TSTP Solution File: ARI616_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI616_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 3.48s 1.20s
% Output : Proof 3.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 18:30:41 EDT 2023
% 0.16/0.35 % 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.
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.22/1.01 Prover 1: Preprocessing ...
% 2.22/1.01 Prover 4: Preprocessing ...
% 2.22/1.05 Prover 0: Preprocessing ...
% 2.22/1.05 Prover 5: Preprocessing ...
% 2.22/1.05 Prover 2: Preprocessing ...
% 2.22/1.05 Prover 6: Preprocessing ...
% 2.22/1.05 Prover 3: Preprocessing ...
% 2.70/1.12 Prover 1: Constructing countermodel ...
% 2.70/1.12 Prover 4: Constructing countermodel ...
% 2.70/1.12 Prover 5: Proving ...
% 2.70/1.12 Prover 2: Proving ...
% 2.70/1.12 Prover 6: Proving ...
% 2.70/1.12 Prover 3: Constructing countermodel ...
% 2.70/1.12 Prover 0: Proving ...
% 3.48/1.20 Prover 3: proved (556ms)
% 3.48/1.20
% 3.48/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.20
% 3.48/1.20 Prover 2: stopped
% 3.48/1.20 Prover 6: stopped
% 3.48/1.21 Prover 0: stopped
% 3.48/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.48/1.21 Prover 5: proved (563ms)
% 3.48/1.21
% 3.48/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.21
% 3.48/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.48/1.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.48/1.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.48/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.65/1.22 Prover 7: Preprocessing ...
% 3.65/1.22 Prover 4: Found proof (size 7)
% 3.65/1.22 Prover 4: proved (581ms)
% 3.69/1.22 Prover 1: Found proof (size 12)
% 3.69/1.22 Prover 1: proved (585ms)
% 3.69/1.22 Prover 8: Preprocessing ...
% 3.69/1.23 Prover 10: Preprocessing ...
% 3.69/1.23 Prover 13: Preprocessing ...
% 3.69/1.24 Prover 11: Preprocessing ...
% 3.69/1.24 Prover 7: Warning: ignoring some quantifiers
% 3.69/1.24 Prover 7: Constructing countermodel ...
% 3.69/1.24 Prover 7: stopped
% 3.69/1.25 Prover 13: Warning: ignoring some quantifiers
% 3.69/1.25 Prover 13: Constructing countermodel ...
% 3.69/1.25 Prover 13: stopped
% 3.69/1.25 Prover 8: Warning: ignoring some quantifiers
% 3.69/1.25 Prover 10: Warning: ignoring some quantifiers
% 3.69/1.25 Prover 10: Constructing countermodel ...
% 3.69/1.26 Prover 10: stopped
% 3.69/1.26 Prover 8: Constructing countermodel ...
% 3.69/1.26 Prover 8: stopped
% 3.69/1.27 Prover 11: Constructing countermodel ...
% 3.69/1.27 Prover 11: stopped
% 3.69/1.27
% 3.69/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/1.27
% 3.69/1.28 % SZS output start Proof for theBenchmark
% 3.69/1.28 Assumptions after simplification:
% 3.69/1.28 ---------------------------------
% 3.69/1.28
% 3.69/1.28 (sum_of_radii_gt_distance_of_centers)
% 3.69/1.30 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] :
% 3.69/1.30 ($lesseq(1, $sum($difference($difference($product(-1, v3), v2), v1), v0)) &
% 3.69/1.30 p(v4, v2, v3) = 0 & p(v4, v0, v1) = 0 & ! [v5: int] : ! [v6: int] : !
% 3.69/1.30 [v7: int] : ! [v8: int] : (v8 = 0 | ~ ($lesseq(0, $sum($difference(v7,
% 3.69/1.30 v6), v5))) | ~ ($lesseq(v5, $sum(v7, v6))) | ~ (p(v5, v6, v7) =
% 3.69/1.30 v8)) & ! [v5: int] : ! [v6: int] : ! [v7: int] : ( ~ ($lesseq(1,
% 3.69/1.30 $sum($difference($product(-1, v7), v6), v5))) | ~ (p(v5, v6, v7) =
% 3.69/1.30 0)) & ! [v5: int] : ! [v6: int] : ! [v7: int] : ( ~ ($lesseq(1,
% 3.69/1.30 $difference($difference(v6, v7), v5))) | ~ (p(v5, v6, v7) = 0)))
% 3.69/1.30
% 3.69/1.30 Those formulas are unsatisfiable:
% 3.69/1.30 ---------------------------------
% 3.69/1.30
% 3.69/1.30 Begin of proof
% 3.69/1.30 |
% 3.69/1.31 | DELTA: instantiating (sum_of_radii_gt_distance_of_centers) with fresh symbols
% 3.69/1.31 | all_3_0, all_3_1, all_3_2, all_3_3, all_3_4 gives:
% 3.69/1.31 | (1) $lesseq(1, $sum($difference($difference($product(-1, all_3_1),
% 3.69/1.31 | all_3_2), all_3_3), all_3_4)) & p(all_3_0, all_3_2, all_3_1) =
% 3.69/1.31 | 0 & p(all_3_0, all_3_4, all_3_3) = 0 & ! [v0: int] : ! [v1: int] : !
% 3.69/1.31 | [v2: int] : ! [v3: int] : (v3 = 0 | ~ ($lesseq(0,
% 3.69/1.31 | $sum($difference(v2, v1), v0))) | ~ ($lesseq(v0, $sum(v2, v1)))
% 3.69/1.31 | | ~ (p(v0, v1, v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 3.69/1.31 | int] : ( ~ ($lesseq(1, $sum($difference($product(-1, v2), v1), v0)))
% 3.69/1.31 | | ~ (p(v0, v1, v2) = 0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 3.69/1.31 | int] : ( ~ ($lesseq(1, $difference($difference(v1, v2), v0))) | ~
% 3.69/1.31 | (p(v0, v1, v2) = 0))
% 3.69/1.31 |
% 3.69/1.31 | ALPHA: (1) implies:
% 3.69/1.31 | (2) $lesseq(1, $sum($difference($difference($product(-1, all_3_1),
% 3.69/1.31 | all_3_2), all_3_3), all_3_4))
% 3.69/1.32 | (3) p(all_3_0, all_3_4, all_3_3) = 0
% 3.69/1.32 | (4) p(all_3_0, all_3_2, all_3_1) = 0
% 3.69/1.32 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 3.69/1.32 | $difference($difference(v1, v2), v0))) | ~ (p(v0, v1, v2) = 0))
% 3.69/1.32 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 3.69/1.32 | $sum($difference($product(-1, v2), v1), v0))) | ~ (p(v0, v1, v2)
% 3.69/1.32 | = 0))
% 3.69/1.32 |
% 3.69/1.32 | GROUND_INST: instantiating (5) with all_3_0, all_3_4, all_3_3, simplifying
% 3.69/1.32 | with (3) gives:
% 3.69/1.32 | (7) $lesseq(all_3_4, $sum(all_3_0, all_3_3))
% 3.69/1.32 |
% 3.69/1.32 | GROUND_INST: instantiating (6) with all_3_0, all_3_2, all_3_1, simplifying
% 3.69/1.32 | with (4) gives:
% 3.69/1.32 | (8) $lesseq(0, $sum($difference(all_3_1, all_3_0), all_3_2))
% 3.69/1.32 |
% 3.69/1.32 | COMBINE_INEQS: (7), (8) imply:
% 3.69/1.32 | (9) $lesseq(all_3_4, $sum($sum(all_3_1, all_3_2), all_3_3))
% 3.69/1.32 |
% 3.69/1.32 | COMBINE_INEQS: (2), (9) imply:
% 3.69/1.32 | (10) $false
% 3.69/1.32 |
% 3.69/1.32 | CLOSE: (10) is inconsistent.
% 3.69/1.32 |
% 3.69/1.32 End of proof
% 3.69/1.32 % SZS output end Proof for theBenchmark
% 3.69/1.32
% 3.69/1.32 703ms
%------------------------------------------------------------------------------