TSTP Solution File: MGT023+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : 600s
% DateTime : Sun Jul 17 22:07:00 EDT 2022
% Result : Theorem 1.89s 1.16s
% Output : Proof 2.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 9 09:44:36 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.89 Prover 0: Preprocessing ...
% 1.54/1.02 Prover 0: Constructing countermodel ...
% 1.89/1.16 Prover 0: proved (523ms)
% 1.89/1.16
% 1.89/1.16 No countermodel exists, formula is valid
% 1.89/1.16 % SZS status Theorem for theBenchmark
% 1.89/1.16
% 1.89/1.16 Generating proof ... found it (size 29)
% 2.64/1.33
% 2.64/1.33 % SZS output start Proof for theBenchmark
% 2.64/1.33 Assumed formulas after preprocessing and simplification:
% 2.64/1.33 | (0) ? [v0] : ? [v1] : (critical_point(v0) = v1 & stable(v0) & environment(v0) & ~ in_environment(v0, v1) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (critical_point(v2) = v5) | ~ (growth_rate(first_movers, v3) = v4) | ~ in_environment(v2, v3) | ~ environment(v2) | ? [v6] : ? [v7] : ? [v8] : ((growth_rate(first_movers, v6) = v8 & growth_rate(efficient_producers, v6) = v7 & subpopulations(first_movers, efficient_producers, v2, v6) & greater(v6, v3) & ~ greater(v7, v8)) | (growth_rate(efficient_producers, v3) = v6 & greater(v6, v4)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (critical_point(v2) = v5) | ~ (growth_rate(efficient_producers, v3) = v4) | ~ in_environment(v2, v3) | ~ environment(v2) | ? [v6] : ? [v7] : ? [v8] : ((growth_rate(first_movers, v6) = v8 & growth_rate(efficient_producers, v6) = v7 & subpopulations(first_movers, efficient_producers, v2, v6) & greater(v6, v3) & ~ greater(v7, v8)) | (growth_rate(first_movers, v3) = v6 & greater(v4, v6)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (growth_rate(v5, v4) = v3) | ~ (growth_rate(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (critical_point(v4) = v3) | ~ (critical_point(v4) = v2)) & ! [v2] : ( ~ stable(v2) | ~ environment(v2) | ? [v3] : ? [v4] : ? [v5] : (growth_rate(first_movers, v3) = v5 & growth_rate(efficient_producers, v3) = v4 & in_environment(v2, v3) & ~ greater(v4, v5) & ! [v6] : ! [v7] : ( ~ (growth_rate(first_movers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v2, v6) | ~ greater(v6, v3) | ? [v8] : (growth_rate(efficient_producers, v6) = v8 & greater(v8, v7))) & ! [v6] : ! [v7] : ( ~ (growth_rate(efficient_producers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v2, v6) | ~ greater(v6, v3) | ? [v8] : (growth_rate(first_movers, v6) = v8 & greater(v7, v8))))))
% 2.64/1.36 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.64/1.36 | (1) critical_point(all_0_1_1) = all_0_0_0 & stable(all_0_1_1) & environment(all_0_1_1) & ~ in_environment(all_0_1_1, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~ (growth_rate(first_movers, v1) = v2) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(first_movers, v4) = v6 & growth_rate(efficient_producers, v4) = v5 & subpopulations(first_movers, efficient_producers, v0, v4) & greater(v4, v1) & ~ greater(v5, v6)) | (growth_rate(efficient_producers, v1) = v4 & greater(v4, v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~ (growth_rate(efficient_producers, v1) = v2) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(first_movers, v4) = v6 & growth_rate(efficient_producers, v4) = v5 & subpopulations(first_movers, efficient_producers, v0, v4) & greater(v4, v1) & ~ greater(v5, v6)) | (growth_rate(first_movers, v1) = v4 & greater(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0)) & ! [v0] : ( ~ stable(v0) | ~ environment(v0) | ? [v1] : ? [v2] : ? [v3] : (growth_rate(first_movers, v1) = v3 & growth_rate(efficient_producers, v1) = v2 & in_environment(v0, v1) & ~ greater(v2, v3) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ~ subpopulations(first_movers, efficient_producers, v0, v4) | ~ greater(v4, v1) | ? [v6] : (growth_rate(efficient_producers, v4) = v6 & greater(v6, v5))) & ! [v4] : ! [v5] : ( ~ (growth_rate(efficient_producers, v4) = v5) | ~ subpopulations(first_movers, efficient_producers, v0, v4) | ~ greater(v4, v1) | ? [v6] : (growth_rate(first_movers, v4) = v6 & greater(v5, v6)))))
% 2.64/1.36 |
% 2.64/1.36 | Applying alpha-rule on (1) yields:
% 2.64/1.36 | (2) stable(all_0_1_1)
% 2.64/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~ (growth_rate(efficient_producers, v1) = v2) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(first_movers, v4) = v6 & growth_rate(efficient_producers, v4) = v5 & subpopulations(first_movers, efficient_producers, v0, v4) & greater(v4, v1) & ~ greater(v5, v6)) | (growth_rate(first_movers, v1) = v4 & greater(v2, v4))))
% 2.64/1.37 | (4) environment(all_0_1_1)
% 2.64/1.37 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 2.64/1.37 | (6) critical_point(all_0_1_1) = all_0_0_0
% 2.64/1.37 | (7) ~ in_environment(all_0_1_1, all_0_0_0)
% 2.64/1.37 | (8) ! [v0] : ( ~ stable(v0) | ~ environment(v0) | ? [v1] : ? [v2] : ? [v3] : (growth_rate(first_movers, v1) = v3 & growth_rate(efficient_producers, v1) = v2 & in_environment(v0, v1) & ~ greater(v2, v3) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ~ subpopulations(first_movers, efficient_producers, v0, v4) | ~ greater(v4, v1) | ? [v6] : (growth_rate(efficient_producers, v4) = v6 & greater(v6, v5))) & ! [v4] : ! [v5] : ( ~ (growth_rate(efficient_producers, v4) = v5) | ~ subpopulations(first_movers, efficient_producers, v0, v4) | ~ greater(v4, v1) | ? [v6] : (growth_rate(first_movers, v4) = v6 & greater(v5, v6)))))
% 2.64/1.37 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0))
% 2.64/1.37 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (critical_point(v0) = v3) | ~ (growth_rate(first_movers, v1) = v2) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(first_movers, v4) = v6 & growth_rate(efficient_producers, v4) = v5 & subpopulations(first_movers, efficient_producers, v0, v4) & greater(v4, v1) & ~ greater(v5, v6)) | (growth_rate(efficient_producers, v1) = v4 & greater(v4, v2))))
% 2.64/1.37 |
% 2.64/1.37 | Instantiating formula (8) with all_0_1_1 and discharging atoms stable(all_0_1_1), environment(all_0_1_1), yields:
% 2.64/1.37 | (11) ? [v0] : ? [v1] : ? [v2] : (growth_rate(first_movers, v0) = v2 & growth_rate(efficient_producers, v0) = v1 & in_environment(all_0_1_1, v0) & ~ greater(v1, v2) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v3) | ~ greater(v3, v0) | ? [v5] : (growth_rate(efficient_producers, v3) = v5 & greater(v5, v4))) & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v3) | ~ greater(v3, v0) | ? [v5] : (growth_rate(first_movers, v3) = v5 & greater(v4, v5))))
% 2.64/1.37 |
% 2.64/1.37 | Instantiating (11) with all_8_0_2, all_8_1_3, all_8_2_4 yields:
% 2.64/1.37 | (12) growth_rate(first_movers, all_8_2_4) = all_8_0_2 & growth_rate(efficient_producers, all_8_2_4) = all_8_1_3 & in_environment(all_0_1_1, all_8_2_4) & ~ greater(all_8_1_3, all_8_0_2) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater(v0, all_8_2_4) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1))) & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater(v0, all_8_2_4) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2)))
% 2.85/1.37 |
% 2.85/1.37 | Applying alpha-rule on (12) yields:
% 2.85/1.37 | (13) growth_rate(first_movers, all_8_2_4) = all_8_0_2
% 2.85/1.37 | (14) ~ greater(all_8_1_3, all_8_0_2)
% 2.85/1.37 | (15) in_environment(all_0_1_1, all_8_2_4)
% 2.85/1.37 | (16) growth_rate(efficient_producers, all_8_2_4) = all_8_1_3
% 2.85/1.37 | (17) ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater(v0, all_8_2_4) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2)))
% 2.85/1.38 | (18) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater(v0, all_8_2_4) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1)))
% 2.85/1.38 |
% 2.85/1.38 | Instantiating formula (10) with all_0_0_0, all_8_0_2, all_8_2_4, all_0_1_1 and discharging atoms critical_point(all_0_1_1) = all_0_0_0, growth_rate(first_movers, all_8_2_4) = all_8_0_2, in_environment(all_0_1_1, all_8_2_4), environment(all_0_1_1), yields:
% 2.85/1.38 | (19) all_8_2_4 = all_0_0_0 | ? [v0] : ? [v1] : ? [v2] : ((growth_rate(first_movers, v0) = v2 & growth_rate(efficient_producers, v0) = v1 & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & greater(v0, all_8_2_4) & ~ greater(v1, v2)) | (growth_rate(efficient_producers, all_8_2_4) = v0 & greater(v0, all_8_0_2)))
% 2.85/1.38 |
% 2.85/1.38 | Instantiating formula (3) with all_0_0_0, all_8_1_3, all_8_2_4, all_0_1_1 and discharging atoms critical_point(all_0_1_1) = all_0_0_0, growth_rate(efficient_producers, all_8_2_4) = all_8_1_3, in_environment(all_0_1_1, all_8_2_4), environment(all_0_1_1), yields:
% 2.85/1.38 | (20) all_8_2_4 = all_0_0_0 | ? [v0] : ? [v1] : ? [v2] : ((growth_rate(first_movers, v0) = v2 & growth_rate(efficient_producers, v0) = v1 & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & greater(v0, all_8_2_4) & ~ greater(v1, v2)) | (growth_rate(first_movers, all_8_2_4) = v0 & greater(all_8_1_3, v0)))
% 2.85/1.38 |
% 2.85/1.38 +-Applying beta-rule and splitting (20), into two cases.
% 2.85/1.38 |-Branch one:
% 2.85/1.38 | (21) all_8_2_4 = all_0_0_0
% 2.85/1.38 |
% 2.85/1.38 | From (21) and (15) follows:
% 2.85/1.38 | (22) in_environment(all_0_1_1, all_0_0_0)
% 2.85/1.38 |
% 2.85/1.38 | Using (22) and (7) yields:
% 2.85/1.38 | (23) $false
% 2.85/1.38 |
% 2.85/1.38 |-The branch is then unsatisfiable
% 2.85/1.38 |-Branch two:
% 2.85/1.38 | (24) ~ (all_8_2_4 = all_0_0_0)
% 2.85/1.38 | (25) ? [v0] : ? [v1] : ? [v2] : ((growth_rate(first_movers, v0) = v2 & growth_rate(efficient_producers, v0) = v1 & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & greater(v0, all_8_2_4) & ~ greater(v1, v2)) | (growth_rate(first_movers, all_8_2_4) = v0 & greater(all_8_1_3, v0)))
% 2.85/1.38 |
% 2.85/1.38 +-Applying beta-rule and splitting (19), into two cases.
% 2.85/1.38 |-Branch one:
% 2.85/1.38 | (21) all_8_2_4 = all_0_0_0
% 2.85/1.38 |
% 2.85/1.38 | Equations (21) can reduce 24 to:
% 2.85/1.38 | (27) $false
% 2.85/1.38 |
% 2.85/1.38 |-The branch is then unsatisfiable
% 2.85/1.38 |-Branch two:
% 2.85/1.38 | (24) ~ (all_8_2_4 = all_0_0_0)
% 2.85/1.38 | (29) ? [v0] : ? [v1] : ? [v2] : ((growth_rate(first_movers, v0) = v2 & growth_rate(efficient_producers, v0) = v1 & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & greater(v0, all_8_2_4) & ~ greater(v1, v2)) | (growth_rate(efficient_producers, all_8_2_4) = v0 & greater(v0, all_8_0_2)))
% 2.85/1.38 |
% 2.85/1.38 | Instantiating (29) with all_26_0_8, all_26_1_9, all_26_2_10 yields:
% 2.85/1.38 | (30) (growth_rate(first_movers, all_26_2_10) = all_26_0_8 & growth_rate(efficient_producers, all_26_2_10) = all_26_1_9 & subpopulations(first_movers, efficient_producers, all_0_1_1, all_26_2_10) & greater(all_26_2_10, all_8_2_4) & ~ greater(all_26_1_9, all_26_0_8)) | (growth_rate(efficient_producers, all_8_2_4) = all_26_2_10 & greater(all_26_2_10, all_8_0_2))
% 2.85/1.38 |
% 2.85/1.38 +-Applying beta-rule and splitting (30), into two cases.
% 2.85/1.38 |-Branch one:
% 2.85/1.38 | (31) growth_rate(first_movers, all_26_2_10) = all_26_0_8 & growth_rate(efficient_producers, all_26_2_10) = all_26_1_9 & subpopulations(first_movers, efficient_producers, all_0_1_1, all_26_2_10) & greater(all_26_2_10, all_8_2_4) & ~ greater(all_26_1_9, all_26_0_8)
% 2.85/1.38 |
% 2.85/1.38 | Applying alpha-rule on (31) yields:
% 2.85/1.38 | (32) ~ greater(all_26_1_9, all_26_0_8)
% 2.85/1.38 | (33) growth_rate(first_movers, all_26_2_10) = all_26_0_8
% 2.85/1.38 | (34) growth_rate(efficient_producers, all_26_2_10) = all_26_1_9
% 2.85/1.38 | (35) greater(all_26_2_10, all_8_2_4)
% 2.85/1.38 | (36) subpopulations(first_movers, efficient_producers, all_0_1_1, all_26_2_10)
% 2.85/1.38 |
% 2.85/1.38 | Instantiating formula (17) with all_26_1_9, all_26_2_10 and discharging atoms growth_rate(efficient_producers, all_26_2_10) = all_26_1_9, subpopulations(first_movers, efficient_producers, all_0_1_1, all_26_2_10), greater(all_26_2_10, all_8_2_4), yields:
% 2.85/1.39 | (37) ? [v0] : (growth_rate(first_movers, all_26_2_10) = v0 & greater(all_26_1_9, v0))
% 2.85/1.39 |
% 2.85/1.39 | Instantiating (37) with all_38_0_12 yields:
% 2.85/1.39 | (38) growth_rate(first_movers, all_26_2_10) = all_38_0_12 & greater(all_26_1_9, all_38_0_12)
% 2.85/1.39 |
% 2.85/1.39 | Applying alpha-rule on (38) yields:
% 2.85/1.39 | (39) growth_rate(first_movers, all_26_2_10) = all_38_0_12
% 2.85/1.39 | (40) greater(all_26_1_9, all_38_0_12)
% 2.85/1.39 |
% 2.85/1.39 | Instantiating formula (5) with first_movers, all_26_2_10, all_38_0_12, all_26_0_8 and discharging atoms growth_rate(first_movers, all_26_2_10) = all_38_0_12, growth_rate(first_movers, all_26_2_10) = all_26_0_8, yields:
% 2.85/1.39 | (41) all_38_0_12 = all_26_0_8
% 2.85/1.39 |
% 2.85/1.39 | From (41) and (40) follows:
% 2.85/1.39 | (42) greater(all_26_1_9, all_26_0_8)
% 2.85/1.39 |
% 2.85/1.39 | Using (42) and (32) yields:
% 2.85/1.39 | (23) $false
% 2.85/1.39 |
% 2.85/1.39 |-The branch is then unsatisfiable
% 2.85/1.39 |-Branch two:
% 2.85/1.39 | (44) growth_rate(efficient_producers, all_8_2_4) = all_26_2_10 & greater(all_26_2_10, all_8_0_2)
% 2.85/1.39 |
% 2.85/1.39 | Applying alpha-rule on (44) yields:
% 2.85/1.39 | (45) growth_rate(efficient_producers, all_8_2_4) = all_26_2_10
% 2.85/1.39 | (46) greater(all_26_2_10, all_8_0_2)
% 2.85/1.39 |
% 2.85/1.39 | Instantiating formula (5) with efficient_producers, all_8_2_4, all_26_2_10, all_8_1_3 and discharging atoms growth_rate(efficient_producers, all_8_2_4) = all_26_2_10, growth_rate(efficient_producers, all_8_2_4) = all_8_1_3, yields:
% 2.85/1.39 | (47) all_26_2_10 = all_8_1_3
% 2.85/1.39 |
% 2.85/1.39 | From (47) and (46) follows:
% 2.85/1.39 | (48) greater(all_8_1_3, all_8_0_2)
% 2.85/1.39 |
% 2.85/1.39 | Using (48) and (14) yields:
% 2.85/1.39 | (23) $false
% 2.85/1.39 |
% 2.85/1.39 |-The branch is then unsatisfiable
% 2.85/1.39 % SZS output end Proof for theBenchmark
% 2.85/1.39
% 2.85/1.39 796ms
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