TSTP Solution File: ARI615_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI615_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 17:48:35 EDT 2023
% Result : Theorem 3.39s 1.20s
% Output : Proof 4.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI615_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.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 : Tue Aug 29 18:34:11 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/sandbox/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 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
% 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
% 2.14/0.96 Prover 1: Preprocessing ...
% 2.14/0.96 Prover 4: Preprocessing ...
% 2.14/1.01 Prover 5: Preprocessing ...
% 2.14/1.01 Prover 6: Preprocessing ...
% 2.14/1.01 Prover 0: Preprocessing ...
% 2.14/1.01 Prover 2: Preprocessing ...
% 2.14/1.01 Prover 3: Preprocessing ...
% 2.85/1.08 Prover 3: Constructing countermodel ...
% 2.85/1.08 Prover 1: Constructing countermodel ...
% 2.85/1.08 Prover 4: Constructing countermodel ...
% 2.85/1.08 Prover 5: Proving ...
% 2.85/1.08 Prover 2: Proving ...
% 2.85/1.08 Prover 6: Proving ...
% 2.85/1.08 Prover 0: Proving ...
% 3.39/1.20 Prover 3: proved (576ms)
% 3.39/1.20
% 3.39/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.20
% 3.39/1.20 Prover 6: stopped
% 3.39/1.20 Prover 5: stopped
% 3.39/1.21 Prover 2: stopped
% 3.39/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.39/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.39/1.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.39/1.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.39/1.22 Prover 0: proved (594ms)
% 3.39/1.22
% 3.39/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.22
% 3.39/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.86/1.22 Prover 8: Preprocessing ...
% 3.86/1.22 Prover 7: Preprocessing ...
% 3.86/1.24 Prover 10: Preprocessing ...
% 3.86/1.24 Prover 13: Preprocessing ...
% 3.86/1.24 Prover 11: Preprocessing ...
% 3.86/1.25 Prover 8: Warning: ignoring some quantifiers
% 3.86/1.25 Prover 8: Constructing countermodel ...
% 3.86/1.25 Prover 10: Warning: ignoring some quantifiers
% 3.86/1.25 Prover 13: Warning: ignoring some quantifiers
% 3.86/1.25 Prover 10: Constructing countermodel ...
% 3.86/1.25 Prover 13: Constructing countermodel ...
% 4.16/1.27 Prover 7: Warning: ignoring some quantifiers
% 4.16/1.27 Prover 7: Constructing countermodel ...
% 4.16/1.27 Prover 4: Found proof (size 21)
% 4.16/1.27 Prover 4: proved (643ms)
% 4.16/1.27 Prover 7: stopped
% 4.16/1.27 Prover 13: stopped
% 4.16/1.27 Prover 1: Found proof (size 22)
% 4.16/1.27 Prover 1: proved (648ms)
% 4.16/1.27 Prover 10: stopped
% 4.16/1.27 Prover 8: stopped
% 4.16/1.28 Prover 11: Constructing countermodel ...
% 4.16/1.28 Prover 11: stopped
% 4.16/1.28
% 4.16/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.16/1.28
% 4.16/1.29 % SZS output start Proof for theBenchmark
% 4.16/1.29 Assumptions after simplification:
% 4.16/1.29 ---------------------------------
% 4.16/1.29
% 4.16/1.29 (interv_with_smaller_radius_contained)
% 4.16/1.31 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ( ~
% 4.16/1.31 (v4 = 0) & $lesseq(v2, v3) & p(v0, v1, v3) = v4 & p(v0, v1, v2) = 0 & !
% 4.16/1.31 [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] : (v8 = 0 | ~
% 4.16/1.31 ($lesseq(0, $sum($difference(v7, v6), v5))) | ~ ($lesseq(v5, $sum(v7,
% 4.16/1.31 v6))) | ~ (p(v5, v6, v7) = v8)) & ! [v5: int] : ! [v6: int] : !
% 4.16/1.31 [v7: int] : ( ~ ($lesseq(1, $sum($difference($product(-1, v7), v6), v5))) |
% 4.16/1.31 ~ (p(v5, v6, v7) = 0)) & ! [v5: int] : ! [v6: int] : ! [v7: int] : ( ~
% 4.16/1.31 ($lesseq(1, $difference($difference(v6, v7), v5))) | ~ (p(v5, v6, v7) =
% 4.16/1.31 0)))
% 4.16/1.31
% 4.16/1.32 (function-axioms)
% 4.16/1.32 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : !
% 4.16/1.32 [v3: int] : ! [v4: int] : (v1 = v0 | ~ (p(v4, v3, v2) = v1) | ~ (p(v4, v3,
% 4.16/1.32 v2) = v0))
% 4.16/1.32
% 4.16/1.32 Those formulas are unsatisfiable:
% 4.16/1.32 ---------------------------------
% 4.16/1.32
% 4.16/1.32 Begin of proof
% 4.16/1.32 |
% 4.16/1.32 | DELTA: instantiating (interv_with_smaller_radius_contained) with fresh symbols
% 4.16/1.32 | all_3_0, all_3_1, all_3_2, all_3_3, all_3_4 gives:
% 4.16/1.32 | (1) ~ (all_3_0 = 0) & $lesseq(all_3_2, all_3_1) & p(all_3_4, all_3_3,
% 4.16/1.32 | all_3_1) = all_3_0 & p(all_3_4, all_3_3, all_3_2) = 0 & ! [v0: int]
% 4.16/1.32 | : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = 0 | ~ ($lesseq(0,
% 4.16/1.32 | $sum($difference(v2, v1), v0))) | ~ ($lesseq(v0, $sum(v2, v1)))
% 4.16/1.32 | | ~ (p(v0, v1, v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 4.16/1.32 | int] : ( ~ ($lesseq(1, $sum($difference($product(-1, v2), v1), v0)))
% 4.16/1.32 | | ~ (p(v0, v1, v2) = 0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 4.16/1.32 | int] : ( ~ ($lesseq(1, $difference($difference(v1, v2), v0))) | ~
% 4.16/1.32 | (p(v0, v1, v2) = 0))
% 4.16/1.32 |
% 4.16/1.32 | ALPHA: (1) implies:
% 4.16/1.33 | (2) ~ (all_3_0 = 0)
% 4.16/1.33 | (3) $lesseq(all_3_2, all_3_1)
% 4.16/1.33 | (4) p(all_3_4, all_3_3, all_3_2) = 0
% 4.16/1.33 | (5) p(all_3_4, all_3_3, all_3_1) = all_3_0
% 4.16/1.33 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 4.16/1.33 | $difference($difference(v1, v2), v0))) | ~ (p(v0, v1, v2) = 0))
% 4.16/1.33 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 4.16/1.33 | $sum($difference($product(-1, v2), v1), v0))) | ~ (p(v0, v1, v2)
% 4.16/1.33 | = 0))
% 4.16/1.33 | (8) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v3 = 0 |
% 4.16/1.33 | ~ ($lesseq(0, $sum($difference(v2, v1), v0))) | ~ ($lesseq(v0,
% 4.16/1.33 | $sum(v2, v1))) | ~ (p(v0, v1, v2) = v3))
% 4.16/1.33 |
% 4.16/1.33 | GROUND_INST: instantiating (7) with all_3_4, all_3_3, all_3_2, simplifying
% 4.16/1.33 | with (4) gives:
% 4.16/1.33 | (9) $lesseq(all_3_4, $sum(all_3_2, all_3_3))
% 4.16/1.33 |
% 4.16/1.33 | GROUND_INST: instantiating (6) with all_3_4, all_3_3, all_3_2, simplifying
% 4.16/1.33 | with (4) gives:
% 4.16/1.33 | (10) $lesseq(0, $sum($difference(all_3_2, all_3_3), all_3_4))
% 4.16/1.33 |
% 4.16/1.33 | GROUND_INST: instantiating (function-axioms) with 0, all_3_0, all_3_2,
% 4.16/1.33 | all_3_3, all_3_4, simplifying with (4) gives:
% 4.16/1.33 | (11) all_3_0 = 0 | ~ (p(all_3_4, all_3_3, all_3_2) = all_3_0)
% 4.16/1.33 |
% 4.16/1.33 | GROUND_INST: instantiating (8) with all_3_4, all_3_3, all_3_1, all_3_0,
% 4.16/1.33 | simplifying with (5) gives:
% 4.16/1.33 | (12) all_3_0 = 0 | ~ ($lesseq(0, $sum($difference(all_3_1, all_3_3),
% 4.16/1.33 | all_3_4))) | ~ ($lesseq(all_3_4, $sum(all_3_1, all_3_3)))
% 4.16/1.33 |
% 4.16/1.33 | BETA: splitting (11) gives:
% 4.16/1.33 |
% 4.16/1.33 | Case 1:
% 4.16/1.33 | |
% 4.16/1.33 | | (13) ~ (p(all_3_4, all_3_3, all_3_2) = all_3_0)
% 4.16/1.33 | |
% 4.16/1.33 | | PRED_UNIFY: (5), (13) imply:
% 4.16/1.33 | | (14) ~ (all_3_1 = all_3_2)
% 4.16/1.33 | |
% 4.16/1.33 | | STRENGTHEN: (3), (14) imply:
% 4.16/1.33 | | (15) $lesseq(1, $difference(all_3_1, all_3_2))
% 4.16/1.33 | |
% 4.16/1.33 | | BETA: splitting (12) gives:
% 4.16/1.33 | |
% 4.16/1.34 | | Case 1:
% 4.16/1.34 | | |
% 4.16/1.34 | | | (16) $lesseq(1, $difference($difference(all_3_3, all_3_1), all_3_4))
% 4.16/1.34 | | |
% 4.16/1.34 | | | COMBINE_INEQS: (15), (16) imply:
% 4.16/1.34 | | | (17) $lesseq(2, $difference($difference(all_3_3, all_3_2), all_3_4))
% 4.16/1.34 | | |
% 4.16/1.34 | | | COMBINE_INEQS: (10), (17) imply:
% 4.16/1.34 | | | (18) $false
% 4.16/1.34 | | |
% 4.16/1.34 | | | CLOSE: (18) is inconsistent.
% 4.16/1.34 | | |
% 4.16/1.34 | | Case 2:
% 4.16/1.34 | | |
% 4.16/1.34 | | | (19) all_3_0 = 0 | ~ ($lesseq(all_3_4, $sum(all_3_1, all_3_3)))
% 4.16/1.34 | | |
% 4.16/1.34 | | | BETA: splitting (19) gives:
% 4.16/1.34 | | |
% 4.16/1.34 | | | Case 1:
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | (20) $lesseq(1, $sum($difference($product(-1, all_3_1), all_3_3),
% 4.16/1.34 | | | | all_3_4))
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | COMBINE_INEQS: (15), (20) imply:
% 4.16/1.34 | | | | (21) $lesseq(2, $sum($difference($product(-1, all_3_2), all_3_3),
% 4.16/1.34 | | | | all_3_4))
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | COMBINE_INEQS: (9), (21) imply:
% 4.16/1.34 | | | | (22) $false
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | CLOSE: (22) is inconsistent.
% 4.16/1.34 | | | |
% 4.16/1.34 | | | Case 2:
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | (23) all_3_0 = 0
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | REDUCE: (2), (23) imply:
% 4.16/1.34 | | | | (24) $false
% 4.16/1.34 | | | |
% 4.16/1.34 | | | | CLOSE: (24) is inconsistent.
% 4.16/1.34 | | | |
% 4.16/1.34 | | | End of split
% 4.16/1.34 | | |
% 4.16/1.34 | | End of split
% 4.16/1.34 | |
% 4.16/1.34 | Case 2:
% 4.16/1.34 | |
% 4.16/1.34 | | (25) all_3_0 = 0
% 4.16/1.34 | |
% 4.16/1.34 | | REDUCE: (2), (25) imply:
% 4.16/1.34 | | (26) $false
% 4.16/1.34 | |
% 4.16/1.34 | | CLOSE: (26) is inconsistent.
% 4.16/1.34 | |
% 4.16/1.34 | End of split
% 4.16/1.34 |
% 4.16/1.34 End of proof
% 4.16/1.34 % SZS output end Proof for theBenchmark
% 4.16/1.34
% 4.16/1.34 737ms
%------------------------------------------------------------------------------