TSTP Solution File: SWW607_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW607_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 : n025.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 00:50:53 EDT 2023
% Result : Theorem 71.01s 10.20s
% Output : Proof 72.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW607_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sun Aug 27 22:03:09 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.73/1.43 Prover 0: Preprocessing ...
% 4.73/1.43 Prover 5: Preprocessing ...
% 4.73/1.44 Prover 3: Preprocessing ...
% 5.18/1.45 Prover 1: Preprocessing ...
% 5.18/1.46 Prover 6: Preprocessing ...
% 5.18/1.46 Prover 4: Preprocessing ...
% 5.18/1.47 Prover 2: Preprocessing ...
% 12.49/2.51 Prover 1: Warning: ignoring some quantifiers
% 13.47/2.59 Prover 6: Proving ...
% 13.47/2.66 Prover 1: Constructing countermodel ...
% 13.47/2.68 Prover 4: Warning: ignoring some quantifiers
% 13.47/2.72 Prover 3: Warning: ignoring some quantifiers
% 14.70/2.79 Prover 5: Proving ...
% 14.70/2.80 Prover 3: Constructing countermodel ...
% 15.13/2.82 Prover 4: Constructing countermodel ...
% 15.40/2.86 Prover 0: Proving ...
% 17.36/3.13 Prover 2: Proving ...
% 18.23/3.32 Prover 3: gave up
% 18.23/3.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.93/3.50 Prover 7: Preprocessing ...
% 22.51/3.89 Prover 7: Warning: ignoring some quantifiers
% 23.23/3.95 Prover 1: gave up
% 23.23/3.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.23/3.98 Prover 7: Constructing countermodel ...
% 23.23/4.11 Prover 8: Preprocessing ...
% 26.59/4.38 Prover 8: Warning: ignoring some quantifiers
% 26.59/4.41 Prover 8: Constructing countermodel ...
% 34.16/5.37 Prover 8: gave up
% 34.16/5.38 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 34.16/5.55 Prover 9: Preprocessing ...
% 37.63/5.84 Prover 9: Warning: ignoring some quantifiers
% 37.63/5.85 Prover 9: Constructing countermodel ...
% 56.57/8.45 Prover 2: stopped
% 56.57/8.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 58.29/8.58 Prover 10: Preprocessing ...
% 59.52/8.75 Prover 10: Warning: ignoring some quantifiers
% 60.40/8.81 Prover 10: Constructing countermodel ...
% 63.74/9.27 Prover 10: gave up
% 63.74/9.29 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.96/9.41 Prover 11: Preprocessing ...
% 67.35/9.70 Prover 11: Warning: ignoring some quantifiers
% 67.35/9.73 Prover 11: Constructing countermodel ...
% 71.01/10.20 Prover 4: Found proof (size 501)
% 71.01/10.20 Prover 4: proved (9574ms)
% 71.01/10.20 Prover 6: stopped
% 71.01/10.20 Prover 5: stopped
% 71.01/10.20 Prover 11: stopped
% 71.01/10.20 Prover 7: stopped
% 71.01/10.20 Prover 9: stopped
% 71.01/10.20 Prover 0: stopped
% 71.01/10.20
% 71.01/10.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.01/10.20
% 71.72/10.30 % SZS output start Proof for theBenchmark
% 71.72/10.31 Assumptions after simplification:
% 71.72/10.31 ---------------------------------
% 71.72/10.31
% 71.72/10.31 (bridgeL)
% 71.72/10.32 ! [v0: int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | tb2t(v1) = v0)
% 71.72/10.32
% 71.72/10.32 (bridgeR3)
% 71.72/10.33 ty(elt) & ty(int) & ? [v0: ty] : (map(int, elt) = v0 & ty(v0) & ! [v1: uni]
% 71.72/10.33 : ! [v2: map_int_elt] : ( ~ (tb2t3(v1) = v2) | ~ uni(v1) | ? [v3: any] :
% 71.72/10.33 ? [v4: uni] : (t2tb3(v2) = v4 & sort1(v0, v1) = v3 & uni(v4) & ( ~ (v3 =
% 71.72/10.33 0) | v4 = v1))) & ! [v1: uni] : ( ~ (sort1(v0, v1) = 0) | ~
% 71.72/10.33 uni(v1) | ? [v2: map_int_elt] : (tb2t3(v1) = v2 & t2tb3(v2) = v1 &
% 71.72/10.33 map_int_elt(v2))))
% 71.72/10.33
% 71.72/10.33 (bridgeR4)
% 71.72/10.33 ty(elt) & ! [v0: uni] : ! [v1: elt1] : ( ~ (tb2t4(v0) = v1) | ~ uni(v0) |
% 71.72/10.33 ? [v2: any] : ? [v3: uni] : (t2tb4(v1) = v3 & sort1(elt, v0) = v2 & uni(v3)
% 71.72/10.33 & ( ~ (v2 = 0) | v3 = v0))) & ! [v0: uni] : ( ~ (sort1(elt, v0) = 0) | ~
% 71.72/10.33 uni(v0) | ? [v1: elt1] : (tb2t4(v0) = v1 & t2tb4(v1) = v0 & elt1(v1)))
% 71.72/10.33
% 71.72/10.33 (elts_def1)
% 71.96/10.33 ty(int) & ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ( ~
% 71.96/10.33 (mk_array1(v0, v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ? [v4: ty] : ?
% 71.96/10.33 [v5: any] : ? [v6: uni] : (elts(v0, v3) = v6 & map(int, v0) = v4 &
% 71.96/10.33 sort1(v4, v2) = v5 & ty(v4) & uni(v6) & ( ~ (v5 = 0) | v6 = v2)))
% 71.96/10.33
% 71.96/10.33 (exchange_def)
% 71.96/10.34 ty(int) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4:
% 71.96/10.34 int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: uni] : (v7 = v6
% 71.96/10.34 | v7 = v5 | ~ ($lesseq(1, $difference(v4, v7))) | ~ ($lesseq(v3, v7)) | ~
% 71.96/10.34 (exchange2(v0, v1, v2, v3, v4, v5, v6) = 0) | ~ (t2tb(v7) = v8) | ~ ty(v0)
% 71.96/10.34 | ~ uni(v2) | ~ uni(v1) | ? [v9: uni] : (get(v0, int, v2, v8) = v9 &
% 71.96/10.34 get(v0, int, v1, v8) = v9 & uni(v9))) & ! [v0: ty] : ! [v1: uni] : !
% 71.96/10.34 [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: int] : !
% 71.96/10.34 [v7: int] : (v7 = 0 | ~ ($lesseq(1, $difference(v4, v6))) | ~ ($lesseq(v3,
% 71.96/10.34 v6)) | ~ ($lesseq(1, $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~
% 71.96/10.34 (exchange2(v0, v1, v2, v3, v4, v5, v6) = v7) | ~ ty(v0) | ~ uni(v2) | ~
% 71.96/10.34 uni(v1) | ? [v8: any] : ? [v9: uni] : ? [v10: uni] : ? [v11: uni] : ?
% 71.96/10.34 [v12: uni] : ? [v13: uni] : (( ~ (v11 = v10) & ~ (v8 = v6) & ~ (v8 = v5)
% 71.96/10.34 & $lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb(v8) = v9 &
% 71.96/10.34 get(v0, int, v2, v9) = v11 & get(v0, int, v1, v9) = v10 & uni(v11) &
% 71.96/10.34 uni(v10) & uni(v9)) | (t2tb(v6) = v10 & t2tb(v5) = v8 & get(v0, int, v2,
% 71.96/10.34 v10) = v11 & get(v0, int, v2, v8) = v13 & get(v0, int, v1, v10) = v12
% 71.96/10.34 & get(v0, int, v1, v8) = v9 & uni(v13) & uni(v12) & uni(v11) & uni(v10)
% 71.96/10.34 & uni(v9) & uni(v8) & ( ~ (v13 = v12) | ~ (v11 = v9))))) & ! [v0: ty]
% 71.96/10.34 : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5: int] :
% 71.96/10.34 ! [v6: int] : ( ~ ($lesseq(1, $difference(v3, v6))) | ~ (exchange2(v0, v1,
% 71.96/10.34 v2, v3, v4, v5, v6) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1)) & !
% 71.96/10.34 [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5:
% 71.96/10.34 int] : ! [v6: int] : ( ~ ($lesseq(v4, v6)) | ~ (exchange2(v0, v1, v2, v3,
% 71.96/10.34 v4, v5, v6) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1)) & ! [v0: ty] :
% 71.96/10.34 ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5: int] : !
% 71.96/10.34 [v6: int] : ( ~ ($lesseq(1, $difference(v3, v5))) | ~ (exchange2(v0, v1, v2,
% 71.96/10.34 v3, v4, v5, v6) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1)) & ! [v0:
% 71.96/10.34 ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5:
% 71.96/10.34 int] : ! [v6: int] : ( ~ ($lesseq(v4, v5)) | ~ (exchange2(v0, v1, v2, v3,
% 71.96/10.34 v4, v5, v6) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1)) & ! [v0: ty] :
% 71.96/10.34 ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5: int] : !
% 71.96/10.34 [v6: int] : ( ~ (exchange2(v0, v1, v2, v3, v4, v5, v6) = 0) | ~ ty(v0) | ~
% 71.96/10.34 uni(v2) | ~ uni(v1) | ? [v7: uni] : ? [v8: uni] : ? [v9: uni] : ? [v10:
% 71.96/10.34 uni] : (t2tb(v6) = v9 & t2tb(v5) = v7 & get(v0, int, v2, v9) = v8 &
% 71.96/10.34 get(v0, int, v2, v7) = v10 & get(v0, int, v1, v9) = v10 & get(v0, int, v1,
% 71.96/10.34 v7) = v8 & uni(v10) & uni(v9) & uni(v8) & uni(v7)))
% 71.96/10.34
% 71.96/10.34 (exchange_def1)
% 72.01/10.34 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : !
% 72.01/10.34 [v5: int] : ! [v6: uni] : ! [v7: uni] : ! [v8: any] : ( ~ (exchange2(v0,
% 72.01/10.34 v6, v7, 0, v5, v3, v4) = v8) | ~ (elts(v0, v2) = v7) | ~ (elts(v0, v1)
% 72.01/10.34 = v6) | ~ (length1(v0, v1) = v5) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) |
% 72.01/10.34 ? [v9: any] : ? [v10: int] : (exchange3(v0, v1, v2, v3, v4) = v9 &
% 72.01/10.34 length1(v0, v2) = v10 & ( ~ (v9 = 0) | (v10 = v5 & v8 = 0)))) & ! [v0:
% 72.01/10.34 ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ! [v5:
% 72.01/10.34 int] : ! [v6: uni] : ! [v7: uni] : ( ~ (exchange2(v0, v6, v7, 0, v5, v3,
% 72.01/10.34 v4) = 0) | ~ (elts(v0, v2) = v7) | ~ (elts(v0, v1) = v6) | ~
% 72.01/10.34 (length1(v0, v1) = v5) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v8: int]
% 72.01/10.34 : ? [v9: any] : (exchange3(v0, v1, v2, v3, v4) = v9 & length1(v0, v2) = v8
% 72.01/10.34 & ( ~ (v8 = v5) | v9 = 0))) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] :
% 72.01/10.34 ! [v3: int] : ! [v4: int] : ! [v5: int] : (v5 = 0 | ~ (exchange3(v0, v1,
% 72.01/10.34 v2, v3, v4) = v5) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v6: int] :
% 72.01/10.34 ? [v7: int] : ? [v8: uni] : ? [v9: uni] : ? [v10: any] : (exchange2(v0,
% 72.01/10.34 v8, v9, 0, v6, v3, v4) = v10 & elts(v0, v2) = v9 & elts(v0, v1) = v8 &
% 72.01/10.34 length1(v0, v2) = v7 & length1(v0, v1) = v6 & uni(v9) & uni(v8) & ( ~ (v10
% 72.01/10.34 = 0) | ~ (v7 = v6)))) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] :
% 72.01/10.34 ! [v3: int] : ! [v4: int] : ( ~ (exchange3(v0, v1, v2, v3, v4) = 0) | ~
% 72.01/10.34 ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v5: int] : ? [v6: uni] : ? [v7:
% 72.01/10.34 uni] : (exchange2(v0, v6, v7, 0, v5, v3, v4) = 0 & elts(v0, v2) = v7 &
% 72.01/10.34 elts(v0, v1) = v6 & length1(v0, v2) = v5 & length1(v0, v1) = v5 & uni(v7)
% 72.01/10.34 & uni(v6)))
% 72.01/10.34
% 72.01/10.34 (exchange_permut_all)
% 72.01/10.34 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int] : ( ~
% 72.01/10.34 (exchange3(v0, v1, v2, v3, v4) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) |
% 72.01/10.34 permut_all(v0, v1, v2) = 0)
% 72.01/10.34
% 72.01/10.34 (get_sort4)
% 72.01/10.34 ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : ( ~
% 72.01/10.34 (get(v1, v0, v2, v3) = v4) | ~ ty(v1) | ~ ty(v0) | ~ uni(v3) | ~ uni(v2)
% 72.01/10.34 | sort1(v1, v4) = 0)
% 72.01/10.34
% 72.01/10.34 (le_asym)
% 72.01/10.34 ! [v0: elt1] : ! [v1: elt1] : ! [v2: int] : (v2 = 0 | ~ (le1(v1, v0) = v2)
% 72.01/10.34 | ~ elt1(v1) | ~ elt1(v0) | le1(v0, v1) = 0) & ! [v0: elt1] : ! [v1:
% 72.01/10.34 elt1] : ! [v2: int] : (v2 = 0 | ~ (le1(v0, v1) = v2) | ~ elt1(v1) | ~
% 72.01/10.34 elt1(v0) | le1(v1, v0) = 0)
% 72.01/10.34
% 72.01/10.35 (le_trans)
% 72.01/10.35 ! [v0: elt1] : ! [v1: elt1] : ! [v2: elt1] : ! [v3: int] : (v3 = 0 | ~
% 72.01/10.35 (le1(v1, v2) = 0) | ~ (le1(v0, v2) = v3) | ~ elt1(v2) | ~ elt1(v1) | ~
% 72.01/10.35 elt1(v0) | ? [v4: int] : ( ~ (v4 = 0) & le1(v0, v1) = v4)) & ! [v0: elt1]
% 72.01/10.35 : ! [v1: elt1] : ! [v2: elt1] : ! [v3: int] : (v3 = 0 | ~ (le1(v0, v2) =
% 72.01/10.35 v3) | ~ (le1(v0, v1) = 0) | ~ elt1(v2) | ~ elt1(v1) | ~ elt1(v0) | ?
% 72.01/10.35 [v4: int] : ( ~ (v4 = 0) & le1(v1, v2) = v4)) & ! [v0: elt1] : ! [v1:
% 72.01/10.35 elt1] : ! [v2: elt1] : ( ~ (le1(v1, v2) = 0) | ~ (le1(v0, v1) = 0) | ~
% 72.01/10.35 elt1(v2) | ~ elt1(v1) | ~ elt1(v0) | le1(v0, v2) = 0)
% 72.01/10.35
% 72.01/10.35 (length_def1)
% 72.01/10.35 ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ( ~ (mk_array1(v0,
% 72.01/10.35 v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | length1(v0, v3) = v1)
% 72.01/10.35
% 72.01/10.35 (permut_all_def)
% 72.01/10.35 ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: uni] : !
% 72.01/10.35 [v5: uni] : ! [v6: any] : ( ~ (permut2(v0, v4, v5, 0, v3) = v6) | ~
% 72.01/10.35 (elts(v0, v2) = v5) | ~ (elts(v0, v1) = v4) | ~ (length1(v0, v1) = v3) |
% 72.01/10.35 ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v7: any] : ? [v8: int] :
% 72.01/10.35 (permut_all(v0, v1, v2) = v7 & length1(v0, v2) = v8 & ( ~ (v7 = 0) | (v8 =
% 72.01/10.35 v3 & v6 = 0)))) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3:
% 72.01/10.35 int] : ! [v4: uni] : ! [v5: uni] : ( ~ (permut2(v0, v4, v5, 0, v3) = 0) |
% 72.01/10.35 ~ (elts(v0, v2) = v5) | ~ (elts(v0, v1) = v4) | ~ (length1(v0, v1) = v3) |
% 72.01/10.35 ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v6: int] : ? [v7: any] :
% 72.01/10.35 (permut_all(v0, v1, v2) = v7 & length1(v0, v2) = v6 & ( ~ (v6 = v3) | v7 =
% 72.01/10.35 0))) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : (v3 =
% 72.01/10.35 0 | ~ (permut_all(v0, v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) |
% 72.01/10.35 ? [v4: int] : ? [v5: int] : ? [v6: uni] : ? [v7: uni] : ? [v8: any] :
% 72.01/10.35 (permut2(v0, v6, v7, 0, v4) = v8 & elts(v0, v2) = v7 & elts(v0, v1) = v6 &
% 72.01/10.35 length1(v0, v2) = v5 & length1(v0, v1) = v4 & uni(v7) & uni(v6) & ( ~ (v8
% 72.01/10.35 = 0) | ~ (v5 = v4)))) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : (
% 72.01/10.35 ~ (permut_all(v0, v1, v2) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ?
% 72.01/10.35 [v3: int] : ? [v4: uni] : ? [v5: uni] : (permut2(v0, v4, v5, 0, v3) = 0 &
% 72.01/10.35 elts(v0, v2) = v5 & elts(v0, v1) = v4 & length1(v0, v2) = v3 & length1(v0,
% 72.01/10.35 v1) = v3 & uni(v5) & uni(v4)))
% 72.01/10.35
% 72.01/10.35 (permut_exists)
% 72.01/10.35 ty(int) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4:
% 72.01/10.35 int] : ! [v5: int] : ! [v6: uni] : ! [v7: uni] : ( ~ ($lesseq(1,
% 72.01/10.35 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (permut2(v0, v1, v2,
% 72.01/10.35 v3, v4) = 0) | ~ (t2tb(v5) = v6) | ~ (get(v0, int, v2, v6) = v7) | ~
% 72.01/10.35 ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v8: int] : ? [v9: uni] : ($lesseq(1,
% 72.01/10.35 $difference(v4, v8)) & $lesseq(v3, v8) & t2tb(v8) = v9 & get(v0, int,
% 72.01/10.35 v1, v9) = v7 & uni(v9) & uni(v7)))
% 72.01/10.35
% 72.01/10.35 (select_eq)
% 72.01/10.35 ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 72.01/10.35 [v5: uni] : ! [v6: uni] : (v6 = v4 | ~ (set(v1, v0, v2, v3, v4) = v5) | ~
% 72.01/10.35 (get(v1, v0, v5, v3) = v6) | ~ ty(v1) | ~ ty(v0) | ~ uni(v4) | ~ uni(v3)
% 72.01/10.35 | ~ uni(v2) | ? [v7: int] : ( ~ (v7 = 0) & sort1(v1, v4) = v7))
% 72.01/10.35
% 72.01/10.35 (select_neq)
% 72.01/10.36 ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 72.01/10.36 [v5: uni] : ! [v6: uni] : ! [v7: uni] : (v4 = v3 | ~ (set(v1, v0, v2, v3,
% 72.01/10.36 v6) = v7) | ~ (get(v1, v0, v2, v4) = v5) | ~ (sort1(v0, v3) = 0) | ~
% 72.01/10.36 ty(v1) | ~ ty(v0) | ~ uni(v6) | ~ uni(v4) | ~ uni(v3) | ~ uni(v2) | ?
% 72.01/10.36 [v8: any] : ((v8 = v5 & get(v1, v0, v7, v4) = v5 & uni(v5)) | ( ~ (v8 = 0) &
% 72.01/10.36 sort1(v0, v4) = v8)))
% 72.01/10.36
% 72.01/10.36 (set_sort4)
% 72.01/10.36 ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 72.01/10.36 [v5: uni] : ( ~ (set(v1, v0, v2, v3, v4) = v5) | ~ ty(v1) | ~ ty(v0) | ~
% 72.01/10.36 uni(v4) | ~ uni(v3) | ~ uni(v2) | ? [v6: ty] : (map(v0, v1) = v6 &
% 72.01/10.36 sort1(v6, v5) = 0 & ty(v6)))
% 72.01/10.36
% 72.01/10.36 (t2tb_sort3)
% 72.01/10.36 ty(int) & ! [v0: int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | sort1(int, v1) =
% 72.01/10.36 0)
% 72.01/10.36
% 72.01/10.36 (t2tb_sort4)
% 72.01/10.36 ty(elt) & ty(int) & ? [v0: ty] : (map(int, elt) = v0 & ty(v0) & ! [v1:
% 72.01/10.36 map_int_elt] : ! [v2: uni] : ( ~ (t2tb3(v1) = v2) | ~ map_int_elt(v1) |
% 72.01/10.36 sort1(v0, v2) = 0))
% 72.01/10.36
% 72.01/10.36 (wP_parameter_insertion_sort1)
% 72.01/10.36 ty(elt) & ty(int) & ? [v0: int] : ? [v1: map_int_elt] : ? [v2: uni] : ?
% 72.01/10.36 [v3: uni] : ? [v4: map_int_elt] : ? [v5: int] : ? [v6: uni] : ? [v7: uni]
% 72.01/10.36 : ? [v8: uni] : ? [v9: uni] : ? [v10: elt1] : ? [v11: int] : ? [v12:
% 72.01/10.36 map_int_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15: uni] : ? [v16: uni]
% 72.01/10.36 : ? [v17: uni] : ? [v18: uni] : ? [v19: elt1] : ? [v20: int] : ? [v21:
% 72.01/10.36 uni] : ? [v22: map_int_elt] : ? [v23: uni] : ? [v24: uni] : ? [v25: uni]
% 72.01/10.36 : ? [v26: int] : ? [v27: uni] : ? [v28: uni] : ? [v29: elt1] : ? [v30:
% 72.01/10.36 int] : ( ~ (v30 = 0) & ~ (v20 = 0) & $lesseq(v26, v5) & $lesseq(v11, v26) &
% 72.01/10.36 $lesseq(1, $difference(v0, v11)) & $lesseq(1, v11) & $lesseq(1,
% 72.01/10.36 $difference(v0, v5)) & sorted_sub6(v4, 0, v5) = 0 & le1(v19, v10) = v20 &
% 72.01/10.36 le1(v10, v29) = v30 & tb2t4(v28) = v29 & tb2t4(v18) = v19 & tb2t4(v9) = v10
% 72.01/10.36 & tb2t3(v21) = v22 & t2tb3(v22) = v23 & t2tb3(v12) = v13 & t2tb3(v4) = v6 &
% 72.01/10.36 t2tb3(v1) = v2 & permut_all(elt, v3, v16) = 0 & permut_all(elt, v3, v7) = 0
% 72.01/10.36 & exchange3(elt, v16, v25, $sum(v11, -1), v11) = 0 & t2tb(v26) = v27 &
% 72.01/10.36 t2tb($sum(v11, -1)) = v17 & t2tb(v11) = v14 & t2tb(v5) = v8 & mk_array1(elt,
% 72.01/10.36 v0, v24) = v25 & mk_array1(elt, v0, v15) = v16 & mk_array1(elt, v0, v6) =
% 72.01/10.36 v7 & mk_array1(elt, v0, v2) = v3 & set(elt, int, v23, v17, v9) = v24 &
% 72.01/10.36 set(elt, int, v13, v14, v18) = v21 & set(elt, int, v13, v14, v9) = v15 &
% 72.01/10.36 get(elt, int, v23, v27) = v28 & get(elt, int, v13, v17) = v18 & get(elt,
% 72.01/10.36 int, v6, v8) = v9 & map_int_elt(v22) & map_int_elt(v12) & map_int_elt(v4)
% 72.01/10.36 & map_int_elt(v1) & elt1(v29) & elt1(v19) & elt1(v10) & uni(v28) & uni(v27)
% 72.01/10.36 & uni(v25) & uni(v24) & uni(v23) & uni(v21) & uni(v18) & uni(v17) & uni(v16)
% 72.01/10.36 & uni(v15) & uni(v14) & uni(v13) & uni(v9) & uni(v8) & uni(v7) & uni(v6) &
% 72.01/10.36 uni(v3) & uni(v2) & ! [v31: int] : ! [v32: int] : ! [v33: uni] : ! [v34:
% 72.01/10.36 uni] : ! [v35: elt1] : ! [v36: uni] : ! [v37: uni] : ! [v38: elt1] :
% 72.01/10.36 ! [v39: int] : (v39 = 0 | v32 = v11 | v31 = v11 | ~ ($lesseq(v32, v5)) | ~
% 72.01/10.36 ($lesseq(v31, v32)) | ~ ($lesseq(0, v31)) | ~ (le1(v35, v38) = v39) | ~
% 72.01/10.36 (tb2t4(v37) = v38) | ~ (tb2t4(v34) = v35) | ~ (t2tb(v32) = v36) | ~
% 72.01/10.36 (t2tb(v31) = v33) | ~ (get(elt, int, v13, v36) = v37) | ~ (get(elt, int,
% 72.01/10.36 v13, v33) = v34)) & ! [v31: int] : ! [v32: uni] : ( ~ ($lesseq(v31,
% 72.01/10.36 v5)) | ~ ($lesseq(1, $difference(v31, v11))) | ~ (t2tb(v31) = v32) |
% 72.01/10.36 ? [v33: uni] : ? [v34: elt1] : (le1(v10, v34) = 0 & tb2t4(v33) = v34 &
% 72.01/10.36 get(elt, int, v13, v32) = v33 & elt1(v34) & uni(v33))))
% 72.01/10.36
% 72.01/10.36 (function-axioms)
% 72.01/10.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : !
% 72.01/10.37 [v3: int] : ! [v4: int] : ! [v5: int] : ! [v6: uni] : ! [v7: uni] : !
% 72.01/10.37 [v8: ty] : (v1 = v0 | ~ (exchange2(v8, v7, v6, v5, v4, v3, v2) = v1) | ~
% 72.01/10.37 (exchange2(v8, v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 72.01/10.37 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : !
% 72.01/10.37 [v5: uni] : ! [v6: ty] : (v1 = v0 | ~ (permut_sub1(v6, v5, v4, v3, v2) = v1)
% 72.01/10.37 | ~ (permut_sub1(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 72.01/10.37 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : !
% 72.01/10.37 [v5: uni] : ! [v6: ty] : (v1 = v0 | ~ (permut3(v6, v5, v4, v3, v2) = v1) |
% 72.01/10.37 ~ (permut3(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 72.01/10.37 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : ! [v5:
% 72.01/10.37 uni] : ! [v6: ty] : (v1 = v0 | ~ (exchange3(v6, v5, v4, v3, v2) = v1) | ~
% 72.01/10.38 (exchange3(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 72.01/10.38 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : ! [v5:
% 72.01/10.38 uni] : ! [v6: ty] : (v1 = v0 | ~ (array_eq_sub1(v6, v5, v4, v3, v2) = v1)
% 72.01/10.38 | ~ (array_eq_sub1(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 72.01/10.38 : ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : !
% 72.01/10.38 [v5: uni] : ! [v6: ty] : (v1 = v0 | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v1)
% 72.01/10.38 | ~ (map_eq_sub1(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 72.01/10.38 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: uni] : !
% 72.01/10.38 [v5: uni] : ! [v6: ty] : (v1 = v0 | ~ (permut2(v6, v5, v4, v3, v2) = v1) |
% 72.01/10.38 ~ (permut2(v6, v5, v4, v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 72.01/10.38 [v2: int] : ! [v3: int] : ! [v4: uni] : ! [v5: uni] : ! [v6: ty] : (v1 =
% 72.01/10.38 v0 | ~ (occ1(v6, v5, v4, v3, v2) = v1) | ~ (occ1(v6, v5, v4, v3, v2) =
% 72.01/10.38 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 72.01/10.38 uni] : ! [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (set(v6, v5, v4, v3, v2) =
% 72.01/10.38 v1) | ~ (set(v6, v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] :
% 72.01/10.38 ! [v2: uni] : ! [v3: int] : ! [v4: uni] : ! [v5: ty] : (v1 = v0 | ~
% 72.01/10.38 (set2(v5, v4, v3, v2) = v1) | ~ (set2(v5, v4, v3, v2) = v0)) & ! [v0: uni]
% 72.01/10.38 : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : ! [v5: ty] : (v1
% 72.01/10.38 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4, v3, v2) = v0)) & !
% 72.01/10.38 [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: bool1] : !
% 72.01/10.38 [v5: ty] : (v1 = v0 | ~ (match_bool1(v5, v4, v3, v2) = v1) | ~
% 72.01/10.38 (match_bool1(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 72.01/10.38 MultipleValueBool] : ! [v2: int] : ! [v3: int] : ! [v4: array_elt] : (v1
% 72.01/10.38 = v0 | ~ (sorted_sub7(v4, v3, v2) = v1) | ~ (sorted_sub7(v4, v3, v2) =
% 72.01/10.38 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 72.01/10.38 int] : ! [v3: int] : ! [v4: map_int_elt] : (v1 = v0 | ~ (sorted_sub6(v4,
% 72.01/10.38 v3, v2) = v1) | ~ (sorted_sub6(v4, v3, v2) = v0)) & ! [v0:
% 72.01/10.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3:
% 72.01/10.38 uni] : ! [v4: ty] : (v1 = v0 | ~ (permut_all(v4, v3, v2) = v1) | ~
% 72.01/10.38 (permut_all(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 72.01/10.38 MultipleValueBool] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 |
% 72.01/10.38 ~ (array_eq(v4, v3, v2) = v1) | ~ (array_eq(v4, v3, v2) = v0)) & ! [v0:
% 72.01/10.38 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: ty] : (v1 = v0 |
% 72.01/10.38 ~ (make1(v4, v3, v2) = v1) | ~ (make1(v4, v3, v2) = v0)) & ! [v0: uni] :
% 72.01/10.38 ! [v1: uni] : ! [v2: int] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~
% 72.01/10.38 (get2(v4, v3, v2) = v1) | ~ (get2(v4, v3, v2) = v0)) & ! [v0: uni] : !
% 72.01/10.38 [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: ty] : (v1 = v0 | ~
% 72.01/10.38 (mk_array1(v4, v3, v2) = v1) | ~ (mk_array1(v4, v3, v2) = v0)) & ! [v0:
% 72.01/10.38 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : ! [v4: ty] : (v1 = v0 |
% 72.01/10.38 ~ (const(v4, v3, v2) = v1) | ~ (const(v4, v3, v2) = v0)) & ! [v0:
% 72.01/10.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: elt1] : ! [v3:
% 72.01/10.38 elt1] : (v1 = v0 | ~ (le1(v3, v2) = v1) | ~ (le1(v3, v2) = v0)) & ! [v0:
% 72.01/10.38 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (elts(v3,
% 72.01/10.38 v2) = v1) | ~ (elts(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 72.01/10.38 [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (length1(v3, v2) = v1) | ~
% 72.01/10.38 (length1(v3, v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3:
% 72.01/10.38 ty] : (v1 = v0 | ~ (map(v3, v2) = v1) | ~ (map(v3, v2) = v0)) & ! [v0:
% 72.01/10.38 uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 72.01/10.38 (contents(v3, v2) = v1) | ~ (contents(v3, v2) = v0)) & ! [v0: uni] : !
% 72.01/10.38 [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) = v1) |
% 72.01/10.38 ~ (mk_ref(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 72.01/10.38 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (sort1(v3,
% 72.01/10.38 v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 72.01/10.38 [v1: MultipleValueBool] : ! [v2: array_elt] : (v1 = v0 | ~ (sorted3(v2) =
% 72.01/10.38 v1) | ~ (sorted3(v2) = v0)) & ! [v0: array_elt] : ! [v1: array_elt] :
% 72.01/10.38 ! [v2: uni] : (v1 = v0 | ~ (tb2t5(v2) = v1) | ~ (tb2t5(v2) = v0)) & ! [v0:
% 72.01/10.38 uni] : ! [v1: uni] : ! [v2: array_elt] : (v1 = v0 | ~ (t2tb5(v2) = v1) |
% 72.01/10.38 ~ (t2tb5(v2) = v0)) & ! [v0: elt1] : ! [v1: elt1] : ! [v2: uni] : (v1 =
% 72.01/10.38 v0 | ~ (tb2t4(v2) = v1) | ~ (tb2t4(v2) = v0)) & ! [v0: uni] : ! [v1:
% 72.01/10.38 uni] : ! [v2: elt1] : (v1 = v0 | ~ (t2tb4(v2) = v1) | ~ (t2tb4(v2) = v0))
% 72.01/10.38 & ! [v0: map_int_elt] : ! [v1: map_int_elt] : ! [v2: uni] : (v1 = v0 | ~
% 72.01/10.38 (tb2t3(v2) = v1) | ~ (tb2t3(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 72.01/10.38 [v2: map_int_elt] : (v1 = v0 | ~ (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0)) & !
% 72.01/10.38 [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~
% 72.01/10.38 (tb2t(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 |
% 72.01/10.38 ~ (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : !
% 72.01/10.38 [v2: ty] : (v1 = v0 | ~ (array(v2) = v1) | ~ (array(v2) = v0)) & ! [v0: ty]
% 72.01/10.38 : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (ref(v2) = v1) | ~ (ref(v2) =
% 72.01/10.38 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~
% 72.01/10.38 (witness1(v2) = v1) | ~ (witness1(v2) = v0))
% 72.01/10.38
% 72.01/10.38 Further assumptions not needed in the proof:
% 72.01/10.38 --------------------------------------------
% 72.01/10.38 array_eq_def, array_eq_sub_def, array_inversion1, bool_inversion, bridgeL3,
% 72.01/10.38 bridgeL4, bridgeL5, bridgeR, bridgeR5, compatOrderMult, const, const_sort2,
% 72.01/10.38 contents_def1, contents_sort2, elts_sort2, exchange_permut_sub, exchange_set,
% 72.01/10.38 get_def, get_sort5, le_refl, make_def, make_sort2, map_eq_sub_def,
% 72.01/10.38 match_bool_False, match_bool_True, match_bool_sort2, mk_array_sort2,
% 72.01/10.38 mk_ref_sort2, occ_append, occ_bounds, occ_empty, occ_eq, occ_exists, occ_neq,
% 72.01/10.38 occ_pos, occ_right_add, occ_right_no_add, permut_def, permut_def1,
% 72.01/10.38 permut_sub_def, permut_sub_weakening, permut_trans, ref_inversion1, set_def,
% 72.01/10.38 set_sort5, sorted_def1, sorted_sub_def2, sorted_sub_def3, t2tb_sort5,
% 72.01/10.38 t2tb_sort6, true_False, tuple0_inversion, witness_sort1
% 72.01/10.38
% 72.01/10.38 Those formulas are unsatisfiable:
% 72.01/10.38 ---------------------------------
% 72.01/10.38
% 72.01/10.38 Begin of proof
% 72.01/10.38 |
% 72.01/10.38 | ALPHA: (elts_def1) implies:
% 72.01/10.38 | (1) ! [v0: ty] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ( ~
% 72.01/10.38 | (mk_array1(v0, v1, v2) = v3) | ~ ty(v0) | ~ uni(v2) | ? [v4: ty] :
% 72.01/10.38 | ? [v5: any] : ? [v6: uni] : (elts(v0, v3) = v6 & map(int, v0) = v4
% 72.01/10.38 | & sort1(v4, v2) = v5 & ty(v4) & uni(v6) & ( ~ (v5 = 0) | v6 = v2)))
% 72.01/10.38 |
% 72.01/10.38 | ALPHA: (t2tb_sort3) implies:
% 72.01/10.38 | (2) ! [v0: int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | sort1(int, v1) = 0)
% 72.01/10.38 |
% 72.01/10.38 | ALPHA: (permut_exists) implies:
% 72.01/10.38 | (3) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int]
% 72.01/10.38 | : ! [v5: int] : ! [v6: uni] : ! [v7: uni] : ( ~ ($lesseq(1,
% 72.01/10.38 | $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (permut2(v0,
% 72.01/10.38 | v1, v2, v3, v4) = 0) | ~ (t2tb(v5) = v6) | ~ (get(v0, int, v2,
% 72.01/10.38 | v6) = v7) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v8: int] :
% 72.01/10.38 | ? [v9: uni] : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) &
% 72.01/10.38 | t2tb(v8) = v9 & get(v0, int, v1, v9) = v7 & uni(v9) & uni(v7)))
% 72.01/10.38 |
% 72.01/10.38 | ALPHA: (exchange_def) implies:
% 72.01/10.38 | (4) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int]
% 72.01/10.38 | : ! [v5: int] : ! [v6: int] : ( ~ (exchange2(v0, v1, v2, v3, v4, v5,
% 72.01/10.38 | v6) = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v7: uni] :
% 72.01/10.38 | ? [v8: uni] : ? [v9: uni] : ? [v10: uni] : (t2tb(v6) = v9 &
% 72.01/10.38 | t2tb(v5) = v7 & get(v0, int, v2, v9) = v8 & get(v0, int, v2, v7) =
% 72.01/10.38 | v10 & get(v0, int, v1, v9) = v10 & get(v0, int, v1, v7) = v8 &
% 72.01/10.38 | uni(v10) & uni(v9) & uni(v8) & uni(v7)))
% 72.01/10.39 | (5) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int]
% 72.01/10.39 | : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: uni] : (v7 = v6
% 72.01/10.39 | | v7 = v5 | ~ ($lesseq(1, $difference(v4, v7))) | ~ ($lesseq(v3,
% 72.01/10.39 | v7)) | ~ (exchange2(v0, v1, v2, v3, v4, v5, v6) = 0) | ~
% 72.01/10.39 | (t2tb(v7) = v8) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v9: uni]
% 72.01/10.39 | : (get(v0, int, v2, v8) = v9 & get(v0, int, v1, v8) = v9 & uni(v9)))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (exchange_def1) implies:
% 72.01/10.39 | (6) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int]
% 72.01/10.39 | : ( ~ (exchange3(v0, v1, v2, v3, v4) = 0) | ~ ty(v0) | ~ uni(v2) | ~
% 72.01/10.39 | uni(v1) | ? [v5: int] : ? [v6: uni] : ? [v7: uni] : (exchange2(v0,
% 72.01/10.39 | v6, v7, 0, v5, v3, v4) = 0 & elts(v0, v2) = v7 & elts(v0, v1) =
% 72.01/10.39 | v6 & length1(v0, v2) = v5 & length1(v0, v1) = v5 & uni(v7) &
% 72.01/10.39 | uni(v6)))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (permut_all_def) implies:
% 72.01/10.39 | (7) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ( ~ (permut_all(v0, v1, v2)
% 72.01/10.39 | = 0) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v3: int] : ? [v4:
% 72.01/10.39 | uni] : ? [v5: uni] : (permut2(v0, v4, v5, 0, v3) = 0 & elts(v0,
% 72.01/10.39 | v2) = v5 & elts(v0, v1) = v4 & length1(v0, v2) = v3 & length1(v0,
% 72.01/10.39 | v1) = v3 & uni(v5) & uni(v4)))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (t2tb_sort4) implies:
% 72.01/10.39 | (8) ? [v0: ty] : (map(int, elt) = v0 & ty(v0) & ! [v1: map_int_elt] : !
% 72.01/10.39 | [v2: uni] : ( ~ (t2tb3(v1) = v2) | ~ map_int_elt(v1) | sort1(v0, v2)
% 72.01/10.39 | = 0))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (bridgeR3) implies:
% 72.01/10.39 | (9) ? [v0: ty] : (map(int, elt) = v0 & ty(v0) & ! [v1: uni] : ! [v2:
% 72.01/10.39 | map_int_elt] : ( ~ (tb2t3(v1) = v2) | ~ uni(v1) | ? [v3: any] :
% 72.01/10.39 | ? [v4: uni] : (t2tb3(v2) = v4 & sort1(v0, v1) = v3 & uni(v4) & ( ~
% 72.01/10.39 | (v3 = 0) | v4 = v1))) & ! [v1: uni] : ( ~ (sort1(v0, v1) = 0)
% 72.01/10.39 | | ~ uni(v1) | ? [v2: map_int_elt] : (tb2t3(v1) = v2 & t2tb3(v2) =
% 72.01/10.39 | v1 & map_int_elt(v2))))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (bridgeR4) implies:
% 72.01/10.39 | (10) ! [v0: uni] : ! [v1: elt1] : ( ~ (tb2t4(v0) = v1) | ~ uni(v0) | ?
% 72.01/10.39 | [v2: any] : ? [v3: uni] : (t2tb4(v1) = v3 & sort1(elt, v0) = v2 &
% 72.01/10.39 | uni(v3) & ( ~ (v2 = 0) | v3 = v0)))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (le_asym) implies:
% 72.01/10.39 | (11) ! [v0: elt1] : ! [v1: elt1] : ! [v2: int] : (v2 = 0 | ~ (le1(v1,
% 72.01/10.39 | v0) = v2) | ~ elt1(v1) | ~ elt1(v0) | le1(v0, v1) = 0)
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (le_trans) implies:
% 72.01/10.39 | (12) ! [v0: elt1] : ! [v1: elt1] : ! [v2: elt1] : ! [v3: int] : (v3 = 0
% 72.01/10.39 | | ~ (le1(v0, v2) = v3) | ~ (le1(v0, v1) = 0) | ~ elt1(v2) | ~
% 72.01/10.39 | elt1(v1) | ~ elt1(v0) | ? [v4: int] : ( ~ (v4 = 0) & le1(v1, v2) =
% 72.01/10.39 | v4))
% 72.01/10.39 | (13) ! [v0: elt1] : ! [v1: elt1] : ! [v2: elt1] : ! [v3: int] : (v3 = 0
% 72.01/10.39 | | ~ (le1(v1, v2) = 0) | ~ (le1(v0, v2) = v3) | ~ elt1(v2) | ~
% 72.01/10.39 | elt1(v1) | ~ elt1(v0) | ? [v4: int] : ( ~ (v4 = 0) & le1(v0, v1) =
% 72.01/10.39 | v4))
% 72.01/10.39 |
% 72.01/10.39 | ALPHA: (wP_parameter_insertion_sort1) implies:
% 72.01/10.39 | (14) ty(int)
% 72.01/10.39 | (15) ty(elt)
% 72.01/10.40 | (16) ? [v0: int] : ? [v1: map_int_elt] : ? [v2: uni] : ? [v3: uni] : ?
% 72.01/10.40 | [v4: map_int_elt] : ? [v5: int] : ? [v6: uni] : ? [v7: uni] : ?
% 72.01/10.40 | [v8: uni] : ? [v9: uni] : ? [v10: elt1] : ? [v11: int] : ? [v12:
% 72.01/10.40 | map_int_elt] : ? [v13: uni] : ? [v14: uni] : ? [v15: uni] : ?
% 72.01/10.40 | [v16: uni] : ? [v17: uni] : ? [v18: uni] : ? [v19: elt1] : ? [v20:
% 72.01/10.40 | int] : ? [v21: uni] : ? [v22: map_int_elt] : ? [v23: uni] : ?
% 72.01/10.40 | [v24: uni] : ? [v25: uni] : ? [v26: int] : ? [v27: uni] : ? [v28:
% 72.01/10.40 | uni] : ? [v29: elt1] : ? [v30: int] : ( ~ (v30 = 0) & ~ (v20 = 0)
% 72.01/10.40 | & $lesseq(v26, v5) & $lesseq(v11, v26) & $lesseq(1, $difference(v0,
% 72.01/10.40 | v11)) & $lesseq(1, v11) & $lesseq(1, $difference(v0, v5)) &
% 72.01/10.40 | sorted_sub6(v4, 0, v5) = 0 & le1(v19, v10) = v20 & le1(v10, v29) =
% 72.01/10.40 | v30 & tb2t4(v28) = v29 & tb2t4(v18) = v19 & tb2t4(v9) = v10 &
% 72.01/10.40 | tb2t3(v21) = v22 & t2tb3(v22) = v23 & t2tb3(v12) = v13 & t2tb3(v4) =
% 72.01/10.40 | v6 & t2tb3(v1) = v2 & permut_all(elt, v3, v16) = 0 & permut_all(elt,
% 72.01/10.40 | v3, v7) = 0 & exchange3(elt, v16, v25, $sum(v11, -1), v11) = 0 &
% 72.01/10.40 | t2tb(v26) = v27 & t2tb($sum(v11, -1)) = v17 & t2tb(v11) = v14 &
% 72.01/10.40 | t2tb(v5) = v8 & mk_array1(elt, v0, v24) = v25 & mk_array1(elt, v0,
% 72.01/10.40 | v15) = v16 & mk_array1(elt, v0, v6) = v7 & mk_array1(elt, v0, v2)
% 72.01/10.40 | = v3 & set(elt, int, v23, v17, v9) = v24 & set(elt, int, v13, v14,
% 72.01/10.40 | v18) = v21 & set(elt, int, v13, v14, v9) = v15 & get(elt, int,
% 72.01/10.40 | v23, v27) = v28 & get(elt, int, v13, v17) = v18 & get(elt, int,
% 72.01/10.40 | v6, v8) = v9 & map_int_elt(v22) & map_int_elt(v12) &
% 72.01/10.40 | map_int_elt(v4) & map_int_elt(v1) & elt1(v29) & elt1(v19) &
% 72.01/10.40 | elt1(v10) & uni(v28) & uni(v27) & uni(v25) & uni(v24) & uni(v23) &
% 72.01/10.40 | uni(v21) & uni(v18) & uni(v17) & uni(v16) & uni(v15) & uni(v14) &
% 72.01/10.40 | uni(v13) & uni(v9) & uni(v8) & uni(v7) & uni(v6) & uni(v3) & uni(v2)
% 72.01/10.40 | & ! [v31: int] : ! [v32: int] : ! [v33: uni] : ! [v34: uni] : !
% 72.01/10.40 | [v35: elt1] : ! [v36: uni] : ! [v37: uni] : ! [v38: elt1] : !
% 72.01/10.40 | [v39: int] : (v39 = 0 | v32 = v11 | v31 = v11 | ~ ($lesseq(v32,
% 72.01/10.40 | v5)) | ~ ($lesseq(v31, v32)) | ~ ($lesseq(0, v31)) | ~
% 72.01/10.40 | (le1(v35, v38) = v39) | ~ (tb2t4(v37) = v38) | ~ (tb2t4(v34) =
% 72.01/10.40 | v35) | ~ (t2tb(v32) = v36) | ~ (t2tb(v31) = v33) | ~
% 72.01/10.40 | (get(elt, int, v13, v36) = v37) | ~ (get(elt, int, v13, v33) =
% 72.01/10.40 | v34)) & ! [v31: int] : ! [v32: uni] : ( ~ ($lesseq(v31, v5)) |
% 72.01/10.40 | ~ ($lesseq(1, $difference(v31, v11))) | ~ (t2tb(v31) = v32) | ?
% 72.01/10.40 | [v33: uni] : ? [v34: elt1] : (le1(v10, v34) = 0 & tb2t4(v33) =
% 72.01/10.40 | v34 & get(elt, int, v13, v32) = v33 & elt1(v34) & uni(v33))))
% 72.01/10.40 |
% 72.01/10.40 | ALPHA: (function-axioms) implies:
% 72.01/10.40 | (17) ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 | ~ (t2tb(v2) =
% 72.01/10.40 | v1) | ~ (t2tb(v2) = v0))
% 72.01/10.40 | (18) ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) =
% 72.01/10.40 | v1) | ~ (tb2t(v2) = v0))
% 72.01/10.40 | (19) ! [v0: uni] : ! [v1: uni] : ! [v2: map_int_elt] : (v1 = v0 | ~
% 72.01/10.40 | (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0))
% 72.01/10.40 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni]
% 72.01/10.40 | : ! [v3: ty] : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2)
% 72.01/10.40 | = v0))
% 72.01/10.40 | (21) ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3: ty] : (v1 = v0 | ~
% 72.01/10.40 | (map(v3, v2) = v1) | ~ (map(v3, v2) = v0))
% 72.01/10.40 | (22) ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 |
% 72.01/10.40 | ~ (length1(v3, v2) = v1) | ~ (length1(v3, v2) = v0))
% 72.01/10.40 | (23) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 |
% 72.01/10.40 | ~ (elts(v3, v2) = v1) | ~ (elts(v3, v2) = v0))
% 72.01/10.40 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 72.01/10.40 | elt1] : ! [v3: elt1] : (v1 = v0 | ~ (le1(v3, v2) = v1) | ~
% 72.01/10.40 | (le1(v3, v2) = v0))
% 72.01/10.40 | (25) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 72.01/10.40 | ty] : ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~
% 72.01/10.40 | (get(v5, v4, v3, v2) = v0))
% 72.01/10.40 |
% 72.01/10.40 | DELTA: instantiating (8) with fresh symbol all_88_0 gives:
% 72.01/10.40 | (26) map(int, elt) = all_88_0 & ty(all_88_0) & ! [v0: map_int_elt] : !
% 72.01/10.40 | [v1: uni] : ( ~ (t2tb3(v0) = v1) | ~ map_int_elt(v0) |
% 72.01/10.40 | sort1(all_88_0, v1) = 0)
% 72.01/10.40 |
% 72.01/10.40 | ALPHA: (26) implies:
% 72.01/10.40 | (27) map(int, elt) = all_88_0
% 72.01/10.40 | (28) ! [v0: map_int_elt] : ! [v1: uni] : ( ~ (t2tb3(v0) = v1) | ~
% 72.01/10.40 | map_int_elt(v0) | sort1(all_88_0, v1) = 0)
% 72.01/10.40 |
% 72.01/10.40 | DELTA: instantiating (9) with fresh symbol all_91_0 gives:
% 72.01/10.40 | (29) map(int, elt) = all_91_0 & ty(all_91_0) & ! [v0: uni] : ! [v1:
% 72.01/10.40 | map_int_elt] : ( ~ (tb2t3(v0) = v1) | ~ uni(v0) | ? [v2: any] : ?
% 72.01/10.40 | [v3: uni] : (t2tb3(v1) = v3 & sort1(all_91_0, v0) = v2 & uni(v3) & (
% 72.01/10.40 | ~ (v2 = 0) | v3 = v0))) & ! [v0: uni] : ( ~ (sort1(all_91_0,
% 72.01/10.40 | v0) = 0) | ~ uni(v0) | ? [v1: map_int_elt] : (tb2t3(v0) = v1 &
% 72.01/10.40 | t2tb3(v1) = v0 & map_int_elt(v1)))
% 72.01/10.40 |
% 72.01/10.40 | ALPHA: (29) implies:
% 72.01/10.40 | (30) map(int, elt) = all_91_0
% 72.01/10.40 | (31) ! [v0: uni] : ! [v1: map_int_elt] : ( ~ (tb2t3(v0) = v1) | ~
% 72.01/10.40 | uni(v0) | ? [v2: any] : ? [v3: uni] : (t2tb3(v1) = v3 &
% 72.01/10.40 | sort1(all_91_0, v0) = v2 & uni(v3) & ( ~ (v2 = 0) | v3 = v0)))
% 72.01/10.40 |
% 72.01/10.40 | DELTA: instantiating (16) with fresh symbols all_94_0, all_94_1, all_94_2,
% 72.01/10.40 | all_94_3, all_94_4, all_94_5, all_94_6, all_94_7, all_94_8, all_94_9,
% 72.01/10.40 | all_94_10, all_94_11, all_94_12, all_94_13, all_94_14, all_94_15,
% 72.01/10.40 | all_94_16, all_94_17, all_94_18, all_94_19, all_94_20, all_94_21,
% 72.01/10.40 | all_94_22, all_94_23, all_94_24, all_94_25, all_94_26, all_94_27,
% 72.01/10.40 | all_94_28, all_94_29, all_94_30 gives:
% 72.01/10.41 | (32) ~ (all_94_0 = 0) & ~ (all_94_10 = 0) & $lesseq(all_94_4, all_94_25)
% 72.01/10.41 | & $lesseq(all_94_19, all_94_4) & $lesseq(1, $difference(all_94_30,
% 72.01/10.41 | all_94_19)) & $lesseq(1, all_94_19) & $lesseq(1,
% 72.01/10.41 | $difference(all_94_30, all_94_25)) & sorted_sub6(all_94_26, 0,
% 72.01/10.41 | all_94_25) = 0 & le1(all_94_11, all_94_20) = all_94_10 &
% 72.01/10.41 | le1(all_94_20, all_94_1) = all_94_0 & tb2t4(all_94_2) = all_94_1 &
% 72.01/10.41 | tb2t4(all_94_12) = all_94_11 & tb2t4(all_94_21) = all_94_20 &
% 72.01/10.41 | tb2t3(all_94_9) = all_94_8 & t2tb3(all_94_8) = all_94_7 &
% 72.01/10.41 | t2tb3(all_94_18) = all_94_17 & t2tb3(all_94_26) = all_94_24 &
% 72.01/10.41 | t2tb3(all_94_29) = all_94_28 & permut_all(elt, all_94_27, all_94_14) =
% 72.01/10.41 | 0 & permut_all(elt, all_94_27, all_94_23) = 0 & exchange3(elt,
% 72.01/10.41 | all_94_14, all_94_5, $sum(all_94_19, -1), all_94_19) = 0 &
% 72.01/10.41 | t2tb(all_94_4) = all_94_3 & t2tb($sum(all_94_19, -1)) = all_94_13 &
% 72.01/10.41 | t2tb(all_94_19) = all_94_16 & t2tb(all_94_25) = all_94_22 &
% 72.01/10.41 | mk_array1(elt, all_94_30, all_94_6) = all_94_5 & mk_array1(elt,
% 72.01/10.41 | all_94_30, all_94_15) = all_94_14 & mk_array1(elt, all_94_30,
% 72.01/10.41 | all_94_24) = all_94_23 & mk_array1(elt, all_94_30, all_94_28) =
% 72.01/10.41 | all_94_27 & set(elt, int, all_94_7, all_94_13, all_94_21) = all_94_6 &
% 72.01/10.41 | set(elt, int, all_94_17, all_94_16, all_94_12) = all_94_9 & set(elt,
% 72.01/10.41 | int, all_94_17, all_94_16, all_94_21) = all_94_15 & get(elt, int,
% 72.01/10.41 | all_94_7, all_94_3) = all_94_2 & get(elt, int, all_94_17, all_94_13)
% 72.01/10.41 | = all_94_12 & get(elt, int, all_94_24, all_94_22) = all_94_21 &
% 72.01/10.41 | map_int_elt(all_94_8) & map_int_elt(all_94_18) &
% 72.01/10.41 | map_int_elt(all_94_26) & map_int_elt(all_94_29) & elt1(all_94_1) &
% 72.01/10.41 | elt1(all_94_11) & elt1(all_94_20) & uni(all_94_2) & uni(all_94_3) &
% 72.01/10.41 | uni(all_94_5) & uni(all_94_6) & uni(all_94_7) & uni(all_94_9) &
% 72.01/10.41 | uni(all_94_12) & uni(all_94_13) & uni(all_94_14) & uni(all_94_15) &
% 72.01/10.41 | uni(all_94_16) & uni(all_94_17) & uni(all_94_21) & uni(all_94_22) &
% 72.01/10.41 | uni(all_94_23) & uni(all_94_24) & uni(all_94_27) & uni(all_94_28) & !
% 72.01/10.41 | [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4: elt1]
% 72.01/10.41 | : ! [v5: uni] : ! [v6: uni] : ! [v7: elt1] : ! [v8: int] : (v8 = 0
% 72.01/10.41 | | v1 = all_94_19 | v0 = all_94_19 | ~ ($lesseq(v1, all_94_25)) | ~
% 72.01/10.41 | ($lesseq(v0, v1)) | ~ ($lesseq(0, v0)) | ~ (le1(v4, v7) = v8) | ~
% 72.01/10.41 | (tb2t4(v6) = v7) | ~ (tb2t4(v3) = v4) | ~ (t2tb(v1) = v5) | ~
% 72.01/10.41 | (t2tb(v0) = v2) | ~ (get(elt, int, all_94_17, v5) = v6) | ~
% 72.01/10.41 | (get(elt, int, all_94_17, v2) = v3)) & ! [v0: int] : ! [v1: uni] :
% 72.01/10.41 | ( ~ ($lesseq(v0, all_94_25)) | ~ ($lesseq(1, $difference(v0,
% 72.01/10.41 | all_94_19))) | ~ (t2tb(v0) = v1) | ? [v2: uni] : ? [v3:
% 72.01/10.41 | elt1] : (le1(all_94_20, v3) = 0 & tb2t4(v2) = v3 & get(elt, int,
% 72.01/10.41 | all_94_17, v1) = v2 & elt1(v3) & uni(v2)))
% 72.01/10.41 |
% 72.01/10.41 | ALPHA: (32) implies:
% 72.01/10.41 | (33) ~ (all_94_10 = 0)
% 72.01/10.41 | (34) ~ (all_94_0 = 0)
% 72.01/10.41 | (35) $lesseq(1, $difference(all_94_30, all_94_25))
% 72.01/10.41 | (36) $lesseq(1, all_94_19)
% 72.01/10.41 | (37) $lesseq(1, $difference(all_94_30, all_94_19))
% 72.01/10.41 | (38) $lesseq(all_94_19, all_94_4)
% 72.01/10.41 | (39) $lesseq(all_94_4, all_94_25)
% 72.01/10.41 | (40) uni(all_94_28)
% 72.01/10.41 | (41) uni(all_94_27)
% 72.01/10.41 | (42) uni(all_94_24)
% 72.01/10.41 | (43) uni(all_94_23)
% 72.01/10.41 | (44) uni(all_94_21)
% 72.01/10.41 | (45) uni(all_94_17)
% 72.01/10.41 | (46) uni(all_94_16)
% 72.01/10.41 | (47) uni(all_94_15)
% 72.01/10.41 | (48) uni(all_94_14)
% 72.01/10.41 | (49) uni(all_94_13)
% 72.01/10.41 | (50) uni(all_94_12)
% 72.01/10.41 | (51) uni(all_94_9)
% 72.01/10.41 | (52) uni(all_94_7)
% 72.01/10.41 | (53) uni(all_94_6)
% 72.01/10.41 | (54) uni(all_94_5)
% 72.01/10.41 | (55) uni(all_94_3)
% 72.01/10.41 | (56) elt1(all_94_20)
% 72.01/10.41 | (57) elt1(all_94_11)
% 72.01/10.41 | (58) elt1(all_94_1)
% 72.01/10.41 | (59) map_int_elt(all_94_29)
% 72.01/10.41 | (60) map_int_elt(all_94_26)
% 72.01/10.41 | (61) get(elt, int, all_94_24, all_94_22) = all_94_21
% 72.01/10.41 | (62) get(elt, int, all_94_17, all_94_13) = all_94_12
% 72.01/10.41 | (63) get(elt, int, all_94_7, all_94_3) = all_94_2
% 72.01/10.41 | (64) set(elt, int, all_94_17, all_94_16, all_94_21) = all_94_15
% 72.01/10.41 | (65) set(elt, int, all_94_17, all_94_16, all_94_12) = all_94_9
% 72.01/10.41 | (66) set(elt, int, all_94_7, all_94_13, all_94_21) = all_94_6
% 72.01/10.41 | (67) mk_array1(elt, all_94_30, all_94_28) = all_94_27
% 72.01/10.41 | (68) mk_array1(elt, all_94_30, all_94_24) = all_94_23
% 72.01/10.41 | (69) mk_array1(elt, all_94_30, all_94_15) = all_94_14
% 72.01/10.41 | (70) mk_array1(elt, all_94_30, all_94_6) = all_94_5
% 72.01/10.41 | (71) t2tb(all_94_25) = all_94_22
% 72.01/10.41 | (72) t2tb(all_94_19) = all_94_16
% 72.01/10.41 | (73) t2tb($sum(all_94_19, -1)) = all_94_13
% 72.01/10.41 | (74) t2tb(all_94_4) = all_94_3
% 72.01/10.41 | (75) exchange3(elt, all_94_14, all_94_5, $sum(all_94_19, -1), all_94_19) =
% 72.01/10.41 | 0
% 72.01/10.41 | (76) permut_all(elt, all_94_27, all_94_23) = 0
% 72.01/10.41 | (77) permut_all(elt, all_94_27, all_94_14) = 0
% 72.01/10.41 | (78) t2tb3(all_94_29) = all_94_28
% 72.01/10.41 | (79) t2tb3(all_94_26) = all_94_24
% 72.01/10.41 | (80) t2tb3(all_94_8) = all_94_7
% 72.01/10.41 | (81) tb2t3(all_94_9) = all_94_8
% 72.01/10.41 | (82) tb2t4(all_94_12) = all_94_11
% 72.01/10.41 | (83) tb2t4(all_94_2) = all_94_1
% 72.01/10.41 | (84) le1(all_94_20, all_94_1) = all_94_0
% 72.01/10.41 | (85) le1(all_94_11, all_94_20) = all_94_10
% 72.01/10.41 | (86) ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(v0, all_94_25)) | ~
% 72.01/10.41 | ($lesseq(1, $difference(v0, all_94_19))) | ~ (t2tb(v0) = v1) | ?
% 72.01/10.41 | [v2: uni] : ? [v3: elt1] : (le1(all_94_20, v3) = 0 & tb2t4(v2) = v3
% 72.01/10.41 | & get(elt, int, all_94_17, v1) = v2 & elt1(v3) & uni(v2)))
% 72.01/10.41 | (87) ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 72.01/10.41 | elt1] : ! [v5: uni] : ! [v6: uni] : ! [v7: elt1] : ! [v8: int] :
% 72.01/10.41 | (v8 = 0 | v1 = all_94_19 | v0 = all_94_19 | ~ ($lesseq(v1,
% 72.01/10.41 | all_94_25)) | ~ ($lesseq(v0, v1)) | ~ ($lesseq(0, v0)) | ~
% 72.01/10.41 | (le1(v4, v7) = v8) | ~ (tb2t4(v6) = v7) | ~ (tb2t4(v3) = v4) | ~
% 72.01/10.41 | (t2tb(v1) = v5) | ~ (t2tb(v0) = v2) | ~ (get(elt, int, all_94_17,
% 72.01/10.41 | v5) = v6) | ~ (get(elt, int, all_94_17, v2) = v3))
% 72.01/10.41 |
% 72.01/10.41 | COMBINE_INEQS: (38), (39) imply:
% 72.01/10.41 | (88) $lesseq(all_94_19, all_94_25)
% 72.01/10.41 |
% 72.01/10.41 | COMBINE_INEQS: (36), (38) imply:
% 72.01/10.41 | (89) $lesseq(1, all_94_4)
% 72.01/10.41 |
% 72.01/10.41 | COMBINE_INEQS: (39), (89) imply:
% 72.01/10.41 | (90) $lesseq(1, all_94_25)
% 72.01/10.41 |
% 72.01/10.41 | GROUND_INST: instantiating (21) with all_88_0, all_91_0, elt, int, simplifying
% 72.01/10.41 | with (27), (30) gives:
% 72.01/10.41 | (91) all_91_0 = all_88_0
% 72.01/10.41 |
% 72.01/10.41 | GROUND_INST: instantiating (17) with all_94_22, all_94_16, all_94_25,
% 72.01/10.42 | simplifying with (71) gives:
% 72.01/10.42 | (92) all_94_16 = all_94_22 | ~ (t2tb(all_94_25) = all_94_16)
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (17) with all_94_16, all_94_3, all_94_19,
% 72.01/10.42 | simplifying with (72) gives:
% 72.01/10.42 | (93) all_94_3 = all_94_16 | ~ (t2tb(all_94_19) = all_94_3)
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (17) with all_94_22, all_94_3, all_94_25,
% 72.01/10.42 | simplifying with (71) gives:
% 72.01/10.42 | (94) all_94_3 = all_94_22 | ~ (t2tb(all_94_25) = all_94_3)
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (get_sort4) with int, elt, all_94_17, all_94_13,
% 72.01/10.42 | all_94_12, simplifying with (14), (15), (45), (49), (62) gives:
% 72.01/10.42 | (95) sort1(elt, all_94_12) = 0
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (set_sort4) with int, elt, all_94_17, all_94_16,
% 72.01/10.42 | all_94_21, all_94_15, simplifying with (14), (15), (44), (45),
% 72.01/10.42 | (46), (64) gives:
% 72.01/10.42 | (96) ? [v0: ty] : (map(int, elt) = v0 & sort1(v0, all_94_15) = 0 & ty(v0))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (set_sort4) with int, elt, all_94_17, all_94_16,
% 72.01/10.42 | all_94_12, all_94_9, simplifying with (14), (15), (45), (46),
% 72.01/10.42 | (50), (65) gives:
% 72.01/10.42 | (97) ? [v0: ty] : (map(int, elt) = v0 & sort1(v0, all_94_9) = 0 & ty(v0))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (set_sort4) with int, elt, all_94_7, all_94_13,
% 72.01/10.42 | all_94_21, all_94_6, simplifying with (14), (15), (44), (49),
% 72.01/10.42 | (52), (66) gives:
% 72.01/10.42 | (98) ? [v0: ty] : (map(int, elt) = v0 & sort1(v0, all_94_6) = 0 & ty(v0))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (1) with elt, all_94_30, all_94_28, all_94_27,
% 72.01/10.42 | simplifying with (15), (40), (67) gives:
% 72.01/10.42 | (99) ? [v0: ty] : ? [v1: any] : ? [v2: uni] : (elts(elt, all_94_27) = v2
% 72.01/10.42 | & map(int, elt) = v0 & sort1(v0, all_94_28) = v1 & ty(v0) & uni(v2)
% 72.01/10.42 | & ( ~ (v1 = 0) | v2 = all_94_28))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (length_def1) with elt, all_94_30, all_94_24,
% 72.01/10.42 | all_94_23, simplifying with (15), (42), (68) gives:
% 72.01/10.42 | (100) length1(elt, all_94_23) = all_94_30
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (1) with elt, all_94_30, all_94_24, all_94_23,
% 72.01/10.42 | simplifying with (15), (42), (68) gives:
% 72.01/10.42 | (101) ? [v0: ty] : ? [v1: any] : ? [v2: uni] : (elts(elt, all_94_23) =
% 72.01/10.42 | v2 & map(int, elt) = v0 & sort1(v0, all_94_24) = v1 & ty(v0) &
% 72.01/10.42 | uni(v2) & ( ~ (v1 = 0) | v2 = all_94_24))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (1) with elt, all_94_30, all_94_15, all_94_14,
% 72.01/10.42 | simplifying with (15), (47), (69) gives:
% 72.01/10.42 | (102) ? [v0: ty] : ? [v1: any] : ? [v2: uni] : (elts(elt, all_94_14) =
% 72.01/10.42 | v2 & map(int, elt) = v0 & sort1(v0, all_94_15) = v1 & ty(v0) &
% 72.01/10.42 | uni(v2) & ( ~ (v1 = 0) | v2 = all_94_15))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (1) with elt, all_94_30, all_94_6, all_94_5,
% 72.01/10.42 | simplifying with (15), (53), (70) gives:
% 72.01/10.42 | (103) ? [v0: ty] : ? [v1: any] : ? [v2: uni] : (elts(elt, all_94_5) = v2
% 72.01/10.42 | & map(int, elt) = v0 & sort1(v0, all_94_6) = v1 & ty(v0) & uni(v2)
% 72.01/10.42 | & ( ~ (v1 = 0) | v2 = all_94_6))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (86) with all_94_25, all_94_22, simplifying with
% 72.01/10.42 | (71) gives:
% 72.01/10.42 | (104) ~ ($lesseq(1, $difference(all_94_25, all_94_19))) | ? [v0: uni] :
% 72.01/10.42 | ? [v1: elt1] : (le1(all_94_20, v1) = 0 & tb2t4(v0) = v1 & get(elt,
% 72.01/10.42 | int, all_94_17, all_94_22) = v0 & elt1(v1) & uni(v0))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (bridgeL) with all_94_25, all_94_22, simplifying
% 72.01/10.42 | with (71) gives:
% 72.01/10.42 | (105) tb2t(all_94_22) = all_94_25
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (bridgeL) with all_94_19, all_94_16, simplifying
% 72.01/10.42 | with (72) gives:
% 72.01/10.42 | (106) tb2t(all_94_16) = all_94_19
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (2) with all_94_19, all_94_16, simplifying with
% 72.01/10.42 | (72) gives:
% 72.01/10.42 | (107) sort1(int, all_94_16) = 0
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (86) with all_94_4, all_94_3, simplifying with (74)
% 72.01/10.42 | gives:
% 72.01/10.42 | (108) ~ ($lesseq(all_94_4, all_94_25)) | ~ ($lesseq(1,
% 72.01/10.42 | $difference(all_94_4, all_94_19))) | ? [v0: uni] : ? [v1: elt1]
% 72.01/10.42 | : (le1(all_94_20, v1) = 0 & tb2t4(v0) = v1 & get(elt, int, all_94_17,
% 72.01/10.42 | all_94_3) = v0 & elt1(v1) & uni(v0))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (bridgeL) with all_94_4, all_94_3, simplifying with
% 72.01/10.42 | (74) gives:
% 72.01/10.42 | (109) tb2t(all_94_3) = all_94_4
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (2) with all_94_4, all_94_3, simplifying with (74)
% 72.01/10.42 | gives:
% 72.01/10.42 | (110) sort1(int, all_94_3) = 0
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (exchange_permut_all) with elt, all_94_14,
% 72.01/10.42 | all_94_5, $sum(all_94_19, -1), all_94_19, simplifying with (15),
% 72.01/10.42 | (48), (54), (75) gives:
% 72.01/10.42 | (111) permut_all(elt, all_94_14, all_94_5) = 0
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (6) with elt, all_94_14, all_94_5, $sum(all_94_19,
% 72.01/10.42 | -1), all_94_19, simplifying with (15), (48), (54), (75) gives:
% 72.01/10.42 | (112) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : (exchange2(elt, v1, v2,
% 72.01/10.42 | 0, v0, $sum(all_94_19, -1), all_94_19) = 0 & elts(elt, all_94_5)
% 72.01/10.42 | = v2 & elts(elt, all_94_14) = v1 & length1(elt, all_94_5) = v0 &
% 72.01/10.42 | length1(elt, all_94_14) = v0 & uni(v2) & uni(v1))
% 72.01/10.42 |
% 72.01/10.42 | GROUND_INST: instantiating (7) with elt, all_94_27, all_94_23, simplifying
% 72.01/10.42 | with (15), (41), (43), (76) gives:
% 72.01/10.43 | (113) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : (permut2(elt, v1, v2, 0,
% 72.01/10.43 | v0) = 0 & elts(elt, all_94_23) = v2 & elts(elt, all_94_27) = v1 &
% 72.01/10.43 | length1(elt, all_94_23) = v0 & length1(elt, all_94_27) = v0 &
% 72.01/10.43 | uni(v2) & uni(v1))
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (7) with elt, all_94_27, all_94_14, simplifying
% 72.01/10.43 | with (15), (41), (48), (77) gives:
% 72.01/10.43 | (114) ? [v0: int] : ? [v1: uni] : ? [v2: uni] : (permut2(elt, v1, v2, 0,
% 72.01/10.43 | v0) = 0 & elts(elt, all_94_14) = v2 & elts(elt, all_94_27) = v1 &
% 72.01/10.43 | length1(elt, all_94_14) = v0 & length1(elt, all_94_27) = v0 &
% 72.01/10.43 | uni(v2) & uni(v1))
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (28) with all_94_29, all_94_28, simplifying with
% 72.01/10.43 | (59), (78) gives:
% 72.01/10.43 | (115) sort1(all_88_0, all_94_28) = 0
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (28) with all_94_26, all_94_24, simplifying with
% 72.01/10.43 | (60), (79) gives:
% 72.01/10.43 | (116) sort1(all_88_0, all_94_24) = 0
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (31) with all_94_9, all_94_8, simplifying with
% 72.01/10.43 | (51), (81) gives:
% 72.01/10.43 | (117) ? [v0: any] : ? [v1: uni] : (t2tb3(all_94_8) = v1 & sort1(all_91_0,
% 72.01/10.43 | all_94_9) = v0 & uni(v1) & ( ~ (v0 = 0) | v1 = all_94_9))
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (10) with all_94_12, all_94_11, simplifying with
% 72.01/10.43 | (50), (82) gives:
% 72.01/10.43 | (118) ? [v0: any] : ? [v1: uni] : (t2tb4(all_94_11) = v1 & sort1(elt,
% 72.01/10.43 | all_94_12) = v0 & uni(v1) & ( ~ (v0 = 0) | v1 = all_94_12))
% 72.01/10.43 |
% 72.01/10.43 | GROUND_INST: instantiating (11) with all_94_1, all_94_20, all_94_0,
% 72.01/10.43 | simplifying with (56), (58), (84) gives:
% 72.01/10.43 | (119) all_94_0 = 0 | le1(all_94_1, all_94_20) = 0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (96) with fresh symbol all_111_0 gives:
% 72.01/10.43 | (120) map(int, elt) = all_111_0 & sort1(all_111_0, all_94_15) = 0 &
% 72.01/10.43 | ty(all_111_0)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (120) implies:
% 72.01/10.43 | (121) sort1(all_111_0, all_94_15) = 0
% 72.01/10.43 | (122) map(int, elt) = all_111_0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (98) with fresh symbol all_113_0 gives:
% 72.01/10.43 | (123) map(int, elt) = all_113_0 & sort1(all_113_0, all_94_6) = 0 &
% 72.01/10.43 | ty(all_113_0)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (123) implies:
% 72.01/10.43 | (124) sort1(all_113_0, all_94_6) = 0
% 72.01/10.43 | (125) map(int, elt) = all_113_0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (97) with fresh symbol all_119_0 gives:
% 72.01/10.43 | (126) map(int, elt) = all_119_0 & sort1(all_119_0, all_94_9) = 0 &
% 72.01/10.43 | ty(all_119_0)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (126) implies:
% 72.01/10.43 | (127) sort1(all_119_0, all_94_9) = 0
% 72.01/10.43 | (128) map(int, elt) = all_119_0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (118) with fresh symbols all_127_0, all_127_1 gives:
% 72.01/10.43 | (129) t2tb4(all_94_11) = all_127_0 & sort1(elt, all_94_12) = all_127_1 &
% 72.01/10.43 | uni(all_127_0) & ( ~ (all_127_1 = 0) | all_127_0 = all_94_12)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (129) implies:
% 72.01/10.43 | (130) sort1(elt, all_94_12) = all_127_1
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (117) with fresh symbols all_131_0, all_131_1 gives:
% 72.01/10.43 | (131) t2tb3(all_94_8) = all_131_0 & sort1(all_91_0, all_94_9) = all_131_1 &
% 72.01/10.43 | uni(all_131_0) & ( ~ (all_131_1 = 0) | all_131_0 = all_94_9)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (131) implies:
% 72.01/10.43 | (132) sort1(all_91_0, all_94_9) = all_131_1
% 72.01/10.43 | (133) t2tb3(all_94_8) = all_131_0
% 72.01/10.43 | (134) ~ (all_131_1 = 0) | all_131_0 = all_94_9
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (112) with fresh symbols all_133_0, all_133_1, all_133_2
% 72.01/10.43 | gives:
% 72.01/10.43 | (135) exchange2(elt, all_133_1, all_133_0, 0, all_133_2, $sum(all_94_19,
% 72.01/10.43 | -1), all_94_19) = 0 & elts(elt, all_94_5) = all_133_0 & elts(elt,
% 72.01/10.43 | all_94_14) = all_133_1 & length1(elt, all_94_5) = all_133_2 &
% 72.01/10.43 | length1(elt, all_94_14) = all_133_2 & uni(all_133_0) & uni(all_133_1)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (135) implies:
% 72.01/10.43 | (136) length1(elt, all_94_14) = all_133_2
% 72.01/10.43 | (137) elts(elt, all_94_14) = all_133_1
% 72.01/10.43 | (138) elts(elt, all_94_5) = all_133_0
% 72.01/10.43 | (139) exchange2(elt, all_133_1, all_133_0, 0, all_133_2, $sum(all_94_19,
% 72.01/10.43 | -1), all_94_19) = 0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (103) with fresh symbols all_135_0, all_135_1, all_135_2
% 72.01/10.43 | gives:
% 72.01/10.43 | (140) elts(elt, all_94_5) = all_135_0 & map(int, elt) = all_135_2 &
% 72.01/10.43 | sort1(all_135_2, all_94_6) = all_135_1 & ty(all_135_2) &
% 72.01/10.43 | uni(all_135_0) & ( ~ (all_135_1 = 0) | all_135_0 = all_94_6)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (140) implies:
% 72.01/10.43 | (141) uni(all_135_0)
% 72.01/10.43 | (142) sort1(all_135_2, all_94_6) = all_135_1
% 72.01/10.43 | (143) map(int, elt) = all_135_2
% 72.01/10.43 | (144) elts(elt, all_94_5) = all_135_0
% 72.01/10.43 | (145) ~ (all_135_1 = 0) | all_135_0 = all_94_6
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (101) with fresh symbols all_137_0, all_137_1, all_137_2
% 72.01/10.43 | gives:
% 72.01/10.43 | (146) elts(elt, all_94_23) = all_137_0 & map(int, elt) = all_137_2 &
% 72.01/10.43 | sort1(all_137_2, all_94_24) = all_137_1 & ty(all_137_2) &
% 72.01/10.43 | uni(all_137_0) & ( ~ (all_137_1 = 0) | all_137_0 = all_94_24)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (146) implies:
% 72.01/10.43 | (147) sort1(all_137_2, all_94_24) = all_137_1
% 72.01/10.43 | (148) map(int, elt) = all_137_2
% 72.01/10.43 | (149) elts(elt, all_94_23) = all_137_0
% 72.01/10.43 | (150) ~ (all_137_1 = 0) | all_137_0 = all_94_24
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (114) with fresh symbols all_139_0, all_139_1, all_139_2
% 72.01/10.43 | gives:
% 72.01/10.43 | (151) permut2(elt, all_139_1, all_139_0, 0, all_139_2) = 0 & elts(elt,
% 72.01/10.43 | all_94_14) = all_139_0 & elts(elt, all_94_27) = all_139_1 &
% 72.01/10.43 | length1(elt, all_94_14) = all_139_2 & length1(elt, all_94_27) =
% 72.01/10.43 | all_139_2 & uni(all_139_0) & uni(all_139_1)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (151) implies:
% 72.01/10.43 | (152) uni(all_139_0)
% 72.01/10.43 | (153) length1(elt, all_94_27) = all_139_2
% 72.01/10.43 | (154) length1(elt, all_94_14) = all_139_2
% 72.01/10.43 | (155) elts(elt, all_94_27) = all_139_1
% 72.01/10.43 | (156) elts(elt, all_94_14) = all_139_0
% 72.01/10.43 | (157) permut2(elt, all_139_1, all_139_0, 0, all_139_2) = 0
% 72.01/10.43 |
% 72.01/10.43 | DELTA: instantiating (99) with fresh symbols all_141_0, all_141_1, all_141_2
% 72.01/10.43 | gives:
% 72.01/10.43 | (158) elts(elt, all_94_27) = all_141_0 & map(int, elt) = all_141_2 &
% 72.01/10.43 | sort1(all_141_2, all_94_28) = all_141_1 & ty(all_141_2) &
% 72.01/10.43 | uni(all_141_0) & ( ~ (all_141_1 = 0) | all_141_0 = all_94_28)
% 72.01/10.43 |
% 72.01/10.43 | ALPHA: (158) implies:
% 72.01/10.43 | (159) uni(all_141_0)
% 72.01/10.43 | (160) sort1(all_141_2, all_94_28) = all_141_1
% 72.01/10.43 | (161) map(int, elt) = all_141_2
% 72.01/10.43 | (162) elts(elt, all_94_27) = all_141_0
% 72.01/10.44 | (163) ~ (all_141_1 = 0) | all_141_0 = all_94_28
% 72.01/10.44 |
% 72.01/10.44 | DELTA: instantiating (102) with fresh symbols all_143_0, all_143_1, all_143_2
% 72.01/10.44 | gives:
% 72.01/10.44 | (164) elts(elt, all_94_14) = all_143_0 & map(int, elt) = all_143_2 &
% 72.01/10.44 | sort1(all_143_2, all_94_15) = all_143_1 & ty(all_143_2) &
% 72.01/10.44 | uni(all_143_0) & ( ~ (all_143_1 = 0) | all_143_0 = all_94_15)
% 72.01/10.44 |
% 72.01/10.44 | ALPHA: (164) implies:
% 72.01/10.44 | (165) sort1(all_143_2, all_94_15) = all_143_1
% 72.01/10.44 | (166) map(int, elt) = all_143_2
% 72.01/10.44 | (167) elts(elt, all_94_14) = all_143_0
% 72.01/10.44 | (168) ~ (all_143_1 = 0) | all_143_0 = all_94_15
% 72.01/10.44 |
% 72.01/10.44 | DELTA: instantiating (113) with fresh symbols all_145_0, all_145_1, all_145_2
% 72.01/10.44 | gives:
% 72.01/10.44 | (169) permut2(elt, all_145_1, all_145_0, 0, all_145_2) = 0 & elts(elt,
% 72.01/10.44 | all_94_23) = all_145_0 & elts(elt, all_94_27) = all_145_1 &
% 72.01/10.44 | length1(elt, all_94_23) = all_145_2 & length1(elt, all_94_27) =
% 72.01/10.44 | all_145_2 & uni(all_145_0) & uni(all_145_1)
% 72.01/10.44 |
% 72.01/10.44 | ALPHA: (169) implies:
% 72.01/10.44 | (170) uni(all_145_0)
% 72.01/10.44 | (171) length1(elt, all_94_27) = all_145_2
% 72.01/10.44 | (172) length1(elt, all_94_23) = all_145_2
% 72.01/10.44 | (173) elts(elt, all_94_27) = all_145_1
% 72.01/10.44 | (174) elts(elt, all_94_23) = all_145_0
% 72.01/10.44 | (175) permut2(elt, all_145_1, all_145_0, 0, all_145_2) = 0
% 72.01/10.44 |
% 72.01/10.44 | REDUCE: (91), (132) imply:
% 72.01/10.44 | (176) sort1(all_88_0, all_94_9) = all_131_1
% 72.01/10.44 |
% 72.01/10.44 | BETA: splitting (119) gives:
% 72.01/10.44 |
% 72.01/10.44 | Case 1:
% 72.01/10.44 | |
% 72.01/10.44 | | (177) le1(all_94_1, all_94_20) = 0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (20) with 0, all_127_1, all_94_12, elt,
% 72.01/10.44 | | simplifying with (95), (130) gives:
% 72.01/10.44 | | (178) all_127_1 = 0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_119_0, all_135_2, elt, int,
% 72.01/10.44 | | simplifying with (128), (143) gives:
% 72.01/10.44 | | (179) all_135_2 = all_119_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_113_0, all_135_2, elt, int,
% 72.01/10.44 | | simplifying with (125), (143) gives:
% 72.01/10.44 | | (180) all_135_2 = all_113_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_135_2, all_137_2, elt, int,
% 72.01/10.44 | | simplifying with (143), (148) gives:
% 72.01/10.44 | | (181) all_137_2 = all_135_2
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_137_2, all_141_2, elt, int,
% 72.01/10.44 | | simplifying with (148), (161) gives:
% 72.01/10.44 | | (182) all_141_2 = all_137_2
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_111_0, all_141_2, elt, int,
% 72.01/10.44 | | simplifying with (122), (161) gives:
% 72.01/10.44 | | (183) all_141_2 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_88_0, all_143_2, elt, int,
% 72.01/10.44 | | simplifying with (27), (166) gives:
% 72.01/10.44 | | (184) all_143_2 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (21) with all_119_0, all_143_2, elt, int,
% 72.01/10.44 | | simplifying with (128), (166) gives:
% 72.01/10.44 | | (185) all_143_2 = all_119_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (22) with all_139_2, all_145_2, all_94_27, elt,
% 72.01/10.44 | | simplifying with (153), (171) gives:
% 72.01/10.44 | | (186) all_145_2 = all_139_2
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (22) with all_94_30, all_145_2, all_94_23, elt,
% 72.01/10.44 | | simplifying with (100), (172) gives:
% 72.01/10.44 | | (187) all_145_2 = all_94_30
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (22) with all_133_2, all_139_2, all_94_14, elt,
% 72.01/10.44 | | simplifying with (136), (154) gives:
% 72.01/10.44 | | (188) all_139_2 = all_133_2
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_141_0, all_145_1, all_94_27, elt,
% 72.01/10.44 | | simplifying with (162), (173) gives:
% 72.01/10.44 | | (189) all_145_1 = all_141_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_139_1, all_145_1, all_94_27, elt,
% 72.01/10.44 | | simplifying with (155), (173) gives:
% 72.01/10.44 | | (190) all_145_1 = all_139_1
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_137_0, all_145_0, all_94_23, elt,
% 72.01/10.44 | | simplifying with (149), (174) gives:
% 72.01/10.44 | | (191) all_145_0 = all_137_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_139_0, all_143_0, all_94_14, elt,
% 72.01/10.44 | | simplifying with (156), (167) gives:
% 72.01/10.44 | | (192) all_143_0 = all_139_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_133_1, all_143_0, all_94_14, elt,
% 72.01/10.44 | | simplifying with (137), (167) gives:
% 72.01/10.44 | | (193) all_143_0 = all_133_1
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (23) with all_133_0, all_135_0, all_94_5, elt,
% 72.01/10.44 | | simplifying with (138), (144) gives:
% 72.01/10.44 | | (194) all_135_0 = all_133_0
% 72.01/10.44 | |
% 72.01/10.44 | | GROUND_INST: instantiating (19) with all_94_7, all_131_0, all_94_8,
% 72.01/10.44 | | simplifying with (80), (133) gives:
% 72.01/10.44 | | (195) all_131_0 = all_94_7
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (189), (190) imply:
% 72.01/10.44 | | (196) all_141_0 = all_139_1
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (196) implies:
% 72.01/10.44 | | (197) all_141_0 = all_139_1
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (186), (187) imply:
% 72.01/10.44 | | (198) all_139_2 = all_94_30
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (192), (193) imply:
% 72.01/10.44 | | (199) all_139_0 = all_133_1
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (199) implies:
% 72.01/10.44 | | (200) all_139_0 = all_133_1
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (184), (185) imply:
% 72.01/10.44 | | (201) all_119_0 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (201) implies:
% 72.01/10.44 | | (202) all_119_0 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (182), (183) imply:
% 72.01/10.44 | | (203) all_137_2 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (203) implies:
% 72.01/10.44 | | (204) all_137_2 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (188), (198) imply:
% 72.01/10.44 | | (205) all_133_2 = all_94_30
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (205) implies:
% 72.01/10.44 | | (206) all_133_2 = all_94_30
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (181), (204) imply:
% 72.01/10.44 | | (207) all_135_2 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (207) implies:
% 72.01/10.44 | | (208) all_135_2 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (179), (180) imply:
% 72.01/10.44 | | (209) all_119_0 = all_113_0
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (209) implies:
% 72.01/10.44 | | (210) all_119_0 = all_113_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (180), (208) imply:
% 72.01/10.44 | | (211) all_113_0 = all_111_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (202), (210) imply:
% 72.01/10.44 | | (212) all_113_0 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | SIMP: (212) implies:
% 72.01/10.44 | | (213) all_113_0 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (211), (213) imply:
% 72.01/10.44 | | (214) all_111_0 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (180), (213) imply:
% 72.01/10.44 | | (215) all_135_2 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (204), (214) imply:
% 72.01/10.44 | | (216) all_137_2 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | COMBINE_EQS: (183), (214) imply:
% 72.01/10.44 | | (217) all_141_2 = all_88_0
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (139), (206) imply:
% 72.01/10.44 | | (218) exchange2(elt, all_133_1, all_133_0, 0, all_94_30, $sum(all_94_19,
% 72.01/10.44 | | -1), all_94_19) = 0
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (175), (187), (190), (191) imply:
% 72.01/10.44 | | (219) permut2(elt, all_139_1, all_137_0, 0, all_94_30) = 0
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (157), (198), (200) imply:
% 72.01/10.44 | | (220) permut2(elt, all_139_1, all_133_1, 0, all_94_30) = 0
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (165), (184) imply:
% 72.01/10.44 | | (221) sort1(all_88_0, all_94_15) = all_143_1
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (160), (217) imply:
% 72.01/10.44 | | (222) sort1(all_88_0, all_94_28) = all_141_1
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (147), (216) imply:
% 72.01/10.44 | | (223) sort1(all_88_0, all_94_24) = all_137_1
% 72.01/10.44 | |
% 72.01/10.44 | | REDUCE: (142), (215) imply:
% 72.01/10.45 | | (224) sort1(all_88_0, all_94_6) = all_135_1
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (127), (202) imply:
% 72.01/10.45 | | (225) sort1(all_88_0, all_94_9) = 0
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (124), (213) imply:
% 72.01/10.45 | | (226) sort1(all_88_0, all_94_6) = 0
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (121), (214) imply:
% 72.01/10.45 | | (227) sort1(all_88_0, all_94_15) = 0
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (170), (191) imply:
% 72.01/10.45 | | (228) uni(all_137_0)
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (159), (197) imply:
% 72.01/10.45 | | (229) uni(all_139_1)
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (152), (200) imply:
% 72.01/10.45 | | (230) uni(all_133_1)
% 72.01/10.45 | |
% 72.01/10.45 | | REDUCE: (141), (194) imply:
% 72.01/10.45 | | (231) uni(all_133_0)
% 72.01/10.45 | |
% 72.01/10.45 | | GROUND_INST: instantiating (20) with 0, all_141_1, all_94_28, all_88_0,
% 72.01/10.45 | | simplifying with (115), (222) gives:
% 72.01/10.45 | | (232) all_141_1 = 0
% 72.01/10.45 | |
% 72.01/10.45 | | GROUND_INST: instantiating (20) with 0, all_137_1, all_94_24, all_88_0,
% 72.01/10.45 | | simplifying with (116), (223) gives:
% 72.01/10.45 | | (233) all_137_1 = 0
% 72.01/10.45 | |
% 72.01/10.45 | | GROUND_INST: instantiating (20) with 0, all_143_1, all_94_15, all_88_0,
% 72.01/10.45 | | simplifying with (221), (227) gives:
% 72.01/10.45 | | (234) all_143_1 = 0
% 72.01/10.45 | |
% 72.01/10.45 | | GROUND_INST: instantiating (20) with all_131_1, 0, all_94_9, all_88_0,
% 72.01/10.45 | | simplifying with (176), (225) gives:
% 72.01/10.45 | | (235) all_131_1 = 0
% 72.01/10.45 | |
% 72.01/10.45 | | GROUND_INST: instantiating (20) with 0, all_135_1, all_94_6, all_88_0,
% 72.01/10.45 | | simplifying with (224), (226) gives:
% 72.01/10.45 | | (236) all_135_1 = 0
% 72.01/10.45 | |
% 72.01/10.45 | | BETA: splitting (145) gives:
% 72.01/10.45 | |
% 72.01/10.45 | | Case 1:
% 72.01/10.45 | | |
% 72.01/10.45 | | | (237) ~ (all_135_1 = 0)
% 72.01/10.45 | | |
% 72.01/10.45 | | | REDUCE: (236), (237) imply:
% 72.01/10.45 | | | (238) $false
% 72.01/10.45 | | |
% 72.01/10.45 | | | CLOSE: (238) is inconsistent.
% 72.01/10.45 | | |
% 72.01/10.45 | | Case 2:
% 72.01/10.45 | | |
% 72.01/10.45 | | | (239) all_135_0 = all_94_6
% 72.01/10.45 | | |
% 72.01/10.45 | | | COMBINE_EQS: (194), (239) imply:
% 72.01/10.45 | | | (240) all_133_0 = all_94_6
% 72.01/10.45 | | |
% 72.01/10.45 | | | SIMP: (240) implies:
% 72.01/10.45 | | | (241) all_133_0 = all_94_6
% 72.01/10.45 | | |
% 72.01/10.45 | | | REDUCE: (218), (241) imply:
% 72.01/10.45 | | | (242) exchange2(elt, all_133_1, all_94_6, 0, all_94_30, $sum(all_94_19,
% 72.01/10.45 | | | -1), all_94_19) = 0
% 72.01/10.45 | | |
% 72.01/10.45 | | | BETA: splitting (134) gives:
% 72.01/10.45 | | |
% 72.01/10.45 | | | Case 1:
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | (243) ~ (all_131_1 = 0)
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | REDUCE: (235), (243) imply:
% 72.01/10.45 | | | | (244) $false
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | CLOSE: (244) is inconsistent.
% 72.01/10.45 | | | |
% 72.01/10.45 | | | Case 2:
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | (245) all_131_0 = all_94_9
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | COMBINE_EQS: (195), (245) imply:
% 72.01/10.45 | | | | (246) all_94_7 = all_94_9
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | SIMP: (246) implies:
% 72.01/10.45 | | | | (247) all_94_7 = all_94_9
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | REDUCE: (63), (247) imply:
% 72.01/10.45 | | | | (248) get(elt, int, all_94_9, all_94_3) = all_94_2
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | BETA: splitting (163) gives:
% 72.01/10.45 | | | |
% 72.01/10.45 | | | | Case 1:
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | (249) ~ (all_141_1 = 0)
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | REDUCE: (232), (249) imply:
% 72.01/10.45 | | | | | (250) $false
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | CLOSE: (250) is inconsistent.
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | Case 2:
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | (251) all_141_0 = all_94_28
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | COMBINE_EQS: (197), (251) imply:
% 72.01/10.45 | | | | | (252) all_139_1 = all_94_28
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | REDUCE: (219), (252) imply:
% 72.01/10.45 | | | | | (253) permut2(elt, all_94_28, all_137_0, 0, all_94_30) = 0
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | REDUCE: (220), (252) imply:
% 72.01/10.45 | | | | | (254) permut2(elt, all_94_28, all_133_1, 0, all_94_30) = 0
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | BETA: splitting (150) gives:
% 72.01/10.45 | | | | |
% 72.01/10.45 | | | | | Case 1:
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | (255) ~ (all_137_1 = 0)
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | REDUCE: (233), (255) imply:
% 72.01/10.45 | | | | | | (256) $false
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | CLOSE: (256) is inconsistent.
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | Case 2:
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | (257) all_137_0 = all_94_24
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | REDUCE: (253), (257) imply:
% 72.01/10.45 | | | | | | (258) permut2(elt, all_94_28, all_94_24, 0, all_94_30) = 0
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | BETA: splitting (168) gives:
% 72.01/10.45 | | | | | |
% 72.01/10.45 | | | | | | Case 1:
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | (259) ~ (all_143_1 = 0)
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | REDUCE: (234), (259) imply:
% 72.01/10.45 | | | | | | | (260) $false
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | CLOSE: (260) is inconsistent.
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | Case 2:
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | (261) all_143_0 = all_94_15
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | COMBINE_EQS: (193), (261) imply:
% 72.01/10.45 | | | | | | | (262) all_133_1 = all_94_15
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | REDUCE: (242), (262) imply:
% 72.01/10.45 | | | | | | | (263) exchange2(elt, all_94_15, all_94_6, 0, all_94_30,
% 72.01/10.45 | | | | | | | $sum(all_94_19, -1), all_94_19) = 0
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | REDUCE: (254), (262) imply:
% 72.01/10.45 | | | | | | | (264) permut2(elt, all_94_28, all_94_15, 0, all_94_30) = 0
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | REDUCE: (137), (262) imply:
% 72.01/10.45 | | | | | | | (265) elts(elt, all_94_14) = all_94_15
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | GROUND_INST: instantiating (3) with elt, all_94_28, all_94_24, 0,
% 72.01/10.45 | | | | | | | all_94_30, all_94_25, all_94_22, all_94_21,
% 72.01/10.45 | | | | | | | simplifying with (15), (40), (42), (61), (71), (258)
% 72.01/10.45 | | | | | | | gives:
% 72.01/10.45 | | | | | | | (266) ~ ($lesseq(1, $difference(all_94_30, all_94_25))) | ~
% 72.01/10.45 | | | | | | | ($lesseq(0, all_94_25)) | ? [v0: int] : ? [v1: uni] :
% 72.01/10.45 | | | | | | | ($lesseq(1, $difference(all_94_30, v0)) & $lesseq(0, v0)
% 72.01/10.45 | | | | | | | & t2tb(v0) = v1 & get(elt, int, all_94_28, v1) =
% 72.01/10.45 | | | | | | | all_94_21 & uni(v1) & uni(all_94_21))
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | GROUND_INST: instantiating (5) with elt, all_94_15, all_94_6, 0,
% 72.01/10.45 | | | | | | | all_94_30, $sum(all_94_19, -1), all_94_19, all_94_4,
% 72.01/10.45 | | | | | | | all_94_3, simplifying with (15), (47), (53), (74),
% 72.01/10.45 | | | | | | | (263) gives:
% 72.01/10.45 | | | | | | | (267) $difference(all_94_4, all_94_19) = -1 | all_94_4 =
% 72.01/10.45 | | | | | | | all_94_19 | ~ ($lesseq(1, $difference(all_94_30,
% 72.01/10.45 | | | | | | | all_94_4))) | ~ ($lesseq(0, all_94_4)) | ? [v0:
% 72.01/10.45 | | | | | | | uni] : (get(elt, int, all_94_6, all_94_3) = v0 &
% 72.01/10.45 | | | | | | | get(elt, int, all_94_15, all_94_3) = v0 & uni(v0))
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | GROUND_INST: instantiating (4) with elt, all_94_15, all_94_6, 0,
% 72.01/10.45 | | | | | | | all_94_30, $sum(all_94_19, -1), all_94_19,
% 72.01/10.45 | | | | | | | simplifying with (15), (47), (53), (263) gives:
% 72.01/10.45 | | | | | | | (268) ? [v0: uni] : ? [v1: uni] : ? [v2: uni] : ? [v3: uni]
% 72.01/10.45 | | | | | | | : (t2tb($sum(all_94_19, -1)) = v0 & t2tb(all_94_19) = v2
% 72.01/10.45 | | | | | | | & get(elt, int, all_94_6, v2) = v1 & get(elt, int,
% 72.01/10.45 | | | | | | | all_94_6, v0) = v3 & get(elt, int, all_94_15, v2) =
% 72.01/10.45 | | | | | | | v3 & get(elt, int, all_94_15, v0) = v1 & uni(v3) &
% 72.01/10.45 | | | | | | | uni(v2) & uni(v1) & uni(v0))
% 72.01/10.45 | | | | | | |
% 72.01/10.45 | | | | | | | GROUND_INST: instantiating (7) with elt, all_94_14, all_94_5,
% 72.01/10.45 | | | | | | | simplifying with (15), (48), (54), (111) gives:
% 72.01/10.46 | | | | | | | (269) ? [v0: int] : ? [v1: uni] : ? [v2: uni] :
% 72.01/10.46 | | | | | | | (permut2(elt, v1, v2, 0, v0) = 0 & elts(elt, all_94_5) =
% 72.01/10.46 | | | | | | | v2 & elts(elt, all_94_14) = v1 & length1(elt, all_94_5)
% 72.01/10.46 | | | | | | | = v0 & length1(elt, all_94_14) = v0 & uni(v2) &
% 72.01/10.46 | | | | | | | uni(v1))
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | GROUND_INST: instantiating (13) with all_94_11, all_94_1,
% 72.01/10.46 | | | | | | | all_94_20, all_94_10, simplifying with (56), (57),
% 72.01/10.46 | | | | | | | (58), (85), (177) gives:
% 72.01/10.46 | | | | | | | (270) all_94_10 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 72.01/10.46 | | | | | | | le1(all_94_11, all_94_1) = v0)
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | DELTA: instantiating (269) with fresh symbols all_251_0,
% 72.01/10.46 | | | | | | | all_251_1, all_251_2 gives:
% 72.01/10.46 | | | | | | | (271) permut2(elt, all_251_1, all_251_0, 0, all_251_2) = 0 &
% 72.01/10.46 | | | | | | | elts(elt, all_94_5) = all_251_0 & elts(elt, all_94_14) =
% 72.01/10.46 | | | | | | | all_251_1 & length1(elt, all_94_5) = all_251_2 &
% 72.01/10.46 | | | | | | | length1(elt, all_94_14) = all_251_2 & uni(all_251_0) &
% 72.01/10.46 | | | | | | | uni(all_251_1)
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | ALPHA: (271) implies:
% 72.01/10.46 | | | | | | | (272) uni(all_251_1)
% 72.01/10.46 | | | | | | | (273) elts(elt, all_94_14) = all_251_1
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | DELTA: instantiating (268) with fresh symbols all_257_0,
% 72.01/10.46 | | | | | | | all_257_1, all_257_2, all_257_3 gives:
% 72.01/10.46 | | | | | | | (274) t2tb($sum(all_94_19, -1)) = all_257_3 & t2tb(all_94_19) =
% 72.01/10.46 | | | | | | | all_257_1 & get(elt, int, all_94_6, all_257_1) =
% 72.01/10.46 | | | | | | | all_257_2 & get(elt, int, all_94_6, all_257_3) =
% 72.01/10.46 | | | | | | | all_257_0 & get(elt, int, all_94_15, all_257_1) =
% 72.01/10.46 | | | | | | | all_257_0 & get(elt, int, all_94_15, all_257_3) =
% 72.01/10.46 | | | | | | | all_257_2 & uni(all_257_0) & uni(all_257_1) &
% 72.01/10.46 | | | | | | | uni(all_257_2) & uni(all_257_3)
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | ALPHA: (274) implies:
% 72.01/10.46 | | | | | | | (275) uni(all_257_1)
% 72.01/10.46 | | | | | | | (276) get(elt, int, all_94_15, all_257_1) = all_257_0
% 72.01/10.46 | | | | | | | (277) t2tb(all_94_19) = all_257_1
% 72.01/10.46 | | | | | | | (278) t2tb($sum(all_94_19, -1)) = all_257_3
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | BETA: splitting (270) gives:
% 72.01/10.46 | | | | | | |
% 72.01/10.46 | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | (279) all_94_10 = 0
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | REDUCE: (33), (279) imply:
% 72.01/10.46 | | | | | | | | (280) $false
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | CLOSE: (280) is inconsistent.
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | Case 2:
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | (281) ? [v0: int] : ( ~ (v0 = 0) & le1(all_94_11, all_94_1)
% 72.01/10.46 | | | | | | | | = v0)
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | DELTA: instantiating (281) with fresh symbol all_264_0 gives:
% 72.01/10.46 | | | | | | | | (282) ~ (all_264_0 = 0) & le1(all_94_11, all_94_1) =
% 72.01/10.46 | | | | | | | | all_264_0
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | ALPHA: (282) implies:
% 72.01/10.46 | | | | | | | | (283) le1(all_94_11, all_94_1) = all_264_0
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | DELTA: instantiating (281) with fresh symbol all_269_0 gives:
% 72.01/10.46 | | | | | | | | (284) ~ (all_269_0 = 0) & le1(all_94_11, all_94_1) =
% 72.01/10.46 | | | | | | | | all_269_0
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | ALPHA: (284) implies:
% 72.01/10.46 | | | | | | | | (285) ~ (all_269_0 = 0)
% 72.01/10.46 | | | | | | | | (286) le1(all_94_11, all_94_1) = all_269_0
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | BETA: splitting (266) gives:
% 72.01/10.46 | | | | | | | |
% 72.01/10.46 | | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | (287) $lesseq(all_94_25, -1)
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | COMBINE_INEQS: (90), (287) imply:
% 72.01/10.46 | | | | | | | | | (288) $false
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | CLOSE: (288) is inconsistent.
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | Case 2:
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | (289) ~ ($lesseq(1, $difference(all_94_30, all_94_25))) |
% 72.01/10.46 | | | | | | | | | ? [v0: int] : ? [v1: uni] : ($lesseq(1,
% 72.01/10.46 | | | | | | | | | $difference(all_94_30, v0)) & $lesseq(0, v0) &
% 72.01/10.46 | | | | | | | | | t2tb(v0) = v1 & get(elt, int, all_94_28, v1) =
% 72.01/10.46 | | | | | | | | | all_94_21 & uni(v1) & uni(all_94_21))
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | BETA: splitting (289) gives:
% 72.01/10.46 | | | | | | | | |
% 72.01/10.46 | | | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | (290) $lesseq(all_94_30, all_94_25)
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | COMBINE_INEQS: (35), (290) imply:
% 72.01/10.46 | | | | | | | | | | (291) $false
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | CLOSE: (291) is inconsistent.
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | Case 2:
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | (292) ? [v0: int] : ? [v1: uni] : ($lesseq(1,
% 72.01/10.46 | | | | | | | | | | $difference(all_94_30, v0)) & $lesseq(0, v0) &
% 72.01/10.46 | | | | | | | | | | t2tb(v0) = v1 & get(elt, int, all_94_28, v1) =
% 72.01/10.46 | | | | | | | | | | all_94_21 & uni(v1) & uni(all_94_21))
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | DELTA: instantiating (292) with fresh symbols all_279_0,
% 72.01/10.46 | | | | | | | | | | all_279_1 gives:
% 72.01/10.46 | | | | | | | | | | (293) $lesseq(1, $difference(all_94_30, all_279_1)) &
% 72.01/10.46 | | | | | | | | | | $lesseq(0, all_279_1) & t2tb(all_279_1) = all_279_0
% 72.01/10.46 | | | | | | | | | | & get(elt, int, all_94_28, all_279_0) = all_94_21 &
% 72.01/10.46 | | | | | | | | | | uni(all_279_0) & uni(all_94_21)
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | GROUND_INST: instantiating (23) with all_94_15, all_251_1,
% 72.01/10.46 | | | | | | | | | | all_94_14, elt, simplifying with (265), (273)
% 72.01/10.46 | | | | | | | | | | gives:
% 72.01/10.46 | | | | | | | | | | (294) all_251_1 = all_94_15
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | GROUND_INST: instantiating (17) with all_94_16, all_257_1,
% 72.01/10.46 | | | | | | | | | | all_94_19, simplifying with (72), (277) gives:
% 72.01/10.46 | | | | | | | | | | (295) all_257_1 = all_94_16
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | GROUND_INST: instantiating (17) with all_94_13, all_257_3,
% 72.01/10.46 | | | | | | | | | | $sum(all_94_19, -1), simplifying with (73), (278)
% 72.01/10.46 | | | | | | | | | | gives:
% 72.01/10.46 | | | | | | | | | | (296) all_257_3 = all_94_13
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | GROUND_INST: instantiating (24) with all_264_0, all_269_0,
% 72.01/10.46 | | | | | | | | | | all_94_1, all_94_11, simplifying with (283), (286)
% 72.01/10.46 | | | | | | | | | | gives:
% 72.01/10.46 | | | | | | | | | | (297) all_269_0 = all_264_0
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | REDUCE: (285), (297) imply:
% 72.01/10.46 | | | | | | | | | | (298) ~ (all_264_0 = 0)
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | REDUCE: (276), (295) imply:
% 72.01/10.46 | | | | | | | | | | (299) get(elt, int, all_94_15, all_94_16) = all_257_0
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | BETA: splitting (92) gives:
% 72.01/10.46 | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | (300) ~ (t2tb(all_94_25) = all_94_16)
% 72.01/10.46 | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | PRED_UNIFY: (72), (300) imply:
% 72.01/10.46 | | | | | | | | | | | (301) ~ (all_94_19 = all_94_25)
% 72.01/10.46 | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | STRENGTHEN: (88), (301) imply:
% 72.01/10.46 | | | | | | | | | | | (302) $lesseq(1, $difference(all_94_25, all_94_19))
% 72.01/10.46 | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | BETA: splitting (104) gives:
% 72.01/10.46 | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | (303) $lesseq(all_94_25, all_94_19)
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | COMBINE_INEQS: (302), (303) imply:
% 72.01/10.46 | | | | | | | | | | | | (304) $false
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | CLOSE: (304) is inconsistent.
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | Case 2:
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | (305) ? [v0: uni] : ? [v1: elt1] : (le1(all_94_20, v1)
% 72.01/10.46 | | | | | | | | | | | | = 0 & tb2t4(v0) = v1 & get(elt, int, all_94_17,
% 72.01/10.46 | | | | | | | | | | | | all_94_22) = v0 & elt1(v1) & uni(v0))
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | DELTA: instantiating (305) with fresh symbols all_376_0,
% 72.01/10.46 | | | | | | | | | | | | all_376_1 gives:
% 72.01/10.46 | | | | | | | | | | | | (306) le1(all_94_20, all_376_0) = 0 & tb2t4(all_376_1) =
% 72.01/10.46 | | | | | | | | | | | | all_376_0 & get(elt, int, all_94_17, all_94_22) =
% 72.01/10.46 | | | | | | | | | | | | all_376_1 & elt1(all_376_0) & uni(all_376_1)
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | ALPHA: (306) implies:
% 72.01/10.46 | | | | | | | | | | | | (307) elt1(all_376_0)
% 72.01/10.46 | | | | | | | | | | | | (308) get(elt, int, all_94_17, all_94_22) = all_376_1
% 72.01/10.46 | | | | | | | | | | | | (309) tb2t4(all_376_1) = all_376_0
% 72.01/10.46 | | | | | | | | | | | | (310) le1(all_94_20, all_376_0) = 0
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | BETA: splitting (94) gives:
% 72.01/10.46 | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | Case 1:
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | (311) ~ (t2tb(all_94_25) = all_94_3)
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | PRED_UNIFY: (74), (311) imply:
% 72.01/10.46 | | | | | | | | | | | | | (312) ~ (all_94_4 = all_94_25)
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REF_CLOSE: (3), (12), (14), (15), (18), (20), (25), (34),
% 72.01/10.46 | | | | | | | | | | | | | (36), (37), (38), (39), (40), (44), (45), (46),
% 72.01/10.46 | | | | | | | | | | | | | (47), (50), (55), (56), (58), (62), (64), (65),
% 72.01/10.46 | | | | | | | | | | | | | (72), (73), (74), (82), (83), (84), (87), (93),
% 72.01/10.46 | | | | | | | | | | | | | (95), (106), (107), (108), (109), (110), (248),
% 72.01/10.46 | | | | | | | | | | | | | (264), (267), (283), (298), (299), (312),
% 72.01/10.46 | | | | | | | | | | | | | (select_eq), (select_neq) are inconsistent by
% 72.01/10.46 | | | | | | | | | | | | | sub-proof #1.
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | Case 2:
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | (313) all_94_3 = all_94_22
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REDUCE: (109), (313) imply:
% 72.01/10.46 | | | | | | | | | | | | | (314) tb2t(all_94_22) = all_94_4
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REDUCE: (74), (313) imply:
% 72.01/10.46 | | | | | | | | | | | | | (315) t2tb(all_94_4) = all_94_22
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REDUCE: (248), (313) imply:
% 72.01/10.46 | | | | | | | | | | | | | (316) get(elt, int, all_94_9, all_94_22) = all_94_2
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REDUCE: (110), (313) imply:
% 72.01/10.46 | | | | | | | | | | | | | (317) sort1(int, all_94_22) = 0
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | REDUCE: (55), (313) imply:
% 72.01/10.46 | | | | | | | | | | | | | (318) uni(all_94_22)
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_94_25, all_94_4,
% 72.01/10.46 | | | | | | | | | | | | | all_94_22, simplifying with (105), (314) gives:
% 72.01/10.46 | | | | | | | | | | | | | (319) all_94_4 = all_94_25
% 72.01/10.46 | | | | | | | | | | | | |
% 72.01/10.46 | | | | | | | | | | | | | COMBINE_INEQS: (36), (302) imply:
% 72.01/10.47 | | | | | | | | | | | | | (320) $lesseq(2, all_94_25)
% 72.01/10.47 | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 72.01/10.47 | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | (321) ~ (t2tb(all_94_19) = all_94_3)
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | REDUCE: (313), (321) imply:
% 72.01/10.47 | | | | | | | | | | | | | | (322) ~ (t2tb(all_94_19) = all_94_22)
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (select_neq) with int, elt,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_17, all_94_16, all_94_22, all_376_1,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_12, all_94_9, simplifying with (14), (15),
% 72.01/10.47 | | | | | | | | | | | | | | (45), (46), (50), (65), (107), (308), (318) gives:
% 72.01/10.47 | | | | | | | | | | | | | | (323) all_94_16 = all_94_22 | ? [v0: int] : ((v0 =
% 72.01/10.47 | | | | | | | | | | | | | | all_376_1 & get(elt, int, all_94_9, all_94_22)
% 72.01/10.47 | | | | | | | | | | | | | | = all_376_1 & uni(all_376_1)) | ( ~ (v0 = 0) &
% 72.01/10.47 | | | | | | | | | | | | | | sort1(int, all_94_22) = v0))
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (select_neq) with int, elt,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_17, all_94_16, all_94_22, all_376_1,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_21, all_94_15, simplifying with (14), (15),
% 72.01/10.47 | | | | | | | | | | | | | | (44), (45), (46), (64), (107), (308), (318) gives:
% 72.01/10.47 | | | | | | | | | | | | | | (324) all_94_16 = all_94_22 | ? [v0: int] : ((v0 =
% 72.01/10.47 | | | | | | | | | | | | | | all_376_1 & get(elt, int, all_94_15,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_22) = all_376_1 & uni(all_376_1)) | (
% 72.01/10.47 | | | | | | | | | | | | | | ~ (v0 = 0) & sort1(int, all_94_22) = v0))
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_94_20, all_376_0,
% 72.01/10.47 | | | | | | | | | | | | | | all_94_1, all_94_0, simplifying with (56), (58),
% 72.01/10.47 | | | | | | | | | | | | | | (84), (307), (310) gives:
% 72.01/10.47 | | | | | | | | | | | | | | (325) all_94_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 72.01/10.47 | | | | | | | | | | | | | | le1(all_376_0, all_94_1) = v0)
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | (326) all_94_0 = 0
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | REDUCE: (34), (326) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | (327) $false
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | (328) ? [v0: int] : ( ~ (v0 = 0) & le1(all_376_0,
% 72.01/10.47 | | | | | | | | | | | | | | | all_94_1) = v0)
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | DELTA: instantiating (328) with fresh symbol all_513_0
% 72.01/10.47 | | | | | | | | | | | | | | | gives:
% 72.01/10.47 | | | | | | | | | | | | | | | (329) ~ (all_513_0 = 0) & le1(all_376_0, all_94_1) =
% 72.01/10.47 | | | | | | | | | | | | | | | all_513_0
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 72.01/10.47 | | | | | | | | | | | | | | | (330) ~ (all_513_0 = 0)
% 72.01/10.47 | | | | | | | | | | | | | | | (331) le1(all_376_0, all_94_1) = all_513_0
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | (332) all_94_16 = all_94_22
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | REDUCE: (72), (332) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | (333) t2tb(all_94_19) = all_94_22
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | PRED_UNIFY: (322), (333) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | (334) $false
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | (335) ~ (all_94_16 = all_94_22)
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | (336) all_94_16 = all_94_22
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | REDUCE: (335), (336) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | (337) $false
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | (338) ? [v0: int] : ((v0 = all_376_1 & get(elt, int,
% 72.01/10.47 | | | | | | | | | | | | | | | | | all_94_9, all_94_22) = all_376_1 &
% 72.01/10.47 | | | | | | | | | | | | | | | | | uni(all_376_1)) | ( ~ (v0 = 0) & sort1(int,
% 72.01/10.47 | | | | | | | | | | | | | | | | | all_94_22) = v0))
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | DELTA: instantiating (338) with fresh symbol all_959_0
% 72.01/10.47 | | | | | | | | | | | | | | | | | gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | (339) (all_959_0 = all_376_1 & get(elt, int, all_94_9,
% 72.01/10.47 | | | | | | | | | | | | | | | | | all_94_22) = all_376_1 & uni(all_376_1)) | ( ~
% 72.01/10.47 | | | | | | | | | | | | | | | | | (all_959_0 = 0) & sort1(int, all_94_22) =
% 72.01/10.47 | | | | | | | | | | | | | | | | | all_959_0)
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (340) all_959_0 = all_376_1 & get(elt, int, all_94_9,
% 72.01/10.47 | | | | | | | | | | | | | | | | | | all_94_22) = all_376_1 & uni(all_376_1)
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | ALPHA: (340) implies:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (341) get(elt, int, all_94_9, all_94_22) = all_376_1
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_94_2, all_376_1,
% 72.01/10.47 | | | | | | | | | | | | | | | | | | all_94_22, all_94_9, int, elt, simplifying with
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (316), (341) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (342) all_376_1 = all_94_2
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | REDUCE: (309), (342) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (343) tb2t4(all_94_2) = all_376_0
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | REDUCE: (308), (342) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (344) get(elt, int, all_94_17, all_94_22) = all_94_2
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (87) with all_94_25, all_94_25,
% 72.01/10.47 | | | | | | | | | | | | | | | | | | all_94_22, all_94_2, all_376_0, all_94_22,
% 72.01/10.47 | | | | | | | | | | | | | | | | | | all_94_2, all_94_1, all_513_0, simplifying with
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (71), (83), (331), (343), (344) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (345) all_513_0 = 0 | all_94_19 = all_94_25 | ~
% 72.01/10.47 | | | | | | | | | | | | | | | | | | ($lesseq(0, all_94_25))
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | (346) $lesseq(all_94_25, -1)
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (320), (346) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | (347) $false
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | (348) all_513_0 = 0 | all_94_19 = all_94_25
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | (349) all_513_0 = 0
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (349) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | (350) $false
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | (351) all_94_19 = all_94_25
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (351) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | (352) $false
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (353) ~ (all_959_0 = 0) & sort1(int, all_94_22) =
% 72.01/10.47 | | | | | | | | | | | | | | | | | | all_959_0
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (354) ~ (all_959_0 = 0)
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (355) sort1(int, all_94_22) = all_959_0
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_959_0, all_94_22,
% 72.01/10.47 | | | | | | | | | | | | | | | | | | int, simplifying with (317), (355) gives:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (356) all_959_0 = 0
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | REDUCE: (354), (356) imply:
% 72.01/10.47 | | | | | | | | | | | | | | | | | | (357) $false
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | (358) all_94_3 = all_94_16
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | COMBINE_EQS: (313), (358) imply:
% 72.01/10.47 | | | | | | | | | | | | | | (359) all_94_16 = all_94_22
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | REDUCE: (300), (359) imply:
% 72.01/10.47 | | | | | | | | | | | | | | (360) ~ (t2tb(all_94_25) = all_94_22)
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | PRED_UNIFY: (71), (360) imply:
% 72.01/10.47 | | | | | | | | | | | | | | (361) $false
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 72.01/10.47 | | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | End of split
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | Case 2:
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | (362) all_94_16 = all_94_22
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | REDUCE: (106), (362) imply:
% 72.01/10.47 | | | | | | | | | | | (363) tb2t(all_94_22) = all_94_19
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | REDUCE: (65), (362) imply:
% 72.01/10.47 | | | | | | | | | | | (364) set(elt, int, all_94_17, all_94_22, all_94_12) =
% 72.01/10.47 | | | | | | | | | | | all_94_9
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_94_25, all_94_19,
% 72.01/10.47 | | | | | | | | | | | all_94_22, simplifying with (105), (363) gives:
% 72.01/10.47 | | | | | | | | | | | (365) all_94_19 = all_94_25
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | REDUCE: (38), (365) imply:
% 72.01/10.47 | | | | | | | | | | | (366) $lesseq(all_94_25, all_94_4)
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | REDUCE: (73), (365) imply:
% 72.01/10.47 | | | | | | | | | | | (367) t2tb($sum(all_94_25, -1)) = all_94_13
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | BETA: splitting (94) gives:
% 72.01/10.47 | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | Case 1:
% 72.01/10.47 | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | (368) ~ (t2tb(all_94_25) = all_94_3)
% 72.01/10.47 | | | | | | | | | | | |
% 72.01/10.47 | | | | | | | | | | | | PRED_UNIFY: (74), (368) imply:
% 72.01/10.47 | | | | | | | | | | | | (369) ~ (all_94_4 = all_94_25)
% 72.01/10.47 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | REF_CLOSE: (3), (12), (14), (15), (18), (20), (25), (34),
% 72.01/10.48 | | | | | | | | | | | | (36), (37), (38), (39), (40), (44), (45), (46),
% 72.01/10.48 | | | | | | | | | | | | (47), (50), (55), (56), (58), (62), (64), (65),
% 72.01/10.48 | | | | | | | | | | | | (72), (73), (74), (82), (83), (84), (87), (93),
% 72.01/10.48 | | | | | | | | | | | | (95), (106), (107), (108), (109), (110), (248),
% 72.01/10.48 | | | | | | | | | | | | (264), (267), (283), (298), (299), (369),
% 72.01/10.48 | | | | | | | | | | | | (select_eq), (select_neq) are inconsistent by
% 72.01/10.48 | | | | | | | | | | | | sub-proof #1.
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | Case 2:
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | (370) all_94_3 = all_94_22
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | REDUCE: (248), (370) imply:
% 72.01/10.48 | | | | | | | | | | | | (371) get(elt, int, all_94_9, all_94_22) = all_94_2
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | REDUCE: (55), (370) imply:
% 72.01/10.48 | | | | | | | | | | | | (372) uni(all_94_22)
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | GROUND_INST: instantiating (select_eq) with int, elt,
% 72.01/10.48 | | | | | | | | | | | | all_94_17, all_94_22, all_94_12, all_94_9,
% 72.01/10.48 | | | | | | | | | | | | all_94_2, simplifying with (14), (15), (45), (50),
% 72.01/10.48 | | | | | | | | | | | | (364), (371), (372) gives:
% 72.01/10.48 | | | | | | | | | | | | (373) all_94_2 = all_94_12 | ? [v0: int] : ( ~ (v0 = 0)
% 72.01/10.48 | | | | | | | | | | | | & sort1(elt, all_94_12) = v0)
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | BETA: splitting (373) gives:
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | Case 1:
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | (374) all_94_2 = all_94_12
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | REDUCE: (83), (374) imply:
% 72.01/10.48 | | | | | | | | | | | | | (375) tb2t4(all_94_12) = all_94_1
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | GROUND_INST: instantiating (87) with $sum(all_94_25, -1),
% 72.01/10.48 | | | | | | | | | | | | | $sum(all_94_25, -1), all_94_13, all_94_12,
% 72.01/10.48 | | | | | | | | | | | | | all_94_11, all_94_13, all_94_12, all_94_1,
% 72.01/10.48 | | | | | | | | | | | | | all_264_0, simplifying with (62), (82), (283),
% 72.01/10.48 | | | | | | | | | | | | | (367), (375) gives:
% 72.01/10.48 | | | | | | | | | | | | | (376) all_264_0 = 0 | $difference(all_94_19, all_94_25)
% 72.01/10.48 | | | | | | | | | | | | | = -1 | ~ ($lesseq(1, all_94_25))
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | BETA: splitting (376) gives:
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | Case 1:
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | (377) $lesseq(all_94_25, 0)
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | COMBINE_INEQS: (90), (377) imply:
% 72.01/10.48 | | | | | | | | | | | | | | (378) $false
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | CLOSE: (378) is inconsistent.
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | Case 2:
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | (379) all_264_0 = 0 | $difference(all_94_19, all_94_25)
% 72.01/10.48 | | | | | | | | | | | | | | = -1
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | Case 1:
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | (380) all_264_0 = 0
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | REDUCE: (298), (380) imply:
% 72.01/10.48 | | | | | | | | | | | | | | | (381) $false
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | CLOSE: (381) is inconsistent.
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | Case 2:
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | (382) $difference(all_94_19, all_94_25) = -1
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | COMBINE_EQS: (365), (382) imply:
% 72.01/10.48 | | | | | | | | | | | | | | | (383) $false
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent.
% 72.01/10.48 | | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | Case 2:
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | (384) ? [v0: int] : ( ~ (v0 = 0) & sort1(elt,
% 72.01/10.48 | | | | | | | | | | | | | all_94_12) = v0)
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | DELTA: instantiating (384) with fresh symbol all_470_0
% 72.01/10.48 | | | | | | | | | | | | | gives:
% 72.01/10.48 | | | | | | | | | | | | | (385) ~ (all_470_0 = 0) & sort1(elt, all_94_12) =
% 72.01/10.48 | | | | | | | | | | | | | all_470_0
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | ALPHA: (385) implies:
% 72.01/10.48 | | | | | | | | | | | | | (386) ~ (all_470_0 = 0)
% 72.01/10.48 | | | | | | | | | | | | | (387) sort1(elt, all_94_12) = all_470_0
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_470_0, all_94_12,
% 72.01/10.48 | | | | | | | | | | | | | elt, simplifying with (95), (387) gives:
% 72.01/10.48 | | | | | | | | | | | | | (388) all_470_0 = 0
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | REDUCE: (386), (388) imply:
% 72.01/10.48 | | | | | | | | | | | | | (389) $false
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | | CLOSE: (389) is inconsistent.
% 72.01/10.48 | | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | | |
% 72.01/10.48 | | | | | | | | | End of split
% 72.01/10.48 | | | | | | | | |
% 72.01/10.48 | | | | | | | | End of split
% 72.01/10.48 | | | | | | | |
% 72.01/10.48 | | | | | | | End of split
% 72.01/10.48 | | | | | | |
% 72.01/10.48 | | | | | | End of split
% 72.01/10.48 | | | | | |
% 72.01/10.48 | | | | | End of split
% 72.01/10.48 | | | | |
% 72.01/10.48 | | | | End of split
% 72.01/10.48 | | | |
% 72.01/10.48 | | | End of split
% 72.01/10.48 | | |
% 72.01/10.48 | | End of split
% 72.01/10.48 | |
% 72.01/10.48 | Case 2:
% 72.01/10.48 | |
% 72.01/10.48 | | (390) all_94_0 = 0
% 72.01/10.48 | |
% 72.01/10.48 | | REDUCE: (34), (390) imply:
% 72.01/10.48 | | (391) $false
% 72.01/10.48 | |
% 72.01/10.48 | | CLOSE: (391) is inconsistent.
% 72.01/10.48 | |
% 72.01/10.48 | End of split
% 72.01/10.48 |
% 72.01/10.48 End of proof
% 72.01/10.48
% 72.01/10.48 Sub-proof #1 shows that the following formulas are inconsistent:
% 72.01/10.48 ----------------------------------------------------------------
% 72.01/10.48 (1) tb2t4(all_94_2) = all_94_1
% 72.01/10.48 (2) ! [v0: elt1] : ! [v1: elt1] : ! [v2: elt1] : ! [v3: int] : (v3 = 0 |
% 72.01/10.48 ~ (le1(v0, v2) = v3) | ~ (le1(v0, v1) = 0) | ~ elt1(v2) | ~ elt1(v1)
% 72.01/10.48 | ~ elt1(v0) | ? [v4: int] : ( ~ (v4 = 0) & le1(v1, v2) = v4))
% 72.01/10.48 (3) ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] :
% 72.01/10.48 ! [v5: uni] : ! [v6: uni] : (v6 = v4 | ~ (set(v1, v0, v2, v3, v4) = v5)
% 72.01/10.48 | ~ (get(v1, v0, v5, v3) = v6) | ~ ty(v1) | ~ ty(v0) | ~ uni(v4) |
% 72.01/10.48 ~ uni(v3) | ~ uni(v2) | ? [v7: int] : ( ~ (v7 = 0) & sort1(v1, v4) =
% 72.01/10.48 v7))
% 72.01/10.48 (4) $lesseq(all_94_4, all_94_25)
% 72.01/10.48 (5) tb2t(all_94_3) = all_94_4
% 72.01/10.48 (6) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] :
% 72.01/10.48 ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4,
% 72.01/10.48 v3, v2) = v0))
% 72.01/10.48 (7) uni(all_94_17)
% 72.01/10.48 (8) ! [v0: int] : ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) =
% 72.01/10.48 v1) | ~ (tb2t(v2) = v0))
% 72.01/10.48 (9) elt1(all_94_1)
% 72.01/10.48 (10) ty(elt)
% 72.01/10.48 (11) ty(int)
% 72.01/10.48 (12) get(elt, int, all_94_17, all_94_13) = all_94_12
% 72.01/10.48 (13) sort1(elt, all_94_12) = 0
% 72.01/10.48 (14) $lesseq(all_94_19, all_94_4)
% 72.01/10.48 (15) t2tb($sum(all_94_19, -1)) = all_94_13
% 72.01/10.48 (16) ~ (all_264_0 = 0)
% 72.01/10.48 (17) $difference(all_94_4, all_94_19) = -1 | all_94_4 = all_94_19 | ~
% 72.01/10.48 ($lesseq(1, $difference(all_94_30, all_94_4))) | ~ ($lesseq(0,
% 72.01/10.48 all_94_4)) | ? [v0: uni] : (get(elt, int, all_94_6, all_94_3) = v0
% 72.01/10.48 & get(elt, int, all_94_15, all_94_3) = v0 & uni(v0))
% 72.01/10.48 (18) uni(all_94_21)
% 72.01/10.48 (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] :
% 72.01/10.48 ! [v3: ty] : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) =
% 72.01/10.48 v0))
% 72.01/10.48 (20) uni(all_94_12)
% 72.01/10.48 (21) t2tb(all_94_4) = all_94_3
% 72.01/10.49 (22) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4: int]
% 72.01/10.49 : ! [v5: int] : ! [v6: uni] : ! [v7: uni] : ( ~ ($lesseq(1,
% 72.01/10.49 $difference(v4, v5))) | ~ ($lesseq(v3, v5)) | ~ (permut2(v0, v1,
% 72.01/10.49 v2, v3, v4) = 0) | ~ (t2tb(v5) = v6) | ~ (get(v0, int, v2, v6) =
% 72.01/10.49 v7) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v8: int] : ? [v9:
% 72.01/10.49 uni] : ($lesseq(1, $difference(v4, v8)) & $lesseq(v3, v8) & t2tb(v8)
% 72.01/10.49 = v9 & get(v0, int, v1, v9) = v7 & uni(v9) & uni(v7)))
% 72.01/10.49 (23) sort1(int, all_94_16) = 0
% 72.01/10.49 (24) set(elt, int, all_94_17, all_94_16, all_94_21) = all_94_15
% 72.01/10.49 (25) ~ (all_94_4 = all_94_25)
% 72.01/10.49 (26) uni(all_94_28)
% 72.01/10.49 (27) ! [v0: ty] : ! [v1: ty] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] :
% 72.01/10.49 ! [v5: uni] : ! [v6: uni] : ! [v7: uni] : (v4 = v3 | ~ (set(v1, v0,
% 72.01/10.49 v2, v3, v6) = v7) | ~ (get(v1, v0, v2, v4) = v5) | ~ (sort1(v0,
% 72.01/10.49 v3) = 0) | ~ ty(v1) | ~ ty(v0) | ~ uni(v6) | ~ uni(v4) | ~
% 72.01/10.49 uni(v3) | ~ uni(v2) | ? [v8: any] : ((v8 = v5 & get(v1, v0, v7, v4)
% 72.01/10.49 = v5 & uni(v5)) | ( ~ (v8 = 0) & sort1(v0, v4) = v8)))
% 72.01/10.49 (28) $lesseq(1, all_94_19)
% 72.01/10.49 (29) le1(all_94_20, all_94_1) = all_94_0
% 72.01/10.49 (30) t2tb(all_94_19) = all_94_16
% 72.01/10.49 (31) permut2(elt, all_94_28, all_94_15, 0, all_94_30) = 0
% 72.01/10.49 (32) ~ ($lesseq(all_94_4, all_94_25)) | ~ ($lesseq(1, $difference(all_94_4,
% 72.01/10.49 all_94_19))) | ? [v0: uni] : ? [v1: elt1] : (le1(all_94_20, v1)
% 72.01/10.49 = 0 & tb2t4(v0) = v1 & get(elt, int, all_94_17, all_94_3) = v0 &
% 72.01/10.49 elt1(v1) & uni(v0))
% 72.01/10.49 (33) uni(all_94_16)
% 72.01/10.49 (34) ~ (all_94_0 = 0)
% 72.01/10.49 (35) elt1(all_94_20)
% 72.01/10.49 (36) uni(all_94_3)
% 72.01/10.49 (37) sort1(int, all_94_3) = 0
% 72.01/10.49 (38) all_94_3 = all_94_16 | ~ (t2tb(all_94_19) = all_94_3)
% 72.01/10.49 (39) get(elt, int, all_94_15, all_94_16) = all_257_0
% 72.01/10.49 (40) get(elt, int, all_94_9, all_94_3) = all_94_2
% 72.01/10.49 (41) tb2t(all_94_16) = all_94_19
% 72.01/10.49 (42) set(elt, int, all_94_17, all_94_16, all_94_12) = all_94_9
% 72.01/10.49 (43) ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 72.01/10.49 elt1] : ! [v5: uni] : ! [v6: uni] : ! [v7: elt1] : ! [v8: int] :
% 72.01/10.49 (v8 = 0 | v1 = all_94_19 | v0 = all_94_19 | ~ ($lesseq(v1, all_94_25))
% 72.01/10.49 | ~ ($lesseq(v0, v1)) | ~ ($lesseq(0, v0)) | ~ (le1(v4, v7) = v8) |
% 72.01/10.49 ~ (tb2t4(v6) = v7) | ~ (tb2t4(v3) = v4) | ~ (t2tb(v1) = v5) | ~
% 72.01/10.49 (t2tb(v0) = v2) | ~ (get(elt, int, all_94_17, v5) = v6) | ~
% 72.01/10.49 (get(elt, int, all_94_17, v2) = v3))
% 72.01/10.49 (44) le1(all_94_11, all_94_1) = all_264_0
% 72.01/10.49 (45) uni(all_94_15)
% 72.01/10.49 (46) tb2t4(all_94_12) = all_94_11
% 72.01/10.49 (47) $lesseq(1, $difference(all_94_30, all_94_19))
% 72.01/10.49
% 72.01/10.49 Begin of proof
% 72.01/10.49 |
% 72.01/10.49 | STRENGTHEN: (4), (25) imply:
% 72.01/10.49 | (48) $lesseq(1, $difference(all_94_25, all_94_4))
% 72.01/10.49 |
% 72.01/10.49 | BETA: splitting (38) gives:
% 72.01/10.49 |
% 72.01/10.49 | Case 1:
% 72.01/10.49 | |
% 72.01/10.49 | | (49) ~ (t2tb(all_94_19) = all_94_3)
% 72.01/10.49 | |
% 72.01/10.49 | | PRED_UNIFY: (21), (49) imply:
% 72.01/10.49 | | (50) ~ (all_94_4 = all_94_19)
% 72.01/10.49 | |
% 72.01/10.49 | | STRENGTHEN: (14), (50) imply:
% 72.01/10.49 | | (51) $lesseq(1, $difference(all_94_4, all_94_19))
% 72.01/10.49 | |
% 72.01/10.49 | | BETA: splitting (32) gives:
% 72.01/10.49 | |
% 72.01/10.49 | | Case 1:
% 72.01/10.49 | | |
% 72.01/10.49 | | | (52) $lesseq(1, $difference(all_94_4, all_94_25))
% 72.01/10.49 | | |
% 72.01/10.49 | | | COMBINE_INEQS: (48), (52) imply:
% 72.01/10.49 | | | (53) $false
% 72.01/10.49 | | |
% 72.01/10.49 | | | CLOSE: (53) is inconsistent.
% 72.01/10.49 | | |
% 72.01/10.49 | | Case 2:
% 72.01/10.49 | | |
% 72.01/10.49 | | | (54) ~ ($lesseq(1, $difference(all_94_4, all_94_19))) | ? [v0: uni] :
% 72.01/10.49 | | | ? [v1: elt1] : (le1(all_94_20, v1) = 0 & tb2t4(v0) = v1 &
% 72.01/10.49 | | | get(elt, int, all_94_17, all_94_3) = v0 & elt1(v1) & uni(v0))
% 72.01/10.49 | | |
% 72.01/10.49 | | | BETA: splitting (54) gives:
% 72.01/10.49 | | |
% 72.01/10.49 | | | Case 1:
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | (55) $lesseq(all_94_4, all_94_19)
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | COMBINE_INEQS: (51), (55) imply:
% 72.01/10.49 | | | | (56) $false
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | CLOSE: (56) is inconsistent.
% 72.01/10.49 | | | |
% 72.01/10.49 | | | Case 2:
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | (57) ? [v0: uni] : ? [v1: elt1] : (le1(all_94_20, v1) = 0 &
% 72.01/10.49 | | | | tb2t4(v0) = v1 & get(elt, int, all_94_17, all_94_3) = v0 &
% 72.01/10.49 | | | | elt1(v1) & uni(v0))
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | DELTA: instantiating (57) with fresh symbols all_432_0, all_432_1 gives:
% 72.01/10.49 | | | | (58) le1(all_94_20, all_432_0) = 0 & tb2t4(all_432_1) = all_432_0 &
% 72.01/10.49 | | | | get(elt, int, all_94_17, all_94_3) = all_432_1 & elt1(all_432_0)
% 72.01/10.49 | | | | & uni(all_432_1)
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | ALPHA: (58) implies:
% 72.01/10.49 | | | | (59) elt1(all_432_0)
% 72.01/10.49 | | | | (60) get(elt, int, all_94_17, all_94_3) = all_432_1
% 72.01/10.49 | | | | (61) tb2t4(all_432_1) = all_432_0
% 72.01/10.49 | | | | (62) le1(all_94_20, all_432_0) = 0
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | GROUND_INST: instantiating (27) with int, elt, all_94_17, all_94_16,
% 72.01/10.49 | | | | all_94_3, all_432_1, all_94_12, all_94_9, simplifying with
% 72.01/10.49 | | | | (7), (10), (11), (20), (23), (33), (36), (42), (60) gives:
% 72.01/10.49 | | | | (63) all_94_3 = all_94_16 | ? [v0: int] : ((v0 = all_432_1 &
% 72.01/10.49 | | | | get(elt, int, all_94_9, all_94_3) = all_432_1 &
% 72.01/10.49 | | | | uni(all_432_1)) | ( ~ (v0 = 0) & sort1(int, all_94_3) = v0))
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | GROUND_INST: instantiating (27) with int, elt, all_94_17, all_94_16,
% 72.01/10.49 | | | | all_94_3, all_432_1, all_94_21, all_94_15, simplifying with
% 72.01/10.49 | | | | (7), (10), (11), (18), (23), (24), (33), (36), (60) gives:
% 72.01/10.49 | | | | (64) all_94_3 = all_94_16 | ? [v0: int] : ((v0 = all_432_1 &
% 72.01/10.49 | | | | get(elt, int, all_94_15, all_94_3) = all_432_1 &
% 72.01/10.49 | | | | uni(all_432_1)) | ( ~ (v0 = 0) & sort1(int, all_94_3) = v0))
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | GROUND_INST: instantiating (2) with all_94_20, all_432_0, all_94_1,
% 72.01/10.49 | | | | all_94_0, simplifying with (9), (29), (35), (59), (62)
% 72.01/10.49 | | | | gives:
% 72.01/10.49 | | | | (65) all_94_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & le1(all_432_0,
% 72.01/10.49 | | | | all_94_1) = v0)
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | BETA: splitting (65) gives:
% 72.01/10.49 | | | |
% 72.01/10.49 | | | | Case 1:
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | (66) all_94_0 = 0
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | REDUCE: (34), (66) imply:
% 72.01/10.49 | | | | | (67) $false
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | CLOSE: (67) is inconsistent.
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | Case 2:
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & le1(all_432_0, all_94_1) = v0)
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | DELTA: instantiating (68) with fresh symbol all_550_0 gives:
% 72.01/10.49 | | | | | (69) ~ (all_550_0 = 0) & le1(all_432_0, all_94_1) = all_550_0
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | ALPHA: (69) implies:
% 72.01/10.49 | | | | | (70) ~ (all_550_0 = 0)
% 72.01/10.49 | | | | | (71) le1(all_432_0, all_94_1) = all_550_0
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | BETA: splitting (17) gives:
% 72.01/10.49 | | | | |
% 72.01/10.49 | | | | | Case 1:
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | (72) $lesseq(all_94_4, -1)
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | COMBINE_INEQS: (51), (72) imply:
% 72.01/10.49 | | | | | | (73) $lesseq(all_94_19, -2)
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | COMBINE_INEQS: (28), (73) imply:
% 72.01/10.49 | | | | | | (74) $false
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | CLOSE: (74) is inconsistent.
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | Case 2:
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | (75) $lesseq(0, all_94_4)
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | BETA: splitting (64) gives:
% 72.01/10.49 | | | | | |
% 72.01/10.49 | | | | | | Case 1:
% 72.01/10.49 | | | | | | |
% 72.01/10.49 | | | | | | | (76) all_94_3 = all_94_16
% 72.01/10.49 | | | | | | |
% 72.01/10.49 | | | | | | | REDUCE: (49), (76) imply:
% 72.01/10.49 | | | | | | | (77) ~ (t2tb(all_94_19) = all_94_16)
% 72.01/10.49 | | | | | | |
% 72.01/10.49 | | | | | | | PRED_UNIFY: (30), (77) imply:
% 72.01/10.49 | | | | | | | (78) $false
% 72.01/10.49 | | | | | | |
% 72.01/10.49 | | | | | | | CLOSE: (78) is inconsistent.
% 72.01/10.49 | | | | | | |
% 72.01/10.49 | | | | | | Case 2:
% 72.01/10.49 | | | | | | |
% 72.01/10.50 | | | | | | | (79) ~ (all_94_3 = all_94_16)
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | BETA: splitting (63) gives:
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | Case 1:
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | (80) all_94_3 = all_94_16
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | REDUCE: (79), (80) imply:
% 72.01/10.50 | | | | | | | | (81) $false
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | CLOSE: (81) is inconsistent.
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | Case 2:
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | (82) ? [v0: int] : ((v0 = all_432_1 & get(elt, int,
% 72.01/10.50 | | | | | | | | all_94_9, all_94_3) = all_432_1 & uni(all_432_1))
% 72.01/10.50 | | | | | | | | | ( ~ (v0 = 0) & sort1(int, all_94_3) = v0))
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | DELTA: instantiating (82) with fresh symbol all_1032_0 gives:
% 72.01/10.50 | | | | | | | | (83) (all_1032_0 = all_432_1 & get(elt, int, all_94_9,
% 72.01/10.50 | | | | | | | | all_94_3) = all_432_1 & uni(all_432_1)) | ( ~
% 72.01/10.50 | | | | | | | | (all_1032_0 = 0) & sort1(int, all_94_3) = all_1032_0)
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | BETA: splitting (83) gives:
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | | Case 1:
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | (84) all_1032_0 = all_432_1 & get(elt, int, all_94_9,
% 72.01/10.50 | | | | | | | | | all_94_3) = all_432_1 & uni(all_432_1)
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | ALPHA: (84) implies:
% 72.01/10.50 | | | | | | | | | (85) get(elt, int, all_94_9, all_94_3) = all_432_1
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | GROUND_INST: instantiating (6) with all_94_2, all_432_1,
% 72.01/10.50 | | | | | | | | | all_94_3, all_94_9, int, elt, simplifying with
% 72.01/10.50 | | | | | | | | | (40), (85) gives:
% 72.01/10.50 | | | | | | | | | (86) all_432_1 = all_94_2
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | REDUCE: (61), (86) imply:
% 72.01/10.50 | | | | | | | | | (87) tb2t4(all_94_2) = all_432_0
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | REDUCE: (60), (86) imply:
% 72.01/10.50 | | | | | | | | | (88) get(elt, int, all_94_17, all_94_3) = all_94_2
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | GROUND_INST: instantiating (43) with all_94_4, all_94_4,
% 72.01/10.50 | | | | | | | | | all_94_3, all_94_2, all_432_0, all_94_3, all_94_2,
% 72.01/10.50 | | | | | | | | | all_94_1, all_550_0, simplifying with (1), (21),
% 72.01/10.50 | | | | | | | | | (71), (87), (88) gives:
% 72.01/10.50 | | | | | | | | | (89) all_550_0 = 0 | all_94_4 = all_94_19 | ~
% 72.01/10.50 | | | | | | | | | ($lesseq(all_94_4, all_94_25)) | ~ ($lesseq(0,
% 72.01/10.50 | | | | | | | | | all_94_4))
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | BETA: splitting (89) gives:
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | Case 1:
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | (90) $lesseq(all_94_4, -1)
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | COMBINE_INEQS: (75), (90) imply:
% 72.01/10.50 | | | | | | | | | | (91) $false
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | CLOSE: (91) is inconsistent.
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | Case 2:
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | (92) all_550_0 = 0 | all_94_4 = all_94_19 | ~
% 72.01/10.50 | | | | | | | | | | ($lesseq(all_94_4, all_94_25))
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | BETA: splitting (92) gives:
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | Case 1:
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | (93) $lesseq(1, $difference(all_94_4, all_94_25))
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | COMBINE_INEQS: (48), (93) imply:
% 72.01/10.50 | | | | | | | | | | | (94) $false
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | CLOSE: (94) is inconsistent.
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | Case 2:
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | (95) all_550_0 = 0 | all_94_4 = all_94_19
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | BETA: splitting (95) gives:
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | Case 1:
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | (96) all_550_0 = 0
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | REDUCE: (70), (96) imply:
% 72.01/10.50 | | | | | | | | | | | | (97) $false
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | CLOSE: (97) is inconsistent.
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | Case 2:
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | (98) all_94_4 = all_94_19
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | REDUCE: (51), (98) imply:
% 72.01/10.50 | | | | | | | | | | | | (99) $false
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 72.01/10.50 | | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | | End of split
% 72.01/10.50 | | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | | End of split
% 72.01/10.50 | | | | | | | | | |
% 72.01/10.50 | | | | | | | | | End of split
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | Case 2:
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | (100) ~ (all_1032_0 = 0) & sort1(int, all_94_3) =
% 72.01/10.50 | | | | | | | | | all_1032_0
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | ALPHA: (100) implies:
% 72.01/10.50 | | | | | | | | | (101) ~ (all_1032_0 = 0)
% 72.01/10.50 | | | | | | | | | (102) sort1(int, all_94_3) = all_1032_0
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1032_0, all_94_3,
% 72.01/10.50 | | | | | | | | | int, simplifying with (37), (102) gives:
% 72.01/10.50 | | | | | | | | | (103) all_1032_0 = 0
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | REDUCE: (101), (103) imply:
% 72.01/10.50 | | | | | | | | | (104) $false
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | | CLOSE: (104) is inconsistent.
% 72.01/10.50 | | | | | | | | |
% 72.01/10.50 | | | | | | | | End of split
% 72.01/10.50 | | | | | | | |
% 72.01/10.50 | | | | | | | End of split
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | End of split
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | End of split
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | End of split
% 72.01/10.50 | | | |
% 72.01/10.50 | | | End of split
% 72.01/10.50 | | |
% 72.01/10.50 | | End of split
% 72.01/10.50 | |
% 72.01/10.50 | Case 2:
% 72.01/10.50 | |
% 72.01/10.50 | | (105) all_94_3 = all_94_16
% 72.01/10.50 | |
% 72.01/10.50 | | REDUCE: (5), (105) imply:
% 72.01/10.50 | | (106) tb2t(all_94_16) = all_94_4
% 72.01/10.50 | |
% 72.01/10.50 | | REDUCE: (21), (105) imply:
% 72.01/10.50 | | (107) t2tb(all_94_4) = all_94_16
% 72.01/10.50 | |
% 72.01/10.50 | | REDUCE: (40), (105) imply:
% 72.01/10.50 | | (108) get(elt, int, all_94_9, all_94_16) = all_94_2
% 72.01/10.50 | |
% 72.01/10.50 | | GROUND_INST: instantiating (8) with all_94_19, all_94_4, all_94_16,
% 72.01/10.50 | | simplifying with (41), (106) gives:
% 72.01/10.50 | | (109) all_94_4 = all_94_19
% 72.01/10.50 | |
% 72.01/10.50 | | REDUCE: (48), (109) imply:
% 72.01/10.50 | | (110) $lesseq(1, $difference(all_94_25, all_94_19))
% 72.01/10.50 | |
% 72.01/10.50 | | GROUND_INST: instantiating (22) with elt, all_94_28, all_94_15, 0,
% 72.01/10.50 | | all_94_30, all_94_19, all_94_16, all_257_0, simplifying with
% 72.01/10.50 | | (10), (26), (30), (31), (39), (45) gives:
% 72.01/10.50 | | (111) ~ ($lesseq(1, $difference(all_94_30, all_94_19))) | ~ ($lesseq(0,
% 72.01/10.50 | | all_94_19)) | ? [v0: int] : ? [v1: uni] : ($lesseq(1,
% 72.01/10.50 | | $difference(all_94_30, v0)) & $lesseq(0, v0) & t2tb(v0) = v1 &
% 72.01/10.50 | | get(elt, int, all_94_28, v1) = all_257_0 & uni(v1) &
% 72.01/10.50 | | uni(all_257_0))
% 72.01/10.50 | |
% 72.01/10.50 | | GROUND_INST: instantiating (3) with int, elt, all_94_17, all_94_16,
% 72.01/10.50 | | all_94_12, all_94_9, all_94_2, simplifying with (7), (10),
% 72.01/10.50 | | (11), (20), (33), (42), (108) gives:
% 72.01/10.50 | | (112) all_94_2 = all_94_12 | ? [v0: int] : ( ~ (v0 = 0) & sort1(elt,
% 72.01/10.50 | | all_94_12) = v0)
% 72.01/10.50 | |
% 72.01/10.50 | | BETA: splitting (112) gives:
% 72.01/10.50 | |
% 72.01/10.50 | | Case 1:
% 72.01/10.50 | | |
% 72.01/10.50 | | | (113) all_94_2 = all_94_12
% 72.01/10.50 | | |
% 72.01/10.50 | | | REDUCE: (1), (113) imply:
% 72.01/10.50 | | | (114) tb2t4(all_94_12) = all_94_1
% 72.01/10.50 | | |
% 72.01/10.50 | | | BETA: splitting (111) gives:
% 72.01/10.50 | | |
% 72.01/10.50 | | | Case 1:
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | (115) $lesseq(all_94_19, -1)
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | COMBINE_INEQS: (28), (115) imply:
% 72.01/10.50 | | | | (116) $false
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | CLOSE: (116) is inconsistent.
% 72.01/10.50 | | | |
% 72.01/10.50 | | | Case 2:
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | (117) ~ ($lesseq(1, $difference(all_94_30, all_94_19))) | ? [v0:
% 72.01/10.50 | | | | int] : ? [v1: uni] : ($lesseq(1, $difference(all_94_30, v0))
% 72.01/10.50 | | | | & $lesseq(0, v0) & t2tb(v0) = v1 & get(elt, int, all_94_28,
% 72.01/10.50 | | | | v1) = all_257_0 & uni(v1) & uni(all_257_0))
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | BETA: splitting (117) gives:
% 72.01/10.50 | | | |
% 72.01/10.50 | | | | Case 1:
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | (118) $lesseq(all_94_30, all_94_19)
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | COMBINE_INEQS: (47), (118) imply:
% 72.01/10.50 | | | | | (119) $false
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | CLOSE: (119) is inconsistent.
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | Case 2:
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | GROUND_INST: instantiating (43) with $sum(all_94_19, -1),
% 72.01/10.50 | | | | | $sum(all_94_19, -1), all_94_13, all_94_12, all_94_11,
% 72.01/10.50 | | | | | all_94_13, all_94_12, all_94_1, all_264_0, simplifying
% 72.01/10.50 | | | | | with (12), (15), (44), (46), (114) gives:
% 72.01/10.50 | | | | | (120) all_264_0 = 0 | ~ ($lesseq(-1, $difference(all_94_25,
% 72.01/10.50 | | | | | all_94_19))) | ~ ($lesseq(1, all_94_19))
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | BETA: splitting (120) gives:
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | | Case 1:
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | (121) $lesseq(all_94_19, 0)
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | COMBINE_INEQS: (28), (121) imply:
% 72.01/10.50 | | | | | | (122) $false
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | CLOSE: (122) is inconsistent.
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | Case 2:
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | (123) all_264_0 = 0 | ~ ($lesseq(-1, $difference(all_94_25,
% 72.01/10.50 | | | | | | all_94_19)))
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | BETA: splitting (123) gives:
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | | Case 1:
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | (124) $lesseq(2, $difference(all_94_19, all_94_25))
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | COMBINE_INEQS: (110), (124) imply:
% 72.01/10.50 | | | | | | | (125) $false
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | CLOSE: (125) is inconsistent.
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | Case 2:
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | (126) all_264_0 = 0
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | REDUCE: (16), (126) imply:
% 72.01/10.50 | | | | | | | (127) $false
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | | CLOSE: (127) is inconsistent.
% 72.01/10.50 | | | | | | |
% 72.01/10.50 | | | | | | End of split
% 72.01/10.50 | | | | | |
% 72.01/10.50 | | | | | End of split
% 72.01/10.50 | | | | |
% 72.01/10.50 | | | | End of split
% 72.01/10.50 | | | |
% 72.01/10.50 | | | End of split
% 72.01/10.50 | | |
% 72.01/10.50 | | Case 2:
% 72.01/10.50 | | |
% 72.01/10.50 | | | (128) ? [v0: int] : ( ~ (v0 = 0) & sort1(elt, all_94_12) = v0)
% 72.01/10.50 | | |
% 72.01/10.50 | | | DELTA: instantiating (128) with fresh symbol all_524_0 gives:
% 72.01/10.50 | | | (129) ~ (all_524_0 = 0) & sort1(elt, all_94_12) = all_524_0
% 72.01/10.50 | | |
% 72.01/10.50 | | | ALPHA: (129) implies:
% 72.01/10.50 | | | (130) ~ (all_524_0 = 0)
% 72.01/10.50 | | | (131) sort1(elt, all_94_12) = all_524_0
% 72.01/10.50 | | |
% 72.01/10.50 | | | GROUND_INST: instantiating (19) with 0, all_524_0, all_94_12, elt,
% 72.01/10.50 | | | simplifying with (13), (131) gives:
% 72.01/10.50 | | | (132) all_524_0 = 0
% 72.01/10.50 | | |
% 72.01/10.50 | | | REDUCE: (130), (132) imply:
% 72.01/10.50 | | | (133) $false
% 72.01/10.50 | | |
% 72.01/10.50 | | | CLOSE: (133) is inconsistent.
% 72.01/10.50 | | |
% 72.01/10.50 | | End of split
% 72.01/10.50 | |
% 72.01/10.50 | End of split
% 72.01/10.50 |
% 72.01/10.50 End of proof
% 72.01/10.50 % SZS output end Proof for theBenchmark
% 72.01/10.51
% 72.01/10.51 9904ms
%------------------------------------------------------------------------------