03/4.43 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 27.03/4.43 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 27.03/4.43 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 27.03/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~
% 27.03/4.43 | (less_than(v3, v2) = v0))
% 27.03/4.43 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 27.03/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~
% 27.03/4.43 | (strictly_less_than(v3, v2) = v0))
% 27.03/4.43 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 27.03/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~
% 27.03/4.43 | (contains_slb(v3, v2) = v0))
% 27.03/4.43 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.43 | (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0))
% 27.03/4.43 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.43 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0))
% 27.03/4.43 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.43 | (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 27.03/4.43 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.03/4.43 | (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0))
% 27.03/4.43 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 27.03/4.43 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2)
% 27.03/4.43 | = v1) | ~ (pair_in_list(v4, v3, v2) = v0))
% 27.03/4.43 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.43 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) =
% 27.03/4.43 | v0))
% 27.03/4.43 |
% 27.03/4.43 | DELTA: instantiating (l32_co) with fresh symbols all_46_0, all_46_1, all_46_2,
% 27.03/4.43 | all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8, all_46_9,
% 27.03/4.43 | all_46_10, all_46_11, all_46_12 gives:
% 27.03/4.44 | (34) ~ (all_46_0 = 0) & ok(all_46_2) = 0 & triple(all_46_11, all_46_4,
% 27.03/4.44 | all_46_10) = all_46_3 & remove_cpq(all_46_3, all_46_9) = all_46_2 &
% 27.03/4.44 | remove_slb(all_46_4, all_46_9) = all_46_1 & pair_in_list(all_46_1,
% 27.03/4.44 | all_46_9, all_46_8) = all_46_0 & pair_in_list(all_46_4, all_46_9,
% 27.03/4.44 | all_46_8) = 0 & pair(all_46_7, all_46_6) = all_46_5 &
% 27.03/4.44 | insert_slb(all_46_12, all_46_5) = all_46_4 &
% 27.03/4.44 | strictly_less_than(all_46_9, all_46_8) = 0 & $i(all_46_1) &
% 27.03/4.44 | $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5) &
% 27.03/4.44 | $i(all_46_6) & $i(all_46_7) & $i(all_46_8) & $i(all_46_9) &
% 27.03/4.44 | $i(all_46_10) & $i(all_46_11) & $i(all_46_12) & ! [v0: $i] : ! [v1:
% 27.03/4.44 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 27.03/4.44 | [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (ok(v5) = 0) | ~ (triple(v0,
% 27.03/4.44 | all_46_12, v1) = v4) | ~ (remove_cpq(v4, v2) = v5) | ~
% 27.03/4.44 | (remove_slb(all_46_12, v2) = v6) | ~ (pair_in_list(v6, v2, v3) =
% 27.03/4.44 | v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any]
% 27.03/4.44 | : ? [v9: any] : (pair_in_list(all_46_12, v2, v3) = v8 &
% 27.03/4.44 | strictly_less_than(v2, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0)))) &
% 27.03/4.44 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.44 | ! [v5: $i] : ( ~ (ok(v5) = 0) | ~ (triple(v0, all_46_12, v1) = v4) |
% 27.03/4.44 | ~ (remove_cpq(v4, v2) = v5) | ~ (pair_in_list(all_46_12, v2, v3) =
% 27.03/4.44 | 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 27.03/4.44 | : ? [v7: $i] : ? [v8: any] : (remove_slb(all_46_12, v2) = v7 &
% 27.03/4.44 | pair_in_list(v7, v2, v3) = v8 & strictly_less_than(v2, v3) = v6 &
% 27.03/4.44 | $i(v7) & ( ~ (v6 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : !
% 27.03/4.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (ok(v5) = 0)
% 27.03/4.44 | | ~ (triple(v0, all_46_12, v1) = v4) | ~ (remove_cpq(v4, v2) = v5)
% 27.03/4.44 | | ~ (strictly_less_than(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 27.03/4.44 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 27.03/4.44 | (remove_slb(all_46_12, v2) = v7 & pair_in_list(v7, v2, v3) = v8 &
% 27.03/4.44 | pair_in_list(all_46_12, v2, v3) = v6 & $i(v7) & ( ~ (v6 = 0) | v8
% 27.03/4.44 | = 0)))
% 27.03/4.44 |
% 27.03/4.44 | ALPHA: (34) implies:
% 27.03/4.44 | (35) ~ (all_46_0 = 0)
% 27.03/4.44 | (36) $i(all_46_12)
% 27.03/4.44 | (37) $i(all_46_11)
% 27.03/4.44 | (38) $i(all_46_10)
% 27.03/4.44 | (39) $i(all_46_9)
% 27.03/4.44 | (40) $i(all_46_8)
% 27.03/4.44 | (41) $i(all_46_7)
% 27.03/4.44 | (42) $i(all_46_6)
% 27.03/4.44 | (43) $i(all_46_4)
% 27.03/4.44 | (44) strictly_less_than(all_46_9, all_46_8) = 0
% 27.03/4.44 | (45) insert_slb(all_46_12, all_46_5) = all_46_4
% 27.03/4.44 | (46) pair(all_46_7, all_46_6) = all_46_5
% 27.03/4.44 | (47) pair_in_list(all_46_4, all_46_9, all_46_8) = 0
% 27.03/4.44 | (48) pair_in_list(all_46_1, all_46_9, all_46_8) = all_46_0
% 27.03/4.44 | (49) remove_slb(all_46_4, all_46_9) = all_46_1
% 27.03/4.44 | (50) remove_cpq(all_46_3, all_46_9) = all_46_2
% 27.03/4.44 | (51) triple(all_46_11, all_46_4, all_46_10) = all_46_3
% 27.03/4.44 | (52) ok(all_46_2) = 0
% 27.03/4.44 | (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.44 | ! [v5: $i] : ( ~ (ok(v5) = 0) | ~ (triple(v0, all_46_12, v1) = v4) |
% 27.03/4.44 | ~ (remove_cpq(v4, v2) = v5) | ~ (strictly_less_than(v2, v3) = 0) |
% 27.03/4.44 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 27.03/4.44 | [v7: $i] : ? [v8: any] : (remove_slb(all_46_12, v2) = v7 &
% 27.03/4.44 | pair_in_list(v7, v2, v3) = v8 & pair_in_list(all_46_12, v2, v3) =
% 27.03/4.44 | v6 & $i(v7) & ( ~ (v6 = 0) | v8 = 0)))
% 27.03/4.44 | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.03/4.44 | ! [v5: $i] : ( ~ (ok(v5) = 0) | ~ (triple(v0, all_46_12, v1) = v4) |
% 27.03/4.44 | ~ (remove_cpq(v4, v2) = v5) | ~ (pair_in_list(all_46_12, v2, v3) =
% 27.03/4.44 | 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 27.03/4.44 | : ? [v7: $i] : ? [v8: any] : (remove_slb(all_46_12, v2) = v7 &
% 27.03/4.44 | pair_in_list(v7, v2, v3) = v8 & strictly_less_than(v2, v3) = v6 &
% 27.03/4.44 | $i(v7) & ( ~ (v6 = 0) | v8 = 0)))
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (6) with all_46_9, all_46_8, simplifying with (39),
% 27.03/4.44 | (40), (44) gives:
% 27.03/4.44 | (55) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_46_8, all_46_9) = v0 &
% 27.03/4.44 | less_than(all_46_9, all_46_8) = 0)
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (ax26) with all_46_12, all_46_7, all_46_6,
% 27.03/4.44 | all_46_5, all_46_4, simplifying with (36), (41), (42), (45), (46)
% 27.03/4.44 | gives:
% 27.03/4.44 | (56) lookup_slb(all_46_4, all_46_7) = all_46_6
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (ax24) with all_46_12, all_46_7, all_46_6,
% 27.03/4.44 | all_46_5, all_46_4, simplifying with (36), (41), (42), (45), (46)
% 27.03/4.44 | gives:
% 27.03/4.44 | (57) remove_slb(all_46_4, all_46_7) = all_46_12
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (14) with all_46_12, all_46_7, all_46_9, all_46_6,
% 27.03/4.44 | all_46_8, all_46_5, all_46_4, simplifying with (36), (39), (40),
% 27.03/4.44 | (41), (42), (45), (46), (47) gives:
% 27.03/4.44 | (58) all_46_6 = all_46_8 | pair_in_list(all_46_12, all_46_9, all_46_8) = 0
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (13) with all_46_12, all_46_7, all_46_9, all_46_6,
% 27.03/4.44 | all_46_8, all_46_5, all_46_4, simplifying with (36), (39), (40),
% 27.03/4.44 | (41), (42), (45), (46), (47) gives:
% 27.03/4.44 | (59) all_46_7 = all_46_9 | pair_in_list(all_46_12, all_46_9, all_46_8) = 0
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (16) with all_46_12, all_46_7, all_46_9, all_46_6,
% 27.03/4.44 | all_46_5, all_46_4, all_46_1, simplifying with (36), (39), (41),
% 27.03/4.44 | (42), (45), (46), (49) gives:
% 27.03/4.44 | (60) all_46_7 = all_46_9 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 27.03/4.44 | (remove_slb(all_46_12, all_46_9) = v1 & contains_slb(all_46_12,
% 27.03/4.44 | all_46_9) = v0 & insert_slb(v1, all_46_5) = v2 & $i(v2) & $i(v1) &
% 27.03/4.44 | ( ~ (v0 = 0) | v2 = all_46_1))
% 27.03/4.44 |
% 27.03/4.44 | GROUND_INST: instantiating (ax37) with all_46_11, all_46_12, all_46_10,
% 27.03/4.44 | all_46_7, all_46_6, all_46_5, all_46_4, all_46_3, simplifying
% 27.03/4.44 | with (36), (37), (38), (41), (42), (45), (46), (51) gives:
% 27.03/4.45 | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 27.03/4.45 | (triple(all_46_11, all_46_12, all_46_10) = v2 & check_cpq(v2) = v3 &
% 27.03/4.45 | check_cpq(all_46_3) = v1 & less_than(all_46_6, all_46_7) = v0 &
% 27.03/4.45 | $i(v2) & ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3
% 27.03/4.45 | = 0))))
% 27.03/4.45 |
% 27.03/4.45 | GROUND_INST: instantiating (ax38) with all_46_11, all_46_12, all_46_10,
% 27.03/4.45 | all_46_7, all_46_6, all_46_5, all_46_4, all_46_3, simplifying
% 27.03/4.45 | with (36), (37), (38), (41), (42), (45), (46), (51) gives:
% 27.03/4.45 | (62) ? [v0: any] : ? [v1: any] : (check_cpq(all_46_3) = v1 &
% 27.03/4.45 | strictly_less_than(all_46_7, all_46_6) = v0 & ( ~ (v1 = 0) | ~ (v0
% 27.03/4.45 | = 0)))
% 27.03/4.45 |
% 27.03/4.45 | GROUND_INST: instantiating (20) with all_46_11, all_46_4, all_46_10, all_46_9,
% 27.03/4.45 | all_46_3, all_46_2, simplifying with (37), (38), (39), (43),
% 27.03/4.45 | (50), (51) gives:
% 27.03/4.45 | (63) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.03/4.45 | : ? [v5: $i] : (remove_pqp(all_46_11, all_46_9) = v3 & triple(v3, v4,
% 27.03/4.45 | all_46_10) = v5 & lookup_slb(all_46_4, all_46_9) = v1 &
% 27.03/4.45 | remove_slb(all_46_4, all_46_9) = v4 & contains_slb(all_46_4,
% 27.03/4.45 | all_46_9) = v0 & less_than(v1, all_46_9) = v2 & $i(v5) & $i(v4) &
% 27.03/4.45 | $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = all_46_2))
% 27.03/4.45 |
% 27.03/4.45 | GROUND_INST: instantiating (22) with all_46_11, all_46_4, all_46_10, all_46_9,
% 27.03/4.45 | all_46_3, all_46_2, simplifying with (37), (38), (39), (43),
% 27.03/4.45 | (50), (51) gives:
% 27.03/4.45 | (64) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.03/4.45 | : ? [v5: $i] : (remove_pqp(all_46_11, all_46_9) = v3 & triple(v3, v4,
% 27.03/4.45 | bad) = v5 & lookup_slb(all_46_4, all_46_9) = v1 &
% 27.03/4.45 | remove_slb(all_46_4, all_46_9) = v4 & contains_slb(all_46_4,
% 27.03/4.45 | all_46_9) = v0 & strictly_less_than(all_46_9, v1) = v2 & $i(v5) &
% 27.03/4.45 | $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 =
% 27.03/4.45 | all_46_2))
% 27.03/4.45 |
% 27.03/4.45 | GROUND_INST: instantiating (19) with all_46_11, all_46_4, all_46_10, all_46_9,
% 27.03/4.45 | all_46_3, all_46_2, simplifying with (37), (38), (39), (43),
% 27.03/4.45 | (50), (51) gives:
% 27.03/4.45 | (65) ? [v0: any] : ? [v1: $i] : (triple(all_46_11, all_46_4, bad) = v1 &
% 27.03/4.45 | contains_slb(all_46_4, all_46_9) = v0 & $i(v1) & (v1 = all_46_2 | v0
% 27.03/4.45 | = 0))
% 27.03/4.45 |
% 27.03/4.45 | DELTA: instantiating (55) with fresh symbol all_55_0 gives:
% 27.03/4.45 | (66) ~ (all_55_0 = 0) & less_than(all_46_8, all_46_9) = all_55_0 &
% 27.03/4.45 | less_than(all_46_9, all_46_8) = 0
% 27.03/4.45 |
% 27.03/4.45 | ALPHA: (66) implies:
% 27.03/4.45 | (67) ~ (all_55_0 = 0)
% 27.03/4.45 | (68) less_than(all_46_9, all_46_8) = 0
% 27.03/4.45 | (69) less_than(all_46_8, all_46_9) = all_55_0
% 27.03/4.45 |
% 27.03/4.45 | DELTA: instantiating (62) with fresh symbols all_57_0, all_57_1 gives:
% 27.03/4.45 | (70) check_cpq(all_46_3) = all_57_0 & strictly_less_than(all_46_7,
% 27.03/4.45 | all_46_6) = all_57_1 & ( ~ (all_57_0 = 0) | ~ (all_57_1 = 0))
% 27.03/4.45 |
% 27.03/4.45 | ALPHA: (70) implies:
% 27.03/4.45 | (71) strictly_less_than(all_46_7, all_46_6) = all_57_1
% 27.03/4.45 |
% 27.03/4.45 | DELTA: instantiating (65) with fresh symbols all_59_0, all_59_1 gives:
% 27.03/4.45 | (72) triple(all_46_11, all_46_4, bad) = all_59_0 & contains_slb(all_46_4,
% 27.03/4.45 | all_46_9) = all_59_1 & $i(all_59_0) & (all_59_0 = all_46_2 |
% 27.03/4.45 | all_59_1 = 0)
% 27.03/4.45 |
% 27.03/4.45 | ALPHA: (72) implies:
% 27.03/4.45 | (73) contains_slb(all_46_4, all_46_9) = all_59_1
% 27.52/4.45 | (74) triple(all_46_11, all_46_4, bad) = all_59_0
% 27.52/4.45 | (75) all_59_0 = all_46_2 | all_59_1 = 0
% 27.52/4.45 |
% 27.52/4.45 | DELTA: instantiating (61) with fresh symbols all_61_0, all_61_1, all_61_2,
% 27.52/4.45 | all_61_3 gives:
% 27.52/4.45 | (76) triple(all_46_11, all_46_12, all_46_10) = all_61_1 &
% 27.52/4.45 | check_cpq(all_61_1) = all_61_0 & check_cpq(all_46_3) = all_61_2 &
% 27.52/4.45 | less_than(all_46_6, all_46_7) = all_61_3 & $i(all_61_1) & ( ~
% 27.52/4.45 | (all_61_3 = 0) | (( ~ (all_61_0 = 0) | all_61_2 = 0) & ( ~ (all_61_2
% 27.52/4.45 | = 0) | all_61_0 = 0)))
% 27.52/4.45 |
% 27.52/4.45 | ALPHA: (76) implies:
% 27.52/4.45 | (77) less_than(all_46_6, all_46_7) = all_61_3
% 27.52/4.45 | (78) triple(all_46_11, all_46_12, all_46_10) = all_61_1
% 27.52/4.45 |
% 27.52/4.45 | DELTA: instantiating (63) with fresh symbols all_63_0, all_63_1, all_63_2,
% 27.52/4.45 | all_63_3, all_63_4, all_63_5 gives:
% 27.52/4.45 | (79) remove_pqp(all_46_11, all_46_9) = all_63_2 & triple(all_63_2,
% 27.52/4.45 | all_63_1, all_46_10) = all_63_0 & lookup_slb(all_46_4, all_46_9) =
% 27.52/4.45 | all_63_4 & remove_slb(all_46_4, all_46_9) = all_63_1 &
% 27.52/4.45 | contains_slb(all_46_4, all_46_9) = all_63_5 & less_than(all_63_4,
% 27.52/4.45 | all_46_9) = all_63_3 & $i(all_63_0) & $i(all_63_1) & $i(all_63_2) &
% 27.52/4.45 | $i(all_63_4) & ( ~ (all_63_3 = 0) | ~ (all_63_5 = 0) | all_63_0 =
% 27.52/4.45 | all_46_2)
% 27.52/4.45 |
% 27.52/4.45 | ALPHA: (79) implies:
% 27.52/4.45 | (80) $i(all_63_1)
% 27.52/4.45 | (81) less_than(all_63_4, all_46_9) = all_63_3
% 27.52/4.45 | (82) contains_slb(all_46_4, all_46_9) = all_63_5
% 27.52/4.45 | (83) remove_slb(all_46_4, all_46_9) = all_63_1
% 27.52/4.45 | (84) lookup_slb(all_46_4, all_46_9) = all_63_4
% 27.52/4.45 | (85) triple(all_63_2, all_63_1, all_46_10) = all_63_0
% 27.52/4.45 | (86) remove_pqp(all_46_11, all_46_9) = all_63_2
% 27.52/4.45 | (87) ~ (all_63_3 = 0) | ~ (all_63_5 = 0) | all_63_0 = all_46_2
% 27.52/4.45 |
% 27.52/4.45 | DELTA: instantiating (64) with fresh symbols all_65_0, all_65_1, all_65_2,
% 27.52/4.45 | all_65_3, all_65_4, all_65_5 gives:
% 27.52/4.45 | (88) remove_pqp(all_46_11, all_46_9) = all_65_2 & triple(all_65_2,
% 27.52/4.45 | all_65_1, bad) = all_65_0 & lookup_slb(all_46_4, all_46_9) =
% 27.52/4.45 | all_65_4 & remove_slb(all_46_4, all_46_9) = all_65_1 &
% 27.52/4.45 | contains_slb(all_46_4, all_46_9) = all_65_5 &
% 27.52/4.45 | strictly_less_than(all_46_9, all_65_4) = all_65_3 & $i(all_65_0) &
% 27.52/4.45 | $i(all_65_1) & $i(all_65_2) & $i(all_65_4) & ( ~ (all_65_3 = 0) | ~
% 27.52/4.45 | (all_65_5 = 0) | all_65_0 = all_46_2)
% 27.52/4.45 |
% 27.52/4.45 | ALPHA: (88) implies:
% 27.52/4.45 | (89) $i(all_65_4)
% 27.52/4.45 | (90) $i(all_65_2)
% 27.52/4.45 | (91) strictly_less_than(all_46_9, all_65_4) = all_65_3
% 27.52/4.45 | (92) contains_slb(all_46_4, all_46_9) = all_65_5
% 27.52/4.45 | (93) remove_slb(all_46_4, all_46_9) = all_65_1
% 27.52/4.45 | (94) lookup_slb(all_46_4, all_46_9) = all_65_4
% 27.52/4.45 | (95) triple(all_65_2, all_65_1, bad) = all_65_0
% 27.52/4.45 | (96) remove_pqp(all_46_11, all_46_9) = all_65_2
% 27.52/4.45 | (97) ~ (all_65_3 = 0) | ~ (all_65_5 = 0) | all_65_0 = all_46_2
% 27.52/4.45 |
% 27.52/4.45 | GROUND_INST: instantiating (27) with all_63_5, all_65_5, all_46_9, all_46_4,
% 27.52/4.45 | simplifying with (82), (92) gives:
% 27.52/4.45 | (98) all_65_5 = all_63_5
% 27.52/4.45 |
% 27.52/4.45 | GROUND_INST: instantiating (27) with all_59_1, all_65_5, all_46_9, all_46_4,
% 27.52/4.45 | simplifying with (73), (92) gives:
% 27.52/4.45 | (99) all_65_5 = all_59_1
% 27.52/4.45 |
% 27.52/4.45 | GROUND_INST: instantiating (28) with all_46_1, all_65_1, all_46_9, all_46_4,
% 27.52/4.45 | simplifying with (49), (93) gives:
% 27.52/4.45 | (100) all_65_1 = all_46_1
% 27.52/4.45 |
% 27.52/4.46 | GROUND_INST: instantiating (28) with all_63_1, all_65_1, all_46_9, all_46_4,
% 27.52/4.46 | simplifying with (83), (93) gives:
% 27.52/4.46 | (101) all_65_1 = all_63_1
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (29) with all_63_4, all_65_4, all_46_9, all_46_4,
% 27.52/4.46 | simplifying with (84), (94) gives:
% 27.52/4.46 | (102) all_65_4 = all_63_4
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (31) with all_63_2, all_65_2, all_46_9, all_46_11,
% 27.52/4.46 | simplifying with (86), (96) gives:
% 27.52/4.46 | (103) all_65_2 = all_63_2
% 27.52/4.46 |
% 27.52/4.46 | COMBINE_EQS: (100), (101) imply:
% 27.52/4.46 | (104) all_63_1 = all_46_1
% 27.52/4.46 |
% 27.52/4.46 | COMBINE_EQS: (98), (99) imply:
% 27.52/4.46 | (105) all_63_5 = all_59_1
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (95), (100), (103) imply:
% 27.52/4.46 | (106) triple(all_63_2, all_46_1, bad) = all_65_0
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (85), (104) imply:
% 27.52/4.46 | (107) triple(all_63_2, all_46_1, all_46_10) = all_63_0
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (91), (102) imply:
% 27.52/4.46 | (108) strictly_less_than(all_46_9, all_63_4) = all_65_3
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (90), (103) imply:
% 27.52/4.46 | (109) $i(all_63_2)
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (89), (102) imply:
% 27.52/4.46 | (110) $i(all_63_4)
% 27.52/4.46 |
% 27.52/4.46 | REDUCE: (80), (104) imply:
% 27.52/4.46 | (111) $i(all_46_1)
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (8) with all_46_8, all_46_9, 0, simplifying with
% 27.52/4.46 | (39), (40), (68) gives:
% 27.52/4.46 | (112) ? [v0: int] : ? [v1: MultipleValueBool] : ( ~ (v0 = 0) &
% 27.52/4.46 | strictly_less_than(all_46_8, all_46_9) = v0 & less_than(all_46_8,
% 27.52/4.46 | all_46_9) = v1)
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (7) with all_46_8, all_46_9, all_55_0, simplifying
% 27.52/4.46 | with (39), (40), (69) gives:
% 27.52/4.46 | (113) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_8, all_46_9)
% 27.52/4.46 | = v0 & less_than(all_46_9, all_46_8) = v1 & ( ~ (v0 = 0) |
% 27.52/4.46 | (all_55_0 = 0 & ~ (v1 = 0))))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (8) with all_46_7, all_46_6, all_61_3, simplifying
% 27.52/4.46 | with (41), (42), (77) gives:
% 27.52/4.46 | (114) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_7, all_46_6)
% 27.52/4.46 | = v0 & less_than(all_46_7, all_46_6) = v1 & ( ~ (v0 = 0) | (v1 = 0
% 27.52/4.46 | & ~ (all_61_3 = 0))))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (7) with all_46_6, all_46_7, all_61_3, simplifying
% 27.52/4.46 | with (41), (42), (77) gives:
% 27.52/4.46 | (115) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_6, all_46_7)
% 27.52/4.46 | = v0 & less_than(all_46_7, all_46_6) = v1 & ( ~ (v0 = 0) |
% 27.52/4.46 | (all_61_3 = 0 & ~ (v1 = 0))))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (4) with all_46_9, all_63_4, all_63_3, simplifying
% 27.52/4.46 | with (39), (81), (110) gives:
% 27.52/4.46 | (116) all_63_3 = 0 | less_than(all_46_9, all_63_4) = 0
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (9) with all_46_9, all_63_4, all_63_3, simplifying
% 27.52/4.46 | with (39), (81), (110) gives:
% 27.52/4.46 | (117) all_63_3 = 0 | ? [v0: any] : ? [v1: any] :
% 27.52/4.46 | (strictly_less_than(all_46_9, all_63_4) = v1 & less_than(all_46_9,
% 27.52/4.46 | all_63_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (8) with all_46_9, all_63_4, all_63_3, simplifying
% 27.52/4.46 | with (39), (81), (110) gives:
% 27.52/4.46 | (118) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_9, all_63_4)
% 27.52/4.46 | = v0 & less_than(all_46_9, all_63_4) = v1 & ( ~ (v0 = 0) | (v1 = 0
% 27.52/4.46 | & ~ (all_63_3 = 0))))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (7) with all_63_4, all_46_9, all_63_3, simplifying
% 27.52/4.46 | with (39), (81), (110) gives:
% 27.52/4.46 | (119) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_63_4, all_46_9)
% 27.52/4.46 | = v0 & less_than(all_46_9, all_63_4) = v1 & ( ~ (v0 = 0) |
% 27.52/4.46 | (all_63_3 = 0 & ~ (v1 = 0))))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (10) with all_46_9, all_63_4, all_65_3, simplifying
% 27.52/4.46 | with (39), (108), (110) gives:
% 27.52/4.46 | (120) all_65_3 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_63_4,
% 27.52/4.46 | all_46_9) = v1 & less_than(all_46_9, all_63_4) = v0 & ( ~ (v0 =
% 27.52/4.46 | 0) | v1 = 0))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (ax27) with all_46_12, all_46_7, all_46_9,
% 27.52/4.46 | all_46_6, all_46_5, all_46_4, all_63_4, simplifying with (36),
% 27.52/4.46 | (39), (41), (42), (45), (46), (84) gives:
% 27.52/4.46 | (121) all_46_7 = all_46_9 | ? [v0: any] : ? [v1: $i] :
% 27.52/4.46 | (lookup_slb(all_46_12, all_46_9) = v1 & contains_slb(all_46_12,
% 27.52/4.46 | all_46_9) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_63_4))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (ax38) with all_46_11, all_46_12, bad, all_46_7,
% 27.52/4.46 | all_46_6, all_46_5, all_46_4, all_59_0, simplifying with (23),
% 27.52/4.46 | (36), (37), (41), (42), (45), (46), (74) gives:
% 27.52/4.46 | (122) ? [v0: any] : ? [v1: any] : (check_cpq(all_59_0) = v1 &
% 27.52/4.46 | strictly_less_than(all_46_7, all_46_6) = v0 & ( ~ (v1 = 0) | ~ (v0
% 27.52/4.46 | = 0)))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (17) with all_46_11, all_46_4, all_59_0,
% 27.52/4.46 | simplifying with (37), (43), (74) gives:
% 27.52/4.46 | (123) ? [v0: int] : ( ~ (v0 = 0) & ok(all_59_0) = v0)
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (17) with all_63_2, all_46_1, all_65_0, simplifying
% 27.52/4.46 | with (106), (109), (111) gives:
% 27.52/4.46 | (124) ? [v0: int] : ( ~ (v0 = 0) & ok(all_65_0) = v0)
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (21) with all_46_11, all_46_4, all_46_10, all_46_9,
% 27.52/4.46 | all_63_2, all_46_1, all_63_0, simplifying with (37), (38), (39),
% 27.52/4.46 | (43), (49), (86), (107) gives:
% 27.52/4.46 | (125) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.52/4.46 | : (triple(all_46_11, all_46_4, all_46_10) = v3 & remove_cpq(v3,
% 27.52/4.46 | all_46_9) = v4 & lookup_slb(all_46_4, all_46_9) = v1 &
% 27.52/4.46 | contains_slb(all_46_4, all_46_9) = v0 & less_than(v1, all_46_9) =
% 27.52/4.46 | v2 & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 =
% 27.52/4.46 | all_63_0))
% 27.52/4.46 |
% 27.52/4.46 | GROUND_INST: instantiating (21) with all_46_11, all_46_4, bad, all_46_9,
% 27.52/4.46 | all_63_2, all_46_1, all_65_0, simplifying with (23), (37), (39),
% 27.52/4.46 | (43), (49), (86), (106) gives:
% 27.52/4.46 | (126) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.52/4.46 | : (triple(all_46_11, all_46_4, bad) = v3 & remove_cpq(v3, all_46_9) =
% 27.52/4.46 | v4 & lookup_slb(all_46_4, all_46_9) = v1 & contains_slb(all_46_4,
% 27.52/4.46 | all_46_9) = v0 & less_than(v1, all_46_9) = v2 & $i(v4) & $i(v3) &
% 27.52/4.46 | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_65_0))
% 27.52/4.46 |
% 27.52/4.46 | DELTA: instantiating (124) with fresh symbol all_76_0 gives:
% 27.52/4.46 | (127) ~ (all_76_0 = 0) & ok(all_65_0) = all_76_0
% 27.52/4.46 |
% 27.52/4.46 | ALPHA: (127) implies:
% 27.52/4.47 | (128) ~ (all_76_0 = 0)
% 27.52/4.47 | (129) ok(all_65_0) = all_76_0
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (123) with fresh symbol all_78_0 gives:
% 27.52/4.47 | (130) ~ (all_78_0 = 0) & ok(all_59_0) = all_78_0
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (130) implies:
% 27.52/4.47 | (131) ~ (all_78_0 = 0)
% 27.52/4.47 | (132) ok(all_59_0) = all_78_0
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (112) with fresh symbols all_80_0, all_80_1 gives:
% 27.52/4.47 | (133) ~ (all_80_1 = 0) & strictly_less_than(all_46_8, all_46_9) = all_80_1
% 27.52/4.47 | & less_than(all_46_8, all_46_9) = all_80_0
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (133) implies:
% 27.52/4.47 | (134) less_than(all_46_8, all_46_9) = all_80_0
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (122) with fresh symbols all_82_0, all_82_1 gives:
% 27.52/4.47 | (135) check_cpq(all_59_0) = all_82_0 & strictly_less_than(all_46_7,
% 27.52/4.47 | all_46_6) = all_82_1 & ( ~ (all_82_0 = 0) | ~ (all_82_1 = 0))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (135) implies:
% 27.52/4.47 | (136) strictly_less_than(all_46_7, all_46_6) = all_82_1
% 27.52/4.47 | (137) ~ (all_82_0 = 0) | ~ (all_82_1 = 0)
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (115) with fresh symbols all_84_0, all_84_1 gives:
% 27.52/4.47 | (138) strictly_less_than(all_46_6, all_46_7) = all_84_1 &
% 27.52/4.47 | less_than(all_46_7, all_46_6) = all_84_0 & ( ~ (all_84_1 = 0) |
% 27.52/4.47 | (all_61_3 = 0 & ~ (all_84_0 = 0)))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (138) implies:
% 27.52/4.47 | (139) less_than(all_46_7, all_46_6) = all_84_0
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (114) with fresh symbols all_86_0, all_86_1 gives:
% 27.52/4.47 | (140) strictly_less_than(all_46_7, all_46_6) = all_86_1 &
% 27.52/4.47 | less_than(all_46_7, all_46_6) = all_86_0 & ( ~ (all_86_1 = 0) |
% 27.52/4.47 | (all_86_0 = 0 & ~ (all_61_3 = 0)))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (140) implies:
% 27.52/4.47 | (141) less_than(all_46_7, all_46_6) = all_86_0
% 27.52/4.47 | (142) strictly_less_than(all_46_7, all_46_6) = all_86_1
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (113) with fresh symbols all_88_0, all_88_1 gives:
% 27.52/4.47 | (143) strictly_less_than(all_46_8, all_46_9) = all_88_1 &
% 27.52/4.47 | less_than(all_46_9, all_46_8) = all_88_0 & ( ~ (all_88_1 = 0) |
% 27.52/4.47 | (all_55_0 = 0 & ~ (all_88_0 = 0)))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (143) implies:
% 27.52/4.47 | (144) less_than(all_46_9, all_46_8) = all_88_0
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (119) with fresh symbols all_90_0, all_90_1 gives:
% 27.52/4.47 | (145) strictly_less_than(all_63_4, all_46_9) = all_90_1 &
% 27.52/4.47 | less_than(all_46_9, all_63_4) = all_90_0 & ( ~ (all_90_1 = 0) |
% 27.52/4.47 | (all_63_3 = 0 & ~ (all_90_0 = 0)))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (145) implies:
% 27.52/4.47 | (146) less_than(all_46_9, all_63_4) = all_90_0
% 27.52/4.47 | (147) strictly_less_than(all_63_4, all_46_9) = all_90_1
% 27.52/4.47 | (148) ~ (all_90_1 = 0) | (all_63_3 = 0 & ~ (all_90_0 = 0))
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (118) with fresh symbols all_92_0, all_92_1 gives:
% 27.52/4.47 | (149) strictly_less_than(all_46_9, all_63_4) = all_92_1 &
% 27.52/4.47 | less_than(all_46_9, all_63_4) = all_92_0 & ( ~ (all_92_1 = 0) |
% 27.52/4.47 | (all_92_0 = 0 & ~ (all_63_3 = 0)))
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (149) implies:
% 27.52/4.47 | (150) less_than(all_46_9, all_63_4) = all_92_0
% 27.52/4.47 | (151) strictly_less_than(all_46_9, all_63_4) = all_92_1
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (126) with fresh symbols all_96_0, all_96_1, all_96_2,
% 27.52/4.47 | all_96_3, all_96_4 gives:
% 27.52/4.47 | (152) triple(all_46_11, all_46_4, bad) = all_96_1 & remove_cpq(all_96_1,
% 27.52/4.47 | all_46_9) = all_96_0 & lookup_slb(all_46_4, all_46_9) = all_96_3 &
% 27.52/4.47 | contains_slb(all_46_4, all_46_9) = all_96_4 & less_than(all_96_3,
% 27.52/4.47 | all_46_9) = all_96_2 & $i(all_96_0) & $i(all_96_1) & $i(all_96_3) &
% 27.52/4.47 | ( ~ (all_96_2 = 0) | ~ (all_96_4 = 0) | all_96_0 = all_65_0)
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (152) implies:
% 27.52/4.47 | (153) $i(all_96_3)
% 27.52/4.47 | (154) less_than(all_96_3, all_46_9) = all_96_2
% 27.52/4.47 | (155) contains_slb(all_46_4, all_46_9) = all_96_4
% 27.52/4.47 | (156) lookup_slb(all_46_4, all_46_9) = all_96_3
% 27.52/4.47 | (157) remove_cpq(all_96_1, all_46_9) = all_96_0
% 27.52/4.47 | (158) triple(all_46_11, all_46_4, bad) = all_96_1
% 27.52/4.47 |
% 27.52/4.47 | DELTA: instantiating (125) with fresh symbols all_98_0, all_98_1, all_98_2,
% 27.52/4.47 | all_98_3, all_98_4 gives:
% 27.52/4.47 | (159) triple(all_46_11, all_46_4, all_46_10) = all_98_1 &
% 27.52/4.47 | remove_cpq(all_98_1, all_46_9) = all_98_0 & lookup_slb(all_46_4,
% 27.52/4.47 | all_46_9) = all_98_3 & contains_slb(all_46_4, all_46_9) = all_98_4
% 27.52/4.47 | & less_than(all_98_3, all_46_9) = all_98_2 & $i(all_98_0) &
% 27.52/4.47 | $i(all_98_1) & $i(all_98_3) & ( ~ (all_98_2 = 0) | ~ (all_98_4 = 0)
% 27.52/4.47 | | all_98_0 = all_63_0)
% 27.52/4.47 |
% 27.52/4.47 | ALPHA: (159) implies:
% 27.52/4.47 | (160) less_than(all_98_3, all_46_9) = all_98_2
% 27.52/4.47 | (161) contains_slb(all_46_4, all_46_9) = all_98_4
% 27.52/4.47 | (162) lookup_slb(all_46_4, all_46_9) = all_98_3
% 27.52/4.47 | (163) remove_cpq(all_98_1, all_46_9) = all_98_0
% 27.52/4.47 | (164) triple(all_46_11, all_46_4, all_46_10) = all_98_1
% 27.52/4.47 | (165) ~ (all_98_2 = 0) | ~ (all_98_4 = 0) | all_98_0 = all_63_0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with 0, all_88_0, all_46_8, all_46_9,
% 27.52/4.47 | simplifying with (68), (144) gives:
% 27.52/4.47 | (166) all_88_0 = 0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with all_90_0, all_92_0, all_63_4, all_46_9,
% 27.52/4.47 | simplifying with (146), (150) gives:
% 27.52/4.47 | (167) all_92_0 = all_90_0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with all_55_0, all_80_0, all_46_9, all_46_8,
% 27.52/4.47 | simplifying with (69), (134) gives:
% 27.52/4.47 | (168) all_80_0 = all_55_0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with all_84_0, all_86_0, all_46_6, all_46_7,
% 27.52/4.47 | simplifying with (139), (141) gives:
% 27.52/4.47 | (169) all_86_0 = all_84_0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (26) with all_65_3, all_92_1, all_63_4, all_46_9,
% 27.52/4.47 | simplifying with (108), (151) gives:
% 27.52/4.47 | (170) all_92_1 = all_65_3
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (26) with all_57_1, all_86_1, all_46_6, all_46_7,
% 27.52/4.47 | simplifying with (71), (142) gives:
% 27.52/4.47 | (171) all_86_1 = all_57_1
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (26) with all_82_1, all_86_1, all_46_6, all_46_7,
% 27.52/4.47 | simplifying with (136), (142) gives:
% 27.52/4.47 | (172) all_86_1 = all_82_1
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (27) with all_59_1, all_98_4, all_46_9, all_46_4,
% 27.52/4.47 | simplifying with (73), (161) gives:
% 27.52/4.47 | (173) all_98_4 = all_59_1
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (27) with all_96_4, all_98_4, all_46_9, all_46_4,
% 27.52/4.47 | simplifying with (155), (161) gives:
% 27.52/4.47 | (174) all_98_4 = all_96_4
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (29) with all_63_4, all_98_3, all_46_9, all_46_4,
% 27.52/4.47 | simplifying with (84), (162) gives:
% 27.52/4.47 | (175) all_98_3 = all_63_4
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (29) with all_96_3, all_98_3, all_46_9, all_46_4,
% 27.52/4.47 | simplifying with (156), (162) gives:
% 27.52/4.47 | (176) all_98_3 = all_96_3
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (33) with all_59_0, all_96_1, bad, all_46_4,
% 27.52/4.47 | all_46_11, simplifying with (74), (158) gives:
% 27.52/4.47 | (177) all_96_1 = all_59_0
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (33) with all_46_3, all_98_1, all_46_10, all_46_4,
% 27.52/4.47 | all_46_11, simplifying with (51), (164) gives:
% 27.52/4.47 | (178) all_98_1 = all_46_3
% 27.52/4.47 |
% 27.52/4.47 | COMBINE_EQS: (175), (176) imply:
% 27.52/4.47 | (179) all_96_3 = all_63_4
% 27.52/4.47 |
% 27.52/4.47 | SIMP: (179) implies:
% 27.52/4.47 | (180) all_96_3 = all_63_4
% 27.52/4.47 |
% 27.52/4.47 | COMBINE_EQS: (173), (174) imply:
% 27.52/4.47 | (181) all_96_4 = all_59_1
% 27.52/4.47 |
% 27.52/4.47 | COMBINE_EQS: (171), (172) imply:
% 27.52/4.47 | (182) all_82_1 = all_57_1
% 27.52/4.47 |
% 27.52/4.47 | REDUCE: (163), (178) imply:
% 27.52/4.47 | (183) remove_cpq(all_46_3, all_46_9) = all_98_0
% 27.52/4.47 |
% 27.52/4.47 | REDUCE: (157), (177) imply:
% 27.52/4.47 | (184) remove_cpq(all_59_0, all_46_9) = all_96_0
% 27.52/4.47 |
% 27.52/4.47 | REDUCE: (160), (175) imply:
% 27.52/4.47 | (185) less_than(all_63_4, all_46_9) = all_98_2
% 27.52/4.47 |
% 27.52/4.47 | REDUCE: (154), (180) imply:
% 27.52/4.47 | (186) less_than(all_63_4, all_46_9) = all_96_2
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with all_63_3, all_98_2, all_46_9, all_63_4,
% 27.52/4.47 | simplifying with (81), (185) gives:
% 27.52/4.47 | (187) all_98_2 = all_63_3
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (25) with all_96_2, all_98_2, all_46_9, all_63_4,
% 27.52/4.47 | simplifying with (185), (186) gives:
% 27.52/4.47 | (188) all_98_2 = all_96_2
% 27.52/4.47 |
% 27.52/4.47 | GROUND_INST: instantiating (30) with all_46_2, all_98_0, all_46_9, all_46_3,
% 27.52/4.47 | simplifying with (50), (183) gives:
% 27.52/4.47 | (189) all_98_0 = all_46_2
% 27.52/4.47 |
% 27.52/4.47 | COMBINE_EQS: (187), (188) imply:
% 27.52/4.47 | (190) all_96_2 = all_63_3
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (2) with all_46_9, all_46_8, all_63_4, all_90_0,
% 27.52/4.48 | simplifying with (39), (40), (68), (110), (146) gives:
% 27.52/4.48 | (191) all_90_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less_than(all_46_8,
% 27.52/4.48 | all_63_4) = v0)
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (8) with all_63_4, all_46_9, all_90_0, simplifying
% 27.52/4.48 | with (39), (110), (146) gives:
% 27.52/4.48 | (192) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_63_4, all_46_9)
% 27.52/4.48 | = v0 & less_than(all_63_4, all_46_9) = v1 & ( ~ (v0 = 0) | (v1 = 0
% 27.52/4.48 | & ~ (all_90_0 = 0))))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (7) with all_46_9, all_63_4, all_90_0, simplifying
% 27.52/4.48 | with (39), (110), (146) gives:
% 27.52/4.48 | (193) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_9, all_63_4)
% 27.52/4.48 | = v0 & less_than(all_63_4, all_46_9) = v1 & ( ~ (v0 = 0) |
% 27.52/4.48 | (all_90_0 = 0 & ~ (v1 = 0))))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (7) with all_46_7, all_46_6, all_84_0, simplifying
% 27.52/4.48 | with (41), (42), (139) gives:
% 27.52/4.48 | (194) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_7, all_46_6)
% 27.52/4.48 | = v0 & less_than(all_46_6, all_46_7) = v1 & ( ~ (v0 = 0) |
% 27.52/4.48 | (all_84_0 = 0 & ~ (v1 = 0))))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (10) with all_63_4, all_46_9, all_90_1, simplifying
% 27.52/4.48 | with (39), (110), (147) gives:
% 27.52/4.48 | (195) all_90_1 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_63_4,
% 27.52/4.48 | all_46_9) = v0 & less_than(all_46_9, all_63_4) = v1 & ( ~ (v0 =
% 27.52/4.48 | 0) | v1 = 0))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (20) with all_46_11, all_46_4, bad, all_46_9,
% 27.52/4.48 | all_59_0, all_96_0, simplifying with (23), (37), (39), (43),
% 27.52/4.48 | (74), (184) gives:
% 27.52/4.48 | (196) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.52/4.48 | : ? [v5: $i] : (remove_pqp(all_46_11, all_46_9) = v3 & triple(v3,
% 27.52/4.48 | v4, bad) = v5 & lookup_slb(all_46_4, all_46_9) = v1 &
% 27.52/4.48 | remove_slb(all_46_4, all_46_9) = v4 & contains_slb(all_46_4,
% 27.52/4.48 | all_46_9) = v0 & less_than(v1, all_46_9) = v2 & $i(v5) & $i(v4) &
% 27.52/4.48 | $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 = all_96_0))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (22) with all_46_11, all_46_4, bad, all_46_9,
% 27.52/4.48 | all_59_0, all_96_0, simplifying with (23), (37), (39), (43),
% 27.52/4.48 | (74), (184) gives:
% 27.52/4.48 | (197) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 27.52/4.48 | : ? [v5: $i] : (remove_pqp(all_46_11, all_46_9) = v3 & triple(v3,
% 27.52/4.48 | v4, bad) = v5 & lookup_slb(all_46_4, all_46_9) = v1 &
% 27.52/4.48 | remove_slb(all_46_4, all_46_9) = v4 & contains_slb(all_46_4,
% 27.52/4.48 | all_46_9) = v0 & strictly_less_than(all_46_9, v1) = v2 & $i(v5) &
% 27.52/4.48 | $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v5 =
% 27.52/4.48 | all_96_0))
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (19) with all_46_11, all_46_4, bad, all_46_9,
% 27.52/4.48 | all_59_0, all_96_0, simplifying with (23), (37), (39), (43),
% 27.52/4.48 | (74), (184) gives:
% 27.52/4.48 | (198) ? [v0: any] : ? [v1: $i] : (triple(all_46_11, all_46_4, bad) = v1 &
% 27.52/4.48 | contains_slb(all_46_4, all_46_9) = v0 & $i(v1) & (v1 = all_96_0 |
% 27.52/4.48 | v0 = 0))
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (194) with fresh symbols all_119_0, all_119_1 gives:
% 27.52/4.48 | (199) strictly_less_than(all_46_7, all_46_6) = all_119_1 &
% 27.52/4.48 | less_than(all_46_6, all_46_7) = all_119_0 & ( ~ (all_119_1 = 0) |
% 27.52/4.48 | (all_84_0 = 0 & ~ (all_119_0 = 0)))
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (199) implies:
% 27.52/4.48 | (200) strictly_less_than(all_46_7, all_46_6) = all_119_1
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (198) with fresh symbols all_121_0, all_121_1 gives:
% 27.52/4.48 | (201) triple(all_46_11, all_46_4, bad) = all_121_0 & contains_slb(all_46_4,
% 27.52/4.48 | all_46_9) = all_121_1 & $i(all_121_0) & (all_121_0 = all_96_0 |
% 27.52/4.48 | all_121_1 = 0)
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (201) implies:
% 27.52/4.48 | (202) contains_slb(all_46_4, all_46_9) = all_121_1
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (193) with fresh symbols all_125_0, all_125_1 gives:
% 27.52/4.48 | (203) strictly_less_than(all_46_9, all_63_4) = all_125_1 &
% 27.52/4.48 | less_than(all_63_4, all_46_9) = all_125_0 & ( ~ (all_125_1 = 0) |
% 27.52/4.48 | (all_90_0 = 0 & ~ (all_125_0 = 0)))
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (203) implies:
% 27.52/4.48 | (204) less_than(all_63_4, all_46_9) = all_125_0
% 27.52/4.48 | (205) strictly_less_than(all_46_9, all_63_4) = all_125_1
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (192) with fresh symbols all_127_0, all_127_1 gives:
% 27.52/4.48 | (206) strictly_less_than(all_63_4, all_46_9) = all_127_1 &
% 27.52/4.48 | less_than(all_63_4, all_46_9) = all_127_0 & ( ~ (all_127_1 = 0) |
% 27.52/4.48 | (all_127_0 = 0 & ~ (all_90_0 = 0)))
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (206) implies:
% 27.52/4.48 | (207) less_than(all_63_4, all_46_9) = all_127_0
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (196) with fresh symbols all_129_0, all_129_1, all_129_2,
% 27.52/4.48 | all_129_3, all_129_4, all_129_5 gives:
% 27.52/4.48 | (208) remove_pqp(all_46_11, all_46_9) = all_129_2 & triple(all_129_2,
% 27.52/4.48 | all_129_1, bad) = all_129_0 & lookup_slb(all_46_4, all_46_9) =
% 27.52/4.48 | all_129_4 & remove_slb(all_46_4, all_46_9) = all_129_1 &
% 27.52/4.48 | contains_slb(all_46_4, all_46_9) = all_129_5 & less_than(all_129_4,
% 27.52/4.48 | all_46_9) = all_129_3 & $i(all_129_0) & $i(all_129_1) &
% 27.52/4.48 | $i(all_129_2) & $i(all_129_4) & ( ~ (all_129_3 = 0) | ~ (all_129_5 =
% 27.52/4.48 | 0) | all_129_0 = all_96_0)
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (208) implies:
% 27.52/4.48 | (209) $i(all_129_4)
% 27.52/4.48 | (210) $i(all_129_2)
% 27.52/4.48 | (211) $i(all_129_1)
% 27.52/4.48 | (212) less_than(all_129_4, all_46_9) = all_129_3
% 27.52/4.48 | (213) contains_slb(all_46_4, all_46_9) = all_129_5
% 27.52/4.48 | (214) remove_slb(all_46_4, all_46_9) = all_129_1
% 27.52/4.48 | (215) lookup_slb(all_46_4, all_46_9) = all_129_4
% 27.52/4.48 | (216) triple(all_129_2, all_129_1, bad) = all_129_0
% 27.52/4.48 | (217) remove_pqp(all_46_11, all_46_9) = all_129_2
% 27.52/4.48 |
% 27.52/4.48 | DELTA: instantiating (197) with fresh symbols all_131_0, all_131_1, all_131_2,
% 27.52/4.48 | all_131_3, all_131_4, all_131_5 gives:
% 27.52/4.48 | (218) remove_pqp(all_46_11, all_46_9) = all_131_2 & triple(all_131_2,
% 27.52/4.48 | all_131_1, bad) = all_131_0 & lookup_slb(all_46_4, all_46_9) =
% 27.52/4.48 | all_131_4 & remove_slb(all_46_4, all_46_9) = all_131_1 &
% 27.52/4.48 | contains_slb(all_46_4, all_46_9) = all_131_5 &
% 27.52/4.48 | strictly_less_than(all_46_9, all_131_4) = all_131_3 & $i(all_131_0) &
% 27.52/4.48 | $i(all_131_1) & $i(all_131_2) & $i(all_131_4) & ( ~ (all_131_3 = 0) |
% 27.52/4.48 | ~ (all_131_5 = 0) | all_131_0 = all_96_0)
% 27.52/4.48 |
% 27.52/4.48 | ALPHA: (218) implies:
% 27.52/4.48 | (219) strictly_less_than(all_46_9, all_131_4) = all_131_3
% 27.52/4.48 | (220) contains_slb(all_46_4, all_46_9) = all_131_5
% 27.52/4.48 | (221) remove_slb(all_46_4, all_46_9) = all_131_1
% 27.52/4.48 | (222) lookup_slb(all_46_4, all_46_9) = all_131_4
% 27.52/4.48 | (223) triple(all_131_2, all_131_1, bad) = all_131_0
% 27.52/4.48 | (224) remove_pqp(all_46_11, all_46_9) = all_131_2
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (25) with all_63_3, all_127_0, all_46_9, all_63_4,
% 27.52/4.48 | simplifying with (81), (207) gives:
% 27.52/4.48 | (225) all_127_0 = all_63_3
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (25) with all_125_0, all_127_0, all_46_9, all_63_4,
% 27.52/4.48 | simplifying with (204), (207) gives:
% 27.52/4.48 | (226) all_127_0 = all_125_0
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (26) with all_65_3, all_125_1, all_63_4, all_46_9,
% 27.52/4.48 | simplifying with (108), (205) gives:
% 27.52/4.48 | (227) all_125_1 = all_65_3
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (26) with all_57_1, all_119_1, all_46_6, all_46_7,
% 27.52/4.48 | simplifying with (71), (200) gives:
% 27.52/4.48 | (228) all_119_1 = all_57_1
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (27) with all_59_1, all_129_5, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (73), (213) gives:
% 27.52/4.48 | (229) all_129_5 = all_59_1
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (27) with all_129_5, all_131_5, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (213), (220) gives:
% 27.52/4.48 | (230) all_131_5 = all_129_5
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (27) with all_121_1, all_131_5, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (202), (220) gives:
% 27.52/4.48 | (231) all_131_5 = all_121_1
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (28) with all_46_1, all_131_1, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (49), (221) gives:
% 27.52/4.48 | (232) all_131_1 = all_46_1
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (28) with all_129_1, all_131_1, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (214), (221) gives:
% 27.52/4.48 | (233) all_131_1 = all_129_1
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (29) with all_63_4, all_131_4, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (84), (222) gives:
% 27.52/4.48 | (234) all_131_4 = all_63_4
% 27.52/4.48 |
% 27.52/4.48 | GROUND_INST: instantiating (29) with all_129_4, all_131_4, all_46_9, all_46_4,
% 27.52/4.48 | simplifying with (215), (222) gives:
% 27.52/4.48 | (235) all_131_4 = all_129_4
% 27.52/4.48 |
% 27.52/4.49 | GROUND_INST: instantiating (31) with all_63_2, all_131_2, all_46_9, all_46_11,
% 27.52/4.49 | simplifying with (86), (224) gives:
% 27.52/4.49 | (236) all_131_2 = all_63_2
% 27.52/4.49 |
% 27.52/4.49 | GROUND_INST: instantiating (31) with all_129_2, all_131_2, all_46_9,
% 27.52/4.49 | all_46_11, simplifying with (217), (224) gives:
% 27.52/4.49 | (237) all_131_2 = all_129_2
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (232), (233) imply:
% 27.52/4.49 | (238) all_129_1 = all_46_1
% 27.52/4.49 |
% 27.52/4.49 | SIMP: (238) implies:
% 27.52/4.49 | (239) all_129_1 = all_46_1
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (236), (237) imply:
% 27.52/4.49 | (240) all_129_2 = all_63_2
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (234), (235) imply:
% 27.52/4.49 | (241) all_129_4 = all_63_4
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (230), (231) imply:
% 27.52/4.49 | (242) all_129_5 = all_121_1
% 27.52/4.49 |
% 27.52/4.49 | SIMP: (242) implies:
% 27.52/4.49 | (243) all_129_5 = all_121_1
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (229), (243) imply:
% 27.52/4.49 | (244) all_121_1 = all_59_1
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (225), (226) imply:
% 27.52/4.49 | (245) all_125_0 = all_63_3
% 27.52/4.49 |
% 27.52/4.49 | SIMP: (245) implies:
% 27.52/4.49 | (246) all_125_0 = all_63_3
% 27.52/4.49 |
% 27.52/4.49 | REDUCE: (223), (232), (236) imply:
% 27.52/4.49 | (247) triple(all_63_2, all_46_1, bad) = all_131_0
% 27.52/4.49 |
% 27.52/4.49 | REDUCE: (216), (239), (240) imply:
% 27.52/4.49 | (248) triple(all_63_2, all_46_1, bad) = all_129_0
% 27.52/4.49 |
% 27.52/4.49 | REDUCE: (219), (234) imply:
% 27.52/4.49 | (249) strictly_less_than(all_46_9, all_63_4) = all_131_3
% 27.52/4.49 |
% 27.52/4.49 | REDUCE: (212), (241) imply:
% 27.52/4.49 | (250) less_than(all_63_4, all_46_9) = all_129_3
% 27.52/4.49 |
% 27.52/4.49 | GROUND_INST: instantiating (25) with all_63_3, all_129_3, all_46_9, all_63_4,
% 27.52/4.49 | simplifying with (81), (250) gives:
% 27.52/4.49 | (251) all_129_3 = all_63_3
% 27.52/4.49 |
% 27.52/4.49 | GROUND_INST: instantiating (26) with all_65_3, all_131_3, all_63_4, all_46_9,
% 27.52/4.49 | simplifying with (108), (249) gives:
% 27.52/4.49 | (252) all_131_3 = all_65_3
% 27.52/4.49 |
% 27.52/4.49 | GROUND_INST: instantiating (33) with all_65_0, all_131_0, bad, all_46_1,
% 27.52/4.49 | all_63_2, simplifying with (106), (247) gives:
% 27.52/4.49 | (253) all_131_0 = all_65_0
% 27.52/4.49 |
% 27.52/4.49 | GROUND_INST: instantiating (33) with all_129_0, all_131_0, bad, all_46_1,
% 27.52/4.49 | all_63_2, simplifying with (247), (248) gives:
% 27.52/4.49 | (254) all_131_0 = all_129_0
% 27.52/4.49 |
% 27.52/4.49 | COMBINE_EQS: (253), (254) imply:
% 27.52/4.49 | (255) all_129_0 = all_65_0
% 27.52/4.49 |
% 27.52/4.49 | BETA: splitting (60) gives:
% 27.52/4.49 |
% 27.52/4.49 | Case 1:
% 27.52/4.49 | |
% 27.52/4.49 | | (256) all_46_7 = all_46_9
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (56), (256) imply:
% 27.52/4.49 | | (257) lookup_slb(all_46_4, all_46_9) = all_46_6
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (57), (256) imply:
% 27.52/4.49 | | (258) remove_slb(all_46_4, all_46_9) = all_46_12
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (46), (256) imply:
% 27.52/4.49 | | (259) pair(all_46_9, all_46_6) = all_46_5
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (71), (256) imply:
% 27.52/4.49 | | (260) strictly_less_than(all_46_9, all_46_6) = all_57_1
% 27.52/4.49 | |
% 27.52/4.49 | | GROUND_INST: instantiating (28) with all_46_1, all_46_12, all_46_9,
% 27.52/4.49 | | all_46_4, simplifying with (49), (258) gives:
% 27.52/4.49 | | (261) all_46_1 = all_46_12
% 27.52/4.49 | |
% 27.52/4.49 | | GROUND_INST: instantiating (29) with all_63_4, all_46_6, all_46_9, all_46_4,
% 27.52/4.49 | | simplifying with (84), (257) gives:
% 27.52/4.49 | | (262) all_63_4 = all_46_6
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (48), (261) imply:
% 27.52/4.49 | | (263) pair_in_list(all_46_12, all_46_9, all_46_8) = all_46_0
% 27.52/4.49 | |
% 27.52/4.49 | | REDUCE: (108), (262) imply:
% 27.52/4.49 | | (264) strictly_less_than(all_46_9, all_46_6) = all_65_3
% 27.52/4.49 | |
% 27.52/4.49 | | BETA: splitting (58) gives:
% 27.52/4.49 | |
% 27.52/4.49 | | Case 1:
% 27.52/4.49 | | |
% 27.52/4.49 | | | (265) pair_in_list(all_46_12, all_46_9, all_46_8) = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | GROUND_INST: instantiating (32) with 0, all_46_0, all_46_8, all_46_9,
% 27.52/4.49 | | | all_46_12, simplifying with (263), (265) gives:
% 27.52/4.49 | | | (266) all_46_0 = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | REDUCE: (35), (266) imply:
% 27.52/4.49 | | | (267) $false
% 27.52/4.49 | | |
% 27.52/4.49 | | | CLOSE: (267) is inconsistent.
% 27.52/4.49 | | |
% 27.52/4.49 | | Case 2:
% 27.52/4.49 | | |
% 27.52/4.49 | | | (268) all_46_6 = all_46_8
% 27.52/4.49 | | |
% 27.52/4.49 | | | REDUCE: (259), (268) imply:
% 27.52/4.49 | | | (269) pair(all_46_9, all_46_8) = all_46_5
% 27.52/4.49 | | |
% 27.52/4.49 | | | REDUCE: (264), (268) imply:
% 27.52/4.49 | | | (270) strictly_less_than(all_46_9, all_46_8) = all_65_3
% 27.52/4.49 | | |
% 27.52/4.49 | | | REDUCE: (260), (268) imply:
% 27.52/4.49 | | | (271) strictly_less_than(all_46_9, all_46_8) = all_57_1
% 27.52/4.49 | | |
% 27.52/4.49 | | | GROUND_INST: instantiating (26) with 0, all_65_3, all_46_8, all_46_9,
% 27.52/4.49 | | | simplifying with (44), (270) gives:
% 27.52/4.49 | | | (272) all_65_3 = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | GROUND_INST: instantiating (26) with all_57_1, all_65_3, all_46_8,
% 27.52/4.49 | | | all_46_9, simplifying with (270), (271) gives:
% 27.52/4.49 | | | (273) all_65_3 = all_57_1
% 27.52/4.49 | | |
% 27.52/4.49 | | | COMBINE_EQS: (272), (273) imply:
% 27.52/4.49 | | | (274) all_57_1 = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | COMBINE_EQS: (182), (274) imply:
% 27.52/4.49 | | | (275) all_82_1 = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | BETA: splitting (137) gives:
% 27.52/4.49 | | |
% 27.52/4.49 | | | Case 1:
% 27.52/4.49 | | | |
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | GROUND_INST: instantiating (12) with all_46_12, all_46_9, all_46_8,
% 27.52/4.49 | | | | all_46_5, all_46_4, all_59_1, simplifying with (36), (39),
% 27.52/4.49 | | | | (40), (45), (73), (269) gives:
% 27.52/4.49 | | | | (276) all_59_1 = 0
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | COMBINE_EQS: (99), (276) imply:
% 27.52/4.49 | | | | (277) all_65_5 = 0
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | REF_CLOSE: (24), (52), (97), (128), (129), (272), (277) are inconsistent
% 27.52/4.49 | | | | by sub-proof #1.
% 27.52/4.49 | | | |
% 27.52/4.49 | | | Case 2:
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | (278) ~ (all_82_1 = 0)
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | REDUCE: (275), (278) imply:
% 27.52/4.49 | | | | (279) $false
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | CLOSE: (279) is inconsistent.
% 27.52/4.49 | | | |
% 27.52/4.49 | | | End of split
% 27.52/4.49 | | |
% 27.52/4.49 | | End of split
% 27.52/4.49 | |
% 27.52/4.49 | Case 2:
% 27.52/4.49 | |
% 27.52/4.49 | | (280) ~ (all_46_7 = all_46_9)
% 27.52/4.49 | | (281) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (remove_slb(all_46_12,
% 27.52/4.49 | | all_46_9) = v1 & contains_slb(all_46_12, all_46_9) = v0 &
% 27.52/4.49 | | insert_slb(v1, all_46_5) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) |
% 27.52/4.49 | | v2 = all_46_1))
% 27.52/4.49 | |
% 27.52/4.49 | | DELTA: instantiating (281) with fresh symbols all_148_0, all_148_1,
% 27.52/4.49 | | all_148_2 gives:
% 27.52/4.49 | | (282) remove_slb(all_46_12, all_46_9) = all_148_1 &
% 27.52/4.49 | | contains_slb(all_46_12, all_46_9) = all_148_2 &
% 27.52/4.49 | | insert_slb(all_148_1, all_46_5) = all_148_0 & $i(all_148_0) &
% 27.52/4.49 | | $i(all_148_1) & ( ~ (all_148_2 = 0) | all_148_0 = all_46_1)
% 27.52/4.49 | |
% 27.52/4.49 | | ALPHA: (282) implies:
% 27.52/4.49 | | (283) $i(all_148_1)
% 27.52/4.49 | | (284) insert_slb(all_148_1, all_46_5) = all_148_0
% 27.52/4.49 | | (285) contains_slb(all_46_12, all_46_9) = all_148_2
% 27.52/4.49 | | (286) remove_slb(all_46_12, all_46_9) = all_148_1
% 27.52/4.49 | | (287) ~ (all_148_2 = 0) | all_148_0 = all_46_1
% 27.52/4.49 | |
% 27.52/4.49 | | BETA: splitting (59) gives:
% 27.52/4.49 | |
% 27.52/4.49 | | Case 1:
% 27.52/4.49 | | |
% 27.52/4.49 | | | (288) pair_in_list(all_46_12, all_46_9, all_46_8) = 0
% 27.52/4.49 | | |
% 27.52/4.49 | | | BETA: splitting (121) gives:
% 27.52/4.49 | | |
% 27.52/4.49 | | | Case 1:
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | (289) all_46_7 = all_46_9
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | REDUCE: (280), (289) imply:
% 27.52/4.49 | | | | (290) $false
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | CLOSE: (290) is inconsistent.
% 27.52/4.49 | | | |
% 27.52/4.49 | | | Case 2:
% 27.52/4.49 | | | |
% 27.52/4.49 | | | | (291) ? [v0: any] : ? [v1: $i] : (lookup_slb(all_46_12, all_46_9) =
% 27.52/4.49 | | | | v1 & contains_slb(all_46_12, all_46_9) = v0 & $i(v1) & ( ~
% 27.52/4.49 | | | | (v0 = 0) | v1 = all_63_4))
% 27.52/4.50 | | | |
% 27.52/4.50 | | | | DELTA: instantiating (291) with fresh symbols all_158_0, all_158_1
% 27.52/4.50 | | | | gives:
% 27.52/4.50 | | | | (292) lookup_slb(all_46_12, all_46_9) = all_158_0 &
% 27.52/4.50 | | | | contains_slb(all_46_12, all_46_9) = all_158_1 & $i(all_158_0) &
% 27.52/4.50 | | | | ( ~ (all_158_1 = 0) | all_158_0 = all_63_4)
% 27.52/4.50 | | | |
% 27.52/4.50 | | | | ALPHA: (292) implies:
% 27.52/4.50 | | | | (293) $i(all_158_0)
% 27.52/4.50 | | | | (294) contains_slb(all_46_12, all_46_9) = all_158_1
% 27.52/4.50 | | | | (295) lookup_slb(all_46_12, all_46_9) = all_158_0
% 27.52/4.50 | | | | (296) ~ (all_158_1 = 0) | all_158_0 = all_63_4
% 27.52/4.50 | | | |
% 27.52/4.50 | | | | GROUND_INST: instantiating (27) with all_148_2, all_158_1, all_46_9,
% 27.52/4.50 | | | | all_46_12, simplifying with (285), (294) gives:
% 27.52/4.50 | | | | (297) all_158_1 = all_148_2
% 27.52/4.50 | | | |
% 27.73/4.50 | | | | BETA: splitting (75) gives:
% 27.73/4.50 | | | |
% 27.73/4.50 | | | | Case 1:
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | (298) all_59_1 = 0
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | COMBINE_EQS: (99), (298) imply:
% 27.73/4.50 | | | | | (299) all_65_5 = 0
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | COMBINE_EQS: (173), (298) imply:
% 27.73/4.50 | | | | | (300) all_98_4 = 0
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | REDUCE: (73), (298) imply:
% 27.73/4.50 | | | | | (301) contains_slb(all_46_4, all_46_9) = 0
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | GROUND_INST: instantiating (11) with all_46_12, all_46_7, all_46_9,
% 27.73/4.50 | | | | | all_46_6, all_46_5, all_46_4, simplifying with (36),
% 27.73/4.50 | | | | | (39), (41), (42), (45), (46), (301) gives:
% 27.73/4.50 | | | | | (302) all_46_7 = all_46_9 | contains_slb(all_46_12, all_46_9) = 0
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | BETA: splitting (87) gives:
% 27.73/4.50 | | | | |
% 27.73/4.50 | | | | | Case 1:
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | (303) ~ (all_63_3 = 0)
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | BETA: splitting (116) gives:
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | Case 1:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | (304) less_than(all_46_9, all_63_4) = 0
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | BETA: splitting (117) gives:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | (305) all_63_3 = 0
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | REDUCE: (303), (305) imply:
% 27.73/4.50 | | | | | | | | (306) $false
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | CLOSE: (306) is inconsistent.
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | (307) ? [v0: any] : ? [v1: any] :
% 27.73/4.50 | | | | | | | | (strictly_less_than(all_46_9, all_63_4) = v1 &
% 27.73/4.50 | | | | | | | | less_than(all_46_9, all_63_4) = v0 & ( ~ (v0 = 0) |
% 27.73/4.50 | | | | | | | | v1 = 0))
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | DELTA: instantiating (307) with fresh symbols all_239_0,
% 27.73/4.50 | | | | | | | | all_239_1 gives:
% 27.73/4.50 | | | | | | | | (308) strictly_less_than(all_46_9, all_63_4) = all_239_0 &
% 27.73/4.50 | | | | | | | | less_than(all_46_9, all_63_4) = all_239_1 & ( ~
% 27.73/4.50 | | | | | | | | (all_239_1 = 0) | all_239_0 = 0)
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | ALPHA: (308) implies:
% 27.73/4.50 | | | | | | | | (309) less_than(all_46_9, all_63_4) = all_239_1
% 27.73/4.50 | | | | | | | | (310) strictly_less_than(all_46_9, all_63_4) = all_239_0
% 27.73/4.50 | | | | | | | | (311) ~ (all_239_1 = 0) | all_239_0 = 0
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | BETA: splitting (120) gives:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | (312) all_65_3 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | REF_CLOSE: (24), (52), (97), (128), (129), (299), (312) are
% 27.73/4.50 | | | | | | | | | inconsistent by sub-proof #1.
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | (313) ~ (all_65_3 = 0)
% 27.73/4.50 | | | | | | | | | (314) ? [v0: any] : ? [v1: any] : (less_than(all_63_4,
% 27.73/4.50 | | | | | | | | | all_46_9) = v1 & less_than(all_46_9, all_63_4) =
% 27.73/4.50 | | | | | | | | | v0 & ( ~ (v0 = 0) | v1 = 0))
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | DELTA: instantiating (314) with fresh symbols all_245_0,
% 27.73/4.50 | | | | | | | | | all_245_1 gives:
% 27.73/4.50 | | | | | | | | | (315) less_than(all_63_4, all_46_9) = all_245_0 &
% 27.73/4.50 | | | | | | | | | less_than(all_46_9, all_63_4) = all_245_1 & ( ~
% 27.73/4.50 | | | | | | | | | (all_245_1 = 0) | all_245_0 = 0)
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | ALPHA: (315) implies:
% 27.73/4.50 | | | | | | | | | (316) less_than(all_46_9, all_63_4) = all_245_1
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | GROUND_INST: instantiating (25) with all_239_1, all_245_1,
% 27.73/4.50 | | | | | | | | | all_63_4, all_46_9, simplifying with (309), (316)
% 27.73/4.50 | | | | | | | | | gives:
% 27.73/4.50 | | | | | | | | | (317) all_245_1 = all_239_1
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_245_1, all_63_4,
% 27.73/4.50 | | | | | | | | | all_46_9, simplifying with (304), (316) gives:
% 27.73/4.50 | | | | | | | | | (318) all_245_1 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | GROUND_INST: instantiating (26) with all_65_3, all_239_0,
% 27.73/4.50 | | | | | | | | | all_63_4, all_46_9, simplifying with (108), (310)
% 27.73/4.50 | | | | | | | | | gives:
% 27.73/4.50 | | | | | | | | | (319) all_239_0 = all_65_3
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | COMBINE_EQS: (317), (318) imply:
% 27.73/4.50 | | | | | | | | | (320) all_239_1 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | SIMP: (320) implies:
% 27.73/4.50 | | | | | | | | | (321) all_239_1 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | BETA: splitting (311) gives:
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | (322) ~ (all_239_1 = 0)
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | REDUCE: (321), (322) imply:
% 27.73/4.50 | | | | | | | | | | (323) $false
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | CLOSE: (323) is inconsistent.
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | (324) all_239_0 = 0
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | COMBINE_EQS: (319), (324) imply:
% 27.73/4.50 | | | | | | | | | | (325) all_65_3 = 0
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | SIMP: (325) implies:
% 27.73/4.50 | | | | | | | | | | (326) all_65_3 = 0
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | REDUCE: (313), (326) imply:
% 27.73/4.50 | | | | | | | | | | (327) $false
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | CLOSE: (327) is inconsistent.
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | End of split
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | End of split
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | End of split
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | Case 2:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | (328) all_63_3 = 0
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | REDUCE: (303), (328) imply:
% 27.73/4.50 | | | | | | | (329) $false
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | CLOSE: (329) is inconsistent.
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | End of split
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | Case 2:
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | (330) all_63_3 = 0
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | COMBINE_EQS: (187), (330) imply:
% 27.73/4.50 | | | | | | (331) all_98_2 = 0
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | REDUCE: (81), (330) imply:
% 27.73/4.50 | | | | | | (332) less_than(all_63_4, all_46_9) = 0
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | BETA: splitting (165) gives:
% 27.73/4.50 | | | | | |
% 27.73/4.50 | | | | | | Case 1:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | (333) ~ (all_98_2 = 0)
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | REDUCE: (331), (333) imply:
% 27.73/4.50 | | | | | | | (334) $false
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | CLOSE: (334) is inconsistent.
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | Case 2:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | (335) ~ (all_98_4 = 0) | all_98_0 = all_63_0
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | BETA: splitting (335) gives:
% 27.73/4.50 | | | | | | |
% 27.73/4.50 | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | (336) ~ (all_98_4 = 0)
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | REDUCE: (300), (336) imply:
% 27.73/4.50 | | | | | | | | (337) $false
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | CLOSE: (337) is inconsistent.
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | (338) all_98_0 = all_63_0
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | COMBINE_EQS: (189), (338) imply:
% 27.73/4.50 | | | | | | | | (339) all_63_0 = all_46_2
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | REDUCE: (107), (339) imply:
% 27.73/4.50 | | | | | | | | (340) triple(all_63_2, all_46_1, all_46_10) = all_46_2
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | BETA: splitting (302) gives:
% 27.73/4.50 | | | | | | | |
% 27.73/4.50 | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | (341) contains_slb(all_46_12, all_46_9) = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | GROUND_INST: instantiating (27) with all_148_2, 0, all_46_9,
% 27.73/4.50 | | | | | | | | | all_46_12, simplifying with (285), (341) gives:
% 27.73/4.50 | | | | | | | | | (342) all_148_2 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | COMBINE_EQS: (297), (342) imply:
% 27.73/4.50 | | | | | | | | | (343) all_158_1 = 0
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | BETA: splitting (287) gives:
% 27.73/4.50 | | | | | | | | |
% 27.73/4.50 | | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | (344) ~ (all_148_2 = 0)
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | REDUCE: (342), (344) imply:
% 27.73/4.50 | | | | | | | | | | (345) $false
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | CLOSE: (345) is inconsistent.
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | (346) all_148_0 = all_46_1
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | REDUCE: (284), (346) imply:
% 27.73/4.50 | | | | | | | | | | (347) insert_slb(all_148_1, all_46_5) = all_46_1
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | BETA: splitting (296) gives:
% 27.73/4.50 | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | (348) ~ (all_158_1 = 0)
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | REDUCE: (343), (348) imply:
% 27.73/4.50 | | | | | | | | | | | (349) $false
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | CLOSE: (349) is inconsistent.
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | (350) all_158_0 = all_63_4
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | REDUCE: (295), (350) imply:
% 27.73/4.50 | | | | | | | | | | | (351) lookup_slb(all_46_12, all_46_9) = all_63_4
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | BETA: splitting (148) gives:
% 27.73/4.50 | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | (352) ~ (all_90_1 = 0)
% 27.73/4.50 | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | BETA: splitting (195) gives:
% 27.73/4.50 | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | Case 1:
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | (353) all_90_1 = 0
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | REDUCE: (352), (353) imply:
% 27.73/4.50 | | | | | | | | | | | | | (354) $false
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | CLOSE: (354) is inconsistent.
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | Case 2:
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | (355) ? [v0: any] : ? [v1: any] : (less_than(all_63_4,
% 27.73/4.50 | | | | | | | | | | | | | all_46_9) = v0 & less_than(all_46_9, all_63_4)
% 27.73/4.50 | | | | | | | | | | | | | = v1 & ( ~ (v0 = 0) | v1 = 0))
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | DELTA: instantiating (355) with fresh symbols all_273_0,
% 27.73/4.50 | | | | | | | | | | | | | all_273_1 gives:
% 27.73/4.50 | | | | | | | | | | | | | (356) less_than(all_63_4, all_46_9) = all_273_1 &
% 27.73/4.50 | | | | | | | | | | | | | less_than(all_46_9, all_63_4) = all_273_0 & ( ~
% 27.73/4.50 | | | | | | | | | | | | | (all_273_1 = 0) | all_273_0 = 0)
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | ALPHA: (356) implies:
% 27.73/4.50 | | | | | | | | | | | | | (357) less_than(all_63_4, all_46_9) = all_273_1
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_273_1, all_46_9,
% 27.73/4.50 | | | | | | | | | | | | | all_63_4, simplifying with (332), (357) gives:
% 27.73/4.50 | | | | | | | | | | | | | (358) all_273_1 = 0
% 27.73/4.50 | | | | | | | | | | | | |
% 27.73/4.50 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_46_8, all_63_4,
% 27.73/4.50 | | | | | | | | | | | | | all_46_9, all_55_0, simplifying with (39), (40),
% 27.73/4.50 | | | | | | | | | | | | | (69), (110), (332) gives:
% 27.73/4.51 | | | | | | | | | | | | | (359) all_55_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 27.73/4.51 | | | | | | | | | | | | | less_than(all_46_8, all_63_4) = v0)
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_63_4, all_46_9,
% 27.73/4.51 | | | | | | | | | | | | | all_46_8, simplifying with (39), (40), (68),
% 27.73/4.51 | | | | | | | | | | | | | (110), (332) gives:
% 27.73/4.51 | | | | | | | | | | | | | (360) less_than(all_63_4, all_46_8) = 0
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_148_1, all_46_7,
% 27.73/4.51 | | | | | | | | | | | | | all_46_9, all_46_6, all_46_8, all_46_5, all_46_1,
% 27.73/4.51 | | | | | | | | | | | | | all_46_0, simplifying with (39), (40), (41), (42),
% 27.73/4.51 | | | | | | | | | | | | | (46), (48), (283), (347) gives:
% 27.73/4.51 | | | | | | | | | | | | | (361) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 27.73/4.51 | | | | | | | | | | | | | pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.51 | | | | | | | | | | | | | v0)
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | GROUND_INST: instantiating (ax37) with all_63_2, all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | bad, all_46_7, all_46_6, all_46_5, all_46_1,
% 27.73/4.51 | | | | | | | | | | | | | all_65_0, simplifying with (23), (41), (42), (46),
% 27.73/4.51 | | | | | | | | | | | | | (106), (109), (283), (347) gives:
% 27.73/4.51 | | | | | | | | | | | | | (362) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.73/4.51 | | | | | | | | | | | | | [v3: any] : (triple(all_63_2, all_148_1, bad) = v2
% 27.73/4.51 | | | | | | | | | | | | | & check_cpq(v2) = v3 & check_cpq(all_65_0) = v1
% 27.73/4.51 | | | | | | | | | | | | | & less_than(all_46_6, all_46_7) = v0 & $i(v2) &
% 27.73/4.51 | | | | | | | | | | | | | ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1
% 27.73/4.51 | | | | | | | | | | | | | = 0) | v3 = 0))))
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | GROUND_INST: instantiating (ax37) with all_63_2, all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | all_46_10, all_46_7, all_46_6, all_46_5, all_46_1,
% 27.73/4.51 | | | | | | | | | | | | | all_46_2, simplifying with (38), (41), (42), (46),
% 27.73/4.51 | | | | | | | | | | | | | (109), (283), (340), (347) gives:
% 27.73/4.51 | | | | | | | | | | | | | (363) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.73/4.51 | | | | | | | | | | | | | [v3: any] : (triple(all_63_2, all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | all_46_10) = v2 & check_cpq(v2) = v3 &
% 27.73/4.51 | | | | | | | | | | | | | check_cpq(all_46_2) = v1 & less_than(all_46_6,
% 27.73/4.51 | | | | | | | | | | | | | all_46_7) = v0 & $i(v2) & ( ~ (v0 = 0) | (( ~
% 27.73/4.51 | | | | | | | | | | | | | (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 27.73/4.51 | | | | | | | | | | | | | 0))))
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | DELTA: instantiating (362) with fresh symbols all_293_0,
% 27.73/4.51 | | | | | | | | | | | | | all_293_1, all_293_2, all_293_3 gives:
% 27.73/4.51 | | | | | | | | | | | | | (364) triple(all_63_2, all_148_1, bad) = all_293_1 &
% 27.73/4.51 | | | | | | | | | | | | | check_cpq(all_293_1) = all_293_0 &
% 27.73/4.51 | | | | | | | | | | | | | check_cpq(all_65_0) = all_293_2 &
% 27.73/4.51 | | | | | | | | | | | | | less_than(all_46_6, all_46_7) = all_293_3 &
% 27.73/4.51 | | | | | | | | | | | | | $i(all_293_1) & ( ~ (all_293_3 = 0) | (( ~
% 27.73/4.51 | | | | | | | | | | | | | (all_293_0 = 0) | all_293_2 = 0) & ( ~
% 27.73/4.51 | | | | | | | | | | | | | (all_293_2 = 0) | all_293_0 = 0)))
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | ALPHA: (364) implies:
% 27.73/4.51 | | | | | | | | | | | | | (365) triple(all_63_2, all_148_1, bad) = all_293_1
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | DELTA: instantiating (363) with fresh symbols all_295_0,
% 27.73/4.51 | | | | | | | | | | | | | all_295_1, all_295_2, all_295_3 gives:
% 27.73/4.51 | | | | | | | | | | | | | (366) triple(all_63_2, all_148_1, all_46_10) = all_295_1
% 27.73/4.51 | | | | | | | | | | | | | & check_cpq(all_295_1) = all_295_0 &
% 27.73/4.51 | | | | | | | | | | | | | check_cpq(all_46_2) = all_295_2 &
% 27.73/4.51 | | | | | | | | | | | | | less_than(all_46_6, all_46_7) = all_295_3 &
% 27.73/4.51 | | | | | | | | | | | | | $i(all_295_1) & ( ~ (all_295_3 = 0) | (( ~
% 27.73/4.51 | | | | | | | | | | | | | (all_295_0 = 0) | all_295_2 = 0) & ( ~
% 27.73/4.51 | | | | | | | | | | | | | (all_295_2 = 0) | all_295_0 = 0)))
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | ALPHA: (366) implies:
% 27.73/4.51 | | | | | | | | | | | | | (367) triple(all_63_2, all_148_1, all_46_10) = all_295_1
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | BETA: splitting (361) gives:
% 27.73/4.51 | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | Case 1:
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | (368) all_46_0 = 0
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | REDUCE: (35), (368) imply:
% 27.73/4.51 | | | | | | | | | | | | | | (369) $false
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | CLOSE: (369) is inconsistent.
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | Case 2:
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | (370) ? [v0: int] : ( ~ (v0 = 0) &
% 27.73/4.51 | | | | | | | | | | | | | | pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.51 | | | | | | | | | | | | | | v0)
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | DELTA: instantiating (370) with fresh symbol all_301_0
% 27.73/4.51 | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | (371) ~ (all_301_0 = 0) & pair_in_list(all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | | all_46_9, all_46_8) = all_301_0
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | ALPHA: (371) implies:
% 27.73/4.51 | | | | | | | | | | | | | | (372) ~ (all_301_0 = 0)
% 27.73/4.51 | | | | | | | | | | | | | | (373) pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.51 | | | | | | | | | | | | | | all_301_0
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | BETA: splitting (359) gives:
% 27.73/4.51 | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | Case 1:
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | (374) all_55_0 = 0
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | REDUCE: (67), (374) imply:
% 27.73/4.51 | | | | | | | | | | | | | | | (375) $false
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | CLOSE: (375) is inconsistent.
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | Case 2:
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | (376) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_46_8,
% 27.73/4.51 | | | | | | | | | | | | | | | all_63_4) = v0)
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | DELTA: instantiating (376) with fresh symbol all_306_0
% 27.73/4.51 | | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (377) ~ (all_306_0 = 0) & less_than(all_46_8, all_63_4)
% 27.73/4.51 | | | | | | | | | | | | | | | = all_306_0
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 27.73/4.51 | | | | | | | | | | | | | | | (378) ~ (all_306_0 = 0)
% 27.73/4.51 | | | | | | | | | | | | | | | (379) less_than(all_46_8, all_63_4) = all_306_0
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_46_8, all_63_4,
% 27.73/4.51 | | | | | | | | | | | | | | | all_306_0, simplifying with (40), (110), (379)
% 27.73/4.51 | | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (380) ? [v0: any] : ? [v1: any] :
% 27.73/4.51 | | | | | | | | | | | | | | | (strictly_less_than(all_46_8, all_63_4) = v0 &
% 27.73/4.51 | | | | | | | | | | | | | | | less_than(all_63_4, all_46_8) = v1 & ( ~ (v0 =
% 27.73/4.51 | | | | | | | | | | | | | | | 0) | (all_306_0 = 0 & ~ (v1 = 0))))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_63_4, all_46_8,
% 27.73/4.51 | | | | | | | | | | | | | | | simplifying with (40), (110), (360) gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (381) ? [v0: any] : ? [v1: any] :
% 27.73/4.51 | | | | | | | | | | | | | | | (strictly_less_than(all_63_4, all_46_8) = v1 &
% 27.73/4.51 | | | | | | | | | | | | | | | less_than(all_46_8, all_63_4) = v0 & (v1 = 0 |
% 27.73/4.51 | | | | | | | | | | | | | | | v0 = 0))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_46_11, all_46_12, bad,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9, all_63_2, all_148_1, all_293_1,
% 27.73/4.51 | | | | | | | | | | | | | | | simplifying with (23), (36), (37), (39), (86),
% 27.73/4.51 | | | | | | | | | | | | | | | (286), (365) gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (382) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ?
% 27.73/4.51 | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (triple(all_46_11,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_12, bad) = v3 & remove_cpq(v3,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v4 & lookup_slb(all_46_12,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v1 & contains_slb(all_46_12,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v0 & less_than(v1, all_46_9) = v2
% 27.73/4.51 | | | | | | | | | | | | | | | & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~
% 27.73/4.51 | | | | | | | | | | | | | | | (v0 = 0) | v4 = all_293_1))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_46_11, all_46_12,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_10, all_46_9, all_63_2, all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | | | all_295_1, simplifying with (36), (37), (38),
% 27.73/4.51 | | | | | | | | | | | | | | | (39), (86), (286), (367) gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (383) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ?
% 27.73/4.51 | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (triple(all_46_11,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_12, all_46_10) = v3 & remove_cpq(v3,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v4 & lookup_slb(all_46_12,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v1 & contains_slb(all_46_12,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_9) = v0 & less_than(v1, all_46_9) = v2
% 27.73/4.51 | | | | | | | | | | | | | | | & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~
% 27.73/4.51 | | | | | | | | | | | | | | | (v0 = 0) | v4 = all_295_1))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_63_2, all_148_1,
% 27.73/4.51 | | | | | | | | | | | | | | | all_46_10, all_295_1, simplifying with (38),
% 27.73/4.51 | | | | | | | | | | | | | | | (109), (283), (367) gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (384) all_46_10 = bad | ok(all_295_1) = 0
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | DELTA: instantiating (381) with fresh symbols all_333_0,
% 27.73/4.51 | | | | | | | | | | | | | | | all_333_1 gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (385) strictly_less_than(all_63_4, all_46_8) = all_333_0
% 27.73/4.51 | | | | | | | | | | | | | | | & less_than(all_46_8, all_63_4) = all_333_1 &
% 27.73/4.51 | | | | | | | | | | | | | | | (all_333_0 = 0 | all_333_1 = 0)
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 27.73/4.51 | | | | | | | | | | | | | | | (386) less_than(all_46_8, all_63_4) = all_333_1
% 27.73/4.51 | | | | | | | | | | | | | | | (387) all_333_0 = 0 | all_333_1 = 0
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | DELTA: instantiating (380) with fresh symbols all_345_0,
% 27.73/4.51 | | | | | | | | | | | | | | | all_345_1 gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (388) strictly_less_than(all_46_8, all_63_4) = all_345_1
% 27.73/4.51 | | | | | | | | | | | | | | | & less_than(all_63_4, all_46_8) = all_345_0 & ( ~
% 27.73/4.51 | | | | | | | | | | | | | | | (all_345_1 = 0) | (all_306_0 = 0 & ~ (all_345_0
% 27.73/4.51 | | | | | | | | | | | | | | | = 0)))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | ALPHA: (388) implies:
% 27.73/4.51 | | | | | | | | | | | | | | | (389) ~ (all_345_1 = 0) | (all_306_0 = 0 & ~
% 27.73/4.51 | | | | | | | | | | | | | | | (all_345_0 = 0))
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | DELTA: instantiating (382) with fresh symbols all_349_0,
% 27.73/4.51 | | | | | | | | | | | | | | | all_349_1, all_349_2, all_349_3, all_349_4 gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (390) triple(all_46_11, all_46_12, bad) = all_349_1 &
% 27.73/4.51 | | | | | | | | | | | | | | | remove_cpq(all_349_1, all_46_9) = all_349_0 &
% 27.73/4.51 | | | | | | | | | | | | | | | lookup_slb(all_46_12, all_46_9) = all_349_3 &
% 27.73/4.51 | | | | | | | | | | | | | | | contains_slb(all_46_12, all_46_9) = all_349_4 &
% 27.73/4.51 | | | | | | | | | | | | | | | less_than(all_349_3, all_46_9) = all_349_2 &
% 27.73/4.51 | | | | | | | | | | | | | | | $i(all_349_0) & $i(all_349_1) & $i(all_349_3) & (
% 27.73/4.51 | | | | | | | | | | | | | | | ~ (all_349_2 = 0) | ~ (all_349_4 = 0) |
% 27.73/4.51 | | | | | | | | | | | | | | | all_349_0 = all_293_1)
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 27.73/4.51 | | | | | | | | | | | | | | | (391) less_than(all_349_3, all_46_9) = all_349_2
% 27.73/4.51 | | | | | | | | | | | | | | | (392) lookup_slb(all_46_12, all_46_9) = all_349_3
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | DELTA: instantiating (383) with fresh symbols all_351_0,
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_1, all_351_2, all_351_3, all_351_4 gives:
% 27.73/4.51 | | | | | | | | | | | | | | | (393) triple(all_46_11, all_46_12, all_46_10) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_1 & remove_cpq(all_351_1, all_46_9) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_0 & lookup_slb(all_46_12, all_46_9) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_3 & contains_slb(all_46_12, all_46_9) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_4 & less_than(all_351_3, all_46_9) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_2 & $i(all_351_0) & $i(all_351_1) &
% 27.73/4.51 | | | | | | | | | | | | | | | $i(all_351_3) & ( ~ (all_351_2 = 0) | ~
% 27.73/4.51 | | | | | | | | | | | | | | | (all_351_4 = 0) | all_351_0 = all_295_1)
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 27.73/4.51 | | | | | | | | | | | | | | | (394) less_than(all_351_3, all_46_9) = all_351_2
% 27.73/4.51 | | | | | | | | | | | | | | | (395) contains_slb(all_46_12, all_46_9) = all_351_4
% 27.73/4.51 | | | | | | | | | | | | | | | (396) lookup_slb(all_46_12, all_46_9) = all_351_3
% 27.73/4.51 | | | | | | | | | | | | | | | (397) remove_cpq(all_351_1, all_46_9) = all_351_0
% 27.73/4.51 | | | | | | | | | | | | | | | (398) triple(all_46_11, all_46_12, all_46_10) =
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_1
% 27.73/4.51 | | | | | | | | | | | | | | | (399) ~ (all_351_2 = 0) | ~ (all_351_4 = 0) |
% 27.73/4.51 | | | | | | | | | | | | | | | all_351_0 = all_295_1
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 27.73/4.51 | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | Case 1:
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_306_0, all_333_1,
% 27.73/4.51 | | | | | | | | | | | | | | | | all_63_4, all_46_8, simplifying with (379), (386)
% 27.73/4.51 | | | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | | | (400) all_333_1 = all_306_0
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_351_4, all_46_9,
% 27.73/4.51 | | | | | | | | | | | | | | | | all_46_12, simplifying with (341), (395) gives:
% 27.73/4.51 | | | | | | | | | | | | | | | | (401) all_351_4 = 0
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_63_4, all_351_3,
% 27.73/4.51 | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (351), (396)
% 27.73/4.51 | | | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | | | (402) all_351_3 = all_63_4
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_349_3, all_351_3,
% 27.73/4.51 | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (392), (396)
% 27.73/4.51 | | | | | | | | | | | | | | | | gives:
% 27.73/4.51 | | | | | | | | | | | | | | | | (403) all_351_3 = all_349_3
% 27.73/4.51 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_61_1, all_351_1,
% 27.73/4.52 | | | | | | | | | | | | | | | | all_46_10, all_46_12, all_46_11, simplifying with
% 27.73/4.52 | | | | | | | | | | | | | | | | (78), (398) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | (404) all_351_1 = all_61_1
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | COMBINE_EQS: (402), (403) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | (405) all_349_3 = all_63_4
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | SIMP: (405) implies:
% 27.73/4.52 | | | | | | | | | | | | | | | | (406) all_349_3 = all_63_4
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | REDUCE: (397), (404) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | (407) remove_cpq(all_61_1, all_46_9) = all_351_0
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | REDUCE: (394), (402) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | (408) less_than(all_63_4, all_46_9) = all_351_2
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | REDUCE: (391), (406) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | (409) less_than(all_63_4, all_46_9) = all_349_2
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | BETA: splitting (387) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_351_2, all_46_9,
% 27.73/4.52 | | | | | | | | | | | | | | | | | all_63_4, simplifying with (332), (408) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (410) all_351_2 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_349_2, all_351_2,
% 27.73/4.52 | | | | | | | | | | | | | | | | | all_46_9, all_63_4, simplifying with (408), (409)
% 27.73/4.52 | | | | | | | | | | | | | | | | | gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (411) all_351_2 = all_349_2
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (411) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (412) all_349_2 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | (413) ~ (all_351_2 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | REDUCE: (410), (413) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | (414) $false
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | (415) ~ (all_351_4 = 0) | all_351_0 = all_295_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | (416) ~ (all_351_4 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | REDUCE: (401), (416) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | (417) $false
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | CLOSE: (417) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | (418) all_351_0 = all_295_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | REDUCE: (407), (418) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | (419) remove_cpq(all_61_1, all_46_9) = all_295_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (420) ok(all_295_1) = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (54) with all_46_11, all_46_10,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_9, all_46_8, all_61_1, all_295_1,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | simplifying with (37), (38), (39), (40), (78),
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (288), (419), (420) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (421) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (remove_slb(all_46_12, all_46_9) = v1 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | pair_in_list(v1, all_46_9, all_46_8) = v2 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | strictly_less_than(all_46_9, all_46_8) = v0 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with all_46_11, all_46_10,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_9, all_46_8, all_61_1, all_295_1,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | simplifying with (37), (38), (39), (40), (44),
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (78), (419), (420) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (422) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (remove_slb(all_46_12, all_46_9) = v1 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | pair_in_list(v1, all_46_9, all_46_8) = v2 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | pair_in_list(all_46_12, all_46_9, all_46_8) = v0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (422) with fresh symbols all_403_0,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_403_1, all_403_2 gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (423) remove_slb(all_46_12, all_46_9) = all_403_1 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | pair_in_list(all_403_1, all_46_9, all_46_8) =
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_403_0 & pair_in_list(all_46_12, all_46_9,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_8) = all_403_2 & $i(all_403_1) & ( ~
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (all_403_2 = 0) | all_403_0 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (424) remove_slb(all_46_12, all_46_9) = all_403_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (421) with fresh symbols all_405_0,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_405_1, all_405_2 gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (425) remove_slb(all_46_12, all_46_9) = all_405_1 &
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | pair_in_list(all_405_1, all_46_9, all_46_8) =
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_405_0 & strictly_less_than(all_46_9, all_46_8)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | = all_405_2 & $i(all_405_1) & ( ~ (all_405_2 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | all_405_0 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (426) strictly_less_than(all_46_9, all_46_8) = all_405_2
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (427) pair_in_list(all_405_1, all_46_9, all_46_8) =
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_405_0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (428) remove_slb(all_46_12, all_46_9) = all_405_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (429) ~ (all_405_2 = 0) | all_405_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_405_2, all_46_8,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_9, simplifying with (44), (426) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (430) all_405_2 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_148_1, all_405_1,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (286), (428)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (431) all_405_1 = all_148_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_403_1, all_405_1,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (424), (428)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (432) all_405_1 = all_403_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (431), (432) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (433) all_403_1 = all_148_1
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (427), (431) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (434) pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_405_0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (435) ~ (all_405_2 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (430), (435) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (436) $false
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (436) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (437) all_405_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (437) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (438) pair_in_list(all_148_1, all_46_9, all_46_8) = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_301_0, 0, all_46_8,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | all_46_9, all_148_1, simplifying with (373), (438)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (439) all_301_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (439) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | (440) $false
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (441) all_46_10 = bad
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (441) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (442) triple(all_63_2, all_46_1, bad) = all_46_2
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_65_0, all_46_2, bad,
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | all_46_1, all_63_2, simplifying with (106), (442)
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | gives:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (443) all_65_0 = all_46_2
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (443) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | (444) ok(all_46_2) = all_76_0
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (52), (128), (444) are inconsistent by
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | (445) all_333_1 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | COMBINE_EQS: (400), (445) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (446) all_306_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | SIMP: (446) implies:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (447) all_306_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | REDUCE: (378), (447) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | | (448) $false
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | | CLOSE: (448) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | (449) all_306_0 = 0 & ~ (all_345_0 = 0)
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | ALPHA: (449) implies:
% 27.73/4.52 | | | | | | | | | | | | | | | | (450) all_306_0 = 0
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | REDUCE: (378), (450) imply:
% 27.73/4.52 | | | | | | | | | | | | | | | | (451) $false
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | End of split
% 27.73/4.52 | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | (452) all_63_3 = 0 & ~ (all_90_0 = 0)
% 27.73/4.52 | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | ALPHA: (452) implies:
% 27.73/4.52 | | | | | | | | | | | | (453) ~ (all_90_0 = 0)
% 27.73/4.52 | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | BETA: splitting (191) gives:
% 27.73/4.52 | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | Case 1:
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | (454) all_90_0 = 0
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | REDUCE: (453), (454) imply:
% 27.73/4.52 | | | | | | | | | | | | | (455) $false
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | CLOSE: (455) is inconsistent.
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | Case 2:
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_148_1, all_46_7,
% 27.73/4.52 | | | | | | | | | | | | | all_46_9, all_46_6, all_46_8, all_46_5, all_46_1,
% 27.73/4.52 | | | | | | | | | | | | | all_46_0, simplifying with (39), (40), (41), (42),
% 27.73/4.52 | | | | | | | | | | | | | (46), (48), (283), (347) gives:
% 27.73/4.52 | | | | | | | | | | | | | (456) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 27.73/4.52 | | | | | | | | | | | | | pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.52 | | | | | | | | | | | | | v0)
% 27.73/4.52 | | | | | | | | | | | | |
% 27.73/4.52 | | | | | | | | | | | | | GROUND_INST: instantiating (ax37) with all_63_2, all_148_1,
% 27.73/4.52 | | | | | | | | | | | | | bad, all_46_7, all_46_6, all_46_5, all_46_1,
% 27.73/4.52 | | | | | | | | | | | | | all_65_0, simplifying with (23), (41), (42), (46),
% 27.73/4.52 | | | | | | | | | | | | | (106), (109), (283), (347) gives:
% 27.73/4.53 | | | | | | | | | | | | | (457) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.73/4.53 | | | | | | | | | | | | | [v3: any] : (triple(all_63_2, all_148_1, bad) = v2
% 27.73/4.53 | | | | | | | | | | | | | & check_cpq(v2) = v3 & check_cpq(all_65_0) = v1
% 27.73/4.53 | | | | | | | | | | | | | & less_than(all_46_6, all_46_7) = v0 & $i(v2) &
% 27.73/4.53 | | | | | | | | | | | | | ( ~ (v0 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1
% 27.73/4.53 | | | | | | | | | | | | | = 0) | v3 = 0))))
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | GROUND_INST: instantiating (ax37) with all_63_2, all_148_1,
% 27.73/4.53 | | | | | | | | | | | | | all_46_10, all_46_7, all_46_6, all_46_5, all_46_1,
% 27.73/4.53 | | | | | | | | | | | | | all_46_2, simplifying with (38), (41), (42), (46),
% 27.73/4.53 | | | | | | | | | | | | | (109), (283), (340), (347) gives:
% 27.73/4.53 | | | | | | | | | | | | | (458) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.73/4.53 | | | | | | | | | | | | | [v3: any] : (triple(all_63_2, all_148_1,
% 27.73/4.53 | | | | | | | | | | | | | all_46_10) = v2 & check_cpq(v2) = v3 &
% 27.73/4.53 | | | | | | | | | | | | | check_cpq(all_46_2) = v1 & less_than(all_46_6,
% 27.73/4.53 | | | | | | | | | | | | | all_46_7) = v0 & $i(v2) & ( ~ (v0 = 0) | (( ~
% 27.73/4.53 | | | | | | | | | | | | | (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 =
% 27.73/4.53 | | | | | | | | | | | | | 0))))
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | DELTA: instantiating (457) with fresh symbols all_289_0,
% 27.73/4.53 | | | | | | | | | | | | | all_289_1, all_289_2, all_289_3 gives:
% 27.73/4.53 | | | | | | | | | | | | | (459) triple(all_63_2, all_148_1, bad) = all_289_1 &
% 27.73/4.53 | | | | | | | | | | | | | check_cpq(all_289_1) = all_289_0 &
% 27.73/4.53 | | | | | | | | | | | | | check_cpq(all_65_0) = all_289_2 &
% 27.73/4.53 | | | | | | | | | | | | | less_than(all_46_6, all_46_7) = all_289_3 &
% 27.73/4.53 | | | | | | | | | | | | | $i(all_289_1) & ( ~ (all_289_3 = 0) | (( ~
% 27.73/4.53 | | | | | | | | | | | | | (all_289_0 = 0) | all_289_2 = 0) & ( ~
% 27.73/4.53 | | | | | | | | | | | | | (all_289_2 = 0) | all_289_0 = 0)))
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | ALPHA: (459) implies:
% 27.73/4.53 | | | | | | | | | | | | | (460) triple(all_63_2, all_148_1, bad) = all_289_1
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | DELTA: instantiating (458) with fresh symbols all_291_0,
% 27.73/4.53 | | | | | | | | | | | | | all_291_1, all_291_2, all_291_3 gives:
% 27.73/4.53 | | | | | | | | | | | | | (461) triple(all_63_2, all_148_1, all_46_10) = all_291_1
% 27.73/4.53 | | | | | | | | | | | | | & check_cpq(all_291_1) = all_291_0 &
% 27.73/4.53 | | | | | | | | | | | | | check_cpq(all_46_2) = all_291_2 &
% 27.73/4.53 | | | | | | | | | | | | | less_than(all_46_6, all_46_7) = all_291_3 &
% 27.73/4.53 | | | | | | | | | | | | | $i(all_291_1) & ( ~ (all_291_3 = 0) | (( ~
% 27.73/4.53 | | | | | | | | | | | | | (all_291_0 = 0) | all_291_2 = 0) & ( ~
% 27.73/4.53 | | | | | | | | | | | | | (all_291_2 = 0) | all_291_0 = 0)))
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | ALPHA: (461) implies:
% 27.73/4.53 | | | | | | | | | | | | | (462) triple(all_63_2, all_148_1, all_46_10) = all_291_1
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | BETA: splitting (456) gives:
% 27.73/4.53 | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | Case 1:
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | (463) all_46_0 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | REDUCE: (35), (463) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (464) $false
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | CLOSE: (464) is inconsistent.
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | Case 2:
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | (465) ? [v0: int] : ( ~ (v0 = 0) &
% 27.73/4.53 | | | | | | | | | | | | | | pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.53 | | | | | | | | | | | | | | v0)
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | DELTA: instantiating (465) with fresh symbol all_300_0
% 27.73/4.53 | | | | | | | | | | | | | | gives:
% 27.73/4.53 | | | | | | | | | | | | | | (466) ~ (all_300_0 = 0) & pair_in_list(all_148_1,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_46_8) = all_300_0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | ALPHA: (466) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (467) ~ (all_300_0 = 0)
% 27.73/4.53 | | | | | | | | | | | | | | (468) pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.53 | | | | | | | | | | | | | | all_300_0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_46_11, all_46_12, bad,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_63_2, all_148_1, all_289_1,
% 27.73/4.53 | | | | | | | | | | | | | | simplifying with (23), (36), (37), (39), (86),
% 27.73/4.53 | | | | | | | | | | | | | | (286), (460) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (469) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ?
% 27.73/4.53 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (triple(all_46_11,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_12, bad) = v3 & remove_cpq(v3,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v4 & lookup_slb(all_46_12,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v1 & contains_slb(all_46_12,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v0 & less_than(v1, all_46_9) = v2
% 27.73/4.53 | | | | | | | | | | | | | | & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~
% 27.73/4.53 | | | | | | | | | | | | | | (v0 = 0) | v4 = all_289_1))
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_46_11, all_46_12,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_10, all_46_9, all_63_2, all_148_1,
% 27.73/4.53 | | | | | | | | | | | | | | all_291_1, simplifying with (36), (37), (38),
% 27.73/4.53 | | | | | | | | | | | | | | (39), (86), (286), (462) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (470) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ?
% 27.73/4.53 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (triple(all_46_11,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_12, all_46_10) = v3 & remove_cpq(v3,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v4 & lookup_slb(all_46_12,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v1 & contains_slb(all_46_12,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9) = v0 & less_than(v1, all_46_9) = v2
% 27.73/4.53 | | | | | | | | | | | | | | & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ~
% 27.73/4.53 | | | | | | | | | | | | | | (v0 = 0) | v4 = all_291_1))
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_63_2, all_148_1,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_10, all_291_1, simplifying with (38),
% 27.73/4.53 | | | | | | | | | | | | | | (109), (283), (462) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (471) all_46_10 = bad | ok(all_291_1) = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | DELTA: instantiating (470) with fresh symbols all_335_0,
% 27.73/4.53 | | | | | | | | | | | | | | all_335_1, all_335_2, all_335_3, all_335_4 gives:
% 27.73/4.53 | | | | | | | | | | | | | | (472) triple(all_46_11, all_46_12, all_46_10) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_1 & remove_cpq(all_335_1, all_46_9) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_0 & lookup_slb(all_46_12, all_46_9) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_3 & contains_slb(all_46_12, all_46_9) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_4 & less_than(all_335_3, all_46_9) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_2 & $i(all_335_0) & $i(all_335_1) &
% 27.73/4.53 | | | | | | | | | | | | | | $i(all_335_3) & ( ~ (all_335_2 = 0) | ~
% 27.73/4.53 | | | | | | | | | | | | | | (all_335_4 = 0) | all_335_0 = all_291_1)
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | ALPHA: (472) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (473) less_than(all_335_3, all_46_9) = all_335_2
% 27.73/4.53 | | | | | | | | | | | | | | (474) contains_slb(all_46_12, all_46_9) = all_335_4
% 27.73/4.53 | | | | | | | | | | | | | | (475) lookup_slb(all_46_12, all_46_9) = all_335_3
% 27.73/4.53 | | | | | | | | | | | | | | (476) remove_cpq(all_335_1, all_46_9) = all_335_0
% 27.73/4.53 | | | | | | | | | | | | | | (477) triple(all_46_11, all_46_12, all_46_10) =
% 27.73/4.53 | | | | | | | | | | | | | | all_335_1
% 27.73/4.53 | | | | | | | | | | | | | | (478) ~ (all_335_2 = 0) | ~ (all_335_4 = 0) |
% 27.73/4.53 | | | | | | | | | | | | | | all_335_0 = all_291_1
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | DELTA: instantiating (469) with fresh symbols all_337_0,
% 27.73/4.53 | | | | | | | | | | | | | | all_337_1, all_337_2, all_337_3, all_337_4 gives:
% 27.73/4.53 | | | | | | | | | | | | | | (479) triple(all_46_11, all_46_12, bad) = all_337_1 &
% 27.73/4.53 | | | | | | | | | | | | | | remove_cpq(all_337_1, all_46_9) = all_337_0 &
% 27.73/4.53 | | | | | | | | | | | | | | lookup_slb(all_46_12, all_46_9) = all_337_3 &
% 27.73/4.53 | | | | | | | | | | | | | | contains_slb(all_46_12, all_46_9) = all_337_4 &
% 27.73/4.53 | | | | | | | | | | | | | | less_than(all_337_3, all_46_9) = all_337_2 &
% 27.73/4.53 | | | | | | | | | | | | | | $i(all_337_0) & $i(all_337_1) & $i(all_337_3) & (
% 27.73/4.53 | | | | | | | | | | | | | | ~ (all_337_2 = 0) | ~ (all_337_4 = 0) |
% 27.73/4.53 | | | | | | | | | | | | | | all_337_0 = all_289_1)
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | ALPHA: (479) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (480) less_than(all_337_3, all_46_9) = all_337_2
% 27.73/4.53 | | | | | | | | | | | | | | (481) contains_slb(all_46_12, all_46_9) = all_337_4
% 27.73/4.53 | | | | | | | | | | | | | | (482) lookup_slb(all_46_12, all_46_9) = all_337_3
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with 0, all_337_4, all_46_9,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_12, simplifying with (341), (481) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (483) all_337_4 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_335_4, all_337_4,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (474), (481)
% 27.73/4.53 | | | | | | | | | | | | | | gives:
% 27.73/4.53 | | | | | | | | | | | | | | (484) all_337_4 = all_335_4
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_63_4, all_337_3,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (351), (482)
% 27.73/4.53 | | | | | | | | | | | | | | gives:
% 27.73/4.53 | | | | | | | | | | | | | | (485) all_337_3 = all_63_4
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_335_3, all_337_3,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (475), (482)
% 27.73/4.53 | | | | | | | | | | | | | | gives:
% 27.73/4.53 | | | | | | | | | | | | | | (486) all_337_3 = all_335_3
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_61_1, all_335_1,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_10, all_46_12, all_46_11, simplifying with
% 27.73/4.53 | | | | | | | | | | | | | | (78), (477) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (487) all_335_1 = all_61_1
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | COMBINE_EQS: (485), (486) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (488) all_335_3 = all_63_4
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | SIMP: (488) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (489) all_335_3 = all_63_4
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | COMBINE_EQS: (483), (484) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (490) all_335_4 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | SIMP: (490) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (491) all_335_4 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | REDUCE: (476), (487) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (492) remove_cpq(all_61_1, all_46_9) = all_335_0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | REDUCE: (480), (485) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (493) less_than(all_63_4, all_46_9) = all_337_2
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | REDUCE: (473), (489) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (494) less_than(all_63_4, all_46_9) = all_335_2
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_337_2, all_46_9,
% 27.73/4.53 | | | | | | | | | | | | | | all_63_4, simplifying with (332), (493) gives:
% 27.73/4.53 | | | | | | | | | | | | | | (495) all_337_2 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_335_2, all_337_2,
% 27.73/4.53 | | | | | | | | | | | | | | all_46_9, all_63_4, simplifying with (493), (494)
% 27.73/4.53 | | | | | | | | | | | | | | gives:
% 27.73/4.53 | | | | | | | | | | | | | | (496) all_337_2 = all_335_2
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | COMBINE_EQS: (495), (496) imply:
% 27.73/4.53 | | | | | | | | | | | | | | (497) all_335_2 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | SIMP: (497) implies:
% 27.73/4.53 | | | | | | | | | | | | | | (498) all_335_2 = 0
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 27.73/4.53 | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | Case 1:
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | (499) ~ (all_335_2 = 0)
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | REDUCE: (498), (499) imply:
% 27.73/4.53 | | | | | | | | | | | | | | | (500) $false
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | CLOSE: (500) is inconsistent.
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | Case 2:
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | (501) ~ (all_335_4 = 0) | all_335_0 = all_291_1
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | BETA: splitting (501) gives:
% 27.73/4.53 | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | Case 1:
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | (502) ~ (all_335_4 = 0)
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | REDUCE: (491), (502) imply:
% 27.73/4.53 | | | | | | | | | | | | | | | | (503) $false
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | CLOSE: (503) is inconsistent.
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | Case 2:
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | (504) all_335_0 = all_291_1
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | REDUCE: (492), (504) imply:
% 27.73/4.53 | | | | | | | | | | | | | | | | (505) remove_cpq(all_61_1, all_46_9) = all_291_1
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | BETA: splitting (471) gives:
% 27.73/4.53 | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.53 | | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | | (506) ok(all_291_1) = 0
% 27.73/4.53 | | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (54) with all_46_11, all_46_10,
% 27.73/4.53 | | | | | | | | | | | | | | | | | all_46_9, all_46_8, all_61_1, all_291_1,
% 27.73/4.53 | | | | | | | | | | | | | | | | | simplifying with (37), (38), (39), (40), (78),
% 27.73/4.53 | | | | | | | | | | | | | | | | | (288), (505), (506) gives:
% 27.73/4.53 | | | | | | | | | | | | | | | | | (507) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 27.73/4.53 | | | | | | | | | | | | | | | | | (remove_slb(all_46_12, all_46_9) = v1 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | pair_in_list(v1, all_46_9, all_46_8) = v2 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | strictly_less_than(all_46_9, all_46_8) = v0 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 27.73/4.53 | | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with all_46_11, all_46_10,
% 27.73/4.53 | | | | | | | | | | | | | | | | | all_46_9, all_46_8, all_61_1, all_291_1,
% 27.73/4.53 | | | | | | | | | | | | | | | | | simplifying with (37), (38), (39), (40), (44),
% 27.73/4.53 | | | | | | | | | | | | | | | | | (78), (505), (506) gives:
% 27.73/4.53 | | | | | | | | | | | | | | | | | (508) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 27.73/4.53 | | | | | | | | | | | | | | | | | (remove_slb(all_46_12, all_46_9) = v1 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | pair_in_list(v1, all_46_9, all_46_8) = v2 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | pair_in_list(all_46_12, all_46_9, all_46_8) = v0
% 27.73/4.53 | | | | | | | | | | | | | | | | | & $i(v1) & ( ~ (v0 = 0) | v2 = 0))
% 27.73/4.53 | | | | | | | | | | | | | | | | |
% 27.73/4.53 | | | | | | | | | | | | | | | | | DELTA: instantiating (508) with fresh symbols all_375_0,
% 27.73/4.53 | | | | | | | | | | | | | | | | | all_375_1, all_375_2 gives:
% 27.73/4.53 | | | | | | | | | | | | | | | | | (509) remove_slb(all_46_12, all_46_9) = all_375_1 &
% 27.73/4.53 | | | | | | | | | | | | | | | | | pair_in_list(all_375_1, all_46_9, all_46_8) =
% 27.73/4.53 | | | | | | | | | | | | | | | | | all_375_0 & pair_in_list(all_46_12, all_46_9,
% 27.73/4.53 | | | | | | | | | | | | | | | | | all_46_8) = all_375_2 & $i(all_375_1) & ( ~
% 27.73/4.53 | | | | | | | | | | | | | | | | | (all_375_2 = 0) | all_375_0 = 0)
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (510) remove_slb(all_46_12, all_46_9) = all_375_1
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | DELTA: instantiating (507) with fresh symbols all_377_0,
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_377_1, all_377_2 gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (511) remove_slb(all_46_12, all_46_9) = all_377_1 &
% 27.73/4.54 | | | | | | | | | | | | | | | | | pair_in_list(all_377_1, all_46_9, all_46_8) =
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_377_0 & strictly_less_than(all_46_9, all_46_8)
% 27.73/4.54 | | | | | | | | | | | | | | | | | = all_377_2 & $i(all_377_1) & ( ~ (all_377_2 = 0)
% 27.73/4.54 | | | | | | | | | | | | | | | | | | all_377_0 = 0)
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | ALPHA: (511) implies:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (512) strictly_less_than(all_46_9, all_46_8) = all_377_2
% 27.73/4.54 | | | | | | | | | | | | | | | | | (513) pair_in_list(all_377_1, all_46_9, all_46_8) =
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_377_0
% 27.73/4.54 | | | | | | | | | | | | | | | | | (514) remove_slb(all_46_12, all_46_9) = all_377_1
% 27.73/4.54 | | | | | | | | | | | | | | | | | (515) ~ (all_377_2 = 0) | all_377_0 = 0
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_377_2, all_46_8,
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_46_9, simplifying with (44), (512) gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (516) all_377_2 = 0
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_148_1, all_377_1,
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (286), (514)
% 27.73/4.54 | | | | | | | | | | | | | | | | | gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (517) all_377_1 = all_148_1
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_375_1, all_377_1,
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_46_9, all_46_12, simplifying with (510), (514)
% 27.73/4.54 | | | | | | | | | | | | | | | | | gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (518) all_377_1 = all_375_1
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (517), (518) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (519) all_375_1 = all_148_1
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | REDUCE: (513), (517) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (520) pair_in_list(all_148_1, all_46_9, all_46_8) =
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_377_0
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | BETA: splitting (515) gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | Case 1:
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (521) ~ (all_377_2 = 0)
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | REDUCE: (516), (521) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (522) $false
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | CLOSE: (522) is inconsistent.
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (523) all_377_0 = 0
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | REDUCE: (520), (523) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (524) pair_in_list(all_148_1, all_46_9, all_46_8) = 0
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_300_0, 0, all_46_8,
% 27.73/4.54 | | | | | | | | | | | | | | | | | | all_46_9, all_148_1, simplifying with (468), (524)
% 27.73/4.54 | | | | | | | | | | | | | | | | | | gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (525) all_300_0 = 0
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | REDUCE: (467), (525) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | | (526) $false
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | | CLOSE: (526) is inconsistent.
% 27.73/4.54 | | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | Case 2:
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | (527) all_46_10 = bad
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | REDUCE: (340), (527) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (528) triple(all_63_2, all_46_1, bad) = all_46_2
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_65_0, all_46_2, bad,
% 27.73/4.54 | | | | | | | | | | | | | | | | | all_46_1, all_63_2, simplifying with (106), (528)
% 27.73/4.54 | | | | | | | | | | | | | | | | | gives:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (529) all_65_0 = all_46_2
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | REDUCE: (129), (529) imply:
% 27.73/4.54 | | | | | | | | | | | | | | | | | (530) ok(all_46_2) = all_76_0
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (52), (128), (530) are inconsistent by
% 27.73/4.54 | | | | | | | | | | | | | | | | | sub-proof #2.
% 27.73/4.54 | | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | | |
% 27.73/4.54 | | | | | | | | | End of split
% 27.73/4.54 | | | | | | | | |
% 27.73/4.54 | | | | | | | | Case 2:
% 27.73/4.54 | | | | | | | | |
% 27.73/4.54 | | | | | | | | | (531) all_46_7 = all_46_9
% 27.73/4.54 | | | | | | | | |
% 27.73/4.54 | | | | | | | | | REDUCE: (280), (531) imply:
% 27.73/4.54 | | | | | | | | | (532) $false
% 27.73/4.54 | | | | | | | | |
% 27.73/4.54 | | | | | | | | | CLOSE: (532) is inconsistent.
% 27.73/4.54 | | | | | | | | |
% 27.73/4.54 | | | | | | | | End of split
% 27.73/4.54 | | | | | | | |
% 27.73/4.54 | | | | | | | End of split
% 27.73/4.54 | | | | | | |
% 27.73/4.54 | | | | | | End of split
% 27.73/4.54 | | | | | |
% 27.73/4.54 | | | | | End of split
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | Case 2:
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | | (533) all_59_0 = all_46_2
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | | REDUCE: (132), (533) imply:
% 27.73/4.54 | | | | | (534) ok(all_46_2) = all_78_0
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | | GROUND_INST: instantiating (24) with 0, all_78_0, all_46_2,
% 27.73/4.54 | | | | | simplifying with (52), (534) gives:
% 27.73/4.54 | | | | | (535) all_78_0 = 0
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | | REDUCE: (131), (535) imply:
% 27.73/4.54 | | | | | (536) $false
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | | CLOSE: (536) is inconsistent.
% 27.73/4.54 | | | | |
% 27.73/4.54 | | | | End of split
% 27.73/4.54 | | | |
% 27.73/4.54 | | | End of split
% 27.73/4.54 | | |
% 27.73/4.54 | | Case 2:
% 27.73/4.54 | | |
% 27.73/4.54 | | | (537) all_46_7 = all_46_9
% 27.73/4.54 | | |
% 27.73/4.54 | | | REDUCE: (280), (537) imply:
% 27.73/4.54 | | | (538) $false
% 27.73/4.54 | | |
% 27.73/4.54 | | | CLOSE: (538) is inconsistent.
% 27.73/4.54 | | |
% 27.73/4.54 | | End of split
% 27.73/4.54 | |
% 27.73/4.54 | End of split
% 27.73/4.54 |
% 27.73/4.54 End of proof
% 27.73/4.54
% 27.73/4.54 Sub-proof #1 shows that the following formulas are inconsistent:
% 27.73/4.54 ----------------------------------------------------------------
% 27.73/4.54 (1) ~ (all_76_0 = 0)
% 27.73/4.54 (2) all_65_5 = 0
% 27.73/4.54 (3) ~ (all_65_3 = 0) | ~ (all_65_5 = 0) | all_65_0 = all_46_2
% 27.73/4.54 (4) all_65_3 = 0
% 27.73/4.54 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.73/4.54 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 27.73/4.54 (6) ok(all_46_2) = 0
% 27.73/4.54 (7) ok(all_65_0) = all_76_0
% 27.73/4.54
% 27.73/4.54 Begin of proof
% 27.73/4.54 |
% 27.73/4.54 | BETA: splitting (3) gives:
% 27.73/4.54 |
% 27.73/4.54 | Case 1:
% 27.73/4.54 | |
% 27.73/4.54 | | (8) ~ (all_65_3 = 0)
% 27.73/4.54 | |
% 27.73/4.54 | | REDUCE: (4), (8) imply:
% 27.73/4.54 | | (9) $false
% 27.73/4.54 | |
% 27.73/4.54 | | CLOSE: (9) is inconsistent.
% 27.73/4.54 | |
% 27.73/4.54 | Case 2:
% 27.73/4.54 | |
% 27.73/4.54 | | (10) ~ (all_65_5 = 0) | all_65_0 = all_46_2
% 27.73/4.54 | |
% 27.73/4.54 | | BETA: splitting (10) gives:
% 27.73/4.54 | |
% 27.73/4.54 | | Case 1:
% 27.73/4.54 | | |
% 27.73/4.54 | | | (11) ~ (all_65_5 = 0)
% 27.73/4.54 | | |
% 27.73/4.54 | | | REDUCE: (2), (11) imply:
% 27.73/4.54 | | | (12) $false
% 27.73/4.54 | | |
% 27.73/4.54 | | | CLOSE: (12) is inconsistent.
% 27.73/4.54 | | |
% 27.73/4.54 | | Case 2:
% 27.73/4.54 | | |
% 27.73/4.54 | | | (13) all_65_0 = all_46_2
% 27.73/4.54 | | |
% 27.73/4.54 | | | REDUCE: (7), (13) imply:
% 27.73/4.54 | | | (14) ok(all_46_2) = all_76_0
% 27.73/4.54 | | |
% 27.73/4.54 | | | REF_CLOSE: (1), (5), (6), (14) are inconsistent by sub-proof #2.
% 27.73/4.54 | | |
% 27.73/4.54 | | End of split
% 27.73/4.54 | |
% 27.73/4.54 | End of split
% 27.73/4.54 |
% 27.73/4.54 End of proof
% 27.73/4.54
% 27.73/4.54 Sub-proof #2 shows that the following formulas are inconsistent:
% 27.73/4.54 ----------------------------------------------------------------
% 27.95/4.54 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.95/4.54 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 27.95/4.54 (2) ok(all_46_2) = all_76_0
% 27.95/4.54 (3) ok(all_46_2) = 0
% 27.95/4.54 (4) ~ (all_76_0 = 0)
% 27.95/4.54
% 27.95/4.54 Begin of proof
% 27.95/4.54 |
% 27.95/4.54 | GROUND_INST: instantiating (1) with 0, all_76_0, all_46_2, simplifying with
% 27.95/4.54 | (2), (3) gives:
% 27.95/4.54 | (5) all_76_0 = 0
% 27.95/4.54 |
% 27.95/4.54 | REDUCE: (4), (5) imply:
% 27.95/4.54 | (6) $false
% 27.95/4.54 |
% 27.95/4.54 | CLOSE: (6) is inconsistent.
% 27.95/4.54 |
% 27.95/4.54 End of proof
% 27.95/4.54 % SZS output end Proof for theBenchmark
% 27.95/4.54
% 27.95/4.54 3942ms
%------------------------------------------------------------------------------