TSTP Solution File: DAT082_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT082_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 : n006.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 22:19:08 EDT 2023
% Result : Theorem 5.78s 1.56s
% Output : Proof 7.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT082_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n006.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 14:03:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.27/1.08 Prover 1: Preprocessing ...
% 2.27/1.08 Prover 4: Preprocessing ...
% 2.89/1.12 Prover 0: Preprocessing ...
% 2.89/1.12 Prover 6: Preprocessing ...
% 2.89/1.12 Prover 2: Preprocessing ...
% 2.89/1.12 Prover 5: Preprocessing ...
% 2.89/1.12 Prover 3: Preprocessing ...
% 5.17/1.44 Prover 1: Constructing countermodel ...
% 5.17/1.45 Prover 3: Constructing countermodel ...
% 5.17/1.46 Prover 6: Proving ...
% 5.17/1.47 Prover 4: Constructing countermodel ...
% 5.17/1.48 Prover 5: Proving ...
% 5.17/1.48 Prover 0: Proving ...
% 5.78/1.53 Prover 2: Proving ...
% 5.78/1.56 Prover 5: proved (900ms)
% 5.78/1.56 Prover 0: proved (909ms)
% 5.78/1.56
% 5.78/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.78/1.56
% 5.78/1.56
% 5.78/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.78/1.56
% 5.78/1.56 Prover 3: stopped
% 5.78/1.56 Prover 2: stopped
% 5.78/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.78/1.56 Prover 6: stopped
% 5.78/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.78/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.78/1.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.78/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.26/1.61 Prover 1: Found proof (size 19)
% 6.26/1.61 Prover 1: proved (963ms)
% 6.26/1.61 Prover 4: stopped
% 6.26/1.62 Prover 7: Preprocessing ...
% 6.26/1.62 Prover 8: Preprocessing ...
% 6.26/1.62 Prover 11: Preprocessing ...
% 6.26/1.62 Prover 13: Preprocessing ...
% 6.26/1.62 Prover 10: Preprocessing ...
% 6.26/1.64 Prover 7: stopped
% 6.26/1.64 Prover 11: stopped
% 6.26/1.65 Prover 10: stopped
% 6.26/1.65 Prover 13: stopped
% 6.92/1.69 Prover 8: Warning: ignoring some quantifiers
% 6.92/1.70 Prover 8: Constructing countermodel ...
% 6.92/1.71 Prover 8: stopped
% 6.92/1.71
% 6.92/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.92/1.71
% 7.08/1.71 % SZS output start Proof for theBenchmark
% 7.08/1.71 Assumptions after simplification:
% 7.08/1.71 ---------------------------------
% 7.08/1.72
% 7.08/1.72 (c)
% 7.17/1.73 list(nil) & ? [v0: list] : ? [v1: list] : ? [v2: int] : ( ~ (v2 = 2) &
% 7.17/1.73 length(v1) = v2 & cons(2, nil) = v0 & cons(1, v0) = v1 & list(v1) &
% 7.17/1.73 list(v0))
% 7.17/1.73
% 7.17/1.74 (l)
% 7.17/1.74 length(nil) = 0 & list(nil)
% 7.17/1.74
% 7.17/1.74 (l_1)
% 7.17/1.74 ! [v0: int] : ! [v1: list] : ! [v2: list] : ( ~ (cons(v0, v1) = v2) | ~
% 7.17/1.74 list(v1) | ? [v3: int] : (length(v2) = v3 & length(v1) = $sum(v3, -1)))
% 7.17/1.74
% 7.17/1.74 (function-axioms)
% 7.17/1.74 ! [v0: list] : ! [v1: list] : ! [v2: list] : ! [v3: list] : (v1 = v0 | ~
% 7.17/1.74 (append(v3, v2) = v1) | ~ (append(v3, v2) = v0)) & ! [v0: int] : ! [v1:
% 7.17/1.74 int] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~ (count(v3, v2) = v1) |
% 7.17/1.74 ~ (count(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.17/1.74 MultipleValueBool] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~
% 7.17/1.74 (inRange(v3, v2) = v1) | ~ (inRange(v3, v2) = v0)) & ! [v0:
% 7.17/1.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: list] : ! [v3:
% 7.17/1.74 int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.17/1.74 list] : ! [v1: list] : ! [v2: list] : ! [v3: int] : (v1 = v0 | ~
% 7.17/1.74 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: int] : ! [v1: int]
% 7.17/1.75 : ! [v2: list] : (v1 = v0 | ~ (length(v2) = v1) | ~ (length(v2) = v0)) & !
% 7.17/1.75 [v0: list] : ! [v1: list] : ! [v2: list] : (v1 = v0 | ~ (tail(v2) = v1) |
% 7.17/1.75 ~ (tail(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0
% 7.17/1.75 | ~ (head(v2) = v1) | ~ (head(v2) = v0))
% 7.17/1.75
% 7.17/1.75 Further assumptions not needed in the proof:
% 7.17/1.75 --------------------------------------------
% 7.17/1.75 a, a_3, a_4, a_8, inRange, in_conv, l1, l2, l3, l4, l_6, l_7
% 7.17/1.75
% 7.17/1.75 Those formulas are unsatisfiable:
% 7.17/1.75 ---------------------------------
% 7.17/1.75
% 7.17/1.75 Begin of proof
% 7.17/1.75 |
% 7.17/1.75 | ALPHA: (l) implies:
% 7.17/1.75 | (1) length(nil) = 0
% 7.17/1.75 |
% 7.17/1.75 | ALPHA: (c) implies:
% 7.17/1.75 | (2) list(nil)
% 7.17/1.75 | (3) ? [v0: list] : ? [v1: list] : ? [v2: int] : ( ~ (v2 = 2) &
% 7.17/1.75 | length(v1) = v2 & cons(2, nil) = v0 & cons(1, v0) = v1 & list(v1) &
% 7.17/1.75 | list(v0))
% 7.17/1.75 |
% 7.17/1.75 | ALPHA: (function-axioms) implies:
% 7.17/1.75 | (4) ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (length(v2)
% 7.17/1.75 | = v1) | ~ (length(v2) = v0))
% 7.17/1.75 |
% 7.17/1.75 | DELTA: instantiating (3) with fresh symbols all_19_0, all_19_1, all_19_2
% 7.17/1.75 | gives:
% 7.17/1.75 | (5) ~ (all_19_0 = 2) & length(all_19_1) = all_19_0 & cons(2, nil) =
% 7.17/1.75 | all_19_2 & cons(1, all_19_2) = all_19_1 & list(all_19_1) &
% 7.17/1.75 | list(all_19_2)
% 7.17/1.75 |
% 7.17/1.75 | ALPHA: (5) implies:
% 7.17/1.76 | (6) ~ (all_19_0 = 2)
% 7.17/1.76 | (7) list(all_19_2)
% 7.17/1.76 | (8) cons(1, all_19_2) = all_19_1
% 7.17/1.76 | (9) cons(2, nil) = all_19_2
% 7.17/1.76 | (10) length(all_19_1) = all_19_0
% 7.17/1.76 |
% 7.17/1.76 | GROUND_INST: instantiating (l_1) with 1, all_19_2, all_19_1, simplifying with
% 7.17/1.76 | (7), (8) gives:
% 7.17/1.76 | (11) ? [v0: int] : (length(all_19_1) = v0 & length(all_19_2) = $sum(v0,
% 7.17/1.76 | -1))
% 7.17/1.76 |
% 7.17/1.76 | GROUND_INST: instantiating (l_1) with 2, nil, all_19_2, simplifying with (2),
% 7.17/1.76 | (9) gives:
% 7.17/1.76 | (12) ? [v0: int] : (length(all_19_2) = v0 & length(nil) = $sum(v0, -1))
% 7.17/1.76 |
% 7.17/1.76 | DELTA: instantiating (11) with fresh symbol all_27_0 gives:
% 7.17/1.76 | (13) length(all_19_1) = all_27_0 & length(all_19_2) = $sum(all_27_0, -1)
% 7.17/1.76 |
% 7.17/1.76 | ALPHA: (13) implies:
% 7.17/1.76 | (14) length(all_19_2) = $sum(all_27_0, -1)
% 7.17/1.76 | (15) length(all_19_1) = all_27_0
% 7.17/1.76 |
% 7.17/1.76 | DELTA: instantiating (12) with fresh symbol all_29_0 gives:
% 7.17/1.76 | (16) length(all_19_2) = all_29_0 & length(nil) = $sum(all_29_0, -1)
% 7.17/1.76 |
% 7.17/1.76 | ALPHA: (16) implies:
% 7.17/1.76 | (17) length(nil) = $sum(all_29_0, -1)
% 7.17/1.76 | (18) length(all_19_2) = all_29_0
% 7.17/1.76 |
% 7.17/1.76 | GROUND_INST: instantiating (4) with 0, $sum(all_29_0, -1), nil, simplifying
% 7.17/1.76 | with (1), (17) gives:
% 7.17/1.76 | (19) all_29_0 = 1
% 7.17/1.76 |
% 7.17/1.76 | GROUND_INST: instantiating (4) with $sum(all_27_0, -1), all_29_0, all_19_2,
% 7.17/1.76 | simplifying with (14), (18) gives:
% 7.17/1.76 | (20) $difference(all_29_0, all_27_0) = -1
% 7.17/1.76 |
% 7.17/1.76 | GROUND_INST: instantiating (4) with all_19_0, all_27_0, all_19_1, simplifying
% 7.17/1.76 | with (10), (15) gives:
% 7.17/1.76 | (21) all_27_0 = all_19_0
% 7.17/1.76 |
% 7.17/1.76 | COMBINE_EQS: (19), (20) imply:
% 7.17/1.76 | (22) all_27_0 = 2
% 7.17/1.76 |
% 7.17/1.76 | SIMP: (22) implies:
% 7.17/1.76 | (23) all_27_0 = 2
% 7.17/1.76 |
% 7.17/1.76 | COMBINE_EQS: (21), (23) imply:
% 7.17/1.76 | (24) all_19_0 = 2
% 7.17/1.76 |
% 7.17/1.76 | REDUCE: (6), (24) imply:
% 7.17/1.76 | (25) $false
% 7.17/1.76 |
% 7.17/1.76 | CLOSE: (25) is inconsistent.
% 7.17/1.76 |
% 7.17/1.76 End of proof
% 7.17/1.76 % SZS output end Proof for theBenchmark
% 7.17/1.77
% 7.17/1.77 1136ms
%------------------------------------------------------------------------------