TSTP Solution File: DAT098_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT098_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 : n016.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 4.19s 1.45s
% Output : Proof 5.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT098_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 14:25:09 EDT 2023
% 0.14/0.36 % 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 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 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 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
% 2.30/1.04 Prover 1: Preprocessing ...
% 2.30/1.04 Prover 4: Preprocessing ...
% 2.30/1.07 Prover 0: Preprocessing ...
% 2.30/1.07 Prover 3: Preprocessing ...
% 2.30/1.07 Prover 2: Preprocessing ...
% 2.30/1.07 Prover 5: Preprocessing ...
% 2.30/1.08 Prover 6: Preprocessing ...
% 3.38/1.25 Prover 5: Proving ...
% 3.38/1.25 Prover 4: Constructing countermodel ...
% 3.38/1.25 Prover 1: Constructing countermodel ...
% 3.38/1.25 Prover 6: Proving ...
% 3.38/1.25 Prover 3: Constructing countermodel ...
% 3.38/1.26 Prover 0: Proving ...
% 3.88/1.26 Prover 2: Proving ...
% 4.19/1.45 Prover 3: proved (806ms)
% 4.19/1.45
% 4.19/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.19/1.45
% 4.19/1.45 Prover 5: stopped
% 4.19/1.45 Prover 6: stopped
% 4.19/1.45 Prover 2: stopped
% 4.19/1.45 Prover 0: proved (816ms)
% 4.19/1.45
% 4.19/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.19/1.45
% 4.19/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.19/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.19/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.19/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.19/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.74/1.48 Prover 4: Found proof (size 25)
% 4.74/1.48 Prover 11: Preprocessing ...
% 4.74/1.49 Prover 7: Preprocessing ...
% 4.74/1.49 Prover 10: Preprocessing ...
% 4.74/1.49 Prover 8: Preprocessing ...
% 4.74/1.50 Prover 4: proved (853ms)
% 4.74/1.50 Prover 1: stopped
% 4.74/1.50 Prover 13: Preprocessing ...
% 4.74/1.50 Prover 10: stopped
% 4.74/1.51 Prover 11: stopped
% 4.74/1.51 Prover 7: stopped
% 4.74/1.52 Prover 13: stopped
% 4.74/1.53 Prover 8: Warning: ignoring some quantifiers
% 4.74/1.53 Prover 8: Constructing countermodel ...
% 4.74/1.54 Prover 8: stopped
% 4.74/1.54
% 4.74/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.74/1.54
% 4.74/1.54 % SZS output start Proof for theBenchmark
% 4.74/1.54 Assumptions after simplification:
% 4.74/1.54 ---------------------------------
% 4.74/1.54
% 4.74/1.54 (c)
% 5.83/1.56 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: list] : ? [v3: int] : ( ~
% 5.83/1.56 (v3 = 0) & inRange(4, v2) = v3 & cons(3, v0) = v1 & cons(2, nil) = v0 &
% 5.83/1.56 cons(1, v1) = v2 & list(v2) & list(v1) & list(v0))
% 5.83/1.56
% 5.83/1.56 (inRange)
% 5.83/1.57 list(nil) & ! [v0: int] : ! [v1: list] : ! [v2: int] : ! [v3: int] : !
% 5.83/1.57 [v4: list] : (v2 = 0 | ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0,
% 5.83/1.57 v3)) | ~ (inRange(v0, v1) = v2) | ~ (cons(v3, v4) = v1) | ~ list(v4)
% 5.83/1.57 | ~ list(v1) | ? [v5: int] : ( ~ (v5 = 0) & inRange(v0, v4) = v5)) & !
% 5.83/1.57 [v0: int] : ! [v1: list] : (v1 = nil | ~ (inRange(v0, v1) = 0) | ~ list(v1)
% 5.83/1.57 | ? [v2: int] : ? [v3: list] : ($lesseq(1, $difference(v0, v2)) &
% 5.83/1.57 $lesseq(0, v2) & inRange(v0, v3) = 0 & cons(v2, v3) = v1 & list(v3))) & !
% 5.83/1.57 [v0: int] : ! [v1: int] : (v1 = 0 | ~ (inRange(v0, nil) = v1))
% 5.83/1.57
% 5.83/1.57 Further assumptions not needed in the proof:
% 5.83/1.57 --------------------------------------------
% 5.83/1.57 l1, l2, l3, l4
% 5.83/1.57
% 5.83/1.57 Those formulas are unsatisfiable:
% 5.83/1.57 ---------------------------------
% 5.83/1.57
% 5.83/1.57 Begin of proof
% 5.83/1.57 |
% 5.83/1.57 | ALPHA: (inRange) implies:
% 5.83/1.57 | (1) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ (inRange(v0, nil) = v1))
% 5.83/1.57 | (2) ! [v0: int] : ! [v1: list] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.83/1.57 | list] : (v2 = 0 | ~ ($lesseq(1, $difference(v0, v3))) | ~
% 5.83/1.57 | ($lesseq(0, v3)) | ~ (inRange(v0, v1) = v2) | ~ (cons(v3, v4) = v1)
% 5.83/1.57 | | ~ list(v4) | ~ list(v1) | ? [v5: int] : ( ~ (v5 = 0) &
% 5.83/1.57 | inRange(v0, v4) = v5))
% 5.83/1.57 |
% 5.83/1.57 | ALPHA: (c) implies:
% 5.83/1.57 | (3) list(nil)
% 5.83/1.58 | (4) ? [v0: list] : ? [v1: list] : ? [v2: list] : ? [v3: int] : ( ~ (v3
% 5.83/1.58 | = 0) & inRange(4, v2) = v3 & cons(3, v0) = v1 & cons(2, nil) = v0 &
% 5.83/1.58 | cons(1, v1) = v2 & list(v2) & list(v1) & list(v0))
% 5.83/1.58 |
% 5.83/1.58 | DELTA: instantiating (4) with fresh symbols all_11_0, all_11_1, all_11_2,
% 5.83/1.58 | all_11_3 gives:
% 5.83/1.58 | (5) ~ (all_11_0 = 0) & inRange(4, all_11_1) = all_11_0 & cons(3, all_11_3)
% 5.83/1.58 | = all_11_2 & cons(2, nil) = all_11_3 & cons(1, all_11_2) = all_11_1 &
% 5.83/1.58 | list(all_11_1) & list(all_11_2) & list(all_11_3)
% 5.83/1.58 |
% 5.83/1.58 | ALPHA: (5) implies:
% 5.83/1.58 | (6) ~ (all_11_0 = 0)
% 5.83/1.58 | (7) list(all_11_3)
% 5.83/1.58 | (8) list(all_11_2)
% 5.83/1.58 | (9) list(all_11_1)
% 5.83/1.58 | (10) cons(1, all_11_2) = all_11_1
% 5.83/1.58 | (11) cons(2, nil) = all_11_3
% 5.83/1.58 | (12) cons(3, all_11_3) = all_11_2
% 5.83/1.58 | (13) inRange(4, all_11_1) = all_11_0
% 5.83/1.58 |
% 5.83/1.58 | GROUND_INST: instantiating (2) with 4, all_11_1, all_11_0, 1, all_11_2,
% 5.83/1.58 | simplifying with (8), (9), (10), (13) gives:
% 5.83/1.58 | (14) all_11_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & inRange(4, all_11_2) =
% 5.83/1.58 | v0)
% 5.83/1.58 |
% 5.83/1.58 | BETA: splitting (14) gives:
% 5.83/1.58 |
% 5.83/1.58 | Case 1:
% 5.83/1.58 | |
% 5.83/1.58 | | (15) all_11_0 = 0
% 5.83/1.58 | |
% 5.83/1.58 | | REDUCE: (6), (15) imply:
% 5.83/1.58 | | (16) $false
% 5.83/1.58 | |
% 5.83/1.58 | | CLOSE: (16) is inconsistent.
% 5.83/1.58 | |
% 5.83/1.58 | Case 2:
% 5.83/1.58 | |
% 5.83/1.59 | | (17) ? [v0: int] : ( ~ (v0 = 0) & inRange(4, all_11_2) = v0)
% 5.83/1.59 | |
% 5.83/1.59 | | DELTA: instantiating (17) with fresh symbol all_23_0 gives:
% 5.83/1.59 | | (18) ~ (all_23_0 = 0) & inRange(4, all_11_2) = all_23_0
% 5.83/1.59 | |
% 5.83/1.59 | | ALPHA: (18) implies:
% 5.83/1.59 | | (19) ~ (all_23_0 = 0)
% 5.83/1.59 | | (20) inRange(4, all_11_2) = all_23_0
% 5.83/1.59 | |
% 5.83/1.59 | | GROUND_INST: instantiating (2) with 4, all_11_2, all_23_0, 3, all_11_3,
% 5.83/1.59 | | simplifying with (7), (8), (12), (20) gives:
% 5.83/1.59 | | (21) all_23_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & inRange(4, all_11_3) =
% 5.83/1.59 | | v0)
% 5.83/1.59 | |
% 5.83/1.59 | | BETA: splitting (21) gives:
% 5.83/1.59 | |
% 5.83/1.59 | | Case 1:
% 5.83/1.59 | | |
% 5.83/1.59 | | | (22) all_23_0 = 0
% 5.83/1.59 | | |
% 5.83/1.59 | | | REDUCE: (19), (22) imply:
% 5.83/1.59 | | | (23) $false
% 5.83/1.59 | | |
% 5.83/1.59 | | | CLOSE: (23) is inconsistent.
% 5.83/1.59 | | |
% 5.83/1.59 | | Case 2:
% 5.83/1.59 | | |
% 5.83/1.59 | | | (24) ? [v0: int] : ( ~ (v0 = 0) & inRange(4, all_11_3) = v0)
% 5.83/1.59 | | |
% 5.83/1.59 | | | DELTA: instantiating (24) with fresh symbol all_32_0 gives:
% 5.83/1.59 | | | (25) ~ (all_32_0 = 0) & inRange(4, all_11_3) = all_32_0
% 5.83/1.59 | | |
% 5.83/1.59 | | | ALPHA: (25) implies:
% 5.83/1.59 | | | (26) ~ (all_32_0 = 0)
% 5.83/1.59 | | | (27) inRange(4, all_11_3) = all_32_0
% 5.83/1.59 | | |
% 5.83/1.59 | | | GROUND_INST: instantiating (2) with 4, all_11_3, all_32_0, 2, nil,
% 5.83/1.59 | | | simplifying with (3), (7), (11), (27) gives:
% 5.83/1.59 | | | (28) all_32_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & inRange(4, nil) = v0)
% 5.83/1.59 | | |
% 5.83/1.59 | | | BETA: splitting (28) gives:
% 5.83/1.59 | | |
% 5.83/1.59 | | | Case 1:
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | (29) all_32_0 = 0
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | REDUCE: (26), (29) imply:
% 5.83/1.59 | | | | (30) $false
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | CLOSE: (30) is inconsistent.
% 5.83/1.59 | | | |
% 5.83/1.59 | | | Case 2:
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & inRange(4, nil) = v0)
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | DELTA: instantiating (31) with fresh symbol all_41_0 gives:
% 5.83/1.59 | | | | (32) ~ (all_41_0 = 0) & inRange(4, nil) = all_41_0
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | ALPHA: (32) implies:
% 5.83/1.59 | | | | (33) ~ (all_41_0 = 0)
% 5.83/1.59 | | | | (34) inRange(4, nil) = all_41_0
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | GROUND_INST: instantiating (1) with 4, all_41_0, simplifying with (34)
% 5.83/1.59 | | | | gives:
% 5.83/1.59 | | | | (35) all_41_0 = 0
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | REDUCE: (33), (35) imply:
% 5.83/1.59 | | | | (36) $false
% 5.83/1.59 | | | |
% 5.83/1.59 | | | | CLOSE: (36) is inconsistent.
% 5.83/1.59 | | | |
% 5.83/1.59 | | | End of split
% 5.83/1.59 | | |
% 5.83/1.59 | | End of split
% 5.83/1.59 | |
% 5.83/1.59 | End of split
% 5.83/1.59 |
% 5.83/1.59 End of proof
% 5.83/1.59 % SZS output end Proof for theBenchmark
% 5.83/1.59
% 5.83/1.59 977ms
%------------------------------------------------------------------------------