TSTP Solution File: DAT099_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT099_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 22:19:10 EDT 2023
% Result : Theorem 5.19s 1.41s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT099_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 14:30:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.83/0.97 Prover 4: Preprocessing ...
% 1.83/0.98 Prover 1: Preprocessing ...
% 2.41/1.01 Prover 6: Preprocessing ...
% 2.41/1.01 Prover 3: Preprocessing ...
% 2.41/1.01 Prover 5: Preprocessing ...
% 2.41/1.01 Prover 2: Preprocessing ...
% 2.41/1.01 Prover 0: Preprocessing ...
% 3.23/1.18 Prover 4: Constructing countermodel ...
% 3.23/1.18 Prover 1: Constructing countermodel ...
% 3.23/1.18 Prover 2: Proving ...
% 3.23/1.18 Prover 3: Constructing countermodel ...
% 3.23/1.18 Prover 6: Proving ...
% 3.23/1.18 Prover 5: Proving ...
% 3.23/1.18 Prover 0: Proving ...
% 5.19/1.41 Prover 0: proved (792ms)
% 5.19/1.41
% 5.19/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.41
% 5.19/1.41 Prover 3: proved (775ms)
% 5.19/1.41
% 5.19/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.41
% 5.19/1.43 Prover 5: stopped
% 5.19/1.45 Prover 2: stopped
% 5.19/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.19/1.45 Prover 6: stopped
% 5.19/1.45 Prover 1: Found proof (size 42)
% 5.19/1.45 Prover 7: Preprocessing ...
% 5.19/1.45 Prover 1: proved (808ms)
% 5.19/1.45 Prover 4: Found proof (size 34)
% 5.19/1.45 Prover 4: proved (799ms)
% 5.19/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.19/1.45 Prover 8: Preprocessing ...
% 5.19/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.19/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.19/1.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.19/1.47 Prover 11: Preprocessing ...
% 5.19/1.47 Prover 13: Preprocessing ...
% 5.19/1.48 Prover 10: Preprocessing ...
% 5.19/1.48 Prover 11: stopped
% 5.19/1.49 Prover 13: stopped
% 5.19/1.49 Prover 7: Warning: ignoring some quantifiers
% 5.19/1.49 Prover 10: stopped
% 5.19/1.49 Prover 7: Constructing countermodel ...
% 5.19/1.49 Prover 7: stopped
% 5.19/1.50 Prover 8: Warning: ignoring some quantifiers
% 5.19/1.50 Prover 8: Constructing countermodel ...
% 5.19/1.51 Prover 8: stopped
% 5.19/1.51
% 5.19/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.51
% 5.19/1.51 % SZS output start Proof for theBenchmark
% 5.19/1.51 Assumptions after simplification:
% 5.19/1.51 ---------------------------------
% 5.19/1.51
% 5.19/1.51 (c)
% 5.86/1.53 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: list] : (cons(3, v0) = v1
% 5.86/1.53 & cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & list(v1) & list(v0) & ?
% 5.86/1.53 [v3: int] : ? [v4: int] : ( ~ (v4 = 0) & $lesseq(4, v3) & inRange(v3, v2) =
% 5.86/1.53 v4))
% 5.86/1.53
% 5.86/1.53 (inRange)
% 6.08/1.54 list(nil) & ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~
% 6.08/1.54 (inRange(v0, v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : !
% 6.08/1.54 [v4: list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, v3)) |
% 6.08/1.54 ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 6.08/1.54 inRange(v0, v4) = v5)))) & ! [v0: int] : ! [v1: list] : (v1 = nil |
% 6.08/1.54 ~ (inRange(v0, v1) = 0) | ~ list(v1) | ? [v2: int] : ? [v3: list] :
% 6.08/1.54 ($lesseq(1, $difference(v0, v2)) & $lesseq(0, v2) & inRange(v0, v3) = 0 &
% 6.08/1.54 cons(v2, v3) = v1 & list(v3)))
% 6.08/1.54
% 6.08/1.54 Further assumptions not needed in the proof:
% 6.08/1.54 --------------------------------------------
% 6.08/1.54 l1, l2, l3, l4
% 6.08/1.54
% 6.08/1.54 Those formulas are unsatisfiable:
% 6.08/1.54 ---------------------------------
% 6.08/1.54
% 6.08/1.54 Begin of proof
% 6.08/1.54 |
% 6.08/1.54 | ALPHA: (inRange) implies:
% 6.08/1.54 | (1) ! [v0: int] : ! [v1: list] : ! [v2: int] : (v2 = 0 | ~ (inRange(v0,
% 6.08/1.54 | v1) = v2) | ~ list(v1) | ( ~ (v1 = nil) & ! [v3: int] : ! [v4:
% 6.08/1.54 | list] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0,
% 6.08/1.54 | v3)) | ~ (cons(v3, v4) = v1) | ~ list(v4) | ? [v5: int] :
% 6.08/1.55 | ( ~ (v5 = 0) & inRange(v0, v4) = v5))))
% 6.08/1.55 |
% 6.08/1.55 | ALPHA: (c) implies:
% 6.08/1.55 | (2) list(nil)
% 6.12/1.55 | (3) ? [v0: list] : ? [v1: list] : ? [v2: list] : (cons(3, v0) = v1 &
% 6.12/1.55 | cons(2, nil) = v0 & cons(1, v1) = v2 & list(v2) & list(v1) & list(v0)
% 6.12/1.55 | & ? [v3: int] : ? [v4: int] : ( ~ (v4 = 0) & $lesseq(4, v3) &
% 6.12/1.55 | inRange(v3, v2) = v4))
% 6.12/1.55 |
% 6.12/1.55 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2
% 6.12/1.55 | gives:
% 6.12/1.55 | (4) cons(3, all_11_2) = all_11_1 & cons(2, nil) = all_11_2 & cons(1,
% 6.12/1.55 | all_11_1) = all_11_0 & list(all_11_0) & list(all_11_1) &
% 6.12/1.55 | list(all_11_2) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 6.12/1.55 | $lesseq(4, v0) & inRange(v0, all_11_0) = v1)
% 6.12/1.55 |
% 6.12/1.55 | ALPHA: (4) implies:
% 6.12/1.55 | (5) list(all_11_2)
% 6.12/1.55 | (6) list(all_11_1)
% 6.12/1.55 | (7) list(all_11_0)
% 6.12/1.55 | (8) cons(1, all_11_1) = all_11_0
% 6.12/1.55 | (9) cons(2, nil) = all_11_2
% 6.12/1.55 | (10) cons(3, all_11_2) = all_11_1
% 6.12/1.55 | (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & $lesseq(4, v0) &
% 6.12/1.55 | inRange(v0, all_11_0) = v1)
% 6.12/1.55 |
% 6.12/1.55 | DELTA: instantiating (11) with fresh symbols all_13_0, all_13_1 gives:
% 6.12/1.55 | (12) ~ (all_13_0 = 0) & $lesseq(4, all_13_1) & inRange(all_13_1, all_11_0)
% 6.12/1.55 | = all_13_0
% 6.12/1.55 |
% 6.12/1.55 | ALPHA: (12) implies:
% 6.12/1.55 | (13) ~ (all_13_0 = 0)
% 6.12/1.56 | (14) $lesseq(4, all_13_1)
% 6.12/1.56 | (15) inRange(all_13_1, all_11_0) = all_13_0
% 6.12/1.56 |
% 6.12/1.56 | GROUND_INST: instantiating (1) with all_13_1, all_11_0, all_13_0, simplifying
% 6.12/1.56 | with (7), (15) gives:
% 6.12/1.56 | (16) all_13_0 = 0 | ( ~ (all_11_0 = nil) & ! [v0: int] : ! [v1: list] : (
% 6.12/1.56 | ~ ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) |
% 6.12/1.56 | ~ (cons(v0, v1) = all_11_0) | ~ list(v1) | ? [v2: int] : ( ~ (v2
% 6.12/1.56 | = 0) & inRange(all_13_1, v1) = v2)))
% 6.12/1.56 |
% 6.12/1.56 | BETA: splitting (16) gives:
% 6.12/1.56 |
% 6.12/1.56 | Case 1:
% 6.12/1.56 | |
% 6.12/1.56 | | (17) all_13_0 = 0
% 6.12/1.56 | |
% 6.12/1.56 | | REDUCE: (13), (17) imply:
% 6.12/1.56 | | (18) $false
% 6.12/1.56 | |
% 6.12/1.56 | | CLOSE: (18) is inconsistent.
% 6.12/1.56 | |
% 6.12/1.56 | Case 2:
% 6.12/1.56 | |
% 6.12/1.56 | | (19) ~ (all_11_0 = nil) & ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1,
% 6.12/1.56 | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~
% 6.12/1.56 | | (cons(v0, v1) = all_11_0) | ~ list(v1) | ? [v2: int] : ( ~ (v2 =
% 6.12/1.56 | | 0) & inRange(all_13_1, v1) = v2))
% 6.12/1.56 | |
% 6.12/1.56 | | ALPHA: (19) implies:
% 6.12/1.56 | | (20) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1, $difference(all_13_1,
% 6.12/1.56 | | v0))) | ~ ($lesseq(0, v0)) | ~ (cons(v0, v1) = all_11_0) |
% 6.12/1.56 | | ~ list(v1) | ? [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1)
% 6.12/1.56 | | = v2))
% 6.12/1.56 | |
% 6.12/1.56 | | GROUND_INST: instantiating (20) with 1, all_11_1, simplifying with (6), (8)
% 6.12/1.56 | | gives:
% 6.12/1.56 | | (21) ~ ($lesseq(2, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) &
% 6.12/1.56 | | inRange(all_13_1, all_11_1) = v0)
% 6.12/1.56 | |
% 6.12/1.56 | | BETA: splitting (21) gives:
% 6.12/1.56 | |
% 6.12/1.56 | | Case 1:
% 6.12/1.56 | | |
% 6.12/1.56 | | | (22) $lesseq(all_13_1, 1)
% 6.12/1.56 | | |
% 6.12/1.57 | | | COMBINE_INEQS: (14), (22) imply:
% 6.12/1.57 | | | (23) $false
% 6.12/1.57 | | |
% 6.12/1.57 | | | CLOSE: (23) is inconsistent.
% 6.12/1.57 | | |
% 6.12/1.57 | | Case 2:
% 6.12/1.57 | | |
% 6.12/1.57 | | | (24) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, all_11_1) = v0)
% 6.12/1.57 | | |
% 6.12/1.57 | | | DELTA: instantiating (24) with fresh symbol all_34_0 gives:
% 6.12/1.57 | | | (25) ~ (all_34_0 = 0) & inRange(all_13_1, all_11_1) = all_34_0
% 6.12/1.57 | | |
% 6.12/1.57 | | | ALPHA: (25) implies:
% 6.12/1.57 | | | (26) ~ (all_34_0 = 0)
% 6.12/1.57 | | | (27) inRange(all_13_1, all_11_1) = all_34_0
% 6.12/1.57 | | |
% 6.12/1.57 | | | GROUND_INST: instantiating (1) with all_13_1, all_11_1, all_34_0,
% 6.12/1.57 | | | simplifying with (6), (27) gives:
% 6.12/1.57 | | | (28) all_34_0 = 0 | ( ~ (all_11_1 = nil) & ! [v0: int] : ! [v1: list]
% 6.12/1.57 | | | : ( ~ ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0,
% 6.12/1.57 | | | v0)) | ~ (cons(v0, v1) = all_11_1) | ~ list(v1) | ?
% 6.12/1.57 | | | [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2)))
% 6.12/1.57 | | |
% 6.12/1.57 | | | BETA: splitting (28) gives:
% 6.12/1.57 | | |
% 6.12/1.57 | | | Case 1:
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | (29) all_34_0 = 0
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | REDUCE: (26), (29) imply:
% 6.12/1.57 | | | | (30) $false
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | CLOSE: (30) is inconsistent.
% 6.12/1.57 | | | |
% 6.12/1.57 | | | Case 2:
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | (31) ~ (all_11_1 = nil) & ! [v0: int] : ! [v1: list] : ( ~
% 6.12/1.57 | | | | ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0, v0))
% 6.12/1.57 | | | | | ~ (cons(v0, v1) = all_11_1) | ~ list(v1) | ? [v2: int] :
% 6.12/1.57 | | | | ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2))
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | ALPHA: (31) implies:
% 6.12/1.57 | | | | (32) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1,
% 6.12/1.57 | | | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~
% 6.12/1.57 | | | | (cons(v0, v1) = all_11_1) | ~ list(v1) | ? [v2: int] : ( ~
% 6.12/1.57 | | | | (v2 = 0) & inRange(all_13_1, v1) = v2))
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | GROUND_INST: instantiating (32) with 3, all_11_2, simplifying with (5),
% 6.12/1.57 | | | | (10) gives:
% 6.12/1.57 | | | | (33) ~ ($lesseq(4, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) &
% 6.12/1.57 | | | | inRange(all_13_1, all_11_2) = v0)
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | BETA: splitting (33) gives:
% 6.12/1.57 | | | |
% 6.12/1.57 | | | | Case 1:
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | (34) $lesseq(all_13_1, 3)
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | COMBINE_INEQS: (14), (34) imply:
% 6.12/1.57 | | | | | (35) $false
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | CLOSE: (35) is inconsistent.
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | Case 2:
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | (36) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, all_11_2) =
% 6.12/1.57 | | | | | v0)
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | DELTA: instantiating (36) with fresh symbol all_48_0 gives:
% 6.12/1.57 | | | | | (37) ~ (all_48_0 = 0) & inRange(all_13_1, all_11_2) = all_48_0
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | ALPHA: (37) implies:
% 6.12/1.57 | | | | | (38) ~ (all_48_0 = 0)
% 6.12/1.57 | | | | | (39) inRange(all_13_1, all_11_2) = all_48_0
% 6.12/1.57 | | | | |
% 6.12/1.57 | | | | | GROUND_INST: instantiating (1) with all_13_1, all_11_2, all_48_0,
% 6.12/1.57 | | | | | simplifying with (5), (39) gives:
% 6.12/1.58 | | | | | (40) all_48_0 = 0 | ( ~ (all_11_2 = nil) & ! [v0: int] : ! [v1:
% 6.12/1.58 | | | | | list] : ( ~ ($lesseq(1, $difference(all_13_1, v0))) | ~
% 6.12/1.58 | | | | | ($lesseq(0, v0)) | ~ (cons(v0, v1) = all_11_2) | ~
% 6.12/1.58 | | | | | list(v1) | ? [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1,
% 6.12/1.58 | | | | | v1) = v2)))
% 6.12/1.58 | | | | |
% 6.12/1.58 | | | | | BETA: splitting (40) gives:
% 6.12/1.58 | | | | |
% 6.12/1.58 | | | | | Case 1:
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | (41) all_48_0 = 0
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | REDUCE: (38), (41) imply:
% 6.12/1.58 | | | | | | (42) $false
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | CLOSE: (42) is inconsistent.
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | Case 2:
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | (43) ~ (all_11_2 = nil) & ! [v0: int] : ! [v1: list] : ( ~
% 6.12/1.58 | | | | | | ($lesseq(1, $difference(all_13_1, v0))) | ~ ($lesseq(0,
% 6.12/1.58 | | | | | | v0)) | ~ (cons(v0, v1) = all_11_2) | ~ list(v1) | ?
% 6.12/1.58 | | | | | | [v2: int] : ( ~ (v2 = 0) & inRange(all_13_1, v1) = v2))
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | ALPHA: (43) implies:
% 6.12/1.58 | | | | | | (44) ! [v0: int] : ! [v1: list] : ( ~ ($lesseq(1,
% 6.12/1.58 | | | | | | $difference(all_13_1, v0))) | ~ ($lesseq(0, v0)) | ~
% 6.12/1.58 | | | | | | (cons(v0, v1) = all_11_2) | ~ list(v1) | ? [v2: int] : (
% 6.12/1.58 | | | | | | ~ (v2 = 0) & inRange(all_13_1, v1) = v2))
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | GROUND_INST: instantiating (44) with 2, nil, simplifying with (2),
% 6.12/1.58 | | | | | | (9) gives:
% 6.12/1.58 | | | | | | (45) ~ ($lesseq(3, all_13_1)) | ? [v0: int] : ( ~ (v0 = 0) &
% 6.12/1.58 | | | | | | inRange(all_13_1, nil) = v0)
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | BETA: splitting (45) gives:
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | | Case 1:
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | (46) $lesseq(all_13_1, 2)
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | COMBINE_INEQS: (14), (46) imply:
% 6.12/1.58 | | | | | | | (47) $false
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | CLOSE: (47) is inconsistent.
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | Case 2:
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & inRange(all_13_1, nil) = v0)
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | DELTA: instantiating (48) with fresh symbol all_62_0 gives:
% 6.12/1.58 | | | | | | | (49) ~ (all_62_0 = 0) & inRange(all_13_1, nil) = all_62_0
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | ALPHA: (49) implies:
% 6.12/1.58 | | | | | | | (50) ~ (all_62_0 = 0)
% 6.12/1.58 | | | | | | | (51) inRange(all_13_1, nil) = all_62_0
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | GROUND_INST: instantiating (1) with all_13_1, nil, all_62_0,
% 6.12/1.58 | | | | | | | simplifying with (2), (51) gives:
% 6.12/1.58 | | | | | | | (52) all_62_0 = 0
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | REDUCE: (50), (52) imply:
% 6.12/1.58 | | | | | | | (53) $false
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | | CLOSE: (53) is inconsistent.
% 6.12/1.58 | | | | | | |
% 6.12/1.58 | | | | | | End of split
% 6.12/1.58 | | | | | |
% 6.12/1.58 | | | | | End of split
% 6.12/1.58 | | | | |
% 6.12/1.58 | | | | End of split
% 6.12/1.58 | | | |
% 6.12/1.58 | | | End of split
% 6.12/1.58 | | |
% 6.12/1.58 | | End of split
% 6.12/1.58 | |
% 6.12/1.58 | End of split
% 6.12/1.58 |
% 6.12/1.58 End of proof
% 6.12/1.58 % SZS output end Proof for theBenchmark
% 6.12/1.58
% 6.12/1.58 982ms
%------------------------------------------------------------------------------