TSTP Solution File: DAT330_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT330_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 : Wed Aug 30 22:19:43 EDT 2023
% Result : Unsatisfiable 67.02s 9.61s
% Output : Proof 67.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT330_1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 15:19:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.82/1.08 Prover 4: Preprocessing ...
% 2.82/1.08 Prover 1: Preprocessing ...
% 2.99/1.11 Prover 5: Preprocessing ...
% 2.99/1.11 Prover 6: Preprocessing ...
% 2.99/1.11 Prover 0: Preprocessing ...
% 2.99/1.11 Prover 3: Preprocessing ...
% 2.99/1.11 Prover 2: Preprocessing ...
% 4.31/1.35 Prover 1: Warning: ignoring some quantifiers
% 4.31/1.36 Prover 4: Warning: ignoring some quantifiers
% 4.85/1.41 Prover 3: Warning: ignoring some quantifiers
% 4.85/1.42 Prover 5: Proving ...
% 4.85/1.42 Prover 1: Constructing countermodel ...
% 4.85/1.43 Prover 6: Proving ...
% 4.85/1.43 Prover 4: Constructing countermodel ...
% 4.85/1.44 Prover 3: Constructing countermodel ...
% 4.85/1.45 Prover 0: Proving ...
% 4.85/1.48 Prover 2: Proving ...
% 8.29/1.91 Prover 3: gave up
% 8.86/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.86/1.93 Prover 1: gave up
% 8.86/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.26/1.98 Prover 7: Preprocessing ...
% 9.26/1.99 Prover 8: Preprocessing ...
% 9.26/2.04 Prover 7: Warning: ignoring some quantifiers
% 9.26/2.05 Prover 7: Constructing countermodel ...
% 9.26/2.12 Prover 8: Warning: ignoring some quantifiers
% 9.26/2.12 Prover 8: Constructing countermodel ...
% 12.00/2.38 Prover 8: gave up
% 12.31/2.39 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 12.31/2.42 Prover 9: Preprocessing ...
% 12.87/2.48 Prover 9: Warning: ignoring some quantifiers
% 12.87/2.48 Prover 9: Constructing countermodel ...
% 62.06/9.10 Prover 2: stopped
% 62.06/9.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 62.06/9.17 Prover 10: Preprocessing ...
% 63.49/9.23 Prover 10: Warning: ignoring some quantifiers
% 63.49/9.24 Prover 10: Constructing countermodel ...
% 67.02/9.60 Prover 10: Found proof (size 266)
% 67.02/9.60 Prover 10: proved (482ms)
% 67.02/9.60 Prover 9: stopped
% 67.02/9.60 Prover 5: stopped
% 67.02/9.60 Prover 0: stopped
% 67.02/9.60 Prover 7: stopped
% 67.02/9.60 Prover 6: stopped
% 67.02/9.61 Prover 4: stopped
% 67.02/9.61
% 67.02/9.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 67.02/9.61
% 67.02/9.62 % SZS output start Proof for theBenchmark
% 67.02/9.62 Assumptions after simplification:
% 67.02/9.62 ---------------------------------
% 67.02/9.62
% 67.02/9.62 (formula_1)
% 67.02/9.64 ! [v0: int] : ! [v1: Set] : ! [v2: Set] : ( ~ (insert(v1, v0) = v2) | ~
% 67.02/9.64 Set(v1) | member(v0, v2))
% 67.02/9.64
% 67.02/9.64 (formula_10)
% 67.02/9.64 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~ (g(v0) = v1))
% 67.02/9.64
% 67.02/9.64 (formula_11)
% 67.02/9.64 Array[Int,Int](arr) & Set(s0) & Set(s1) & ? [v0: int] : ? [v1: Set] : ((s0 =
% 67.02/9.64 s1 | ~ ($lesseq(i1, 0)) & ( ~ ($lesseq(1, i1)) | (v1 = s1 &
% 67.02/9.64 select:(Array[Int,Int]*Int)>Int(arr, i1) = v0 & insert(s0, v0) = s1)))
% 67.02/9.64
% 67.02/9.64 (formula_12)
% 67.02/9.64 Array[Int,Int](arr) & Set(s2) & Set(s1) & ? [v0: int] : ? [v1: int] : (g(i2)
% 67.02/9.64 = v0 & select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s1, v1) = s2)
% 67.02/9.64
% 67.02/9.64 (formula_13)
% 67.02/9.65 Array[Int,Int](arr) & Set(s3) & Set(s2) & ? [v0: int] : ? [v1: int] : (g(i3)
% 67.02/9.65 = v0 & select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s2, v1) = s3)
% 67.02/9.65
% 67.02/9.65 (formula_15)
% 67.02/9.65 Set(s3) & Set(s0) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & sup(s3) = v0
% 67.02/9.65 & sup(s0) = v1)
% 67.02/9.65
% 67.02/9.65 (formula_2)
% 67.02/9.65 ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | ~
% 67.02/9.65 (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0, v2)) &
% 67.02/9.65 ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 | ~
% 67.02/9.65 (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v2) | member(v0, v3))
% 67.02/9.65
% 67.02/9.65 (formula_6)
% 67.02/9.65 ! [v0: Set] : ! [v1: int] : ( ~ (sup(v0) = v1) | ~ Set(v0) | member(v1,
% 67.02/9.65 v0))
% 67.02/9.65
% 67.02/9.65 (formula_7)
% 67.02/9.65 ! [v0: Set] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, $difference(v1,
% 67.02/9.65 v2))) | ~ (sup(v0) = v2) | ~ Set(v0) | ~ member(v1, v0))
% 67.02/9.65
% 67.02/9.65 (formula_8)
% 67.02/9.65 ! [v0: Set] : ! [v1: int] : ! [v2: Set] : ( ~ (insert(v0, v1) = v2) | ~
% 67.02/9.65 Set(v0) | ? [v3: int] : ? [v4: int] : ((v4 = v1 & sup(v2) = v1) |
% 67.02/9.65 ($lesseq(v1, v3) & sup(v0) = v3)))
% 67.02/9.65
% 67.02/9.65 (formula_9)
% 67.02/9.65 Array[Int,Int](arr) & Set(s0) & ? [v0: int] : (sup(s0) = v0 & ! [v1: int] :
% 67.02/9.65 ! [v2: int] : ( ~ ($lesseq(v0, v2)) | ~ ($lesseq(1, v1)) | ~
% 67.02/9.65 (select:(Array[Int,Int]*Int)>Int(arr, v1) = v2)))
% 67.02/9.65
% 67.02/9.65 (function-axioms)
% 67.61/9.65 ! [v0: Array[Int,Int]] : ! [v1: Array[Int,Int]] : ! [v2: int] : ! [v3:
% 67.61/9.65 int] : ! [v4: Array[Int,Int]] : (v1 = v0 | ~
% 67.61/9.65 (store:(Array[Int,Int]*Int*Int)>Array[Int,Int](v4, v3, v2) = v1) | ~
% 67.61/9.65 (store:(Array[Int,Int]*Int*Int)>Array[Int,Int](v4, v3, v2) = v0)) & ! [v0:
% 67.61/9.65 int] : ! [v1: int] : ! [v2: int] : ! [v3: Array[Int,Int]] : (v1 = v0 | ~
% 67.61/9.65 (select:(Array[Int,Int]*Int)>Int(v3, v2) = v1) | ~
% 67.61/9.65 (select:(Array[Int,Int]*Int)>Int(v3, v2) = v0)) & ! [v0: Set] : ! [v1:
% 67.61/9.65 Set] : ! [v2: int] : ! [v3: Set] : (v1 = v0 | ~ (delete(v3, v2) = v1) |
% 67.61/9.65 ~ (delete(v3, v2) = v0)) & ! [v0: Set] : ! [v1: Set] : ! [v2: int] : !
% 67.61/9.65 [v3: Set] : (v1 = v0 | ~ (insert(v3, v2) = v1) | ~ (insert(v3, v2) = v0)) &
% 67.61/9.65 ! [v0: Array[Int,Int]] : ! [v1: Array[Int,Int]] : ! [v2: int] : (v1 = v0 |
% 67.61/9.65 ~ (const:(Int)>Array[Int,Int](v2) = v1) | ~ (const:(Int)>Array[Int,Int](v2)
% 67.61/9.65 = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (g(v2)
% 67.61/9.65 = v1) | ~ (g(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Set] :
% 67.61/9.65 (v1 = v0 | ~ (sup(v2) = v1) | ~ (sup(v2) = v0))
% 67.61/9.65
% 67.61/9.65 Further assumptions not needed in the proof:
% 67.61/9.65 --------------------------------------------
% 67.61/9.65 formula_14, formula_16, formula_17, formula_18, formula_19, formula_3,
% 67.61/9.65 formula_4, formula_5
% 67.61/9.65
% 67.61/9.65 Those formulas are unsatisfiable:
% 67.61/9.65 ---------------------------------
% 67.61/9.65
% 67.61/9.65 Begin of proof
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_2) implies:
% 67.61/9.66 | (1) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 |
% 67.61/9.66 | ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v2) | member(v0,
% 67.61/9.66 | v3))
% 67.61/9.66 | (2) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 |
% 67.61/9.66 | ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0,
% 67.61/9.66 | v2))
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_9) implies:
% 67.61/9.66 | (3) ? [v0: int] : (sup(s0) = v0 & ! [v1: int] : ! [v2: int] : ( ~
% 67.61/9.66 | ($lesseq(v0, v2)) | ~ ($lesseq(1, v1)) | ~
% 67.61/9.66 | (select:(Array[Int,Int]*Int)>Int(arr, v1) = v2)))
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_11) implies:
% 67.61/9.66 | (4) ? [v0: int] : ? [v1: Set] : ((s0 = s1 | ~ ($lesseq(i1, 0)) & ( ~
% 67.61/9.66 | ($lesseq(1, i1)) | (v1 = s1 &
% 67.61/9.66 | select:(Array[Int,Int]*Int)>Int(arr, i1) = v0 & insert(s0, v0)
% 67.61/9.66 | = s1)))
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_12) implies:
% 67.61/9.66 | (5) Set(s1)
% 67.61/9.66 | (6) ? [v0: int] : ? [v1: int] : (g(i2) = v0 &
% 67.61/9.66 | select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s1, v1) = s2)
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_13) implies:
% 67.61/9.66 | (7) Set(s2)
% 67.61/9.66 | (8) ? [v0: int] : ? [v1: int] : (g(i3) = v0 &
% 67.61/9.66 | select:(Array[Int,Int]*Int)>Int(arr, v0) = v1 & insert(s2, v1) = s3)
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (formula_15) implies:
% 67.61/9.66 | (9) Set(s0)
% 67.61/9.66 | (10) Set(s3)
% 67.61/9.66 | (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & sup(s3) = v0 & sup(s0) =
% 67.61/9.66 | v1)
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (function-axioms) implies:
% 67.61/9.66 | (12) ! [v0: int] : ! [v1: int] : ! [v2: Set] : (v1 = v0 | ~ (sup(v2) =
% 67.61/9.66 | v1) | ~ (sup(v2) = v0))
% 67.61/9.66 | (13) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: Array[Int,Int]] :
% 67.61/9.66 | (v1 = v0 | ~ (select:(Array[Int,Int]*Int)>Int(v3, v2) = v1) | ~
% 67.61/9.66 | (select:(Array[Int,Int]*Int)>Int(v3, v2) = v0))
% 67.61/9.66 |
% 67.61/9.66 | DELTA: instantiating (11) with fresh symbols all_20_0, all_20_1 gives:
% 67.61/9.66 | (14) ~ (all_20_0 = all_20_1) & sup(s3) = all_20_1 & sup(s0) = all_20_0
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (14) implies:
% 67.61/9.66 | (15) ~ (all_20_0 = all_20_1)
% 67.61/9.66 | (16) sup(s0) = all_20_0
% 67.61/9.66 | (17) sup(s3) = all_20_1
% 67.61/9.66 |
% 67.61/9.66 | DELTA: instantiating (6) with fresh symbols all_22_0, all_22_1 gives:
% 67.61/9.66 | (18) g(i2) = all_22_1 & select:(Array[Int,Int]*Int)>Int(arr, all_22_1) =
% 67.61/9.66 | all_22_0 & insert(s1, all_22_0) = s2
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (18) implies:
% 67.61/9.66 | (19) insert(s1, all_22_0) = s2
% 67.61/9.66 | (20) select:(Array[Int,Int]*Int)>Int(arr, all_22_1) = all_22_0
% 67.61/9.66 | (21) g(i2) = all_22_1
% 67.61/9.66 |
% 67.61/9.66 | DELTA: instantiating (8) with fresh symbols all_24_0, all_24_1 gives:
% 67.61/9.66 | (22) g(i3) = all_24_1 & select:(Array[Int,Int]*Int)>Int(arr, all_24_1) =
% 67.61/9.66 | all_24_0 & insert(s2, all_24_0) = s3
% 67.61/9.66 |
% 67.61/9.66 | ALPHA: (22) implies:
% 67.61/9.66 | (23) insert(s2, all_24_0) = s3
% 67.61/9.66 | (24) select:(Array[Int,Int]*Int)>Int(arr, all_24_1) = all_24_0
% 67.61/9.66 | (25) g(i3) = all_24_1
% 67.61/9.66 |
% 67.61/9.66 | DELTA: instantiating (3) with fresh symbol all_28_0 gives:
% 67.61/9.67 | (26) sup(s0) = all_28_0 & ! [v0: int] : ! [v1: int] : ( ~
% 67.61/9.67 | ($lesseq(all_28_0, v1)) | ~ ($lesseq(1, v0)) | ~
% 67.61/9.67 | (select:(Array[Int,Int]*Int)>Int(arr, v0) = v1))
% 67.61/9.67 |
% 67.61/9.67 | ALPHA: (26) implies:
% 67.61/9.67 | (27) sup(s0) = all_28_0
% 67.61/9.67 | (28) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(all_28_0, v1)) | ~
% 67.61/9.67 | ($lesseq(1, v0)) | ~ (select:(Array[Int,Int]*Int)>Int(arr, v0) =
% 67.61/9.67 | v1))
% 67.61/9.67 |
% 67.61/9.67 | DELTA: instantiating (4) with fresh symbols all_32_0, all_32_1 gives:
% 67.61/9.67 | (29) (s0 = s1 | ~ ($lesseq(i1, 0)) & ( ~ ($lesseq(1, i1)) | (all_32_0 = s1
% 67.61/9.67 | & select:(Array[Int,Int]*Int)>Int(arr, i1) = all_32_1 &
% 67.61/9.67 | insert(s0, all_32_1) = s1))
% 67.61/9.67 |
% 67.61/9.67 | ALPHA: (29) implies:
% 67.61/9.67 | (30) ~ ($lesseq(1, i1)) | (all_32_0 = s1 &
% 67.61/9.67 | select:(Array[Int,Int]*Int)>Int(arr, i1) = all_32_1 & insert(s0,
% 67.61/9.67 | all_32_1) = s1)
% 67.61/9.67 | (31) s0 = s1 | ~ ($lesseq(i1, 0)
% 67.61/9.67 |
% 67.61/9.67 | GROUND_INST: instantiating (12) with all_20_0, all_28_0, s0, simplifying with
% 67.61/9.67 | (16), (27) gives:
% 67.61/9.67 | (32) all_28_0 = all_20_0
% 67.61/9.67 |
% 67.61/9.67 | GROUND_INST: instantiating (28) with all_22_1, all_22_0, simplifying with (20)
% 67.61/9.67 | gives:
% 67.61/9.67 | (33) ~ ($lesseq(all_28_0, all_22_0)) | ~ ($lesseq(1, all_22_1))
% 67.61/9.67 |
% 67.61/9.67 | GROUND_INST: instantiating (28) with all_24_1, all_24_0, simplifying with (24)
% 67.61/9.67 | gives:
% 67.61/9.67 | (34) ~ ($lesseq(all_28_0, all_24_0)) | ~ ($lesseq(1, all_24_1))
% 67.61/9.67 |
% 67.61/9.67 | GROUND_INST: instantiating (formula_10) with i3, all_24_1, simplifying with
% 67.61/9.67 | (25) gives:
% 67.61/9.67 | (35) $lesseq(1, all_24_1)
% 67.61/9.67 |
% 67.61/9.67 | GROUND_INST: instantiating (formula_10) with i2, all_22_1, simplifying with
% 67.61/9.67 | (21) gives:
% 67.61/9.67 | (36) $lesseq(1, all_22_1)
% 67.61/9.67 |
% 67.61/9.67 | BETA: splitting (33) gives:
% 67.61/9.67 |
% 67.61/9.67 | Case 1:
% 67.61/9.67 | |
% 67.61/9.67 | | (37) $lesseq(1, $difference(all_28_0, all_22_0))
% 67.61/9.67 | |
% 67.61/9.67 | | REDUCE: (32), (37) imply:
% 67.61/9.67 | | (38) $lesseq(1, $difference(all_20_0, all_22_0))
% 67.61/9.67 | |
% 67.61/9.67 | | BETA: splitting (34) gives:
% 67.61/9.67 | |
% 67.61/9.67 | | Case 1:
% 67.61/9.67 | | |
% 67.61/9.67 | | | (39) $lesseq(1, $difference(all_28_0, all_24_0))
% 67.61/9.67 | | |
% 67.61/9.67 | | | REDUCE: (32), (39) imply:
% 67.61/9.67 | | | (40) $lesseq(1, $difference(all_20_0, all_24_0))
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (13) with all_22_0, all_24_0, all_22_1, arr,
% 67.61/9.67 | | | simplifying with (20) gives:
% 67.61/9.67 | | | (41) all_24_0 = all_22_0 | ~ (select:(Array[Int,Int]*Int)>Int(arr,
% 67.61/9.67 | | | all_22_1) = all_24_0)
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (formula_1) with all_22_0, s1, s2, simplifying
% 67.61/9.67 | | | with (5), (19) gives:
% 67.61/9.67 | | | (42) member(all_22_0, s2)
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (formula_8) with s1, all_22_0, s2, simplifying
% 67.61/9.67 | | | with (5), (19) gives:
% 67.61/9.67 | | | (43) ? [v0: int] : ? [v1: int] : ((v1 = all_22_0 & sup(s2) =
% 67.61/9.67 | | | all_22_0) | ($lesseq(all_22_0, v0) & sup(s1) = v0))
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (formula_8) with s2, all_24_0, s3, simplifying
% 67.61/9.67 | | | with (7), (23) gives:
% 67.61/9.67 | | | (44) ? [v0: int] : ? [v1: int] : ((v1 = all_24_0 & sup(s3) =
% 67.61/9.67 | | | all_24_0) | ($lesseq(all_24_0, v0) & sup(s2) = v0))
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (formula_6) with s0, all_20_0, simplifying with
% 67.61/9.67 | | | (9), (16) gives:
% 67.61/9.67 | | | (45) member(all_20_0, s0)
% 67.61/9.67 | | |
% 67.61/9.67 | | | GROUND_INST: instantiating (formula_6) with s3, all_20_1, simplifying with
% 67.61/9.67 | | | (10), (17) gives:
% 67.61/9.67 | | | (46) member(all_20_1, s3)
% 67.61/9.67 | | |
% 67.61/9.67 | | | DELTA: instantiating (44) with fresh symbols all_59_0, all_59_1 gives:
% 67.61/9.67 | | | (47) (all_59_0 = all_24_0 & sup(s3) = all_24_0) | ($lesseq(all_24_0,
% 67.61/9.67 | | | all_59_1) & sup(s2) = all_59_1)
% 67.61/9.67 | | |
% 67.61/9.67 | | | DELTA: instantiating (43) with fresh symbols all_61_0, all_61_1 gives:
% 67.61/9.67 | | | (48) (all_61_0 = all_22_0 & sup(s2) = all_22_0) | ($lesseq(all_22_0,
% 67.61/9.67 | | | all_61_1) & sup(s1) = all_61_1)
% 67.61/9.67 | | |
% 67.61/9.68 | | | GROUND_INST: instantiating (2) with all_20_1, all_24_0, s2, s3,
% 67.61/9.68 | | | simplifying with (7), (23), (46) gives:
% 67.61/9.68 | | | (49) all_24_0 = all_20_1 | member(all_20_1, s2)
% 67.61/9.68 | | |
% 67.61/9.68 | | | GROUND_INST: instantiating (1) with all_22_0, all_24_0, s2, s3,
% 67.61/9.68 | | | simplifying with (7), (23), (42) gives:
% 67.61/9.68 | | | (50) all_24_0 = all_22_0 | member(all_22_0, s3)
% 67.61/9.68 | | |
% 67.61/9.68 | | | BETA: splitting (30) gives:
% 67.61/9.68 | | |
% 67.61/9.68 | | | Case 1:
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | (51) $lesseq(i1, 0)
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | REF_CLOSE: (1), (2), (7), (9), (10), (12), (15), (16), (17), (19), (23),
% 67.61/9.68 | | | | (31), (38), (40), (45), (47), (48), (49), (51), (formula_6),
% 67.61/9.68 | | | | (formula_7) are inconsistent by sub-proof #2.
% 67.61/9.68 | | | |
% 67.61/9.68 | | | Case 2:
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | (52) all_32_0 = s1 & select:(Array[Int,Int]*Int)>Int(arr, i1) =
% 67.61/9.68 | | | | all_32_1 & insert(s0, all_32_1) = s1
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | ALPHA: (52) implies:
% 67.61/9.68 | | | | (53) insert(s0, all_32_1) = s1
% 67.61/9.68 | | | | (54) select:(Array[Int,Int]*Int)>Int(arr, i1) = all_32_1
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | GROUND_INST: instantiating (28) with i1, all_32_1, simplifying with (54)
% 67.61/9.68 | | | | gives:
% 67.61/9.68 | | | | (55) ~ ($lesseq(all_28_0, all_32_1)) | ~ ($lesseq(1, i1))
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | BETA: splitting (55) gives:
% 67.61/9.68 | | | |
% 67.61/9.68 | | | | Case 1:
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | (56) $lesseq(1, $difference(all_28_0, all_32_1))
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | REDUCE: (32), (56) imply:
% 67.61/9.68 | | | | | (57) $lesseq(1, $difference(all_20_0, all_32_1))
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | GROUND_INST: instantiating (1) with all_20_0, all_32_1, s0, s1,
% 67.61/9.68 | | | | | simplifying with (9), (45), (53) gives:
% 67.61/9.68 | | | | | (58) all_32_1 = all_20_0 | member(all_20_0, s1)
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | GROUND_INST: instantiating (formula_8) with s0, all_32_1, s1,
% 67.61/9.68 | | | | | simplifying with (9), (53) gives:
% 67.61/9.68 | | | | | (59) ? [v0: int] : ? [v1: int] : ((v1 = all_32_1 & sup(s1) =
% 67.61/9.68 | | | | | all_32_1) | ($lesseq(all_32_1, v0) & sup(s0) = v0))
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | DELTA: instantiating (59) with fresh symbols all_97_0, all_97_1 gives:
% 67.61/9.68 | | | | | (60) (all_97_0 = all_32_1 & sup(s1) = all_32_1) |
% 67.61/9.68 | | | | | ($lesseq(all_32_1, all_97_1) & sup(s0) = all_97_1)
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | BETA: splitting (58) gives:
% 67.61/9.68 | | | | |
% 67.61/9.68 | | | | | Case 1:
% 67.61/9.68 | | | | | |
% 67.61/9.68 | | | | | | (61) member(all_20_0, s1)
% 67.61/9.68 | | | | | |
% 67.61/9.68 | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_22_0, s1, s2,
% 67.61/9.68 | | | | | | simplifying with (5), (19), (61) gives:
% 67.61/9.68 | | | | | | (62) all_22_0 = all_20_0 | member(all_20_0, s2)
% 67.61/9.68 | | | | | |
% 67.61/9.68 | | | | | | BETA: splitting (62) gives:
% 67.61/9.68 | | | | | |
% 67.61/9.68 | | | | | | Case 1:
% 67.61/9.68 | | | | | | |
% 67.61/9.68 | | | | | | | (63) member(all_20_0, s2)
% 67.61/9.68 | | | | | | |
% 67.61/9.68 | | | | | | | GROUND_INST: instantiating (1) with all_20_0, all_24_0, s2, s3,
% 67.61/9.68 | | | | | | | simplifying with (7), (23), (63) gives:
% 67.61/9.68 | | | | | | | (64) all_24_0 = all_20_0 | member(all_20_0, s3)
% 67.61/9.68 | | | | | | |
% 67.61/9.68 | | | | | | | BETA: splitting (41) gives:
% 67.61/9.68 | | | | | | |
% 67.61/9.68 | | | | | | | Case 1:
% 67.61/9.68 | | | | | | | |
% 67.61/9.68 | | | | | | | | (65) ~ (select:(Array[Int,Int]*Int)>Int(arr, all_22_1) =
% 67.61/9.68 | | | | | | | | all_24_0)
% 67.61/9.68 | | | | | | | |
% 67.61/9.68 | | | | | | | | BETA: splitting (64) gives:
% 67.61/9.68 | | | | | | | |
% 67.61/9.68 | | | | | | | | Case 1:
% 67.61/9.68 | | | | | | | | |
% 67.61/9.68 | | | | | | | | | (66) member(all_20_0, s3)
% 67.61/9.68 | | | | | | | | |
% 67.61/9.68 | | | | | | | | | PRED_UNIFY: (20), (65) imply:
% 67.61/9.69 | | | | | | | | | (67) ~ (all_24_0 = all_22_0)
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | BETA: splitting (50) gives:
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | Case 1:
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (10), (12), (15), (16), (17),
% 67.61/9.69 | | | | | | | | | | (19), (38), (40), (48), (49), (53), (57), (60),
% 67.61/9.69 | | | | | | | | | | (61), (63), (66), (formula_6), (formula_7) are
% 67.61/9.69 | | | | | | | | | | inconsistent by sub-proof #1.
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | Case 2:
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | | (68) all_24_0 = all_22_0
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | | REDUCE: (67), (68) imply:
% 67.61/9.69 | | | | | | | | | | (69) $false
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | | CLOSE: (69) is inconsistent.
% 67.61/9.69 | | | | | | | | | |
% 67.61/9.69 | | | | | | | | | End of split
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | Case 2:
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | (70) all_24_0 = all_20_0
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | REDUCE: (40), (70) imply:
% 67.61/9.69 | | | | | | | | | (71) $false
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | CLOSE: (71) is inconsistent.
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | End of split
% 67.61/9.69 | | | | | | | |
% 67.61/9.69 | | | | | | | Case 2:
% 67.61/9.69 | | | | | | | |
% 67.61/9.69 | | | | | | | | (72) all_24_0 = all_22_0
% 67.61/9.69 | | | | | | | |
% 67.61/9.69 | | | | | | | | BETA: splitting (64) gives:
% 67.61/9.69 | | | | | | | |
% 67.61/9.69 | | | | | | | | Case 1:
% 67.61/9.69 | | | | | | | | |
% 67.61/9.69 | | | | | | | | | (73) member(all_20_0, s3)
% 67.61/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (10), (12), (15), (16), (17),
% 67.80/9.69 | | | | | | | | | (19), (38), (40), (48), (49), (53), (57), (60),
% 67.80/9.69 | | | | | | | | | (61), (63), (73), (formula_6), (formula_7) are
% 67.80/9.69 | | | | | | | | | inconsistent by sub-proof #1.
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | Case 2:
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | (74) all_24_0 = all_20_0
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | COMBINE_EQS: (72), (74) imply:
% 67.80/9.69 | | | | | | | | | (75) all_22_0 = all_20_0
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | SIMP: (75) implies:
% 67.80/9.69 | | | | | | | | | (76) all_22_0 = all_20_0
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | REDUCE: (38), (76) imply:
% 67.80/9.69 | | | | | | | | | (77) $false
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | | CLOSE: (77) is inconsistent.
% 67.80/9.69 | | | | | | | | |
% 67.80/9.69 | | | | | | | | End of split
% 67.80/9.69 | | | | | | | |
% 67.80/9.69 | | | | | | | End of split
% 67.80/9.69 | | | | | | |
% 67.80/9.69 | | | | | | Case 2:
% 67.80/9.69 | | | | | | |
% 67.80/9.69 | | | | | | | (78) all_22_0 = all_20_0
% 67.80/9.69 | | | | | | |
% 67.80/9.69 | | | | | | | REDUCE: (38), (78) imply:
% 67.80/9.69 | | | | | | | (79) $false
% 67.80/9.69 | | | | | | |
% 67.80/9.69 | | | | | | | CLOSE: (79) is inconsistent.
% 67.80/9.69 | | | | | | |
% 67.80/9.69 | | | | | | End of split
% 67.80/9.69 | | | | | |
% 67.80/9.69 | | | | | Case 2:
% 67.80/9.69 | | | | | |
% 67.80/9.69 | | | | | | (80) all_32_1 = all_20_0
% 67.80/9.69 | | | | | |
% 67.80/9.69 | | | | | | REDUCE: (57), (80) imply:
% 67.80/9.69 | | | | | | (81) $false
% 67.80/9.69 | | | | | |
% 67.80/9.69 | | | | | | CLOSE: (81) is inconsistent.
% 67.80/9.69 | | | | | |
% 67.80/9.69 | | | | | End of split
% 67.80/9.69 | | | | |
% 67.80/9.69 | | | | Case 2:
% 67.80/9.69 | | | | |
% 67.80/9.69 | | | | | (82) $lesseq(i1, 0)
% 67.80/9.69 | | | | |
% 67.80/9.70 | | | | | REF_CLOSE: (1), (2), (7), (9), (10), (12), (15), (16), (17), (19),
% 67.80/9.70 | | | | | (23), (31), (38), (40), (45), (47), (48), (49), (82),
% 67.80/9.70 | | | | | (formula_6), (formula_7) are inconsistent by sub-proof #2.
% 67.80/9.70 | | | | |
% 67.80/9.70 | | | | End of split
% 67.80/9.70 | | | |
% 67.80/9.70 | | | End of split
% 67.80/9.70 | | |
% 67.80/9.70 | | Case 2:
% 67.80/9.70 | | |
% 67.80/9.70 | | | (83) $lesseq(all_24_1, 0)
% 67.80/9.70 | | |
% 67.80/9.70 | | | COMBINE_INEQS: (35), (83) imply:
% 67.80/9.70 | | | (84) $false
% 67.80/9.70 | | |
% 67.80/9.70 | | | CLOSE: (84) is inconsistent.
% 67.80/9.70 | | |
% 67.80/9.70 | | End of split
% 67.80/9.70 | |
% 67.80/9.70 | Case 2:
% 67.80/9.70 | |
% 67.80/9.70 | | (85) $lesseq(all_22_1, 0)
% 67.80/9.70 | |
% 67.80/9.70 | | COMBINE_INEQS: (36), (85) imply:
% 67.80/9.70 | | (86) $false
% 67.80/9.70 | |
% 67.80/9.70 | | CLOSE: (86) is inconsistent.
% 67.80/9.70 | |
% 67.80/9.70 | End of split
% 67.80/9.70 |
% 67.80/9.70 End of proof
% 67.80/9.70
% 67.80/9.70 Sub-proof #1 shows that the following formulas are inconsistent:
% 67.80/9.70 ----------------------------------------------------------------
% 67.80/9.70 (1) member(all_20_0, s3)
% 67.80/9.70 (2) all_24_0 = all_20_1 | member(all_20_1, s2)
% 67.80/9.70 (3) ! [v0: Set] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 67.80/9.70 $difference(v1, v2))) | ~ (sup(v0) = v2) | ~ Set(v0) | ~
% 67.80/9.70 member(v1, v0))
% 67.80/9.70 (4) sup(s0) = all_20_0
% 67.80/9.70 (5) insert(s0, all_32_1) = s1
% 67.80/9.70 (6) $lesseq(1, $difference(all_20_0, all_24_0))
% 67.80/9.70 (7) ~ (all_20_0 = all_20_1)
% 67.80/9.70 (8) ! [v0: int] : ! [v1: int] : ! [v2: Set] : (v1 = v0 | ~ (sup(v2) = v1)
% 67.80/9.70 | ~ (sup(v2) = v0))
% 67.80/9.70 (9) ! [v0: Set] : ! [v1: int] : ( ~ (sup(v0) = v1) | ~ Set(v0) |
% 67.80/9.70 member(v1, v0))
% 67.80/9.70 (10) $lesseq(1, $difference(all_20_0, all_32_1))
% 67.80/9.70 (11) member(all_20_0, s1)
% 67.80/9.70 (12) Set(s3)
% 67.80/9.70 (13) Set(s0)
% 67.80/9.70 (14) member(all_20_0, s2)
% 67.80/9.70 (15) Set(s2)
% 67.80/9.70 (16) (all_61_0 = all_22_0 & sup(s2) = all_22_0) | ($lesseq(all_22_0,
% 67.80/9.70 all_61_1) & sup(s1) = all_61_1)
% 67.80/9.70 (17) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 |
% 67.80/9.70 ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0,
% 67.80/9.70 v2))
% 67.80/9.70 (18) sup(s3) = all_20_1
% 67.80/9.70 (19) (all_97_0 = all_32_1 & sup(s1) = all_32_1) | ($lesseq(all_32_1,
% 67.80/9.70 all_97_1) & sup(s0) = all_97_1)
% 67.80/9.70 (20) insert(s1, all_22_0) = s2
% 67.80/9.70 (21) $lesseq(1, $difference(all_20_0, all_22_0))
% 67.80/9.70 (22) Set(s1)
% 67.80/9.70
% 67.80/9.70 Begin of proof
% 67.80/9.70 |
% 67.80/9.70 | GROUND_INST: instantiating (3) with s3, all_20_0, all_20_1, simplifying with
% 67.80/9.70 | (1), (12), (18) gives:
% 67.80/9.70 | (23) $lesseq(all_20_0, all_20_1)
% 67.80/9.70 |
% 67.80/9.70 | STRENGTHEN: (7), (23) imply:
% 67.80/9.70 | (24) $lesseq(1, $difference(all_20_1, all_20_0))
% 67.80/9.70 |
% 67.80/9.70 | BETA: splitting (16) gives:
% 67.80/9.70 |
% 67.80/9.70 | Case 1:
% 67.80/9.70 | |
% 67.80/9.70 | | (25) all_61_0 = all_22_0 & sup(s2) = all_22_0
% 67.80/9.70 | |
% 67.80/9.70 | | ALPHA: (25) implies:
% 67.80/9.70 | | (26) sup(s2) = all_22_0
% 67.80/9.70 | |
% 67.80/9.70 | | GROUND_INST: instantiating (3) with s2, all_20_0, all_22_0, simplifying with
% 67.80/9.70 | | (14), (15), (26) gives:
% 67.80/9.70 | | (27) $lesseq(all_20_0, all_22_0)
% 67.80/9.70 | |
% 67.80/9.70 | | COMBINE_INEQS: (21), (27) imply:
% 67.80/9.70 | | (28) $false
% 67.80/9.70 | |
% 67.80/9.70 | | CLOSE: (28) is inconsistent.
% 67.80/9.70 | |
% 67.80/9.70 | Case 2:
% 67.80/9.70 | |
% 67.80/9.71 | | (29) $lesseq(all_22_0, all_61_1) & sup(s1) = all_61_1
% 67.80/9.71 | |
% 67.80/9.71 | | ALPHA: (29) implies:
% 67.80/9.71 | | (30) sup(s1) = all_61_1
% 67.80/9.71 | |
% 67.80/9.71 | | BETA: splitting (2) gives:
% 67.80/9.71 | |
% 67.80/9.71 | | Case 1:
% 67.80/9.71 | | |
% 67.80/9.71 | | | (31) member(all_20_1, s2)
% 67.80/9.71 | | |
% 67.80/9.71 | | | GROUND_INST: instantiating (17) with all_20_1, all_22_0, s1, s2,
% 67.80/9.71 | | | simplifying with (20), (22), (31) gives:
% 67.80/9.71 | | | (32) all_22_0 = all_20_1 | member(all_20_1, s1)
% 67.80/9.71 | | |
% 67.80/9.71 | | | GROUND_INST: instantiating (3) with s1, all_20_0, all_61_1, simplifying
% 67.80/9.71 | | | with (11), (22), (30) gives:
% 67.80/9.71 | | | (33) $lesseq(all_20_0, all_61_1)
% 67.80/9.71 | | |
% 67.80/9.71 | | | GROUND_INST: instantiating (9) with s1, all_61_1, simplifying with (22),
% 67.80/9.71 | | | (30) gives:
% 67.80/9.71 | | | (34) member(all_61_1, s1)
% 67.80/9.71 | | |
% 67.80/9.71 | | | BETA: splitting (19) gives:
% 67.80/9.71 | | |
% 67.80/9.71 | | | Case 1:
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | (35) all_97_0 = all_32_1 & sup(s1) = all_32_1
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | ALPHA: (35) implies:
% 67.80/9.71 | | | | (36) sup(s1) = all_32_1
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | GROUND_INST: instantiating (8) with all_61_1, all_32_1, s1, simplifying
% 67.80/9.71 | | | | with (30), (36) gives:
% 67.80/9.71 | | | | (37) all_61_1 = all_32_1
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | REDUCE: (33), (37) imply:
% 67.80/9.71 | | | | (38) $lesseq(all_20_0, all_32_1)
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | COMBINE_INEQS: (10), (38) imply:
% 67.80/9.71 | | | | (39) $false
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | CLOSE: (39) is inconsistent.
% 67.80/9.71 | | | |
% 67.80/9.71 | | | Case 2:
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | (40) $lesseq(all_32_1, all_97_1) & sup(s0) = all_97_1
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | ALPHA: (40) implies:
% 67.80/9.71 | | | | (41) sup(s0) = all_97_1
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | GROUND_INST: instantiating (8) with all_20_0, all_97_1, s0, simplifying
% 67.80/9.71 | | | | with (4), (41) gives:
% 67.80/9.71 | | | | (42) all_97_1 = all_20_0
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | GROUND_INST: instantiating (17) with all_61_1, all_32_1, s0, s1,
% 67.80/9.71 | | | | simplifying with (5), (13), (34) gives:
% 67.80/9.71 | | | | (43) all_61_1 = all_32_1 | member(all_61_1, s0)
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | BETA: splitting (32) gives:
% 67.80/9.71 | | | |
% 67.80/9.71 | | | | Case 1:
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | (44) member(all_20_1, s1)
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | GROUND_INST: instantiating (3) with s1, all_20_1, all_61_1,
% 67.80/9.71 | | | | | simplifying with (22), (30), (44) gives:
% 67.80/9.71 | | | | | (45) $lesseq(all_20_1, all_61_1)
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | BETA: splitting (43) gives:
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | Case 1:
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | (46) member(all_61_1, s0)
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | GROUND_INST: instantiating (3) with s0, all_61_1, all_20_0,
% 67.80/9.71 | | | | | | simplifying with (4), (13), (46) gives:
% 67.80/9.71 | | | | | | (47) $lesseq(all_61_1, all_20_0)
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | COMBINE_INEQS: (45), (47) imply:
% 67.80/9.71 | | | | | | (48) $lesseq(all_20_1, all_20_0)
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | COMBINE_INEQS: (24), (48) imply:
% 67.80/9.71 | | | | | | (49) $false
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | CLOSE: (49) is inconsistent.
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | Case 2:
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | (50) all_61_1 = all_32_1
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | REDUCE: (33), (50) imply:
% 67.80/9.71 | | | | | | (51) $lesseq(all_20_0, all_32_1)
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | COMBINE_INEQS: (10), (51) imply:
% 67.80/9.71 | | | | | | (52) $false
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | | CLOSE: (52) is inconsistent.
% 67.80/9.71 | | | | | |
% 67.80/9.71 | | | | | End of split
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | Case 2:
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | (53) all_22_0 = all_20_1
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | REDUCE: (21), (53) imply:
% 67.80/9.71 | | | | | (54) $lesseq(1, $difference(all_20_0, all_20_1))
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | COMBINE_INEQS: (24), (54) imply:
% 67.80/9.71 | | | | | (55) $false
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | | CLOSE: (55) is inconsistent.
% 67.80/9.71 | | | | |
% 67.80/9.71 | | | | End of split
% 67.80/9.71 | | | |
% 67.80/9.71 | | | End of split
% 67.80/9.71 | | |
% 67.80/9.71 | | Case 2:
% 67.80/9.71 | | |
% 67.80/9.71 | | | (56) all_24_0 = all_20_1
% 67.80/9.71 | | |
% 67.80/9.71 | | | REDUCE: (6), (56) imply:
% 67.80/9.71 | | | (57) $lesseq(1, $difference(all_20_0, all_20_1))
% 67.80/9.71 | | |
% 67.80/9.71 | | | COMBINE_INEQS: (24), (57) imply:
% 67.80/9.71 | | | (58) $false
% 67.80/9.71 | | |
% 67.80/9.71 | | | CLOSE: (58) is inconsistent.
% 67.80/9.71 | | |
% 67.80/9.71 | | End of split
% 67.80/9.71 | |
% 67.80/9.71 | End of split
% 67.80/9.71 |
% 67.80/9.71 End of proof
% 67.80/9.71
% 67.80/9.71 Sub-proof #2 shows that the following formulas are inconsistent:
% 67.80/9.71 ----------------------------------------------------------------
% 67.80/9.71 (1) all_24_0 = all_20_1 | member(all_20_1, s2)
% 67.80/9.71 (2) ! [v0: Set] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 67.80/9.71 $difference(v1, v2))) | ~ (sup(v0) = v2) | ~ Set(v0) | ~
% 67.80/9.71 member(v1, v0))
% 67.80/9.71 (3) s0 = s1 | ~ ($lesseq(i1, 0)
% 67.80/9.71 (4) sup(s0) = all_20_0
% 67.80/9.71 (5) $lesseq(i1, 0)
% 67.80/9.71 (6) $lesseq(1, $difference(all_20_0, all_24_0))
% 67.80/9.71 (7) ~ (all_20_0 = all_20_1)
% 67.80/9.71 (8) ! [v0: int] : ! [v1: int] : ! [v2: Set] : (v1 = v0 | ~ (sup(v2) = v1)
% 67.80/9.71 | ~ (sup(v2) = v0))
% 67.80/9.71 (9) ! [v0: Set] : ! [v1: int] : ( ~ (sup(v0) = v1) | ~ Set(v0) |
% 67.80/9.71 member(v1, v0))
% 67.80/9.71 (10) Set(s3)
% 67.80/9.71 (11) Set(s0)
% 67.80/9.71 (12) (all_59_0 = all_24_0 & sup(s3) = all_24_0) | ($lesseq(all_24_0,
% 67.80/9.71 all_59_1) & sup(s2) = all_59_1)
% 67.80/9.71 (13) Set(s2)
% 67.80/9.71 (14) (all_61_0 = all_22_0 & sup(s2) = all_22_0) | ($lesseq(all_22_0,
% 67.80/9.71 all_61_1) & sup(s1) = all_61_1)
% 67.80/9.71 (15) member(all_20_0, s0)
% 67.80/9.71 (16) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 |
% 67.80/9.71 ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v2) | member(v0,
% 67.80/9.71 v3))
% 67.80/9.72 (17) ! [v0: int] : ! [v1: int] : ! [v2: Set] : ! [v3: Set] : (v1 = v0 |
% 67.80/9.72 ~ (insert(v2, v1) = v3) | ~ Set(v2) | ~ member(v0, v3) | member(v0,
% 67.80/9.72 v2))
% 67.80/9.72 (18) sup(s3) = all_20_1
% 67.80/9.72 (19) insert(s1, all_22_0) = s2
% 67.80/9.72 (20) $lesseq(1, $difference(all_20_0, all_22_0))
% 67.80/9.72 (21) insert(s2, all_24_0) = s3
% 67.80/9.72
% 67.80/9.72 Begin of proof
% 67.80/9.72 |
% 67.80/9.72 | BETA: splitting (3) gives:
% 67.80/9.72 |
% 67.80/9.72 | Case 1:
% 67.80/9.72 | |
% 67.80/9.72 | | (22) $lesseq(1, i1)
% 67.80/9.72 | |
% 67.80/9.72 | | COMBINE_INEQS: (5), (22) imply:
% 67.80/9.72 | | (23) $false
% 67.80/9.72 | |
% 67.80/9.72 | | CLOSE: (23) is inconsistent.
% 67.80/9.72 | |
% 67.80/9.72 | Case 2:
% 67.80/9.72 | |
% 67.80/9.72 | | (24) s0 = s1
% 67.80/9.72 | |
% 67.80/9.72 | | REDUCE: (4), (24) imply:
% 67.80/9.72 | | (25) sup(s1) = all_20_0
% 67.80/9.72 | |
% 67.80/9.72 | | REDUCE: (11), (24) imply:
% 67.80/9.72 | | (26) Set(s1)
% 67.80/9.72 | |
% 67.80/9.72 | | REDUCE: (15), (24) imply:
% 67.80/9.72 | | (27) member(all_20_0, s1)
% 67.80/9.72 | |
% 67.80/9.72 | | GROUND_INST: instantiating (16) with all_20_0, all_22_0, s1, s2, simplifying
% 67.80/9.72 | | with (19), (26), (27) gives:
% 67.80/9.72 | | (28) all_22_0 = all_20_0 | member(all_20_0, s2)
% 67.80/9.72 | |
% 67.80/9.72 | | BETA: splitting (28) gives:
% 67.80/9.72 | |
% 67.80/9.72 | | Case 1:
% 67.80/9.72 | | |
% 67.80/9.72 | | | (29) member(all_20_0, s2)
% 67.80/9.72 | | |
% 67.80/9.72 | | | GROUND_INST: instantiating (16) with all_20_0, all_24_0, s2, s3,
% 67.80/9.72 | | | simplifying with (13), (21), (29) gives:
% 67.80/9.72 | | | (30) all_24_0 = all_20_0 | member(all_20_0, s3)
% 67.80/9.72 | | |
% 67.80/9.72 | | | BETA: splitting (30) gives:
% 67.80/9.72 | | |
% 67.80/9.72 | | | Case 1:
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | (31) member(all_20_0, s3)
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | GROUND_INST: instantiating (2) with s3, all_20_0, all_20_1, simplifying
% 67.80/9.72 | | | | with (10), (18), (31) gives:
% 67.80/9.72 | | | | (32) $lesseq(all_20_0, all_20_1)
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | STRENGTHEN: (7), (32) imply:
% 67.80/9.72 | | | | (33) $lesseq(1, $difference(all_20_1, all_20_0))
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | BETA: splitting (12) gives:
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | Case 1:
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | (34) all_59_0 = all_24_0 & sup(s3) = all_24_0
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | ALPHA: (34) implies:
% 67.80/9.72 | | | | | (35) sup(s3) = all_24_0
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | GROUND_INST: instantiating (8) with all_20_1, all_24_0, s3,
% 67.80/9.72 | | | | | simplifying with (18), (35) gives:
% 67.80/9.72 | | | | | (36) all_24_0 = all_20_1
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | REDUCE: (6), (36) imply:
% 67.80/9.72 | | | | | (37) $lesseq(1, $difference(all_20_0, all_20_1))
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | COMBINE_INEQS: (33), (37) imply:
% 67.80/9.72 | | | | | (38) $false
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | CLOSE: (38) is inconsistent.
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | Case 2:
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | (39) $lesseq(all_24_0, all_59_1) & sup(s2) = all_59_1
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | ALPHA: (39) implies:
% 67.80/9.72 | | | | | (40) sup(s2) = all_59_1
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | GROUND_INST: instantiating (2) with s2, all_20_0, all_59_1,
% 67.80/9.72 | | | | | simplifying with (13), (29), (40) gives:
% 67.80/9.72 | | | | | (41) $lesseq(all_20_0, all_59_1)
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | GROUND_INST: instantiating (9) with s2, all_59_1, simplifying with
% 67.80/9.72 | | | | | (13), (40) gives:
% 67.80/9.72 | | | | | (42) member(all_59_1, s2)
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | BETA: splitting (14) gives:
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | | Case 1:
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | (43) all_61_0 = all_22_0 & sup(s2) = all_22_0
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | ALPHA: (43) implies:
% 67.80/9.72 | | | | | | (44) sup(s2) = all_22_0
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | GROUND_INST: instantiating (8) with all_59_1, all_22_0, s2,
% 67.80/9.72 | | | | | | simplifying with (40), (44) gives:
% 67.80/9.72 | | | | | | (45) all_59_1 = all_22_0
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | REDUCE: (41), (45) imply:
% 67.80/9.72 | | | | | | (46) $lesseq(all_20_0, all_22_0)
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | COMBINE_INEQS: (20), (46) imply:
% 67.80/9.72 | | | | | | (47) $false
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | CLOSE: (47) is inconsistent.
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | Case 2:
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | (48) $lesseq(all_22_0, all_61_1) & sup(s1) = all_61_1
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | ALPHA: (48) implies:
% 67.80/9.72 | | | | | | (49) sup(s1) = all_61_1
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | GROUND_INST: instantiating (8) with all_20_0, all_61_1, s1,
% 67.80/9.72 | | | | | | simplifying with (25), (49) gives:
% 67.80/9.72 | | | | | | (50) all_61_1 = all_20_0
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | GROUND_INST: instantiating (17) with all_59_1, all_22_0, s1, s2,
% 67.80/9.72 | | | | | | simplifying with (19), (26), (42) gives:
% 67.80/9.72 | | | | | | (51) all_59_1 = all_22_0 | member(all_59_1, s1)
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | BETA: splitting (1) gives:
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | | Case 1:
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | (52) member(all_20_1, s2)
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | GROUND_INST: instantiating (2) with s2, all_20_1, all_59_1,
% 67.80/9.72 | | | | | | | simplifying with (13), (40), (52) gives:
% 67.80/9.72 | | | | | | | (53) $lesseq(all_20_1, all_59_1)
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | BETA: splitting (51) gives:
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | Case 1:
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | (54) member(all_59_1, s1)
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | GROUND_INST: instantiating (2) with s1, all_59_1, all_20_0,
% 67.80/9.72 | | | | | | | | simplifying with (25), (26), (54) gives:
% 67.80/9.72 | | | | | | | | (55) $lesseq(all_59_1, all_20_0)
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | COMBINE_INEQS: (53), (55) imply:
% 67.80/9.72 | | | | | | | | (56) $lesseq(all_20_1, all_20_0)
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | COMBINE_INEQS: (33), (56) imply:
% 67.80/9.72 | | | | | | | | (57) $false
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | CLOSE: (57) is inconsistent.
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | Case 2:
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | (58) all_59_1 = all_22_0
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | REDUCE: (41), (58) imply:
% 67.80/9.72 | | | | | | | | (59) $lesseq(all_20_0, all_22_0)
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | COMBINE_INEQS: (20), (59) imply:
% 67.80/9.72 | | | | | | | | (60) $false
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | | CLOSE: (60) is inconsistent.
% 67.80/9.72 | | | | | | | |
% 67.80/9.72 | | | | | | | End of split
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | Case 2:
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | (61) all_24_0 = all_20_1
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | REDUCE: (6), (61) imply:
% 67.80/9.72 | | | | | | | (62) $lesseq(1, $difference(all_20_0, all_20_1))
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | COMBINE_INEQS: (33), (62) imply:
% 67.80/9.72 | | | | | | | (63) $false
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | | CLOSE: (63) is inconsistent.
% 67.80/9.72 | | | | | | |
% 67.80/9.72 | | | | | | End of split
% 67.80/9.72 | | | | | |
% 67.80/9.72 | | | | | End of split
% 67.80/9.72 | | | | |
% 67.80/9.72 | | | | End of split
% 67.80/9.72 | | | |
% 67.80/9.72 | | | Case 2:
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | (64) all_24_0 = all_20_0
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | REDUCE: (6), (64) imply:
% 67.80/9.72 | | | | (65) $false
% 67.80/9.72 | | | |
% 67.80/9.72 | | | | CLOSE: (65) is inconsistent.
% 67.80/9.72 | | | |
% 67.80/9.72 | | | End of split
% 67.80/9.72 | | |
% 67.80/9.72 | | Case 2:
% 67.80/9.72 | | |
% 67.80/9.72 | | | (66) all_22_0 = all_20_0
% 67.80/9.72 | | |
% 67.80/9.72 | | | REDUCE: (20), (66) imply:
% 67.80/9.72 | | | (67) $false
% 67.80/9.72 | | |
% 67.80/9.72 | | | CLOSE: (67) is inconsistent.
% 67.80/9.72 | | |
% 67.80/9.72 | | End of split
% 67.80/9.72 | |
% 67.80/9.72 | End of split
% 67.80/9.72 |
% 67.80/9.72 End of proof
% 67.80/9.72 % SZS output end Proof for theBenchmark
% 67.80/9.72
% 67.80/9.72 9103ms
%------------------------------------------------------------------------------