TSTP Solution File: SWW631_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW631_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 : Fri Sep 1 00:50:57 EDT 2023
% Result : Theorem 22.76s 3.87s
% Output : Proof 26.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW631_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 19:11:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.08/1.34 Prover 5: Preprocessing ...
% 4.08/1.34 Prover 3: Preprocessing ...
% 4.08/1.34 Prover 4: Preprocessing ...
% 4.08/1.34 Prover 6: Preprocessing ...
% 4.08/1.34 Prover 0: Preprocessing ...
% 4.08/1.34 Prover 2: Preprocessing ...
% 4.08/1.34 Prover 1: Preprocessing ...
% 8.64/2.09 Prover 1: Warning: ignoring some quantifiers
% 8.64/2.09 Prover 4: Warning: ignoring some quantifiers
% 9.69/2.15 Prover 3: Warning: ignoring some quantifiers
% 9.69/2.17 Prover 4: Constructing countermodel ...
% 9.69/2.17 Prover 6: Proving ...
% 9.69/2.18 Prover 3: Constructing countermodel ...
% 9.69/2.19 Prover 1: Constructing countermodel ...
% 10.46/2.21 Prover 0: Proving ...
% 10.46/2.27 Prover 5: Proving ...
% 10.46/2.29 Prover 2: Proving ...
% 22.76/3.87 Prover 3: proved (3223ms)
% 22.76/3.87
% 22.76/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.76/3.87
% 22.76/3.87 Prover 2: stopped
% 22.76/3.87 Prover 5: stopped
% 22.76/3.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.76/3.87 Prover 6: stopped
% 22.76/3.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.76/3.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.76/3.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.76/3.91 Prover 0: stopped
% 22.76/3.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.30/4.06 Prover 11: Preprocessing ...
% 24.30/4.06 Prover 8: Preprocessing ...
% 24.30/4.06 Prover 7: Preprocessing ...
% 24.50/4.07 Prover 13: Preprocessing ...
% 24.50/4.09 Prover 10: Preprocessing ...
% 25.09/4.16 Prover 8: Warning: ignoring some quantifiers
% 25.09/4.18 Prover 8: Constructing countermodel ...
% 25.09/4.19 Prover 11: Warning: ignoring some quantifiers
% 25.09/4.20 Prover 13: Warning: ignoring some quantifiers
% 25.09/4.20 Prover 11: Constructing countermodel ...
% 25.09/4.20 Prover 7: Warning: ignoring some quantifiers
% 25.09/4.20 Prover 10: Warning: ignoring some quantifiers
% 25.09/4.21 Prover 7: Constructing countermodel ...
% 25.09/4.21 Prover 10: Constructing countermodel ...
% 25.09/4.22 Prover 13: Constructing countermodel ...
% 25.69/4.29 Prover 1: Found proof (size 277)
% 25.69/4.29 Prover 1: proved (3652ms)
% 25.69/4.29 Prover 10: stopped
% 25.69/4.29 Prover 11: stopped
% 25.69/4.29 Prover 7: stopped
% 25.69/4.29 Prover 8: stopped
% 25.69/4.29 Prover 13: stopped
% 25.69/4.29 Prover 4: stopped
% 25.69/4.29
% 25.69/4.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.69/4.29
% 25.69/4.31 % SZS output start Proof for theBenchmark
% 25.69/4.32 Assumptions after simplification:
% 25.69/4.32 ---------------------------------
% 25.69/4.32
% 25.69/4.32 (bridgeL)
% 25.69/4.33 ! [v0: int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | tb2t(v1) = v0)
% 25.69/4.33
% 25.69/4.33 (bridgeR)
% 25.69/4.33 ! [v0: uni] : ! [v1: int] : ( ~ (tb2t(v0) = v1) | ~ uni(v0) | t2tb(v1) =
% 25.69/4.33 v0)
% 25.69/4.33
% 25.69/4.33 (f_prop)
% 25.69/4.33 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference(n, v0))) | ~
% 25.69/4.33 ($lesseq(1, v0)) | ~ (f(v0) = v1) | ($lesseq(1, $difference(v0, v1)) &
% 25.69/4.33 $lesseq(0, v1)))
% 25.69/4.33
% 25.69/4.33 (wP_parameter_distance)
% 25.69/4.34 ty(int) & ? [v0: uni] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? [v4:
% 25.69/4.34 map_int_int] : ($lesseq(2, n) & tb2t1(v3) = v4 & t2tb(-1) = v2 & t2tb(0) =
% 25.69/4.34 v0 & const(int, int, v0) = v1 & set(int, int, v1, v0, v2) = v3 &
% 25.69/4.34 map_int_int(v4) & uni(v3) & uni(v2) & uni(v1) & uni(v0) & ? [v5:
% 25.69/4.34 map_int_int] : ? [v6: map_int_int] : ? [v7: int] : ? [v8: uni] : ?
% 25.69/4.34 [v9: uni] : ? [v10: uni] : ? [v11: uni] : ? [v12: uni] : ? [v13: uni] :
% 25.69/4.34 ? [v14: int] : ? [v15: int] : ($lesseq(1, $difference(n, v7)) & $lesseq(1,
% 25.69/4.34 v7) & t2tb1(v6) = v10 & t2tb1(v5) = v8 & f(v7) = v15 & tb2t(v13) = v14 &
% 25.69/4.34 tb2t(v11) = -1 & tb2t(v9) = 0 & t2tb($sum(v7, -1)) = v12 & get(int, int,
% 25.69/4.34 v10, v0) = v11 & get(int, int, v8, v12) = v13 & get(int, int, v8, v0) =
% 25.69/4.34 v9 & map_int_int(v6) & map_int_int(v5) & uni(v13) & uni(v12) & uni(v11) &
% 25.69/4.34 uni(v10) & uni(v9) & uni(v8) & ! [v16: int] : ! [v17: uni] : ! [v18:
% 25.69/4.34 uni] : ! [v19: int] : ! [v20: int] : (v20 = 0 | ~ ($lesseq(1,
% 25.69/4.34 $difference(v7, v16))) | ~ ($lesseq(0, v16)) | ~ (path(v19, v16) =
% 25.69/4.34 v20) | ~ (tb2t(v18) = v19) | ~ (t2tb(v16) = v17) | ~ (get(int, int,
% 25.69/4.34 v8, v17) = v18)) & ! [v16: int] : ! [v17: uni] : ! [v18: uni] :
% 25.69/4.34 ! [v19: uni] : ( ~ ($lesseq(1, $difference(v7, v16))) | ~ ($lesseq(1,
% 25.69/4.34 v16)) | ~ (t2tb(v16) = v17) | ~ (get(int, int, v10, v17) = v18) |
% 25.69/4.34 ~ (get(int, int, v8, v18) = v19) | ? [v20: int] : ? [v21: uni] : ?
% 25.69/4.34 [v22: int] : ? [v23: int] : ? [v24: uni] : ? [v25: int] : ($lesseq(1,
% 25.69/4.34 v25) & $lesseq(1, $difference(v16, v23)) & $lesseq(v20, v23) &
% 25.69/4.34 $lesseq(1, $difference(v20, v22)) & f(v16) = v20 & tb2t(v24) = v25 &
% 25.69/4.34 tb2t(v21) = v22 & tb2t(v19) = $sum(v25, -1) & tb2t(v18) = v23 &
% 25.69/4.34 get(int, int, v10, v18) = v21 & get(int, int, v8, v17) = v24 &
% 25.69/4.34 uni(v24) & uni(v21) & ! [v26: int] : ! [v27: uni] : ! [v28: uni] :
% 25.69/4.34 ( ~ ($lesseq(1, $difference(v16, v26))) | ~ ($lesseq(1,
% 25.69/4.34 $difference(v26, v23))) | ~ (t2tb(v26) = v27) | ~ (get(int,
% 25.69/4.34 int, v8, v27) = v28) | ? [v29: int] : ($lesseq(v25, v29) &
% 25.69/4.34 tb2t(v28) = v29)))) & ? [v16: int] : ? [v17: uni] : ? [v18:
% 25.69/4.34 uni] : ? [v19: int] : ? [v20: uni] : ? [v21: int] : ($lesseq(v15,
% 25.69/4.34 v21) & $lesseq(1, $difference(v7, v16)) & $lesseq(1, $difference(n,
% 25.69/4.34 v16)) & $lesseq(v15, v16) & $lesseq(0, v16) & tb2t(v20) = v21 &
% 25.69/4.34 tb2t(v18) = v19 & t2tb(v16) = v17 & get(int, int, v10, v17) = v20 &
% 25.69/4.34 get(int, int, v8, v17) = v18 & uni(v20) & uni(v18) & uni(v17) & ! [v22:
% 25.69/4.34 int] : ! [v23: uni] : ! [v24: uni] : ( ~ ($lesseq(1, $difference(v7,
% 25.69/4.35 v22))) | ~ ($lesseq(1, $difference(v22, v16))) | ~ (t2tb(v22)
% 25.69/4.35 = v23) | ~ (get(int, int, v8, v23) = v24) | ? [v25: int] :
% 25.69/4.35 ($lesseq(1, $difference(v25, v19)) & tb2t(v24) = v25)) & ? [v22: uni]
% 25.69/4.35 : ? [v23: uni] : ? [v24: int] : (tb2t(v23) = v24 & t2tb(v21) = v22 &
% 25.69/4.35 get(int, int, v8, v22) = v23 & uni(v23) & uni(v22) & ? [v25: int] :
% 25.69/4.35 ? [v26: uni] : ? [v27: uni] : ? [v28: int] : ($lesseq(v28, v24) &
% 25.69/4.35 $lesseq(1, $difference(v7, v25)) & $lesseq(1, $difference(v25, v21))
% 25.69/4.35 & tb2t(v27) = v28 & t2tb(v25) = v26 & get(int, int, v8, v26) = v27 &
% 25.69/4.35 uni(v27) & uni(v26))))))
% 25.69/4.35
% 25.69/4.35 (function-axioms)
% 25.69/4.35 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 25.69/4.35 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (set(v6, v5, v4, v3, v2) = v1) | ~
% 25.69/4.35 (set(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni]
% 25.69/4.35 : ! [v3: int] : ! [v4: uni] : ! [v5: ty] : (v1 = v0 | ~ (set1(v5, v4, v3,
% 25.69/4.35 v2) = v1) | ~ (set1(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1:
% 25.69/4.35 uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : ! [v5: ty] : (v1 = v0 |
% 25.69/4.35 ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4, v3, v2) = v0)) & ! [v0: uni]
% 25.69/4.35 : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool] : ! [v5: ty] :
% 25.69/4.35 (v1 = v0 | ~ (match_bool(v5, v4, v3, v2) = v1) | ~ (match_bool(v5, v4, v3,
% 25.69/4.35 v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] :
% 25.69/4.35 ! [v4: ty] : (v1 = v0 | ~ (make(v4, v3, v2) = v1) | ~ (make(v4, v3, v2) =
% 25.69/4.35 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: int] : ! [v3: uni] : ! [v4:
% 25.69/4.35 ty] : (v1 = v0 | ~ (get1(v4, v3, v2) = v1) | ~ (get1(v4, v3, v2) = v0)) &
% 25.69/4.35 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: ty] : (v1 =
% 25.69/4.35 v0 | ~ (mk_array(v4, v3, v2) = v1) | ~ (mk_array(v4, v3, v2) = v0)) & !
% 25.69/4.35 [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : ! [v4: ty] : (v1 = v0
% 25.69/4.35 | ~ (const(v4, v3, v2) = v1) | ~ (const(v4, v3, v2) = v0)) & ! [v0:
% 25.69/4.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3:
% 25.69/4.35 int] : (v1 = v0 | ~ (distance(v3, v2) = v1) | ~ (distance(v3, v2) = v0)) &
% 25.69/4.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : !
% 25.69/4.35 [v3: int] : (v1 = v0 | ~ (path(v3, v2) = v1) | ~ (path(v3, v2) = v0)) & !
% 25.69/4.35 [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 25.69/4.35 (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0)) & ! [v0: int] : ! [v1: int]
% 25.69/4.35 : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length(v3, v2) = v1) | ~
% 25.69/4.35 (length(v3, v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3:
% 25.69/4.35 ty] : (v1 = v0 | ~ (map(v3, v2) = v1) | ~ (map(v3, v2) = v0)) & ! [v0:
% 25.69/4.35 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 25.69/4.35 (contents(v3, v2) = v1) | ~ (contents(v3, v2) = v0)) & ! [v0: uni] : !
% 25.69/4.35 [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) = v1) |
% 25.69/4.35 ~ (mk_ref(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.69/4.35 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (sort(v3,
% 25.69/4.35 v2) = v1) | ~ (sort(v3, v2) = v0)) & ! [v0: map_int_int] : ! [v1:
% 25.69/4.35 map_int_int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t1(v2) = v1) | ~ (tb2t1(v2)
% 25.69/4.35 = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: map_int_int] : (v1 = v0 |
% 25.69/4.35 ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 25.69/4.35 [v2: int] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0: int] : !
% 25.69/4.35 [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) = v0))
% 25.69/4.35 & ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 | ~ (t2tb(v2) = v1) |
% 25.69/4.35 ~ (t2tb(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 = v0 |
% 25.69/4.35 ~ (array(v2) = v1) | ~ (array(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : !
% 25.69/4.35 [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~ (ref(v2) = v0)) & ! [v0: uni] :
% 25.69/4.35 ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness(v2) = v1) | ~ (witness(v2)
% 25.69/4.35 = v0))
% 25.69/4.35
% 25.69/4.35 Further assumptions not needed in the proof:
% 25.69/4.35 --------------------------------------------
% 25.69/4.35 array_inversion, bool_inversion, bridgeL1, bridgeR1, compatOrderMult, const1,
% 25.69/4.35 const_sort, contents_def, contents_sort, distance_def, elts_def, elts_sort,
% 25.69/4.35 get_def, get_sort, get_sort1, length_def, make_def, make_sort, match_bool_False,
% 25.69/4.35 match_bool_True, match_bool_sort, mk_array_sort, mk_ref_sort, n_nonneg, path0,
% 25.69/4.35 path_inversion, paths, ref_inversion, select_eq, select_neq, set_def, set_sort,
% 25.69/4.35 set_sort1, t2tb_sort, t2tb_sort1, true_False, tuple0_inversion, witness_sort
% 25.69/4.35
% 25.69/4.35 Those formulas are unsatisfiable:
% 25.69/4.35 ---------------------------------
% 25.69/4.35
% 25.69/4.35 Begin of proof
% 25.69/4.35 |
% 25.69/4.35 | ALPHA: (wP_parameter_distance) implies:
% 25.69/4.36 | (1) ? [v0: uni] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni] : ? [v4:
% 25.69/4.36 | map_int_int] : ($lesseq(2, n) & tb2t1(v3) = v4 & t2tb(-1) = v2 &
% 25.69/4.36 | t2tb(0) = v0 & const(int, int, v0) = v1 & set(int, int, v1, v0, v2) =
% 25.69/4.36 | v3 & map_int_int(v4) & uni(v3) & uni(v2) & uni(v1) & uni(v0) & ?
% 25.69/4.36 | [v5: map_int_int] : ? [v6: map_int_int] : ? [v7: int] : ? [v8:
% 25.69/4.36 | uni] : ? [v9: uni] : ? [v10: uni] : ? [v11: uni] : ? [v12: uni]
% 25.69/4.36 | : ? [v13: uni] : ? [v14: int] : ? [v15: int] : ($lesseq(1,
% 25.69/4.36 | $difference(n, v7)) & $lesseq(1, v7) & t2tb1(v6) = v10 &
% 25.69/4.36 | t2tb1(v5) = v8 & f(v7) = v15 & tb2t(v13) = v14 & tb2t(v11) = -1 &
% 25.69/4.36 | tb2t(v9) = 0 & t2tb($sum(v7, -1)) = v12 & get(int, int, v10, v0) =
% 25.69/4.36 | v11 & get(int, int, v8, v12) = v13 & get(int, int, v8, v0) = v9 &
% 25.69/4.36 | map_int_int(v6) & map_int_int(v5) & uni(v13) & uni(v12) & uni(v11)
% 25.69/4.36 | & uni(v10) & uni(v9) & uni(v8) & ! [v16: int] : ! [v17: uni] : !
% 25.69/4.36 | [v18: uni] : ! [v19: int] : ! [v20: int] : (v20 = 0 | ~
% 25.69/4.36 | ($lesseq(1, $difference(v7, v16))) | ~ ($lesseq(0, v16)) | ~
% 25.69/4.36 | (path(v19, v16) = v20) | ~ (tb2t(v18) = v19) | ~ (t2tb(v16) =
% 25.69/4.36 | v17) | ~ (get(int, int, v8, v17) = v18)) & ! [v16: int] : !
% 25.69/4.36 | [v17: uni] : ! [v18: uni] : ! [v19: uni] : ( ~ ($lesseq(1,
% 25.69/4.36 | $difference(v7, v16))) | ~ ($lesseq(1, v16)) | ~ (t2tb(v16)
% 25.69/4.36 | = v17) | ~ (get(int, int, v10, v17) = v18) | ~ (get(int, int,
% 25.69/4.36 | v8, v18) = v19) | ? [v20: int] : ? [v21: uni] : ? [v22:
% 25.69/4.36 | int] : ? [v23: int] : ? [v24: uni] : ? [v25: int] :
% 25.69/4.36 | ($lesseq(1, v25) & $lesseq(1, $difference(v16, v23)) &
% 25.69/4.36 | $lesseq(v20, v23) & $lesseq(1, $difference(v20, v22)) & f(v16)
% 25.69/4.36 | = v20 & tb2t(v24) = v25 & tb2t(v21) = v22 & tb2t(v19) =
% 25.69/4.36 | $sum(v25, -1) & tb2t(v18) = v23 & get(int, int, v10, v18) = v21
% 25.69/4.36 | & get(int, int, v8, v17) = v24 & uni(v24) & uni(v21) & ! [v26:
% 25.69/4.36 | int] : ! [v27: uni] : ! [v28: uni] : ( ~ ($lesseq(1,
% 25.69/4.36 | $difference(v16, v26))) | ~ ($lesseq(1, $difference(v26,
% 25.69/4.36 | v23))) | ~ (t2tb(v26) = v27) | ~ (get(int, int, v8,
% 25.69/4.36 | v27) = v28) | ? [v29: int] : ($lesseq(v25, v29) &
% 25.69/4.36 | tb2t(v28) = v29)))) & ? [v16: int] : ? [v17: uni] : ?
% 25.69/4.36 | [v18: uni] : ? [v19: int] : ? [v20: uni] : ? [v21: int] :
% 25.69/4.36 | ($lesseq(v15, v21) & $lesseq(1, $difference(v7, v16)) & $lesseq(1,
% 25.69/4.36 | $difference(n, v16)) & $lesseq(v15, v16) & $lesseq(0, v16) &
% 25.69/4.36 | tb2t(v20) = v21 & tb2t(v18) = v19 & t2tb(v16) = v17 & get(int,
% 25.69/4.36 | int, v10, v17) = v20 & get(int, int, v8, v17) = v18 & uni(v20)
% 25.69/4.36 | & uni(v18) & uni(v17) & ! [v22: int] : ! [v23: uni] : ! [v24:
% 25.69/4.36 | uni] : ( ~ ($lesseq(1, $difference(v7, v22))) | ~ ($lesseq(1,
% 25.69/4.36 | $difference(v22, v16))) | ~ (t2tb(v22) = v23) | ~
% 25.69/4.36 | (get(int, int, v8, v23) = v24) | ? [v25: int] : ($lesseq(1,
% 25.69/4.36 | $difference(v25, v19)) & tb2t(v24) = v25)) & ? [v22: uni]
% 25.69/4.36 | : ? [v23: uni] : ? [v24: int] : (tb2t(v23) = v24 & t2tb(v21) =
% 25.69/4.36 | v22 & get(int, int, v8, v22) = v23 & uni(v23) & uni(v22) & ?
% 25.69/4.36 | [v25: int] : ? [v26: uni] : ? [v27: uni] : ? [v28: int] :
% 25.69/4.36 | ($lesseq(v28, v24) & $lesseq(1, $difference(v7, v25)) &
% 25.69/4.36 | $lesseq(1, $difference(v25, v21)) & tb2t(v27) = v28 &
% 25.69/4.36 | t2tb(v25) = v26 & get(int, int, v8, v26) = v27 & uni(v27) &
% 25.69/4.36 | uni(v26))))))
% 25.69/4.36 |
% 25.69/4.36 | ALPHA: (function-axioms) implies:
% 25.69/4.36 | (2) ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 | ~ (t2tb(v2) =
% 25.69/4.36 | v1) | ~ (t2tb(v2) = v0))
% 25.69/4.36 | (3) ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) =
% 25.69/4.36 | v1) | ~ (tb2t(v2) = v0))
% 25.69/4.36 | (4) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty]
% 25.69/4.36 | : ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5,
% 25.69/4.36 | v4, v3, v2) = v0))
% 25.69/4.36 |
% 25.69/4.36 | DELTA: instantiating (1) with fresh symbols all_55_0, all_55_1, all_55_2,
% 25.69/4.36 | all_55_3, all_55_4 gives:
% 25.69/4.37 | (5) $lesseq(2, n) & tb2t1(all_55_1) = all_55_0 & t2tb(-1) = all_55_2 &
% 25.69/4.37 | t2tb(0) = all_55_4 & const(int, int, all_55_4) = all_55_3 & set(int,
% 25.69/4.37 | int, all_55_3, all_55_4, all_55_2) = all_55_1 & map_int_int(all_55_0)
% 25.69/4.37 | & uni(all_55_1) & uni(all_55_2) & uni(all_55_3) & uni(all_55_4) & ?
% 25.69/4.37 | [v0: map_int_int] : ? [v1: map_int_int] : ? [v2: int] : ? [v3: uni]
% 25.69/4.37 | : ? [v4: uni] : ? [v5: uni] : ? [v6: uni] : ? [v7: uni] : ? [v8:
% 25.69/4.37 | uni] : ? [v9: int] : ? [v10: int] : ($lesseq(1, $difference(n, v2))
% 25.69/4.37 | & $lesseq(1, v2) & t2tb1(v1) = v5 & t2tb1(v0) = v3 & f(v2) = v10 &
% 25.69/4.37 | tb2t(v8) = v9 & tb2t(v6) = -1 & tb2t(v4) = 0 & t2tb($sum(v2, -1)) =
% 25.69/4.37 | v7 & get(int, int, v5, all_55_4) = v6 & get(int, int, v3, v7) = v8 &
% 25.69/4.37 | get(int, int, v3, all_55_4) = v4 & map_int_int(v1) & map_int_int(v0)
% 25.69/4.37 | & uni(v8) & uni(v7) & uni(v6) & uni(v5) & uni(v4) & uni(v3) & !
% 25.69/4.37 | [v11: int] : ! [v12: uni] : ! [v13: uni] : ! [v14: int] : ! [v15:
% 25.69/4.37 | int] : (v15 = 0 | ~ ($lesseq(1, $difference(v2, v11))) | ~
% 25.69/4.37 | ($lesseq(0, v11)) | ~ (path(v14, v11) = v15) | ~ (tb2t(v13) =
% 25.69/4.37 | v14) | ~ (t2tb(v11) = v12) | ~ (get(int, int, v3, v12) = v13))
% 25.69/4.37 | & ! [v11: int] : ! [v12: uni] : ! [v13: uni] : ! [v14: uni] : ( ~
% 25.69/4.37 | ($lesseq(1, $difference(v2, v11))) | ~ ($lesseq(1, v11)) | ~
% 25.69/4.37 | (t2tb(v11) = v12) | ~ (get(int, int, v5, v12) = v13) | ~
% 25.69/4.37 | (get(int, int, v3, v13) = v14) | ? [v15: int] : ? [v16: uni] : ?
% 25.69/4.37 | [v17: int] : ? [v18: int] : ? [v19: uni] : ? [v20: int] :
% 25.69/4.37 | ($lesseq(1, v20) & $lesseq(1, $difference(v11, v18)) & $lesseq(v15,
% 25.69/4.37 | v18) & $lesseq(1, $difference(v15, v17)) & f(v11) = v15 &
% 25.69/4.37 | tb2t(v19) = v20 & tb2t(v16) = v17 & tb2t(v14) = $sum(v20, -1) &
% 25.69/4.37 | tb2t(v13) = v18 & get(int, int, v5, v13) = v16 & get(int, int,
% 25.69/4.37 | v3, v12) = v19 & uni(v19) & uni(v16) & ! [v21: int] : ! [v22:
% 25.69/4.37 | uni] : ! [v23: uni] : ( ~ ($lesseq(1, $difference(v11, v21)))
% 25.69/4.37 | | ~ ($lesseq(1, $difference(v21, v18))) | ~ (t2tb(v21) = v22)
% 25.69/4.37 | | ~ (get(int, int, v3, v22) = v23) | ? [v24: int] :
% 25.69/4.37 | ($lesseq(v20, v24) & tb2t(v23) = v24)))) & ? [v11: int] : ?
% 25.69/4.37 | [v12: uni] : ? [v13: uni] : ? [v14: int] : ? [v15: uni] : ? [v16:
% 25.69/4.37 | int] : ($lesseq(v10, v16) & $lesseq(1, $difference(v2, v11)) &
% 25.69/4.37 | $lesseq(1, $difference(n, v11)) & $lesseq(v10, v11) & $lesseq(0,
% 25.69/4.37 | v11) & tb2t(v15) = v16 & tb2t(v13) = v14 & t2tb(v11) = v12 &
% 25.69/4.37 | get(int, int, v5, v12) = v15 & get(int, int, v3, v12) = v13 &
% 25.69/4.37 | uni(v15) & uni(v13) & uni(v12) & ! [v17: int] : ! [v18: uni] : !
% 25.69/4.37 | [v19: uni] : ( ~ ($lesseq(1, $difference(v2, v17))) | ~
% 25.69/4.37 | ($lesseq(1, $difference(v17, v11))) | ~ (t2tb(v17) = v18) | ~
% 25.69/4.37 | (get(int, int, v3, v18) = v19) | ? [v20: int] : ($lesseq(1,
% 25.69/4.37 | $difference(v20, v14)) & tb2t(v19) = v20)) & ? [v17: uni] :
% 25.69/4.37 | ? [v18: uni] : ? [v19: int] : (tb2t(v18) = v19 & t2tb(v16) = v17 &
% 25.69/4.37 | get(int, int, v3, v17) = v18 & uni(v18) & uni(v17) & ? [v20:
% 25.69/4.37 | int] : ? [v21: uni] : ? [v22: uni] : ? [v23: int] :
% 25.69/4.37 | ($lesseq(v23, v19) & $lesseq(1, $difference(v2, v20)) &
% 25.69/4.37 | $lesseq(1, $difference(v20, v16)) & tb2t(v22) = v23 & t2tb(v20)
% 25.69/4.37 | = v21 & get(int, int, v3, v21) = v22 & uni(v22) & uni(v21)))))
% 25.69/4.37 |
% 25.69/4.37 | ALPHA: (5) implies:
% 25.69/4.37 | (6) t2tb(0) = all_55_4
% 25.69/4.37 | (7) t2tb(-1) = all_55_2
% 25.69/4.38 | (8) ? [v0: map_int_int] : ? [v1: map_int_int] : ? [v2: int] : ? [v3:
% 25.69/4.38 | uni] : ? [v4: uni] : ? [v5: uni] : ? [v6: uni] : ? [v7: uni] : ?
% 25.69/4.38 | [v8: uni] : ? [v9: int] : ? [v10: int] : ($lesseq(1, $difference(n,
% 25.69/4.38 | v2)) & $lesseq(1, v2) & t2tb1(v1) = v5 & t2tb1(v0) = v3 & f(v2) =
% 25.69/4.38 | v10 & tb2t(v8) = v9 & tb2t(v6) = -1 & tb2t(v4) = 0 & t2tb($sum(v2,
% 25.69/4.38 | -1)) = v7 & get(int, int, v5, all_55_4) = v6 & get(int, int, v3,
% 25.69/4.38 | v7) = v8 & get(int, int, v3, all_55_4) = v4 & map_int_int(v1) &
% 25.69/4.38 | map_int_int(v0) & uni(v8) & uni(v7) & uni(v6) & uni(v5) & uni(v4) &
% 25.69/4.38 | uni(v3) & ! [v11: int] : ! [v12: uni] : ! [v13: uni] : ! [v14:
% 25.69/4.38 | int] : ! [v15: int] : (v15 = 0 | ~ ($lesseq(1, $difference(v2,
% 25.69/4.38 | v11))) | ~ ($lesseq(0, v11)) | ~ (path(v14, v11) = v15) |
% 25.69/4.38 | ~ (tb2t(v13) = v14) | ~ (t2tb(v11) = v12) | ~ (get(int, int, v3,
% 25.69/4.38 | v12) = v13)) & ! [v11: int] : ! [v12: uni] : ! [v13: uni] :
% 25.69/4.38 | ! [v14: uni] : ( ~ ($lesseq(1, $difference(v2, v11))) | ~
% 25.69/4.38 | ($lesseq(1, v11)) | ~ (t2tb(v11) = v12) | ~ (get(int, int, v5,
% 25.69/4.38 | v12) = v13) | ~ (get(int, int, v3, v13) = v14) | ? [v15: int]
% 25.69/4.38 | : ? [v16: uni] : ? [v17: int] : ? [v18: int] : ? [v19: uni] :
% 25.69/4.38 | ? [v20: int] : ($lesseq(1, v20) & $lesseq(1, $difference(v11, v18))
% 25.69/4.38 | & $lesseq(v15, v18) & $lesseq(1, $difference(v15, v17)) & f(v11)
% 25.69/4.38 | = v15 & tb2t(v19) = v20 & tb2t(v16) = v17 & tb2t(v14) = $sum(v20,
% 25.69/4.38 | -1) & tb2t(v13) = v18 & get(int, int, v5, v13) = v16 & get(int,
% 25.69/4.38 | int, v3, v12) = v19 & uni(v19) & uni(v16) & ! [v21: int] : !
% 25.69/4.38 | [v22: uni] : ! [v23: uni] : ( ~ ($lesseq(1, $difference(v11,
% 25.69/4.38 | v21))) | ~ ($lesseq(1, $difference(v21, v18))) | ~
% 25.69/4.38 | (t2tb(v21) = v22) | ~ (get(int, int, v3, v22) = v23) | ?
% 25.69/4.38 | [v24: int] : ($lesseq(v20, v24) & tb2t(v23) = v24)))) & ?
% 25.69/4.38 | [v11: int] : ? [v12: uni] : ? [v13: uni] : ? [v14: int] : ? [v15:
% 25.69/4.38 | uni] : ? [v16: int] : ($lesseq(v10, v16) & $lesseq(1,
% 25.69/4.38 | $difference(v2, v11)) & $lesseq(1, $difference(n, v11)) &
% 25.69/4.38 | $lesseq(v10, v11) & $lesseq(0, v11) & tb2t(v15) = v16 & tb2t(v13) =
% 25.69/4.38 | v14 & t2tb(v11) = v12 & get(int, int, v5, v12) = v15 & get(int,
% 25.69/4.38 | int, v3, v12) = v13 & uni(v15) & uni(v13) & uni(v12) & ! [v17:
% 25.69/4.38 | int] : ! [v18: uni] : ! [v19: uni] : ( ~ ($lesseq(1,
% 25.69/4.38 | $difference(v2, v17))) | ~ ($lesseq(1, $difference(v17,
% 25.69/4.38 | v11))) | ~ (t2tb(v17) = v18) | ~ (get(int, int, v3, v18)
% 25.69/4.38 | = v19) | ? [v20: int] : ($lesseq(1, $difference(v20, v14)) &
% 25.69/4.38 | tb2t(v19) = v20)) & ? [v17: uni] : ? [v18: uni] : ? [v19:
% 25.69/4.38 | int] : (tb2t(v18) = v19 & t2tb(v16) = v17 & get(int, int, v3,
% 25.69/4.38 | v17) = v18 & uni(v18) & uni(v17) & ? [v20: int] : ? [v21:
% 25.69/4.38 | uni] : ? [v22: uni] : ? [v23: int] : ($lesseq(v23, v19) &
% 25.69/4.38 | $lesseq(1, $difference(v2, v20)) & $lesseq(1, $difference(v20,
% 25.69/4.38 | v16)) & tb2t(v22) = v23 & t2tb(v20) = v21 & get(int, int,
% 25.69/4.38 | v3, v21) = v22 & uni(v22) & uni(v21)))))
% 25.69/4.38 |
% 25.69/4.38 | DELTA: instantiating (8) with fresh symbols all_57_0, all_57_1, all_57_2,
% 25.69/4.38 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 25.69/4.38 | all_57_10 gives:
% 25.69/4.38 | (9) $lesseq(1, $difference(n, all_57_8)) & $lesseq(1, all_57_8) &
% 25.69/4.38 | t2tb1(all_57_9) = all_57_5 & t2tb1(all_57_10) = all_57_7 & f(all_57_8)
% 25.69/4.38 | = all_57_0 & tb2t(all_57_2) = all_57_1 & tb2t(all_57_4) = -1 &
% 25.69/4.38 | tb2t(all_57_6) = 0 & t2tb($sum(all_57_8, -1)) = all_57_3 & get(int,
% 25.69/4.38 | int, all_57_5, all_55_4) = all_57_4 & get(int, int, all_57_7,
% 25.69/4.38 | all_57_3) = all_57_2 & get(int, int, all_57_7, all_55_4) = all_57_6 &
% 25.69/4.38 | map_int_int(all_57_9) & map_int_int(all_57_10) & uni(all_57_2) &
% 25.69/4.38 | uni(all_57_3) & uni(all_57_4) & uni(all_57_5) & uni(all_57_6) &
% 25.69/4.38 | uni(all_57_7) & ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ! [v3:
% 25.69/4.38 | int] : ! [v4: int] : (v4 = 0 | ~ ($lesseq(1, $difference(all_57_8,
% 25.69/4.38 | v0))) | ~ ($lesseq(0, v0)) | ~ (path(v3, v0) = v4) | ~
% 25.69/4.39 | (tb2t(v2) = v3) | ~ (t2tb(v0) = v1) | ~ (get(int, int, all_57_7,
% 25.69/4.39 | v1) = v2)) & ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ! [v3:
% 25.69/4.39 | uni] : ( ~ ($lesseq(1, $difference(all_57_8, v0))) | ~ ($lesseq(1,
% 25.69/4.39 | v0)) | ~ (t2tb(v0) = v1) | ~ (get(int, int, all_57_5, v1) = v2)
% 25.69/4.39 | | ~ (get(int, int, all_57_7, v2) = v3) | ? [v4: int] : ? [v5: uni]
% 25.69/4.39 | : ? [v6: int] : ? [v7: int] : ? [v8: uni] : ? [v9: int] :
% 25.69/4.39 | ($lesseq(1, v9) & $lesseq(1, $difference(v0, v7)) & $lesseq(v4, v7) &
% 25.69/4.39 | $lesseq(1, $difference(v4, v6)) & f(v0) = v4 & tb2t(v8) = v9 &
% 25.69/4.39 | tb2t(v5) = v6 & tb2t(v3) = $sum(v9, -1) & tb2t(v2) = v7 & get(int,
% 25.69/4.39 | int, all_57_5, v2) = v5 & get(int, int, all_57_7, v1) = v8 &
% 25.69/4.39 | uni(v8) & uni(v5) & ! [v10: int] : ! [v11: uni] : ! [v12: uni] :
% 25.69/4.39 | ( ~ ($lesseq(1, $difference(v0, v10))) | ~ ($lesseq(1,
% 25.69/4.39 | $difference(v10, v7))) | ~ (t2tb(v10) = v11) | ~ (get(int,
% 25.69/4.39 | int, all_57_7, v11) = v12) | ? [v13: int] : ($lesseq(v9,
% 25.69/4.39 | v13) & tb2t(v12) = v13)))) & ? [v0: int] : ? [v1: uni] : ?
% 25.69/4.39 | [v2: uni] : ? [v3: int] : ? [v4: uni] : ? [v5: int] :
% 25.69/4.39 | ($lesseq(all_57_0, v5) & $lesseq(1, $difference(all_57_8, v0)) &
% 25.69/4.39 | $lesseq(1, $difference(n, v0)) & $lesseq(all_57_0, v0) & $lesseq(0,
% 25.69/4.39 | v0) & tb2t(v4) = v5 & tb2t(v2) = v3 & t2tb(v0) = v1 & get(int, int,
% 25.69/4.39 | all_57_5, v1) = v4 & get(int, int, all_57_7, v1) = v2 & uni(v4) &
% 25.69/4.39 | uni(v2) & uni(v1) & ! [v6: int] : ! [v7: uni] : ! [v8: uni] : ( ~
% 25.69/4.39 | ($lesseq(1, $difference(all_57_8, v6))) | ~ ($lesseq(1,
% 25.69/4.39 | $difference(v6, v0))) | ~ (t2tb(v6) = v7) | ~ (get(int, int,
% 25.69/4.39 | all_57_7, v7) = v8) | ? [v9: int] : ($lesseq(1,
% 25.69/4.39 | $difference(v9, v3)) & tb2t(v8) = v9)) & ? [v6: uni] : ? [v7:
% 25.69/4.39 | uni] : ? [v8: int] : (tb2t(v7) = v8 & t2tb(v5) = v6 & get(int,
% 25.69/4.39 | int, all_57_7, v6) = v7 & uni(v7) & uni(v6) & ? [v9: int] : ?
% 25.69/4.39 | [v10: uni] : ? [v11: uni] : ? [v12: int] : ($lesseq(v12, v8) &
% 25.69/4.39 | $lesseq(1, $difference(all_57_8, v9)) & $lesseq(1,
% 25.69/4.39 | $difference(v9, v5)) & tb2t(v11) = v12 & t2tb(v9) = v10 &
% 25.69/4.39 | get(int, int, all_57_7, v10) = v11 & uni(v11) & uni(v10))))
% 25.69/4.39 |
% 25.69/4.39 | ALPHA: (9) implies:
% 25.69/4.39 | (10) $lesseq(1, $difference(n, all_57_8))
% 25.69/4.39 | (11) uni(all_57_6)
% 25.69/4.39 | (12) uni(all_57_4)
% 25.69/4.39 | (13) get(int, int, all_57_7, all_57_3) = all_57_2
% 25.69/4.39 | (14) get(int, int, all_57_5, all_55_4) = all_57_4
% 25.69/4.39 | (15) t2tb($sum(all_57_8, -1)) = all_57_3
% 25.69/4.39 | (16) tb2t(all_57_6) = 0
% 25.69/4.39 | (17) tb2t(all_57_4) = -1
% 25.69/4.39 | (18) f(all_57_8) = all_57_0
% 25.69/4.39 | (19) ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ( ~
% 25.69/4.39 | ($lesseq(1, $difference(all_57_8, v0))) | ~ ($lesseq(1, v0)) | ~
% 25.69/4.39 | (t2tb(v0) = v1) | ~ (get(int, int, all_57_5, v1) = v2) | ~
% 25.69/4.39 | (get(int, int, all_57_7, v2) = v3) | ? [v4: int] : ? [v5: uni] :
% 25.69/4.39 | ? [v6: int] : ? [v7: int] : ? [v8: uni] : ? [v9: int] :
% 25.69/4.39 | ($lesseq(1, v9) & $lesseq(1, $difference(v0, v7)) & $lesseq(v4, v7)
% 25.69/4.39 | & $lesseq(1, $difference(v4, v6)) & f(v0) = v4 & tb2t(v8) = v9 &
% 25.69/4.39 | tb2t(v5) = v6 & tb2t(v3) = $sum(v9, -1) & tb2t(v2) = v7 & get(int,
% 25.69/4.39 | int, all_57_5, v2) = v5 & get(int, int, all_57_7, v1) = v8 &
% 25.69/4.39 | uni(v8) & uni(v5) & ! [v10: int] : ! [v11: uni] : ! [v12: uni]
% 25.69/4.39 | : ( ~ ($lesseq(1, $difference(v0, v10))) | ~ ($lesseq(1,
% 25.69/4.39 | $difference(v10, v7))) | ~ (t2tb(v10) = v11) | ~ (get(int,
% 25.69/4.39 | int, all_57_7, v11) = v12) | ? [v13: int] : ($lesseq(v9,
% 25.69/4.39 | v13) & tb2t(v12) = v13))))
% 26.49/4.39 | (20) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: int] : ? [v4:
% 26.49/4.39 | uni] : ? [v5: int] : ($lesseq(all_57_0, v5) & $lesseq(1,
% 26.49/4.39 | $difference(all_57_8, v0)) & $lesseq(1, $difference(n, v0)) &
% 26.49/4.39 | $lesseq(all_57_0, v0) & $lesseq(0, v0) & tb2t(v4) = v5 & tb2t(v2) =
% 26.49/4.39 | v3 & t2tb(v0) = v1 & get(int, int, all_57_5, v1) = v4 & get(int,
% 26.49/4.39 | int, all_57_7, v1) = v2 & uni(v4) & uni(v2) & uni(v1) & ! [v6:
% 26.49/4.39 | int] : ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.39 | $difference(all_57_8, v6))) | ~ ($lesseq(1, $difference(v6,
% 26.49/4.39 | v0))) | ~ (t2tb(v6) = v7) | ~ (get(int, int, all_57_7, v7)
% 26.49/4.39 | = v8) | ? [v9: int] : ($lesseq(1, $difference(v9, v3)) &
% 26.49/4.39 | tb2t(v8) = v9)) & ? [v6: uni] : ? [v7: uni] : ? [v8: int] :
% 26.49/4.39 | (tb2t(v7) = v8 & t2tb(v5) = v6 & get(int, int, all_57_7, v6) = v7 &
% 26.49/4.39 | uni(v7) & uni(v6) & ? [v9: int] : ? [v10: uni] : ? [v11: uni] :
% 26.49/4.39 | ? [v12: int] : ($lesseq(v12, v8) & $lesseq(1,
% 26.49/4.39 | $difference(all_57_8, v9)) & $lesseq(1, $difference(v9, v5)) &
% 26.49/4.39 | tb2t(v11) = v12 & t2tb(v9) = v10 & get(int, int, all_57_7, v10)
% 26.49/4.39 | = v11 & uni(v11) & uni(v10))))
% 26.49/4.39 |
% 26.49/4.39 | DELTA: instantiating (20) with fresh symbols all_61_0, all_61_1, all_61_2,
% 26.49/4.39 | all_61_3, all_61_4, all_61_5 gives:
% 26.49/4.39 | (21) $lesseq(all_57_0, all_61_0) & $lesseq(1, $difference(all_57_8,
% 26.49/4.39 | all_61_5)) & $lesseq(1, $difference(n, all_61_5)) &
% 26.49/4.39 | $lesseq(all_57_0, all_61_5) & $lesseq(0, all_61_5) & tb2t(all_61_1) =
% 26.49/4.39 | all_61_0 & tb2t(all_61_3) = all_61_2 & t2tb(all_61_5) = all_61_4 &
% 26.49/4.39 | get(int, int, all_57_5, all_61_4) = all_61_1 & get(int, int, all_57_7,
% 26.49/4.40 | all_61_4) = all_61_3 & uni(all_61_1) & uni(all_61_3) & uni(all_61_4)
% 26.49/4.40 | & ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ( ~ ($lesseq(1,
% 26.49/4.40 | $difference(all_57_8, v0))) | ~ ($lesseq(1, $difference(v0,
% 26.49/4.40 | all_61_5))) | ~ (t2tb(v0) = v1) | ~ (get(int, int, all_57_7,
% 26.49/4.40 | v1) = v2) | ? [v3: int] : ($lesseq(1, $difference(v3,
% 26.49/4.40 | all_61_2)) & tb2t(v2) = v3)) & ? [v0: uni] : ? [v1: uni] :
% 26.49/4.40 | ? [v2: int] : (tb2t(v1) = v2 & t2tb(all_61_0) = v0 & get(int, int,
% 26.49/4.40 | all_57_7, v0) = v1 & uni(v1) & uni(v0) & ? [v3: int] : ? [v4:
% 26.49/4.40 | uni] : ? [v5: uni] : ? [v6: int] : ($lesseq(v6, v2) & $lesseq(1,
% 26.49/4.40 | $difference(all_57_8, v3)) & $lesseq(1, $difference(v3,
% 26.49/4.40 | all_61_0)) & tb2t(v5) = v6 & t2tb(v3) = v4 & get(int, int,
% 26.49/4.40 | all_57_7, v4) = v5 & uni(v5) & uni(v4)))
% 26.49/4.40 |
% 26.49/4.40 | ALPHA: (21) implies:
% 26.49/4.40 | (22) $lesseq(0, all_61_5)
% 26.49/4.40 | (23) $lesseq(all_57_0, all_61_5)
% 26.49/4.40 | (24) $lesseq(1, $difference(all_57_8, all_61_5))
% 26.49/4.40 | (25) $lesseq(all_57_0, all_61_0)
% 26.49/4.40 | (26) uni(all_61_1)
% 26.49/4.40 | (27) get(int, int, all_57_7, all_61_4) = all_61_3
% 26.49/4.40 | (28) get(int, int, all_57_5, all_61_4) = all_61_1
% 26.49/4.40 | (29) t2tb(all_61_5) = all_61_4
% 26.49/4.40 | (30) tb2t(all_61_3) = all_61_2
% 26.49/4.40 | (31) tb2t(all_61_1) = all_61_0
% 26.49/4.40 | (32) ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ( ~ ($lesseq(1,
% 26.49/4.40 | $difference(all_57_8, v0))) | ~ ($lesseq(1, $difference(v0,
% 26.49/4.40 | all_61_5))) | ~ (t2tb(v0) = v1) | ~ (get(int, int, all_57_7,
% 26.49/4.40 | v1) = v2) | ? [v3: int] : ($lesseq(1, $difference(v3,
% 26.49/4.40 | all_61_2)) & tb2t(v2) = v3))
% 26.49/4.40 | (33) ? [v0: uni] : ? [v1: uni] : ? [v2: int] : (tb2t(v1) = v2 &
% 26.49/4.40 | t2tb(all_61_0) = v0 & get(int, int, all_57_7, v0) = v1 & uni(v1) &
% 26.49/4.40 | uni(v0) & ? [v3: int] : ? [v4: uni] : ? [v5: uni] : ? [v6: int]
% 26.49/4.40 | : ($lesseq(v6, v2) & $lesseq(1, $difference(all_57_8, v3)) &
% 26.49/4.40 | $lesseq(1, $difference(v3, all_61_0)) & tb2t(v5) = v6 & t2tb(v3) =
% 26.49/4.40 | v4 & get(int, int, all_57_7, v4) = v5 & uni(v5) & uni(v4)))
% 26.49/4.40 |
% 26.49/4.40 | DELTA: instantiating (33) with fresh symbols all_65_0, all_65_1, all_65_2
% 26.49/4.40 | gives:
% 26.49/4.40 | (34) tb2t(all_65_1) = all_65_0 & t2tb(all_61_0) = all_65_2 & get(int, int,
% 26.49/4.40 | all_57_7, all_65_2) = all_65_1 & uni(all_65_1) & uni(all_65_2) & ?
% 26.49/4.40 | [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: int] : ($lesseq(v3,
% 26.49/4.40 | all_65_0) & $lesseq(1, $difference(all_57_8, v0)) & $lesseq(1,
% 26.49/4.40 | $difference(v0, all_61_0)) & tb2t(v2) = v3 & t2tb(v0) = v1 &
% 26.49/4.40 | get(int, int, all_57_7, v1) = v2 & uni(v2) & uni(v1))
% 26.49/4.40 |
% 26.49/4.40 | ALPHA: (34) implies:
% 26.49/4.40 | (35) get(int, int, all_57_7, all_65_2) = all_65_1
% 26.49/4.40 | (36) t2tb(all_61_0) = all_65_2
% 26.49/4.40 | (37) tb2t(all_65_1) = all_65_0
% 26.49/4.40 | (38) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : ? [v3: int] :
% 26.49/4.40 | ($lesseq(v3, all_65_0) & $lesseq(1, $difference(all_57_8, v0)) &
% 26.49/4.40 | $lesseq(1, $difference(v0, all_61_0)) & tb2t(v2) = v3 & t2tb(v0) =
% 26.49/4.40 | v1 & get(int, int, all_57_7, v1) = v2 & uni(v2) & uni(v1))
% 26.49/4.40 |
% 26.49/4.40 | DELTA: instantiating (38) with fresh symbols all_67_0, all_67_1, all_67_2,
% 26.49/4.40 | all_67_3 gives:
% 26.49/4.40 | (39) $lesseq(all_67_0, all_65_0) & $lesseq(1, $difference(all_57_8,
% 26.49/4.40 | all_67_3)) & $lesseq(1, $difference(all_67_3, all_61_0)) &
% 26.49/4.40 | tb2t(all_67_1) = all_67_0 & t2tb(all_67_3) = all_67_2 & get(int, int,
% 26.49/4.40 | all_57_7, all_67_2) = all_67_1 & uni(all_67_1) & uni(all_67_2)
% 26.49/4.40 |
% 26.49/4.40 | ALPHA: (39) implies:
% 26.49/4.40 | (40) $lesseq(1, $difference(all_67_3, all_61_0))
% 26.49/4.40 | (41) $lesseq(1, $difference(all_57_8, all_67_3))
% 26.49/4.40 | (42) $lesseq(all_67_0, all_65_0)
% 26.49/4.40 | (43) get(int, int, all_57_7, all_67_2) = all_67_1
% 26.49/4.40 | (44) t2tb(all_67_3) = all_67_2
% 26.49/4.40 | (45) tb2t(all_67_1) = all_67_0
% 26.49/4.40 |
% 26.49/4.40 | COMBINE_INEQS: (22), (24) imply:
% 26.49/4.40 | (46) $lesseq(1, all_57_8)
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (2) with all_57_3, all_61_4, $sum(all_57_8, -1),
% 26.49/4.40 | simplifying with (15) gives:
% 26.49/4.40 | (47) all_61_4 = all_57_3 | ~ (t2tb($sum(all_57_8, -1)) = all_61_4)
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (2) with all_55_4, all_61_4, 0, simplifying with
% 26.49/4.40 | (6) gives:
% 26.49/4.40 | (48) all_61_4 = all_55_4 | ~ (t2tb(0) = all_61_4)
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (2) with all_61_4, all_67_2, all_61_5, simplifying
% 26.49/4.40 | with (29) gives:
% 26.49/4.40 | (49) all_67_2 = all_61_4 | ~ (t2tb(all_61_5) = all_67_2)
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (2) with all_57_3, all_67_2, $sum(all_57_8, -1),
% 26.49/4.40 | simplifying with (15) gives:
% 26.49/4.40 | (50) all_67_2 = all_57_3 | ~ (t2tb($sum(all_57_8, -1)) = all_67_2)
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (f_prop) with all_57_8, all_57_0, simplifying with
% 26.49/4.40 | (18) gives:
% 26.49/4.40 | (51) ~ ($lesseq(1, $difference(n, all_57_8))) | ~ ($lesseq(1, all_57_8))
% 26.49/4.40 | | ($lesseq(1, $difference(all_57_8, all_57_0)) & $lesseq(0, all_57_0))
% 26.49/4.40 |
% 26.49/4.40 | GROUND_INST: instantiating (32) with $sum(all_57_8, -1), all_57_3, all_57_2,
% 26.49/4.40 | simplifying with (13), (15) gives:
% 26.49/4.41 | (52) ~ ($lesseq(2, $difference(all_57_8, all_61_5))) | ? [v0: int] :
% 26.49/4.41 | ($lesseq(1, $difference(v0, all_61_2)) & tb2t(all_57_2) = v0)
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeL) with $sum(all_57_8, -1), all_57_3,
% 26.49/4.41 | simplifying with (15) gives:
% 26.49/4.41 | (53) tb2t(all_57_3) = $sum(all_57_8, -1)
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeL) with all_61_5, all_61_4, simplifying with
% 26.49/4.41 | (29) gives:
% 26.49/4.41 | (54) tb2t(all_61_4) = all_61_5
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeL) with all_61_0, all_65_2, simplifying with
% 26.49/4.41 | (36) gives:
% 26.49/4.41 | (55) tb2t(all_65_2) = all_61_0
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (32) with all_67_3, all_67_2, all_67_1, simplifying
% 26.49/4.41 | with (43), (44) gives:
% 26.49/4.41 | (56) ~ ($lesseq(1, $difference(all_57_8, all_67_3))) | ~ ($lesseq(1,
% 26.49/4.41 | $difference(all_67_3, all_61_5))) | ? [v0: int] : ($lesseq(1,
% 26.49/4.41 | $difference(v0, all_61_2)) & tb2t(all_67_1) = v0)
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeL) with all_67_3, all_67_2, simplifying with
% 26.49/4.41 | (44) gives:
% 26.49/4.41 | (57) tb2t(all_67_2) = all_67_3
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeR) with all_57_6, 0, simplifying with (11),
% 26.49/4.41 | (16) gives:
% 26.49/4.41 | (58) t2tb(0) = all_57_6
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeR) with all_57_4, -1, simplifying with (12),
% 26.49/4.41 | (17) gives:
% 26.49/4.41 | (59) t2tb(-1) = all_57_4
% 26.49/4.41 |
% 26.49/4.41 | GROUND_INST: instantiating (bridgeR) with all_61_1, all_61_0, simplifying with
% 26.49/4.41 | (26), (31) gives:
% 26.49/4.41 | (60) t2tb(all_61_0) = all_61_1
% 26.49/4.41 |
% 26.49/4.41 | BETA: splitting (51) gives:
% 26.49/4.41 |
% 26.49/4.41 | Case 1:
% 26.49/4.41 | |
% 26.49/4.41 | | (61) $lesseq(all_57_8, 0)
% 26.49/4.41 | |
% 26.49/4.41 | | COMBINE_INEQS: (46), (61) imply:
% 26.49/4.41 | | (62) $false
% 26.49/4.41 | |
% 26.49/4.41 | | CLOSE: (62) is inconsistent.
% 26.49/4.41 | |
% 26.49/4.41 | Case 2:
% 26.49/4.41 | |
% 26.49/4.41 | | (63) ~ ($lesseq(1, $difference(n, all_57_8))) | ($lesseq(1,
% 26.49/4.41 | | $difference(all_57_8, all_57_0)) & $lesseq(0, all_57_0))
% 26.49/4.41 | |
% 26.49/4.41 | | BETA: splitting (63) gives:
% 26.49/4.41 | |
% 26.49/4.41 | | Case 1:
% 26.49/4.41 | | |
% 26.49/4.41 | | | (64) $lesseq(n, all_57_8)
% 26.49/4.41 | | |
% 26.49/4.41 | | | COMBINE_INEQS: (10), (64) imply:
% 26.49/4.41 | | | (65) $false
% 26.49/4.41 | | |
% 26.49/4.41 | | | CLOSE: (65) is inconsistent.
% 26.49/4.41 | | |
% 26.49/4.41 | | Case 2:
% 26.49/4.41 | | |
% 26.49/4.41 | | | (66) $lesseq(1, $difference(all_57_8, all_57_0)) & $lesseq(0, all_57_0)
% 26.49/4.41 | | |
% 26.49/4.41 | | | ALPHA: (66) implies:
% 26.49/4.41 | | | (67) $lesseq(0, all_57_0)
% 26.49/4.41 | | |
% 26.49/4.41 | | | GROUND_INST: instantiating (2) with all_61_4, all_57_6, 0, simplifying
% 26.49/4.41 | | | with (58) gives:
% 26.49/4.41 | | | (68) all_61_4 = all_57_6 | ~ (t2tb(0) = all_61_4)
% 26.49/4.41 | | |
% 26.49/4.41 | | | GROUND_INST: instantiating (2) with all_55_4, all_57_6, 0, simplifying
% 26.49/4.41 | | | with (6), (58) gives:
% 26.49/4.41 | | | (69) all_57_6 = all_55_4
% 26.49/4.41 | | |
% 26.49/4.41 | | | GROUND_INST: instantiating (2) with all_55_2, all_57_4, -1, simplifying
% 26.49/4.41 | | | with (7), (59) gives:
% 26.49/4.41 | | | (70) all_57_4 = all_55_2
% 26.49/4.41 | | |
% 26.49/4.41 | | | GROUND_INST: instantiating (2) with all_65_2, all_61_1, all_61_0,
% 26.49/4.41 | | | simplifying with (36), (60) gives:
% 26.49/4.41 | | | (71) all_65_2 = all_61_1
% 26.49/4.41 | | |
% 26.49/4.41 | | | REDUCE: (17), (70) imply:
% 26.49/4.41 | | | (72) tb2t(all_55_2) = -1
% 26.49/4.41 | | |
% 26.49/4.41 | | | REDUCE: (14), (70) imply:
% 26.49/4.41 | | | (73) get(int, int, all_57_5, all_55_4) = all_55_2
% 26.49/4.41 | | |
% 26.49/4.41 | | | REDUCE: (35), (71) imply:
% 26.49/4.41 | | | (74) get(int, int, all_57_7, all_61_1) = all_65_1
% 26.49/4.41 | | |
% 26.49/4.41 | | | GROUND_INST: instantiating (19) with all_61_5, all_61_4, all_61_1,
% 26.49/4.41 | | | all_65_1, simplifying with (28), (29), (74) gives:
% 26.49/4.41 | | | (75) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ~ ($lesseq(1,
% 26.49/4.41 | | | all_61_5)) | ? [v0: int] : ? [v1: uni] : ? [v2: int] : ?
% 26.49/4.41 | | | [v3: int] : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) &
% 26.49/4.41 | | | $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0, v3) &
% 26.49/4.41 | | | $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 & tb2t(v4) =
% 26.49/4.41 | | | v5 & tb2t(v1) = v2 & tb2t(all_65_1) = $sum(v5, -1) &
% 26.49/4.41 | | | tb2t(all_61_1) = v3 & get(int, int, all_57_5, all_61_1) = v1 &
% 26.49/4.41 | | | get(int, int, all_57_7, all_61_4) = v4 & uni(v4) & uni(v1) & !
% 26.49/4.41 | | | [v6: int] : ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.41 | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.41 | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~ (get(int,
% 26.49/4.41 | | | int, all_57_7, v7) = v8) | ? [v9: int] : ($lesseq(v5, v9)
% 26.49/4.41 | | | & tb2t(v8) = v9)))
% 26.49/4.41 | | |
% 26.49/4.41 | | | BETA: splitting (50) gives:
% 26.49/4.41 | | |
% 26.49/4.41 | | | Case 1:
% 26.49/4.41 | | | |
% 26.49/4.41 | | | | (76) ~ (t2tb($sum(all_57_8, -1)) = all_67_2)
% 26.49/4.41 | | | |
% 26.49/4.41 | | | | PRED_UNIFY: (44), (76) imply:
% 26.49/4.41 | | | | (77) ~ ($difference(all_67_3, all_57_8) = -1)
% 26.49/4.41 | | | |
% 26.49/4.41 | | | | STRENGTHEN: (41), (77) imply:
% 26.49/4.41 | | | | (78) $lesseq(2, $difference(all_57_8, all_67_3))
% 26.49/4.41 | | | |
% 26.49/4.41 | | | | BETA: splitting (49) gives:
% 26.49/4.41 | | | |
% 26.49/4.41 | | | | Case 1:
% 26.49/4.41 | | | | |
% 26.49/4.42 | | | | | (79) ~ (t2tb(all_61_5) = all_67_2)
% 26.49/4.42 | | | | |
% 26.49/4.42 | | | | | PRED_UNIFY: (44), (79) imply:
% 26.49/4.42 | | | | | (80) ~ (all_67_3 = all_61_5)
% 26.49/4.42 | | | | |
% 26.49/4.42 | | | | | BETA: splitting (47) gives:
% 26.49/4.42 | | | | |
% 26.49/4.42 | | | | | Case 1:
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | (81) ~ (t2tb($sum(all_57_8, -1)) = all_61_4)
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | PRED_UNIFY: (29), (81) imply:
% 26.49/4.42 | | | | | | (82) ~ ($difference(all_61_5, all_57_8) = -1)
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | STRENGTHEN: (24), (82) imply:
% 26.49/4.42 | | | | | | (83) $lesseq(2, $difference(all_57_8, all_61_5))
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | COMBINE_INEQS: (25), (67) imply:
% 26.49/4.42 | | | | | | (84) $lesseq(0, all_61_0)
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | BETA: splitting (48) gives:
% 26.49/4.42 | | | | | |
% 26.49/4.42 | | | | | | Case 1:
% 26.49/4.42 | | | | | | |
% 26.49/4.42 | | | | | | | (85) ~ (t2tb(0) = all_61_4)
% 26.49/4.42 | | | | | | |
% 26.49/4.42 | | | | | | | PRED_UNIFY: (29), (85) imply:
% 26.49/4.42 | | | | | | | (86) ~ (all_61_5 = 0)
% 26.49/4.42 | | | | | | |
% 26.49/4.42 | | | | | | | STRENGTHEN: (22), (86) imply:
% 26.49/4.42 | | | | | | | (87) $lesseq(1, all_61_5)
% 26.49/4.42 | | | | | | |
% 26.49/4.42 | | | | | | | BETA: splitting (75) gives:
% 26.49/4.42 | | | | | | |
% 26.49/4.42 | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | (88) $lesseq(all_61_5, 0)
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | COMBINE_INEQS: (87), (88) imply:
% 26.49/4.42 | | | | | | | | (89) $false
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | CLOSE: (89) is inconsistent.
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | Case 2:
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | (90) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ?
% 26.49/4.42 | | | | | | | | [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3: int] :
% 26.49/4.42 | | | | | | | | ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) &
% 26.49/4.42 | | | | | | | | $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0,
% 26.49/4.42 | | | | | | | | v3) & $lesseq(1, $difference(v0, v2)) & f(all_61_5)
% 26.49/4.42 | | | | | | | | = v0 & tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1)
% 26.49/4.42 | | | | | | | | = $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.42 | | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.42 | | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.42 | | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.42 | | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.42 | | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.42 | | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.42 | | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | BETA: splitting (90) gives:
% 26.49/4.42 | | | | | | | |
% 26.49/4.42 | | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | (91) $lesseq(all_57_8, all_61_5)
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | COMBINE_INEQS: (83), (91) imply:
% 26.49/4.42 | | | | | | | | | (92) $false
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | CLOSE: (92) is inconsistent.
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | Case 2:
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | (93) ? [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3:
% 26.49/4.42 | | | | | | | | | int] : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5)
% 26.49/4.42 | | | | | | | | | & $lesseq(1, $difference(all_61_5, v3)) &
% 26.49/4.42 | | | | | | | | | $lesseq(v0, v3) & $lesseq(1, $difference(v0, v2)) &
% 26.49/4.42 | | | | | | | | | f(all_61_5) = v0 & tb2t(v4) = v5 & tb2t(v1) = v2 &
% 26.49/4.42 | | | | | | | | | tb2t(all_65_1) = $sum(v5, -1) & tb2t(all_61_1) = v3
% 26.49/4.42 | | | | | | | | | & get(int, int, all_57_5, all_61_1) = v1 & get(int,
% 26.49/4.42 | | | | | | | | | int, all_57_7, all_61_4) = v4 & uni(v4) & uni(v1)
% 26.49/4.42 | | | | | | | | | & ! [v6: int] : ! [v7: uni] : ! [v8: uni] : ( ~
% 26.49/4.42 | | | | | | | | | ($lesseq(1, $difference(all_61_5, v6))) | ~
% 26.49/4.42 | | | | | | | | | ($lesseq(1, $difference(v6, v3))) | ~ (t2tb(v6) =
% 26.49/4.42 | | | | | | | | | v7) | ~ (get(int, int, all_57_7, v7) = v8) | ?
% 26.49/4.42 | | | | | | | | | [v9: int] : ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | DELTA: instantiating (93) with fresh symbols all_343_0,
% 26.49/4.42 | | | | | | | | | all_343_1, all_343_2, all_343_3, all_343_4, all_343_5
% 26.49/4.42 | | | | | | | | | gives:
% 26.49/4.42 | | | | | | | | | (94) $lesseq(1, all_343_0) & $lesseq(1,
% 26.49/4.42 | | | | | | | | | $difference(all_61_5, all_343_2)) &
% 26.49/4.42 | | | | | | | | | $lesseq(all_343_5, all_343_2) & $lesseq(1,
% 26.49/4.42 | | | | | | | | | $difference(all_343_5, all_343_3)) & f(all_61_5) =
% 26.49/4.42 | | | | | | | | | all_343_5 & tb2t(all_343_1) = all_343_0 &
% 26.49/4.42 | | | | | | | | | tb2t(all_343_4) = all_343_3 & tb2t(all_65_1) =
% 26.49/4.42 | | | | | | | | | $sum(all_343_0, -1) & tb2t(all_61_1) = all_343_2 &
% 26.49/4.42 | | | | | | | | | get(int, int, all_57_5, all_61_1) = all_343_4 &
% 26.49/4.42 | | | | | | | | | get(int, int, all_57_7, all_61_4) = all_343_1 &
% 26.49/4.42 | | | | | | | | | uni(all_343_1) & uni(all_343_4) & ! [v0: int] : !
% 26.49/4.42 | | | | | | | | | [v1: uni] : ! [v2: uni] : ( ~ ($lesseq(1,
% 26.49/4.42 | | | | | | | | | $difference(all_61_5, v0))) | ~ ($lesseq(1,
% 26.49/4.42 | | | | | | | | | $difference(v0, all_343_2))) | ~ (t2tb(v0) =
% 26.49/4.42 | | | | | | | | | v1) | ~ (get(int, int, all_57_7, v1) = v2) | ?
% 26.49/4.42 | | | | | | | | | [v3: int] : ($lesseq(all_343_0, v3) & tb2t(v2) =
% 26.49/4.42 | | | | | | | | | v3))
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | ALPHA: (94) implies:
% 26.49/4.42 | | | | | | | | | (95) get(int, int, all_57_7, all_61_4) = all_343_1
% 26.49/4.42 | | | | | | | | | (96) tb2t(all_61_1) = all_343_2
% 26.49/4.42 | | | | | | | | | (97) tb2t(all_65_1) = $sum(all_343_0, -1)
% 26.49/4.42 | | | | | | | | | (98) tb2t(all_343_1) = all_343_0
% 26.49/4.42 | | | | | | | | | (99) ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ( ~
% 26.49/4.42 | | | | | | | | | ($lesseq(1, $difference(all_61_5, v0))) | ~
% 26.49/4.42 | | | | | | | | | ($lesseq(1, $difference(v0, all_343_2))) | ~
% 26.49/4.42 | | | | | | | | | (t2tb(v0) = v1) | ~ (get(int, int, all_57_7, v1) =
% 26.49/4.42 | | | | | | | | | v2) | ? [v3: int] : ($lesseq(all_343_0, v3) &
% 26.49/4.42 | | | | | | | | | tb2t(v2) = v3))
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | GROUND_INST: instantiating (99) with all_67_3, all_67_2,
% 26.49/4.42 | | | | | | | | | all_67_1, simplifying with (43), (44) gives:
% 26.49/4.42 | | | | | | | | | (100) ~ ($lesseq(1, $difference(all_67_3, all_343_2))) |
% 26.49/4.42 | | | | | | | | | ~ ($lesseq(1, $difference(all_61_5, all_67_3))) | ?
% 26.49/4.42 | | | | | | | | | [v0: int] : ($lesseq(all_343_0, v0) & tb2t(all_67_1)
% 26.49/4.42 | | | | | | | | | = v0)
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | GROUND_INST: instantiating (4) with all_61_3, all_343_1,
% 26.49/4.42 | | | | | | | | | all_61_4, all_57_7, int, int, simplifying with
% 26.49/4.42 | | | | | | | | | (27), (95) gives:
% 26.49/4.42 | | | | | | | | | (101) all_343_1 = all_61_3
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | GROUND_INST: instantiating (3) with all_61_0, all_343_2,
% 26.49/4.42 | | | | | | | | | all_61_1, simplifying with (31), (96) gives:
% 26.49/4.42 | | | | | | | | | (102) all_343_2 = all_61_0
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | GROUND_INST: instantiating (3) with all_65_0, $sum(all_343_0,
% 26.49/4.42 | | | | | | | | | -1), all_65_1, simplifying with (37), (97)
% 26.49/4.42 | | | | | | | | | gives:
% 26.49/4.42 | | | | | | | | | (103) $difference(all_343_0, all_65_0) = 1
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | REDUCE: (98), (101), (103) imply:
% 26.49/4.42 | | | | | | | | | (104) tb2t(all_61_3) = $sum(all_65_0, 1)
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | BETA: splitting (100) gives:
% 26.49/4.42 | | | | | | | | |
% 26.49/4.42 | | | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | (105) $lesseq(all_67_3, all_343_2)
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | REDUCE: (102), (105) imply:
% 26.49/4.42 | | | | | | | | | | (106) $lesseq(all_67_3, all_61_0)
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | COMBINE_INEQS: (40), (106) imply:
% 26.49/4.42 | | | | | | | | | | (107) $false
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | CLOSE: (107) is inconsistent.
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | Case 2:
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | (108) ~ ($lesseq(1, $difference(all_61_5, all_67_3))) |
% 26.49/4.42 | | | | | | | | | | ? [v0: int] : ($lesseq(all_343_0, v0) &
% 26.49/4.42 | | | | | | | | | | tb2t(all_67_1) = v0)
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | BETA: splitting (108) gives:
% 26.49/4.42 | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | (109) $lesseq(all_61_5, all_67_3)
% 26.49/4.42 | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | STRENGTHEN: (80), (109) imply:
% 26.49/4.42 | | | | | | | | | | | (110) $lesseq(1, $difference(all_67_3, all_61_5))
% 26.49/4.42 | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | BETA: splitting (56) gives:
% 26.49/4.42 | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | (111) $lesseq(all_57_8, all_67_3)
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | COMBINE_INEQS: (78), (111) imply:
% 26.49/4.42 | | | | | | | | | | | | (112) $false
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | Case 2:
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | (113) ~ ($lesseq(1, $difference(all_67_3, all_61_5))) |
% 26.49/4.42 | | | | | | | | | | | | ? [v0: int] : ($lesseq(1, $difference(v0,
% 26.49/4.42 | | | | | | | | | | | | all_61_2)) & tb2t(all_67_1) = v0)
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | BETA: splitting (113) gives:
% 26.49/4.42 | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | Case 1:
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | | (114) $lesseq(all_67_3, all_61_5)
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | | COMBINE_INEQS: (110), (114) imply:
% 26.49/4.42 | | | | | | | | | | | | | (115) $false
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | Case 2:
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | | (116) ? [v0: int] : ($lesseq(1, $difference(v0,
% 26.49/4.42 | | | | | | | | | | | | | all_61_2)) & tb2t(all_67_1) = v0)
% 26.49/4.42 | | | | | | | | | | | | |
% 26.49/4.42 | | | | | | | | | | | | | DELTA: instantiating (116) with fresh symbol all_387_0
% 26.49/4.42 | | | | | | | | | | | | | gives:
% 26.49/4.43 | | | | | | | | | | | | | (117) $lesseq(1, $difference(all_387_0, all_61_2)) &
% 26.49/4.43 | | | | | | | | | | | | | tb2t(all_67_1) = all_387_0
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | ALPHA: (117) implies:
% 26.49/4.43 | | | | | | | | | | | | | (118) $lesseq(1, $difference(all_387_0, all_61_2))
% 26.49/4.43 | | | | | | | | | | | | | (119) tb2t(all_67_1) = all_387_0
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0,
% 26.49/4.43 | | | | | | | | | | | | | 1), all_61_3, simplifying with (30), (104)
% 26.49/4.43 | | | | | | | | | | | | | gives:
% 26.49/4.43 | | | | | | | | | | | | | (120) $difference(all_65_0, all_61_2) = -1
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_67_0, all_387_0,
% 26.49/4.43 | | | | | | | | | | | | | all_67_1, simplifying with (45), (119) gives:
% 26.49/4.43 | | | | | | | | | | | | | (121) all_387_0 = all_67_0
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | REDUCE: (118), (121) imply:
% 26.49/4.43 | | | | | | | | | | | | | (122) $lesseq(1, $difference(all_67_0, all_61_2))
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | REDUCE: (42), (120) imply:
% 26.49/4.43 | | | | | | | | | | | | | (123) $lesseq(1, $difference(all_61_2, all_67_0))
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | COMBINE_INEQS: (122), (123) imply:
% 26.49/4.43 | | | | | | | | | | | | | (124) $false
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 26.49/4.43 | | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | | End of split
% 26.49/4.43 | | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | End of split
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | Case 2:
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | (125) ? [v0: int] : ($lesseq(all_343_0, v0) &
% 26.49/4.43 | | | | | | | | | | | tb2t(all_67_1) = v0)
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | DELTA: instantiating (125) with fresh symbol all_367_0
% 26.49/4.43 | | | | | | | | | | | gives:
% 26.49/4.43 | | | | | | | | | | | (126) $lesseq(all_343_0, all_367_0) & tb2t(all_67_1) =
% 26.49/4.43 | | | | | | | | | | | all_367_0
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | ALPHA: (126) implies:
% 26.49/4.43 | | | | | | | | | | | (127) $lesseq(all_343_0, all_367_0)
% 26.49/4.43 | | | | | | | | | | | (128) tb2t(all_67_1) = all_367_0
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | REDUCE: (103), (127) imply:
% 26.49/4.43 | | | | | | | | | | | (129) $lesseq(1, $difference(all_367_0, all_65_0))
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0,
% 26.49/4.43 | | | | | | | | | | | 1), all_61_3, simplifying with (30), (104)
% 26.49/4.43 | | | | | | | | | | | gives:
% 26.49/4.43 | | | | | | | | | | | (130) $difference(all_65_0, all_61_2) = -1
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_67_0, all_367_0,
% 26.49/4.43 | | | | | | | | | | | all_67_1, simplifying with (45), (128) gives:
% 26.49/4.43 | | | | | | | | | | | (131) all_367_0 = all_67_0
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | REDUCE: (129), (130), (131) imply:
% 26.49/4.43 | | | | | | | | | | | (132) $lesseq(all_61_2, all_67_0)
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | REDUCE: (42), (130) imply:
% 26.49/4.43 | | | | | | | | | | | (133) $lesseq(1, $difference(all_61_2, all_67_0))
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | COMBINE_INEQS: (132), (133) imply:
% 26.49/4.43 | | | | | | | | | | | (134) $false
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 26.49/4.43 | | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | | End of split
% 26.49/4.43 | | | | | | | | | |
% 26.49/4.43 | | | | | | | | | End of split
% 26.49/4.43 | | | | | | | | |
% 26.49/4.43 | | | | | | | | End of split
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | End of split
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | Case 2:
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | (135) t2tb(0) = all_61_4
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | REF_CLOSE: (3), (4), (28), (31), (68), (69), (72), (73), (84),
% 26.49/4.43 | | | | | | | (135) are inconsistent by sub-proof #1.
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | End of split
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | Case 2:
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | (136) all_61_4 = all_57_3
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | REDUCE: (54), (136) imply:
% 26.49/4.43 | | | | | | (137) tb2t(all_57_3) = all_61_5
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | REDUCE: (27), (136) imply:
% 26.49/4.43 | | | | | | (138) get(int, int, all_57_7, all_57_3) = all_61_3
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | GROUND_INST: instantiating (4) with all_57_2, all_61_3, all_57_3,
% 26.49/4.43 | | | | | | all_57_7, int, int, simplifying with (13), (138) gives:
% 26.49/4.43 | | | | | | (139) all_61_3 = all_57_2
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | GROUND_INST: instantiating (3) with $sum(all_57_8, -1), all_61_5,
% 26.49/4.43 | | | | | | all_57_3, simplifying with (53), (137) gives:
% 26.49/4.43 | | | | | | (140) $difference(all_61_5, all_57_8) = -1
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | REDUCE: (30), (139) imply:
% 26.49/4.43 | | | | | | (141) tb2t(all_57_2) = all_61_2
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | BETA: splitting (75) gives:
% 26.49/4.43 | | | | | |
% 26.49/4.43 | | | | | | Case 1:
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | (142) $lesseq(all_61_5, 0)
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | REDUCE: (140), (142) imply:
% 26.49/4.43 | | | | | | | (143) $lesseq(all_57_8, 1)
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | COMBINE_INEQS: (40), (78) imply:
% 26.49/4.43 | | | | | | | (144) $lesseq(3, $difference(all_57_8, all_61_0))
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | COMBINE_INEQS: (25), (144) imply:
% 26.49/4.43 | | | | | | | (145) $lesseq(3, $difference(all_57_8, all_57_0))
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | COMBINE_INEQS: (67), (145) imply:
% 26.49/4.43 | | | | | | | (146) $lesseq(3, all_57_8)
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | COMBINE_INEQS: (143), (146) imply:
% 26.49/4.43 | | | | | | | (147) $false
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | CLOSE: (147) is inconsistent.
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | Case 2:
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | (148) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ?
% 26.49/4.43 | | | | | | | [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3: int] :
% 26.49/4.43 | | | | | | | ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) & $lesseq(1,
% 26.49/4.43 | | | | | | | $difference(all_61_5, v3)) & $lesseq(v0, v3) &
% 26.49/4.43 | | | | | | | $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.43 | | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) =
% 26.49/4.43 | | | | | | | $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.43 | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.43 | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.43 | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.43 | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.43 | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | BETA: splitting (148) gives:
% 26.49/4.43 | | | | | | |
% 26.49/4.43 | | | | | | | Case 1:
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | (149) $lesseq(all_57_8, all_61_5)
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | REDUCE: (140), (149) imply:
% 26.49/4.43 | | | | | | | | (150) $false
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | CLOSE: (150) is inconsistent.
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | Case 2:
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | (151) ? [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3:
% 26.49/4.43 | | | | | | | | int] : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5)
% 26.49/4.43 | | | | | | | | & $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0,
% 26.49/4.43 | | | | | | | | v3) & $lesseq(1, $difference(v0, v2)) & f(all_61_5)
% 26.49/4.43 | | | | | | | | = v0 & tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1)
% 26.49/4.43 | | | | | | | | = $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.43 | | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.43 | | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.43 | | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.43 | | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.43 | | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | DELTA: instantiating (151) with fresh symbols all_308_0,
% 26.49/4.43 | | | | | | | | all_308_1, all_308_2, all_308_3, all_308_4, all_308_5
% 26.49/4.43 | | | | | | | | gives:
% 26.49/4.43 | | | | | | | | (152) $lesseq(1, all_308_0) & $lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(all_61_5, all_308_2)) &
% 26.49/4.43 | | | | | | | | $lesseq(all_308_5, all_308_2) & $lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(all_308_5, all_308_3)) & f(all_61_5) =
% 26.49/4.43 | | | | | | | | all_308_5 & tb2t(all_308_1) = all_308_0 &
% 26.49/4.43 | | | | | | | | tb2t(all_308_4) = all_308_3 & tb2t(all_65_1) =
% 26.49/4.43 | | | | | | | | $sum(all_308_0, -1) & tb2t(all_61_1) = all_308_2 &
% 26.49/4.43 | | | | | | | | get(int, int, all_57_5, all_61_1) = all_308_4 &
% 26.49/4.43 | | | | | | | | get(int, int, all_57_7, all_61_4) = all_308_1 &
% 26.49/4.43 | | | | | | | | uni(all_308_1) & uni(all_308_4) & ! [v0: int] : !
% 26.49/4.43 | | | | | | | | [v1: uni] : ! [v2: uni] : ( ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(all_61_5, v0))) | ~ ($lesseq(1,
% 26.49/4.43 | | | | | | | | $difference(v0, all_308_2))) | ~ (t2tb(v0) = v1)
% 26.49/4.43 | | | | | | | | | ~ (get(int, int, all_57_7, v1) = v2) | ? [v3:
% 26.49/4.43 | | | | | | | | int] : ($lesseq(all_308_0, v3) & tb2t(v2) = v3))
% 26.49/4.43 | | | | | | | |
% 26.49/4.43 | | | | | | | | ALPHA: (152) implies:
% 26.49/4.43 | | | | | | | | (153) get(int, int, all_57_7, all_61_4) = all_308_1
% 26.49/4.43 | | | | | | | | (154) tb2t(all_61_1) = all_308_2
% 26.49/4.43 | | | | | | | | (155) tb2t(all_65_1) = $sum(all_308_0, -1)
% 26.49/4.43 | | | | | | | | (156) tb2t(all_308_1) = all_308_0
% 26.49/4.43 | | | | | | | | (157) ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ( ~
% 26.49/4.43 | | | | | | | | ($lesseq(1, $difference(all_61_5, v0))) | ~
% 26.49/4.43 | | | | | | | | ($lesseq(1, $difference(v0, all_308_2))) | ~
% 26.49/4.44 | | | | | | | | (t2tb(v0) = v1) | ~ (get(int, int, all_57_7, v1) =
% 26.49/4.44 | | | | | | | | v2) | ? [v3: int] : ($lesseq(all_308_0, v3) &
% 26.49/4.44 | | | | | | | | tb2t(v2) = v3))
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | GROUND_INST: instantiating (157) with all_67_3, all_67_2,
% 26.49/4.44 | | | | | | | | all_67_1, simplifying with (43), (44) gives:
% 26.49/4.44 | | | | | | | | (158) ~ ($lesseq(1, $difference(all_67_3, all_308_2))) | ~
% 26.49/4.44 | | | | | | | | ($lesseq(1, $difference(all_61_5, all_67_3))) | ? [v0:
% 26.49/4.44 | | | | | | | | int] : ($lesseq(all_308_0, v0) & tb2t(all_67_1) = v0)
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | REDUCE: (136), (153) imply:
% 26.49/4.44 | | | | | | | | (159) get(int, int, all_57_7, all_57_3) = all_308_1
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | GROUND_INST: instantiating (4) with all_57_2, all_308_1,
% 26.49/4.44 | | | | | | | | all_57_3, all_57_7, int, int, simplifying with
% 26.49/4.44 | | | | | | | | (13), (159) gives:
% 26.49/4.44 | | | | | | | | (160) all_308_1 = all_57_2
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | GROUND_INST: instantiating (3) with all_61_0, all_308_2,
% 26.49/4.44 | | | | | | | | all_61_1, simplifying with (31), (154) gives:
% 26.49/4.44 | | | | | | | | (161) all_308_2 = all_61_0
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | GROUND_INST: instantiating (3) with all_65_0, $sum(all_308_0,
% 26.49/4.44 | | | | | | | | -1), all_65_1, simplifying with (37), (155)
% 26.49/4.44 | | | | | | | | gives:
% 26.49/4.44 | | | | | | | | (162) $difference(all_308_0, all_65_0) = 1
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | REDUCE: (156), (160), (162) imply:
% 26.49/4.44 | | | | | | | | (163) tb2t(all_57_2) = $sum(all_65_0, 1)
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | BETA: splitting (158) gives:
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | | Case 1:
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | (164) $lesseq(all_67_3, all_308_2)
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | REDUCE: (161), (164) imply:
% 26.49/4.44 | | | | | | | | | (165) $lesseq(all_67_3, all_61_0)
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | COMBINE_INEQS: (40), (165) imply:
% 26.49/4.44 | | | | | | | | | (166) $false
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | CLOSE: (166) is inconsistent.
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | Case 2:
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | (167) ~ ($lesseq(1, $difference(all_61_5, all_67_3))) | ?
% 26.49/4.44 | | | | | | | | | [v0: int] : ($lesseq(all_308_0, v0) & tb2t(all_67_1)
% 26.49/4.44 | | | | | | | | | = v0)
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | BETA: splitting (167) gives:
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | | Case 1:
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | (168) $lesseq(all_61_5, all_67_3)
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | REDUCE: (140), (168) imply:
% 26.49/4.44 | | | | | | | | | | (169) $lesseq(-1, $difference(all_67_3, all_57_8))
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | COMBINE_INEQS: (78), (169) imply:
% 26.49/4.44 | | | | | | | | | | (170) $false
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | CLOSE: (170) is inconsistent.
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | Case 2:
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | (171) ? [v0: int] : ($lesseq(all_308_0, v0) &
% 26.49/4.44 | | | | | | | | | | tb2t(all_67_1) = v0)
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | DELTA: instantiating (171) with fresh symbol all_332_0
% 26.49/4.44 | | | | | | | | | | gives:
% 26.49/4.44 | | | | | | | | | | (172) $lesseq(all_308_0, all_332_0) & tb2t(all_67_1) =
% 26.49/4.44 | | | | | | | | | | all_332_0
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | ALPHA: (172) implies:
% 26.49/4.44 | | | | | | | | | | (173) $lesseq(all_308_0, all_332_0)
% 26.49/4.44 | | | | | | | | | | (174) tb2t(all_67_1) = all_332_0
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | REDUCE: (162), (173) imply:
% 26.49/4.44 | | | | | | | | | | (175) $lesseq(1, $difference(all_332_0, all_65_0))
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0,
% 26.49/4.44 | | | | | | | | | | 1), all_57_2, simplifying with (141), (163)
% 26.49/4.44 | | | | | | | | | | gives:
% 26.49/4.44 | | | | | | | | | | (176) $difference(all_65_0, all_61_2) = -1
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | GROUND_INST: instantiating (3) with all_67_0, all_332_0,
% 26.49/4.44 | | | | | | | | | | all_67_1, simplifying with (45), (174) gives:
% 26.49/4.44 | | | | | | | | | | (177) all_332_0 = all_67_0
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | REDUCE: (175), (176), (177) imply:
% 26.49/4.44 | | | | | | | | | | (178) $lesseq(all_61_2, all_67_0)
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | REDUCE: (42), (176) imply:
% 26.49/4.44 | | | | | | | | | | (179) $lesseq(1, $difference(all_61_2, all_67_0))
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | COMBINE_INEQS: (178), (179) imply:
% 26.49/4.44 | | | | | | | | | | (180) $false
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | | CLOSE: (180) is inconsistent.
% 26.49/4.44 | | | | | | | | | |
% 26.49/4.44 | | | | | | | | | End of split
% 26.49/4.44 | | | | | | | | |
% 26.49/4.44 | | | | | | | | End of split
% 26.49/4.44 | | | | | | | |
% 26.49/4.44 | | | | | | | End of split
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | End of split
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | End of split
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | Case 2:
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | (181) all_67_2 = all_61_4
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | REDUCE: (57), (181) imply:
% 26.49/4.44 | | | | | (182) tb2t(all_61_4) = all_67_3
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | REDUCE: (43), (181) imply:
% 26.49/4.44 | | | | | (183) get(int, int, all_57_7, all_61_4) = all_67_1
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | GROUND_INST: instantiating (4) with all_61_3, all_67_1, all_61_4,
% 26.49/4.44 | | | | | all_57_7, int, int, simplifying with (27), (183) gives:
% 26.49/4.44 | | | | | (184) all_67_1 = all_61_3
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | GROUND_INST: instantiating (3) with all_61_5, all_67_3, all_61_4,
% 26.49/4.44 | | | | | simplifying with (54), (182) gives:
% 26.49/4.44 | | | | | (185) all_67_3 = all_61_5
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | REDUCE: (78), (185) imply:
% 26.49/4.44 | | | | | (186) $lesseq(2, $difference(all_57_8, all_61_5))
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | REDUCE: (40), (185) imply:
% 26.49/4.44 | | | | | (187) $lesseq(1, $difference(all_61_5, all_61_0))
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | COMBINE_INEQS: (25), (187) imply:
% 26.49/4.44 | | | | | (188) $lesseq(1, $difference(all_61_5, all_57_0))
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | REDUCE: (45), (184) imply:
% 26.49/4.44 | | | | | (189) tb2t(all_61_3) = all_67_0
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | BETA: splitting (75) gives:
% 26.49/4.44 | | | | |
% 26.49/4.44 | | | | | Case 1:
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | (190) $lesseq(all_61_5, 0)
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | COMBINE_INEQS: (188), (190) imply:
% 26.49/4.44 | | | | | | (191) $lesseq(all_57_0, -1)
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | COMBINE_INEQS: (67), (191) imply:
% 26.49/4.44 | | | | | | (192) $false
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | CLOSE: (192) is inconsistent.
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | Case 2:
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | (193) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ? [v0:
% 26.49/4.44 | | | | | | int] : ? [v1: uni] : ? [v2: int] : ? [v3: int] : ?
% 26.49/4.44 | | | | | | [v4: uni] : ? [v5: int] : ($lesseq(1, v5) & $lesseq(1,
% 26.49/4.44 | | | | | | $difference(all_61_5, v3)) & $lesseq(v0, v3) &
% 26.49/4.44 | | | | | | $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.44 | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) = $sum(v5,
% 26.49/4.44 | | | | | | -1) & tb2t(all_61_1) = v3 & get(int, int, all_57_5,
% 26.49/4.44 | | | | | | all_61_1) = v1 & get(int, int, all_57_7, all_61_4) = v4
% 26.49/4.44 | | | | | | & uni(v4) & uni(v1) & ! [v6: int] : ! [v7: uni] : !
% 26.49/4.44 | | | | | | [v8: uni] : ( ~ ($lesseq(1, $difference(all_61_5, v6))) |
% 26.49/4.44 | | | | | | ~ ($lesseq(1, $difference(v6, v3))) | ~ (t2tb(v6) =
% 26.49/4.44 | | | | | | v7) | ~ (get(int, int, all_57_7, v7) = v8) | ? [v9:
% 26.49/4.44 | | | | | | int] : ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | BETA: splitting (193) gives:
% 26.49/4.44 | | | | | |
% 26.49/4.44 | | | | | | Case 1:
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | (194) $lesseq(all_57_8, all_61_5)
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | COMBINE_INEQS: (186), (194) imply:
% 26.49/4.44 | | | | | | | (195) $false
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | CLOSE: (195) is inconsistent.
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | Case 2:
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | (196) ? [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3: int]
% 26.49/4.44 | | | | | | | : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) &
% 26.49/4.44 | | | | | | | $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0, v3)
% 26.49/4.44 | | | | | | | & $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.44 | | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) =
% 26.49/4.44 | | | | | | | $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.44 | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.44 | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.44 | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.44 | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.44 | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.44 | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.44 | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | DELTA: instantiating (196) with fresh symbols all_291_0,
% 26.49/4.44 | | | | | | | all_291_1, all_291_2, all_291_3, all_291_4, all_291_5
% 26.49/4.44 | | | | | | | gives:
% 26.49/4.44 | | | | | | | (197) $lesseq(1, all_291_0) & $lesseq(1, $difference(all_61_5,
% 26.49/4.44 | | | | | | | all_291_2)) & $lesseq(all_291_5, all_291_2) &
% 26.49/4.44 | | | | | | | $lesseq(1, $difference(all_291_5, all_291_3)) &
% 26.49/4.44 | | | | | | | f(all_61_5) = all_291_5 & tb2t(all_291_1) = all_291_0 &
% 26.49/4.44 | | | | | | | tb2t(all_291_4) = all_291_3 & tb2t(all_65_1) =
% 26.49/4.44 | | | | | | | $sum(all_291_0, -1) & tb2t(all_61_1) = all_291_2 &
% 26.49/4.44 | | | | | | | get(int, int, all_57_5, all_61_1) = all_291_4 & get(int,
% 26.49/4.44 | | | | | | | int, all_57_7, all_61_4) = all_291_1 & uni(all_291_1) &
% 26.49/4.44 | | | | | | | uni(all_291_4) & ! [v0: int] : ! [v1: uni] : ! [v2:
% 26.49/4.44 | | | | | | | uni] : ( ~ ($lesseq(1, $difference(all_61_5, v0))) | ~
% 26.49/4.44 | | | | | | | ($lesseq(1, $difference(v0, all_291_2))) | ~ (t2tb(v0)
% 26.49/4.44 | | | | | | | = v1) | ~ (get(int, int, all_57_7, v1) = v2) | ?
% 26.49/4.44 | | | | | | | [v3: int] : ($lesseq(all_291_0, v3) & tb2t(v2) = v3))
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | ALPHA: (197) implies:
% 26.49/4.44 | | | | | | | (198) get(int, int, all_57_7, all_61_4) = all_291_1
% 26.49/4.44 | | | | | | | (199) tb2t(all_65_1) = $sum(all_291_0, -1)
% 26.49/4.44 | | | | | | | (200) tb2t(all_291_1) = all_291_0
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | GROUND_INST: instantiating (4) with all_61_3, all_291_1, all_61_4,
% 26.49/4.44 | | | | | | | all_57_7, int, int, simplifying with (27), (198)
% 26.49/4.44 | | | | | | | gives:
% 26.49/4.44 | | | | | | | (201) all_291_1 = all_61_3
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | GROUND_INST: instantiating (3) with all_61_2, all_67_0, all_61_3,
% 26.49/4.44 | | | | | | | simplifying with (30), (189) gives:
% 26.49/4.44 | | | | | | | (202) all_67_0 = all_61_2
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | GROUND_INST: instantiating (3) with all_65_0, $sum(all_291_0, -1),
% 26.49/4.44 | | | | | | | all_65_1, simplifying with (37), (199) gives:
% 26.49/4.44 | | | | | | | (203) $difference(all_291_0, all_65_0) = 1
% 26.49/4.44 | | | | | | |
% 26.49/4.44 | | | | | | | REDUCE: (42), (202) imply:
% 26.49/4.44 | | | | | | | (204) $lesseq(all_61_2, all_65_0)
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | REDUCE: (200), (201), (203) imply:
% 26.49/4.45 | | | | | | | (205) tb2t(all_61_3) = $sum(all_65_0, 1)
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0, 1),
% 26.49/4.45 | | | | | | | all_61_3, simplifying with (30), (205) gives:
% 26.49/4.45 | | | | | | | (206) $difference(all_65_0, all_61_2) = -1
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | REDUCE: (204), (206) imply:
% 26.49/4.45 | | | | | | | (207) $false
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | CLOSE: (207) is inconsistent.
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | End of split
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | End of split
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | End of split
% 26.49/4.45 | | | |
% 26.49/4.45 | | | Case 2:
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | (208) all_67_2 = all_57_3
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | REDUCE: (57), (208) imply:
% 26.49/4.45 | | | | (209) tb2t(all_57_3) = all_67_3
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | REDUCE: (44), (208) imply:
% 26.49/4.45 | | | | (210) t2tb(all_67_3) = all_57_3
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | REDUCE: (43), (208) imply:
% 26.49/4.45 | | | | (211) get(int, int, all_57_7, all_57_3) = all_67_1
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | GROUND_INST: instantiating (4) with all_57_2, all_67_1, all_57_3,
% 26.49/4.45 | | | | all_57_7, int, int, simplifying with (13), (211) gives:
% 26.49/4.45 | | | | (212) all_67_1 = all_57_2
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | GROUND_INST: instantiating (3) with $sum(all_57_8, -1), all_67_3,
% 26.49/4.45 | | | | all_57_3, simplifying with (53), (209) gives:
% 26.49/4.45 | | | | (213) $difference(all_67_3, all_57_8) = -1
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | REDUCE: (40), (213) imply:
% 26.49/4.45 | | | | (214) $lesseq(2, $difference(all_57_8, all_61_0))
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | REDUCE: (45), (212) imply:
% 26.49/4.45 | | | | (215) tb2t(all_57_2) = all_67_0
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | BETA: splitting (49) gives:
% 26.49/4.45 | | | |
% 26.49/4.45 | | | | Case 1:
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | (216) ~ (t2tb(all_61_5) = all_67_2)
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | REDUCE: (208), (216) imply:
% 26.49/4.45 | | | | | (217) ~ (t2tb(all_61_5) = all_57_3)
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | PRED_UNIFY: (15), (217) imply:
% 26.49/4.45 | | | | | (218) ~ ($difference(all_61_5, all_57_8) = -1)
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | STRENGTHEN: (24), (218) imply:
% 26.49/4.45 | | | | | (219) $lesseq(2, $difference(all_57_8, all_61_5))
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | BETA: splitting (52) gives:
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | Case 1:
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | (220) $lesseq(-1, $difference(all_61_5, all_57_8))
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | COMBINE_INEQS: (219), (220) imply:
% 26.49/4.45 | | | | | | (221) $false
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | CLOSE: (221) is inconsistent.
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | Case 2:
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | (222) ? [v0: int] : ($lesseq(1, $difference(v0, all_61_2)) &
% 26.49/4.45 | | | | | | tb2t(all_57_2) = v0)
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | DELTA: instantiating (222) with fresh symbol all_279_0 gives:
% 26.49/4.45 | | | | | | (223) $lesseq(1, $difference(all_279_0, all_61_2)) &
% 26.49/4.45 | | | | | | tb2t(all_57_2) = all_279_0
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | ALPHA: (223) implies:
% 26.49/4.45 | | | | | | (224) $lesseq(1, $difference(all_279_0, all_61_2))
% 26.49/4.45 | | | | | | (225) tb2t(all_57_2) = all_279_0
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | GROUND_INST: instantiating (3) with all_67_0, all_279_0, all_57_2,
% 26.49/4.45 | | | | | | simplifying with (215), (225) gives:
% 26.49/4.45 | | | | | | (226) all_279_0 = all_67_0
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | REDUCE: (224), (226) imply:
% 26.49/4.45 | | | | | | (227) $lesseq(1, $difference(all_67_0, all_61_2))
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | BETA: splitting (75) gives:
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | | Case 1:
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | (228) $lesseq(all_61_5, 0)
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | COMBINE_INEQS: (23), (228) imply:
% 26.49/4.45 | | | | | | | (229) $lesseq(all_57_0, 0)
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | ANTI_SYMM: (22), (228) imply:
% 26.49/4.45 | | | | | | | (230) all_61_5 = 0
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | ANTI_SYMM: (67), (229) imply:
% 26.49/4.45 | | | | | | | (231) all_57_0 = 0
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | REDUCE: (25), (231) imply:
% 26.49/4.45 | | | | | | | (232) $lesseq(0, all_61_0)
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | REDUCE: (29), (230) imply:
% 26.49/4.45 | | | | | | | (233) t2tb(0) = all_61_4
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | REF_CLOSE: (3), (4), (28), (31), (68), (69), (72), (73), (232),
% 26.49/4.45 | | | | | | | (233) are inconsistent by sub-proof #1.
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | Case 2:
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | (234) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ?
% 26.49/4.45 | | | | | | | [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3: int] :
% 26.49/4.45 | | | | | | | ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) & $lesseq(1,
% 26.49/4.45 | | | | | | | $difference(all_61_5, v3)) & $lesseq(v0, v3) &
% 26.49/4.45 | | | | | | | $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.45 | | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) =
% 26.49/4.45 | | | | | | | $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.45 | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.45 | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.45 | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.45 | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.45 | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | BETA: splitting (234) gives:
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | | Case 1:
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | (235) $lesseq(all_57_8, all_61_5)
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | COMBINE_INEQS: (219), (235) imply:
% 26.49/4.45 | | | | | | | | (236) $false
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | CLOSE: (236) is inconsistent.
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | Case 2:
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | (237) ? [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3:
% 26.49/4.45 | | | | | | | | int] : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5)
% 26.49/4.45 | | | | | | | | & $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0,
% 26.49/4.45 | | | | | | | | v3) & $lesseq(1, $difference(v0, v2)) & f(all_61_5)
% 26.49/4.45 | | | | | | | | = v0 & tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1)
% 26.49/4.45 | | | | | | | | = $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.45 | | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.45 | | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.45 | | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.45 | | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.45 | | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | DELTA: instantiating (237) with fresh symbols all_303_0,
% 26.49/4.45 | | | | | | | | all_303_1, all_303_2, all_303_3, all_303_4, all_303_5
% 26.49/4.45 | | | | | | | | gives:
% 26.49/4.45 | | | | | | | | (238) $lesseq(1, all_303_0) & $lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(all_61_5, all_303_2)) &
% 26.49/4.45 | | | | | | | | $lesseq(all_303_5, all_303_2) & $lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(all_303_5, all_303_3)) & f(all_61_5) =
% 26.49/4.45 | | | | | | | | all_303_5 & tb2t(all_303_1) = all_303_0 &
% 26.49/4.45 | | | | | | | | tb2t(all_303_4) = all_303_3 & tb2t(all_65_1) =
% 26.49/4.45 | | | | | | | | $sum(all_303_0, -1) & tb2t(all_61_1) = all_303_2 &
% 26.49/4.45 | | | | | | | | get(int, int, all_57_5, all_61_1) = all_303_4 &
% 26.49/4.45 | | | | | | | | get(int, int, all_57_7, all_61_4) = all_303_1 &
% 26.49/4.45 | | | | | | | | uni(all_303_1) & uni(all_303_4) & ! [v0: int] : !
% 26.49/4.45 | | | | | | | | [v1: uni] : ! [v2: uni] : ( ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(all_61_5, v0))) | ~ ($lesseq(1,
% 26.49/4.45 | | | | | | | | $difference(v0, all_303_2))) | ~ (t2tb(v0) = v1)
% 26.49/4.45 | | | | | | | | | ~ (get(int, int, all_57_7, v1) = v2) | ? [v3:
% 26.49/4.45 | | | | | | | | int] : ($lesseq(all_303_0, v3) & tb2t(v2) = v3))
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | ALPHA: (238) implies:
% 26.49/4.45 | | | | | | | | (239) get(int, int, all_57_7, all_61_4) = all_303_1
% 26.49/4.45 | | | | | | | | (240) tb2t(all_65_1) = $sum(all_303_0, -1)
% 26.49/4.45 | | | | | | | | (241) tb2t(all_303_1) = all_303_0
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | GROUND_INST: instantiating (4) with all_61_3, all_303_1,
% 26.49/4.45 | | | | | | | | all_61_4, all_57_7, int, int, simplifying with
% 26.49/4.45 | | | | | | | | (27), (239) gives:
% 26.49/4.45 | | | | | | | | (242) all_303_1 = all_61_3
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | GROUND_INST: instantiating (3) with all_65_0, $sum(all_303_0,
% 26.49/4.45 | | | | | | | | -1), all_65_1, simplifying with (37), (240)
% 26.49/4.45 | | | | | | | | gives:
% 26.49/4.45 | | | | | | | | (243) $difference(all_303_0, all_65_0) = 1
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | REDUCE: (241), (242), (243) imply:
% 26.49/4.45 | | | | | | | | (244) tb2t(all_61_3) = $sum(all_65_0, 1)
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0, 1),
% 26.49/4.45 | | | | | | | | all_61_3, simplifying with (30), (244) gives:
% 26.49/4.45 | | | | | | | | (245) $difference(all_65_0, all_61_2) = -1
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | REDUCE: (42), (245) imply:
% 26.49/4.45 | | | | | | | | (246) $lesseq(1, $difference(all_61_2, all_67_0))
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | COMBINE_INEQS: (227), (246) imply:
% 26.49/4.45 | | | | | | | | (247) $false
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | | CLOSE: (247) is inconsistent.
% 26.49/4.45 | | | | | | | |
% 26.49/4.45 | | | | | | | End of split
% 26.49/4.45 | | | | | | |
% 26.49/4.45 | | | | | | End of split
% 26.49/4.45 | | | | | |
% 26.49/4.45 | | | | | End of split
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | Case 2:
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | (248) all_67_2 = all_61_4
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | COMBINE_EQS: (208), (248) imply:
% 26.49/4.45 | | | | | (249) all_61_4 = all_57_3
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | SIMP: (249) implies:
% 26.49/4.45 | | | | | (250) all_61_4 = all_57_3
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | REDUCE: (54), (250) imply:
% 26.49/4.45 | | | | | (251) tb2t(all_57_3) = all_61_5
% 26.49/4.45 | | | | |
% 26.49/4.45 | | | | | REDUCE: (27), (250) imply:
% 26.49/4.46 | | | | | (252) get(int, int, all_57_7, all_57_3) = all_61_3
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | | GROUND_INST: instantiating (4) with all_57_2, all_61_3, all_57_3,
% 26.49/4.46 | | | | | all_57_7, int, int, simplifying with (13), (252) gives:
% 26.49/4.46 | | | | | (253) all_61_3 = all_57_2
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | | GROUND_INST: instantiating (3) with $sum(all_57_8, -1), all_61_5,
% 26.49/4.46 | | | | | all_57_3, simplifying with (53), (251) gives:
% 26.49/4.46 | | | | | (254) $difference(all_61_5, all_57_8) = -1
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | | REDUCE: (30), (253) imply:
% 26.49/4.46 | | | | | (255) tb2t(all_57_2) = all_61_2
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | | BETA: splitting (75) gives:
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | | Case 1:
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | (256) $lesseq(all_61_5, 0)
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | REDUCE: (254), (256) imply:
% 26.49/4.46 | | | | | | (257) $lesseq(all_57_8, 1)
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | COMBINE_INEQS: (25), (214) imply:
% 26.49/4.46 | | | | | | (258) $lesseq(2, $difference(all_57_8, all_57_0))
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | COMBINE_INEQS: (67), (258) imply:
% 26.49/4.46 | | | | | | (259) $lesseq(2, all_57_8)
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | COMBINE_INEQS: (257), (259) imply:
% 26.49/4.46 | | | | | | (260) $false
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | CLOSE: (260) is inconsistent.
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | Case 2:
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | (261) ~ ($lesseq(1, $difference(all_57_8, all_61_5))) | ? [v0:
% 26.49/4.46 | | | | | | int] : ? [v1: uni] : ? [v2: int] : ? [v3: int] : ?
% 26.49/4.46 | | | | | | [v4: uni] : ? [v5: int] : ($lesseq(1, v5) & $lesseq(1,
% 26.49/4.46 | | | | | | $difference(all_61_5, v3)) & $lesseq(v0, v3) &
% 26.49/4.46 | | | | | | $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.46 | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) = $sum(v5,
% 26.49/4.46 | | | | | | -1) & tb2t(all_61_1) = v3 & get(int, int, all_57_5,
% 26.49/4.46 | | | | | | all_61_1) = v1 & get(int, int, all_57_7, all_61_4) = v4
% 26.49/4.46 | | | | | | & uni(v4) & uni(v1) & ! [v6: int] : ! [v7: uni] : !
% 26.49/4.46 | | | | | | [v8: uni] : ( ~ ($lesseq(1, $difference(all_61_5, v6))) |
% 26.49/4.46 | | | | | | ~ ($lesseq(1, $difference(v6, v3))) | ~ (t2tb(v6) =
% 26.49/4.46 | | | | | | v7) | ~ (get(int, int, all_57_7, v7) = v8) | ? [v9:
% 26.49/4.46 | | | | | | int] : ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | BETA: splitting (261) gives:
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | | Case 1:
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | (262) $lesseq(all_57_8, all_61_5)
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | REDUCE: (254), (262) imply:
% 26.49/4.46 | | | | | | | (263) $false
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | CLOSE: (263) is inconsistent.
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | Case 2:
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | (264) ? [v0: int] : ? [v1: uni] : ? [v2: int] : ? [v3: int]
% 26.49/4.46 | | | | | | | : ? [v4: uni] : ? [v5: int] : ($lesseq(1, v5) &
% 26.49/4.46 | | | | | | | $lesseq(1, $difference(all_61_5, v3)) & $lesseq(v0, v3)
% 26.49/4.46 | | | | | | | & $lesseq(1, $difference(v0, v2)) & f(all_61_5) = v0 &
% 26.49/4.46 | | | | | | | tb2t(v4) = v5 & tb2t(v1) = v2 & tb2t(all_65_1) =
% 26.49/4.46 | | | | | | | $sum(v5, -1) & tb2t(all_61_1) = v3 & get(int, int,
% 26.49/4.46 | | | | | | | all_57_5, all_61_1) = v1 & get(int, int, all_57_7,
% 26.49/4.46 | | | | | | | all_61_4) = v4 & uni(v4) & uni(v1) & ! [v6: int] :
% 26.49/4.46 | | | | | | | ! [v7: uni] : ! [v8: uni] : ( ~ ($lesseq(1,
% 26.49/4.46 | | | | | | | $difference(all_61_5, v6))) | ~ ($lesseq(1,
% 26.49/4.46 | | | | | | | $difference(v6, v3))) | ~ (t2tb(v6) = v7) | ~
% 26.49/4.46 | | | | | | | (get(int, int, all_57_7, v7) = v8) | ? [v9: int] :
% 26.49/4.46 | | | | | | | ($lesseq(v5, v9) & tb2t(v8) = v9)))
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | DELTA: instantiating (264) with fresh symbols all_284_0,
% 26.49/4.46 | | | | | | | all_284_1, all_284_2, all_284_3, all_284_4, all_284_5
% 26.49/4.46 | | | | | | | gives:
% 26.49/4.46 | | | | | | | (265) $lesseq(1, all_284_0) & $lesseq(1, $difference(all_61_5,
% 26.49/4.46 | | | | | | | all_284_2)) & $lesseq(all_284_5, all_284_2) &
% 26.49/4.46 | | | | | | | $lesseq(1, $difference(all_284_5, all_284_3)) &
% 26.49/4.46 | | | | | | | f(all_61_5) = all_284_5 & tb2t(all_284_1) = all_284_0 &
% 26.49/4.46 | | | | | | | tb2t(all_284_4) = all_284_3 & tb2t(all_65_1) =
% 26.49/4.46 | | | | | | | $sum(all_284_0, -1) & tb2t(all_61_1) = all_284_2 &
% 26.49/4.46 | | | | | | | get(int, int, all_57_5, all_61_1) = all_284_4 & get(int,
% 26.49/4.46 | | | | | | | int, all_57_7, all_61_4) = all_284_1 & uni(all_284_1) &
% 26.49/4.46 | | | | | | | uni(all_284_4) & ! [v0: int] : ! [v1: uni] : ! [v2:
% 26.49/4.46 | | | | | | | uni] : ( ~ ($lesseq(1, $difference(all_61_5, v0))) | ~
% 26.49/4.46 | | | | | | | ($lesseq(1, $difference(v0, all_284_2))) | ~ (t2tb(v0)
% 26.49/4.46 | | | | | | | = v1) | ~ (get(int, int, all_57_7, v1) = v2) | ?
% 26.49/4.46 | | | | | | | [v3: int] : ($lesseq(all_284_0, v3) & tb2t(v2) = v3))
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | ALPHA: (265) implies:
% 26.49/4.46 | | | | | | | (266) get(int, int, all_57_7, all_61_4) = all_284_1
% 26.49/4.46 | | | | | | | (267) tb2t(all_61_1) = all_284_2
% 26.49/4.46 | | | | | | | (268) tb2t(all_65_1) = $sum(all_284_0, -1)
% 26.49/4.46 | | | | | | | (269) tb2t(all_284_1) = all_284_0
% 26.49/4.46 | | | | | | | (270) ! [v0: int] : ! [v1: uni] : ! [v2: uni] : ( ~
% 26.49/4.46 | | | | | | | ($lesseq(1, $difference(all_61_5, v0))) | ~
% 26.49/4.46 | | | | | | | ($lesseq(1, $difference(v0, all_284_2))) | ~ (t2tb(v0)
% 26.49/4.46 | | | | | | | = v1) | ~ (get(int, int, all_57_7, v1) = v2) | ?
% 26.49/4.46 | | | | | | | [v3: int] : ($lesseq(all_284_0, v3) & tb2t(v2) = v3))
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | GROUND_INST: instantiating (270) with all_61_0, all_61_1,
% 26.49/4.46 | | | | | | | all_65_1, simplifying with (60), (74) gives:
% 26.49/4.46 | | | | | | | (271) ~ ($lesseq(1, $difference(all_61_0, all_284_2))) | ~
% 26.49/4.46 | | | | | | | ($lesseq(1, $difference(all_61_5, all_61_0))) | ? [v0:
% 26.49/4.46 | | | | | | | int] : ($lesseq(all_284_0, v0) & tb2t(all_65_1) = v0)
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | REDUCE: (250), (266) imply:
% 26.49/4.46 | | | | | | | (272) get(int, int, all_57_7, all_57_3) = all_284_1
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | BETA: splitting (271) gives:
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | | Case 1:
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | GROUND_INST: instantiating (4) with all_57_2, all_284_1,
% 26.49/4.46 | | | | | | | | all_57_3, all_57_7, int, int, simplifying with
% 26.49/4.46 | | | | | | | | (13), (272) gives:
% 26.49/4.46 | | | | | | | | (273) all_284_1 = all_57_2
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | GROUND_INST: instantiating (3) with all_67_0, all_61_2,
% 26.49/4.46 | | | | | | | | all_57_2, simplifying with (215), (255) gives:
% 26.49/4.46 | | | | | | | | (274) all_67_0 = all_61_2
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | GROUND_INST: instantiating (3) with all_65_0, $sum(all_284_0,
% 26.49/4.46 | | | | | | | | -1), all_65_1, simplifying with (37), (268)
% 26.49/4.46 | | | | | | | | gives:
% 26.49/4.46 | | | | | | | | (275) $difference(all_284_0, all_65_0) = 1
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | REDUCE: (42), (274) imply:
% 26.49/4.46 | | | | | | | | (276) $lesseq(all_61_2, all_65_0)
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | REDUCE: (269), (273), (275) imply:
% 26.49/4.46 | | | | | | | | (277) tb2t(all_57_2) = $sum(all_65_0, 1)
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | GROUND_INST: instantiating (3) with all_61_2, $sum(all_65_0, 1),
% 26.49/4.46 | | | | | | | | all_57_2, simplifying with (255), (277) gives:
% 26.49/4.46 | | | | | | | | (278) $difference(all_65_0, all_61_2) = -1
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | REDUCE: (276), (278) imply:
% 26.49/4.46 | | | | | | | | (279) $false
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | CLOSE: (279) is inconsistent.
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | Case 2:
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | (280) $lesseq(1, $difference(all_61_0, all_284_2))
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | GROUND_INST: instantiating (3) with all_61_0, all_284_2,
% 26.49/4.46 | | | | | | | | all_61_1, simplifying with (31), (267) gives:
% 26.49/4.46 | | | | | | | | (281) all_284_2 = all_61_0
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | REDUCE: (280), (281) imply:
% 26.49/4.46 | | | | | | | | (282) $false
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | | CLOSE: (282) is inconsistent.
% 26.49/4.46 | | | | | | | |
% 26.49/4.46 | | | | | | | End of split
% 26.49/4.46 | | | | | | |
% 26.49/4.46 | | | | | | End of split
% 26.49/4.46 | | | | | |
% 26.49/4.46 | | | | | End of split
% 26.49/4.46 | | | | |
% 26.49/4.46 | | | | End of split
% 26.49/4.46 | | | |
% 26.49/4.46 | | | End of split
% 26.49/4.46 | | |
% 26.49/4.46 | | End of split
% 26.49/4.46 | |
% 26.49/4.46 | End of split
% 26.49/4.46 |
% 26.49/4.46 End of proof
% 26.49/4.46
% 26.49/4.46 Sub-proof #1 shows that the following formulas are inconsistent:
% 26.49/4.46 ----------------------------------------------------------------
% 26.49/4.46 (1) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] :
% 26.49/4.46 ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4,
% 26.49/4.46 v3, v2) = v0))
% 26.49/4.46 (2) all_61_4 = all_57_6 | ~ (t2tb(0) = all_61_4)
% 26.49/4.46 (3) t2tb(0) = all_61_4
% 26.49/4.46 (4) tb2t(all_55_2) = -1
% 26.49/4.46 (5) $lesseq(0, all_61_0)
% 26.49/4.46 (6) tb2t(all_61_1) = all_61_0
% 26.49/4.46 (7) get(int, int, all_57_5, all_55_4) = all_55_2
% 26.49/4.46 (8) get(int, int, all_57_5, all_61_4) = all_61_1
% 26.49/4.46 (9) ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) =
% 26.49/4.46 v1) | ~ (tb2t(v2) = v0))
% 26.49/4.46 (10) all_57_6 = all_55_4
% 26.49/4.46
% 26.49/4.46 Begin of proof
% 26.49/4.46 |
% 26.49/4.46 | BETA: splitting (2) gives:
% 26.49/4.46 |
% 26.49/4.46 | Case 1:
% 26.49/4.46 | |
% 26.49/4.46 | | (11) ~ (t2tb(0) = all_61_4)
% 26.49/4.46 | |
% 26.49/4.46 | | PRED_UNIFY: (3), (11) imply:
% 26.49/4.46 | | (12) $false
% 26.49/4.46 | |
% 26.49/4.46 | | CLOSE: (12) is inconsistent.
% 26.49/4.46 | |
% 26.49/4.46 | Case 2:
% 26.49/4.46 | |
% 26.49/4.46 | | (13) all_61_4 = all_57_6
% 26.49/4.46 | |
% 26.49/4.46 | | COMBINE_EQS: (10), (13) imply:
% 26.49/4.46 | | (14) all_61_4 = all_55_4
% 26.49/4.46 | |
% 26.49/4.46 | | REDUCE: (8), (14) imply:
% 26.49/4.46 | | (15) get(int, int, all_57_5, all_55_4) = all_61_1
% 26.49/4.46 | |
% 26.49/4.46 | | GROUND_INST: instantiating (1) with all_55_2, all_61_1, all_55_4, all_57_5,
% 26.49/4.46 | | int, int, simplifying with (7), (15) gives:
% 26.49/4.46 | | (16) all_61_1 = all_55_2
% 26.49/4.46 | |
% 26.49/4.46 | | REDUCE: (6), (16) imply:
% 26.49/4.46 | | (17) tb2t(all_55_2) = all_61_0
% 26.49/4.46 | |
% 26.49/4.46 | | GROUND_INST: instantiating (9) with -1, all_61_0, all_55_2, simplifying with
% 26.49/4.47 | | (4), (17) gives:
% 26.49/4.47 | | (18) all_61_0 = -1
% 26.49/4.47 | |
% 26.49/4.47 | | REDUCE: (5), (18) imply:
% 26.49/4.47 | | (19) $false
% 26.49/4.47 | |
% 26.49/4.47 | | CLOSE: (19) is inconsistent.
% 26.49/4.47 | |
% 26.49/4.47 | End of split
% 26.49/4.47 |
% 26.49/4.47 End of proof
% 26.49/4.47 % SZS output end Proof for theBenchmark
% 26.49/4.47
% 26.49/4.47 3848ms
%------------------------------------------------------------------------------