TSTP Solution File: MGT023+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT023+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 22:07:01 EDT 2022
% Result : Theorem 2.69s 1.36s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT023+2 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 9 10:25:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.57/0.60 ____ _
% 0.57/0.60 ___ / __ \_____(_)___ ________ __________
% 0.57/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic
% 0.57/0.60 (ePrincess v.1.0)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2015
% 0.57/0.60 (c) Peter Backeman, 2014-2015
% 0.57/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.60 Bug reports to peter@backeman.se
% 0.57/0.60
% 0.57/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.78/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.95 Prover 0: Preprocessing ...
% 1.88/1.11 Prover 0: Constructing countermodel ...
% 2.69/1.36 Prover 0: proved (707ms)
% 2.69/1.36
% 2.69/1.36 No countermodel exists, formula is valid
% 2.69/1.36 % SZS status Theorem for theBenchmark
% 2.69/1.36
% 2.69/1.36 Generating proof ... found it (size 41)
% 3.58/1.62
% 3.58/1.62 % SZS output start Proof for theBenchmark
% 3.58/1.62 Assumed formulas after preprocessing and simplification:
% 3.58/1.62 | (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(efficient_producers, v3) = v4) | ~ in_environment(v2, v3) | ~ environment(v2) | ? [v6] : ? [v7] : ? [v8] : ((growth_rate(efficient_producers, v6) = v7 & growth_rate(first_movers, v6) = v8 & greater(v6, v3) & subpopulations(first_movers, efficient_producers, v2, v6) & ~ greater(v7, v8)) | (growth_rate(first_movers, v3) = v6 & greater(v4, v6)))) & ! [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(efficient_producers, v6) = v7 & growth_rate(first_movers, v6) = v8 & greater(v6, v3) & subpopulations(first_movers, efficient_producers, v2, v6) & ~ greater(v7, v8)) | (growth_rate(efficient_producers, v3) = v6 & greater(v6, v4)))) & ! [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] : ! [v3] : ( ~ in_environment(v2, v3) | ~ environment(v2) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater_or_equal(v4, v3) & subpopulations(first_movers, efficient_producers, v2, v4) & ~ greater(v5, v6)) | (growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & in_environment(v2, v4) & ~ greater(v5, v6) & ! [v7] : ! [v8] : ( ~ (growth_rate(efficient_producers, v7) = v8) | ~ greater(v7, v4) | ~ subpopulations(first_movers, efficient_producers, v2, v7) | ? [v9] : (growth_rate(first_movers, v7) = v9 & greater(v8, v9))) & ! [v7] : ! [v8] : ( ~ (growth_rate(first_movers, v7) = v8) | ~ greater(v7, v4) | ~ subpopulations(first_movers, efficient_producers, v2, v7) | ? [v9] : (growth_rate(efficient_producers, v7) = v9 & greater(v9, v8)))))) & ! [v2] : ( ~ stable(v2) | ~ environment(v2) | ? [v3] : (in_environment(v2, v3) & ! [v4] : ! [v5] : ( ~ (growth_rate(efficient_producers, v4) = v5) | ~ greater_or_equal(v4, v3) | ~ subpopulations(first_movers, efficient_producers, v2, v4) | ? [v6] : (growth_rate(first_movers, v4) = v6 & greater(v5, v6))) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ~ greater_or_equal(v4, v3) | ~ subpopulations(first_movers, efficient_producers, v2, v4) | ? [v6] : (growth_rate(efficient_producers, v4) = v6 & greater(v6, v5))))))
% 3.74/1.66 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.74/1.66 | (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(efficient_producers, v1) = v2) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v4] : ? [v5] : ? [v6] : ((growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v4, v1) & subpopulations(first_movers, efficient_producers, v0, v4) & ~ greater(v5, v6)) | (growth_rate(first_movers, v1) = v4 & greater(v2, v4)))) & ! [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(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v4, v1) & subpopulations(first_movers, efficient_producers, v0, v4) & ~ greater(v5, v6)) | (growth_rate(efficient_producers, v1) = v4 & greater(v4, v2)))) & ! [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] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : ? [v3] : ? [v4] : ((growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater_or_equal(v2, v1) & subpopulations(first_movers, efficient_producers, v0, v2) & ~ greater(v3, v4)) | (growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & in_environment(v0, v2) & ~ greater(v3, v4) & ! [v5] : ! [v6] : ( ~ (growth_rate(efficient_producers, v5) = v6) | ~ greater(v5, v2) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | ? [v7] : (growth_rate(first_movers, v5) = v7 & greater(v6, v7))) & ! [v5] : ! [v6] : ( ~ (growth_rate(first_movers, v5) = v6) | ~ greater(v5, v2) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | ? [v7] : (growth_rate(efficient_producers, v5) = v7 & greater(v7, v6)))))) & ! [v0] : ( ~ stable(v0) | ~ environment(v0) | ? [v1] : (in_environment(v0, v1) & ! [v2] : ! [v3] : ( ~ (growth_rate(efficient_producers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ? [v4] : (growth_rate(first_movers, v2) = v4 & greater(v3, v4))) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ? [v4] : (growth_rate(efficient_producers, v2) = v4 & greater(v4, v3)))))
% 3.74/1.67 |
% 3.74/1.67 | Applying alpha-rule on (1) yields:
% 3.74/1.67 | (2) ~ in_environment(all_0_1_1, all_0_0_0)
% 3.74/1.67 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0))
% 3.74/1.67 | (4) ! [v0] : ( ~ stable(v0) | ~ environment(v0) | ? [v1] : (in_environment(v0, v1) & ! [v2] : ! [v3] : ( ~ (growth_rate(efficient_producers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ? [v4] : (growth_rate(first_movers, v2) = v4 & greater(v3, v4))) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | ? [v4] : (growth_rate(efficient_producers, v2) = v4 & greater(v4, v3)))))
% 3.74/1.68 | (5) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : ? [v3] : ? [v4] : ((growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater_or_equal(v2, v1) & subpopulations(first_movers, efficient_producers, v0, v2) & ~ greater(v3, v4)) | (growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & in_environment(v0, v2) & ~ greater(v3, v4) & ! [v5] : ! [v6] : ( ~ (growth_rate(efficient_producers, v5) = v6) | ~ greater(v5, v2) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | ? [v7] : (growth_rate(first_movers, v5) = v7 & greater(v6, v7))) & ! [v5] : ! [v6] : ( ~ (growth_rate(first_movers, v5) = v6) | ~ greater(v5, v2) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | ? [v7] : (growth_rate(efficient_producers, v5) = v7 & greater(v7, v6))))))
% 3.74/1.68 | (6) stable(all_0_1_1)
% 3.74/1.68 | (7) critical_point(all_0_1_1) = all_0_0_0
% 3.74/1.68 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 3.74/1.68 | (9) ! [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(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v4, v1) & subpopulations(first_movers, efficient_producers, v0, v4) & ~ greater(v5, v6)) | (growth_rate(efficient_producers, v1) = v4 & greater(v4, v2))))
% 3.74/1.68 | (10) ! [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(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v4, v1) & subpopulations(first_movers, efficient_producers, v0, v4) & ~ greater(v5, v6)) | (growth_rate(first_movers, v1) = v4 & greater(v2, v4))))
% 3.74/1.68 | (11) environment(all_0_1_1)
% 3.74/1.68 |
% 3.74/1.68 | Instantiating formula (4) with all_0_1_1 and discharging atoms stable(all_0_1_1), environment(all_0_1_1), yields:
% 3.74/1.68 | (12) ? [v0] : (in_environment(all_0_1_1, v0) & ! [v1] : ! [v2] : ( ~ (growth_rate(efficient_producers, v1) = v2) | ~ greater_or_equal(v1, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v1) | ? [v3] : (growth_rate(first_movers, v1) = v3 & greater(v2, v3))) & ! [v1] : ! [v2] : ( ~ (growth_rate(first_movers, v1) = v2) | ~ greater_or_equal(v1, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v1) | ? [v3] : (growth_rate(efficient_producers, v1) = v3 & greater(v3, v2))))
% 3.74/1.68 |
% 3.74/1.68 | Instantiating (12) with all_8_0_2 yields:
% 3.74/1.68 | (13) in_environment(all_0_1_1, all_8_0_2) & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ greater_or_equal(v0, all_8_0_2) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2))) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater_or_equal(v0, all_8_0_2) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1)))
% 3.74/1.68 |
% 3.74/1.68 | Applying alpha-rule on (13) yields:
% 3.74/1.68 | (14) in_environment(all_0_1_1, all_8_0_2)
% 3.74/1.68 | (15) ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ greater_or_equal(v0, all_8_0_2) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2)))
% 3.74/1.68 | (16) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater_or_equal(v0, all_8_0_2) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1)))
% 3.74/1.69 |
% 3.74/1.69 | Instantiating formula (5) with all_8_0_2, all_0_1_1 and discharging atoms in_environment(all_0_1_1, all_8_0_2), environment(all_0_1_1), yields:
% 3.74/1.69 | (17) ? [v0] : ? [v1] : ? [v2] : ((growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater_or_equal(v0, all_8_0_2) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(v1, v2)) | (growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & in_environment(all_0_1_1, v0) & ~ greater(v1, v2) & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ~ greater(v3, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v3) | ? [v5] : (growth_rate(first_movers, v3) = v5 & greater(v4, v5))) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ~ greater(v3, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v3) | ? [v5] : (growth_rate(efficient_producers, v3) = v5 & greater(v5, v4)))))
% 3.74/1.69 |
% 3.74/1.69 | Instantiating (17) with all_16_0_3, all_16_1_4, all_16_2_5 yields:
% 3.74/1.69 | (18) (growth_rate(efficient_producers, all_16_2_5) = all_16_1_4 & growth_rate(first_movers, all_16_2_5) = all_16_0_3 & greater_or_equal(all_16_2_5, all_8_0_2) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_2_5) & ~ greater(all_16_1_4, all_16_0_3)) | (growth_rate(efficient_producers, all_16_2_5) = all_16_1_4 & growth_rate(first_movers, all_16_2_5) = all_16_0_3 & in_environment(all_0_1_1, all_16_2_5) & ~ greater(all_16_1_4, all_16_0_3) & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2))) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1))))
% 3.74/1.69 |
% 3.74/1.69 +-Applying beta-rule and splitting (18), into two cases.
% 3.74/1.69 |-Branch one:
% 3.74/1.69 | (19) growth_rate(efficient_producers, all_16_2_5) = all_16_1_4 & growth_rate(first_movers, all_16_2_5) = all_16_0_3 & greater_or_equal(all_16_2_5, all_8_0_2) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_2_5) & ~ greater(all_16_1_4, all_16_0_3)
% 3.74/1.69 |
% 3.74/1.69 | Applying alpha-rule on (19) yields:
% 3.74/1.69 | (20) greater_or_equal(all_16_2_5, all_8_0_2)
% 3.74/1.69 | (21) growth_rate(first_movers, all_16_2_5) = all_16_0_3
% 3.74/1.69 | (22) subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_2_5)
% 3.74/1.69 | (23) ~ greater(all_16_1_4, all_16_0_3)
% 3.74/1.69 | (24) growth_rate(efficient_producers, all_16_2_5) = all_16_1_4
% 3.74/1.69 |
% 3.74/1.69 | Instantiating formula (15) with all_16_1_4, all_16_2_5 and discharging atoms growth_rate(efficient_producers, all_16_2_5) = all_16_1_4, greater_or_equal(all_16_2_5, all_8_0_2), subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_2_5), yields:
% 3.74/1.69 | (25) ? [v0] : (growth_rate(first_movers, all_16_2_5) = v0 & greater(all_16_1_4, v0))
% 3.74/1.69 |
% 3.74/1.69 | Instantiating (25) with all_26_0_7 yields:
% 3.74/1.69 | (26) growth_rate(first_movers, all_16_2_5) = all_26_0_7 & greater(all_16_1_4, all_26_0_7)
% 3.74/1.69 |
% 3.74/1.69 | Applying alpha-rule on (26) yields:
% 3.74/1.69 | (27) growth_rate(first_movers, all_16_2_5) = all_26_0_7
% 3.74/1.69 | (28) greater(all_16_1_4, all_26_0_7)
% 3.74/1.69 |
% 3.74/1.69 | Instantiating formula (8) with first_movers, all_16_2_5, all_26_0_7, all_16_0_3 and discharging atoms growth_rate(first_movers, all_16_2_5) = all_26_0_7, growth_rate(first_movers, all_16_2_5) = all_16_0_3, yields:
% 3.74/1.69 | (29) all_26_0_7 = all_16_0_3
% 3.74/1.69 |
% 3.74/1.69 | From (29) and (28) follows:
% 3.74/1.69 | (30) greater(all_16_1_4, all_16_0_3)
% 3.74/1.69 |
% 3.74/1.69 | Using (30) and (23) yields:
% 3.74/1.69 | (31) $false
% 3.74/1.69 |
% 3.74/1.69 |-The branch is then unsatisfiable
% 3.74/1.69 |-Branch two:
% 3.74/1.69 | (32) growth_rate(efficient_producers, all_16_2_5) = all_16_1_4 & growth_rate(first_movers, all_16_2_5) = all_16_0_3 & in_environment(all_0_1_1, all_16_2_5) & ~ greater(all_16_1_4, all_16_0_3) & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2))) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1)))
% 3.74/1.70 |
% 3.74/1.70 | Applying alpha-rule on (32) yields:
% 3.74/1.70 | (21) growth_rate(first_movers, all_16_2_5) = all_16_0_3
% 3.74/1.70 | (23) ~ greater(all_16_1_4, all_16_0_3)
% 3.74/1.70 | (35) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(efficient_producers, v0) = v2 & greater(v2, v1)))
% 3.74/1.70 | (36) in_environment(all_0_1_1, all_16_2_5)
% 3.74/1.70 | (37) ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ~ greater(v0, all_16_2_5) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ? [v2] : (growth_rate(first_movers, v0) = v2 & greater(v1, v2)))
% 3.74/1.70 | (24) growth_rate(efficient_producers, all_16_2_5) = all_16_1_4
% 3.74/1.70 |
% 3.74/1.70 | Instantiating formula (10) with all_0_0_0, all_16_1_4, all_16_2_5, all_0_1_1 and discharging atoms critical_point(all_0_1_1) = all_0_0_0, growth_rate(efficient_producers, all_16_2_5) = all_16_1_4, in_environment(all_0_1_1, all_16_2_5), environment(all_0_1_1), yields:
% 3.74/1.70 | (39) all_16_2_5 = all_0_0_0 | ? [v0] : ? [v1] : ? [v2] : ((growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v0, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(v1, v2)) | (growth_rate(first_movers, all_16_2_5) = v0 & greater(all_16_1_4, v0)))
% 3.74/1.70 |
% 3.74/1.70 | Instantiating formula (9) with all_0_0_0, all_16_0_3, all_16_2_5, all_0_1_1 and discharging atoms critical_point(all_0_1_1) = all_0_0_0, growth_rate(first_movers, all_16_2_5) = all_16_0_3, in_environment(all_0_1_1, all_16_2_5), environment(all_0_1_1), yields:
% 3.74/1.70 | (40) all_16_2_5 = all_0_0_0 | ? [v0] : ? [v1] : ? [v2] : ((growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v0, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(v1, v2)) | (growth_rate(efficient_producers, all_16_2_5) = v0 & greater(v0, all_16_0_3)))
% 3.74/1.70 |
% 3.74/1.70 +-Applying beta-rule and splitting (40), into two cases.
% 3.74/1.70 |-Branch one:
% 3.74/1.70 | (41) all_16_2_5 = all_0_0_0
% 3.74/1.70 |
% 3.74/1.70 | From (41) and (36) follows:
% 3.74/1.70 | (42) in_environment(all_0_1_1, all_0_0_0)
% 3.74/1.70 |
% 3.74/1.70 | Using (42) and (2) yields:
% 3.74/1.70 | (31) $false
% 3.74/1.70 |
% 3.74/1.70 |-The branch is then unsatisfiable
% 3.74/1.70 |-Branch two:
% 3.74/1.70 | (44) ~ (all_16_2_5 = all_0_0_0)
% 3.74/1.70 | (45) ? [v0] : ? [v1] : ? [v2] : ((growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v0, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(v1, v2)) | (growth_rate(efficient_producers, all_16_2_5) = v0 & greater(v0, all_16_0_3)))
% 3.74/1.70 |
% 3.74/1.70 +-Applying beta-rule and splitting (39), into two cases.
% 3.74/1.70 |-Branch one:
% 3.74/1.70 | (41) all_16_2_5 = all_0_0_0
% 3.74/1.70 |
% 3.74/1.70 | Equations (41) can reduce 44 to:
% 3.74/1.70 | (47) $false
% 3.74/1.70 |
% 3.74/1.70 |-The branch is then unsatisfiable
% 3.74/1.70 |-Branch two:
% 3.74/1.70 | (44) ~ (all_16_2_5 = all_0_0_0)
% 3.74/1.70 | (49) ? [v0] : ? [v1] : ? [v2] : ((growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v0, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(v1, v2)) | (growth_rate(first_movers, all_16_2_5) = v0 & greater(all_16_1_4, v0)))
% 3.74/1.70 |
% 3.74/1.70 | Instantiating (49) with all_36_0_14, all_36_1_15, all_36_2_16 yields:
% 3.74/1.70 | (50) (growth_rate(efficient_producers, all_36_2_16) = all_36_1_15 & growth_rate(first_movers, all_36_2_16) = all_36_0_14 & greater(all_36_2_16, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_36_2_16) & ~ greater(all_36_1_15, all_36_0_14)) | (growth_rate(first_movers, all_16_2_5) = all_36_2_16 & greater(all_16_1_4, all_36_2_16))
% 3.74/1.70 |
% 3.74/1.70 +-Applying beta-rule and splitting (50), into two cases.
% 3.74/1.70 |-Branch one:
% 3.74/1.70 | (51) growth_rate(efficient_producers, all_36_2_16) = all_36_1_15 & growth_rate(first_movers, all_36_2_16) = all_36_0_14 & greater(all_36_2_16, all_16_2_5) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_36_2_16) & ~ greater(all_36_1_15, all_36_0_14)
% 3.74/1.71 |
% 3.74/1.71 | Applying alpha-rule on (51) yields:
% 3.74/1.71 | (52) greater(all_36_2_16, all_16_2_5)
% 3.74/1.71 | (53) growth_rate(efficient_producers, all_36_2_16) = all_36_1_15
% 3.74/1.71 | (54) ~ greater(all_36_1_15, all_36_0_14)
% 3.74/1.71 | (55) growth_rate(first_movers, all_36_2_16) = all_36_0_14
% 3.74/1.71 | (56) subpopulations(first_movers, efficient_producers, all_0_1_1, all_36_2_16)
% 3.74/1.71 |
% 3.74/1.71 | Instantiating formula (37) with all_36_1_15, all_36_2_16 and discharging atoms growth_rate(efficient_producers, all_36_2_16) = all_36_1_15, greater(all_36_2_16, all_16_2_5), subpopulations(first_movers, efficient_producers, all_0_1_1, all_36_2_16), yields:
% 3.74/1.71 | (57) ? [v0] : (growth_rate(first_movers, all_36_2_16) = v0 & greater(all_36_1_15, v0))
% 3.74/1.71 |
% 3.74/1.71 | Instantiating (57) with all_52_0_20 yields:
% 3.74/1.71 | (58) growth_rate(first_movers, all_36_2_16) = all_52_0_20 & greater(all_36_1_15, all_52_0_20)
% 3.74/1.71 |
% 3.74/1.71 | Applying alpha-rule on (58) yields:
% 3.74/1.71 | (59) growth_rate(first_movers, all_36_2_16) = all_52_0_20
% 3.74/1.71 | (60) greater(all_36_1_15, all_52_0_20)
% 3.74/1.71 |
% 3.74/1.71 | Instantiating formula (8) with first_movers, all_36_2_16, all_52_0_20, all_36_0_14 and discharging atoms growth_rate(first_movers, all_36_2_16) = all_52_0_20, growth_rate(first_movers, all_36_2_16) = all_36_0_14, yields:
% 3.74/1.71 | (61) all_52_0_20 = all_36_0_14
% 3.74/1.71 |
% 3.74/1.71 | From (61) and (60) follows:
% 3.74/1.71 | (62) greater(all_36_1_15, all_36_0_14)
% 3.74/1.71 |
% 3.74/1.71 | Using (62) and (54) yields:
% 3.74/1.71 | (31) $false
% 3.74/1.71 |
% 3.74/1.71 |-The branch is then unsatisfiable
% 3.74/1.71 |-Branch two:
% 3.74/1.71 | (64) growth_rate(first_movers, all_16_2_5) = all_36_2_16 & greater(all_16_1_4, all_36_2_16)
% 3.74/1.71 |
% 3.74/1.71 | Applying alpha-rule on (64) yields:
% 3.74/1.71 | (65) growth_rate(first_movers, all_16_2_5) = all_36_2_16
% 3.74/1.71 | (66) greater(all_16_1_4, all_36_2_16)
% 3.74/1.71 |
% 3.74/1.71 | Instantiating formula (8) with first_movers, all_16_2_5, all_36_2_16, all_16_0_3 and discharging atoms growth_rate(first_movers, all_16_2_5) = all_36_2_16, growth_rate(first_movers, all_16_2_5) = all_16_0_3, yields:
% 3.74/1.71 | (67) all_36_2_16 = all_16_0_3
% 3.74/1.71 |
% 3.74/1.71 | From (67) and (66) follows:
% 3.74/1.71 | (30) greater(all_16_1_4, all_16_0_3)
% 3.74/1.71 |
% 3.74/1.71 | Using (30) and (23) yields:
% 3.74/1.71 | (31) $false
% 3.74/1.71 |
% 3.74/1.71 |-The branch is then unsatisfiable
% 3.74/1.71 % SZS output end Proof for theBenchmark
% 3.74/1.71
% 3.74/1.71 1102ms
%------------------------------------------------------------------------------