TSTP Solution File: MGT028+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 22:07:02 EDT 2022
% Result : Theorem 2.28s 1.32s
% Output : Proof 3.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n026.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 : 600
% 0.13/0.34 % DateTime : Thu Jun 9 09:46:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.61 ____ _
% 0.47/0.61 ___ / __ \_____(_)___ ________ __________
% 0.47/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.61
% 0.47/0.61 A Theorem Prover for First-Order Logic
% 0.47/0.61 (ePrincess v.1.0)
% 0.47/0.61
% 0.47/0.61 (c) Philipp Rümmer, 2009-2015
% 0.47/0.61 (c) Peter Backeman, 2014-2015
% 0.47/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.61 Bug reports to peter@backeman.se
% 0.47/0.61
% 0.47/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.61
% 0.47/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.95 Prover 0: Preprocessing ...
% 1.79/1.12 Prover 0: Constructing countermodel ...
% 2.28/1.31 Prover 0: proved (649ms)
% 2.28/1.32
% 2.28/1.32 No countermodel exists, formula is valid
% 2.28/1.32 % SZS status Theorem for theBenchmark
% 2.28/1.32
% 2.28/1.32 Generating proof ... found it (size 17)
% 2.93/1.50
% 2.93/1.50 % SZS output start Proof for theBenchmark
% 2.93/1.50 Assumed formulas after preprocessing and simplification:
% 2.93/1.50 | (0) ? [v0] : ? [v1] : (appear(efficient_producers, v0) = v1 & stable(v0) & environment(v0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (appear(v5, v4) = v3) | ~ (appear(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (growth_rate(v5, v4) = v3) | ~ (growth_rate(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (appear(efficient_producers, v2) = v3) | ~ in_environment(v2, v4) | ~ stable(v2) | ~ environment(v2) | ? [v5] : ? [v6] : ((growth_rate(first_movers, v5) = v6 & greater_or_equal(v5, v4) & subpopulations(first_movers, efficient_producers, v2, v5) & ~ greater(zero, v6)) | (greater(v5, v3) & ! [v7] : ! [v8] : ( ~ (growth_rate(first_movers, v7) = v8) | ~ greater_or_equal(v7, v5) | ~ subpopulations(first_movers, efficient_producers, v2, v7) | greater(zero, v8))))) & ! [v2] : ( ~ greater(v2, v1) | ? [v3] : ? [v4] : (growth_rate(first_movers, v3) = v4 & greater_or_equal(v3, v2) & subpopulations(first_movers, efficient_producers, v0, v3) & ~ greater(zero, v4))) & ! [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) | greater(v5, zero)) & ! [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(zero, v6))) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ~ greater_or_equal(v4, v3) | ~ subpopulations(first_movers, efficient_producers, v2, v4) | greater(zero, v5)) & ! [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, zero))))))
% 3.15/1.54 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.15/1.54 | (1) appear(efficient_producers, all_0_1_1) = all_0_0_0 & stable(all_0_1_1) & environment(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (appear(v3, v2) = v1) | ~ (appear(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (appear(efficient_producers, v0) = v1) | ~ in_environment(v0, v2) | ~ stable(v0) | ~ environment(v0) | ? [v3] : ? [v4] : ((growth_rate(first_movers, v3) = v4 & greater_or_equal(v3, v2) & subpopulations(first_movers, efficient_producers, v0, v3) & ~ greater(zero, v4)) | (greater(v3, v1) & ! [v5] : ! [v6] : ( ~ (growth_rate(first_movers, v5) = v6) | ~ greater_or_equal(v5, v3) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | greater(zero, v6))))) & ! [v0] : ( ~ greater(v0, all_0_0_0) | ? [v1] : ? [v2] : (growth_rate(first_movers, v1) = v2 & greater_or_equal(v1, v0) & subpopulations(first_movers, efficient_producers, all_0_1_1, v1) & ~ greater(zero, v2))) & ! [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) | greater(v3, zero)) & ! [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(zero, v4))) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | greater(zero, v3)) & ! [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, zero)))))
% 3.15/1.55 |
% 3.15/1.55 | Applying alpha-rule on (1) yields:
% 3.15/1.55 | (2) appear(efficient_producers, all_0_1_1) = all_0_0_0
% 3.15/1.55 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (appear(efficient_producers, v0) = v1) | ~ in_environment(v0, v2) | ~ stable(v0) | ~ environment(v0) | ? [v3] : ? [v4] : ((growth_rate(first_movers, v3) = v4 & greater_or_equal(v3, v2) & subpopulations(first_movers, efficient_producers, v0, v3) & ~ greater(zero, v4)) | (greater(v3, v1) & ! [v5] : ! [v6] : ( ~ (growth_rate(first_movers, v5) = v6) | ~ greater_or_equal(v5, v3) | ~ subpopulations(first_movers, efficient_producers, v0, v5) | greater(zero, v6)))))
% 3.15/1.55 | (4) environment(all_0_1_1)
% 3.15/1.55 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (appear(v3, v2) = v1) | ~ (appear(v3, v2) = v0))
% 3.15/1.55 | (6) ! [v0] : ( ~ greater(v0, all_0_0_0) | ? [v1] : ? [v2] : (growth_rate(first_movers, v1) = v2 & greater_or_equal(v1, v0) & subpopulations(first_movers, efficient_producers, all_0_1_1, v1) & ~ greater(zero, v2)))
% 3.15/1.55 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 3.15/1.55 | (8) stable(all_0_1_1)
% 3.15/1.55 | (9) ! [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) | greater(v3, zero)) & ! [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(zero, v4))) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ greater_or_equal(v2, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v2) | greater(zero, v3)) & ! [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, zero)))))
% 3.15/1.55 |
% 3.15/1.55 | Instantiating formula (9) with all_0_1_1 and discharging atoms stable(all_0_1_1), environment(all_0_1_1), yields:
% 3.15/1.55 | (10) ? [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) | greater(v2, zero)) & ! [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(zero, v3))) & ! [v1] : ! [v2] : ( ~ (growth_rate(first_movers, v1) = v2) | ~ greater_or_equal(v1, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v1) | greater(zero, v2)) & ! [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, zero))))
% 3.15/1.56 |
% 3.15/1.56 | Instantiating (10) with all_8_0_2 yields:
% 3.15/1.56 | (11) 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) | greater(v1, zero)) & ! [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(zero, 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) | greater(zero, v1)) & ! [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, zero)))
% 3.15/1.56 |
% 3.15/1.56 | Applying alpha-rule on (11) yields:
% 3.15/1.56 | (12) in_environment(all_0_1_1, all_8_0_2)
% 3.15/1.56 | (13) ! [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) | greater(zero, v1))
% 3.15/1.56 | (14) ! [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) | greater(v1, zero))
% 3.15/1.56 | (15) ! [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, zero)))
% 3.15/1.56 | (16) ! [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(zero, v2)))
% 3.15/1.56 |
% 3.15/1.56 | Instantiating formula (3) with all_8_0_2, all_0_0_0, all_0_1_1 and discharging atoms appear(efficient_producers, all_0_1_1) = all_0_0_0, in_environment(all_0_1_1, all_8_0_2), stable(all_0_1_1), environment(all_0_1_1), yields:
% 3.15/1.56 | (17) ? [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) & ~ greater(zero, v1)) | (greater(v0, all_0_0_0) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ~ greater_or_equal(v2, v0) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v2) | greater(zero, v3))))
% 3.15/1.56 |
% 3.15/1.56 | Instantiating (17) with all_16_0_3, all_16_1_4 yields:
% 3.15/1.56 | (18) (growth_rate(first_movers, all_16_1_4) = all_16_0_3 & greater_or_equal(all_16_1_4, all_8_0_2) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_1_4) & ~ greater(zero, all_16_0_3)) | (greater(all_16_1_4, all_0_0_0) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater_or_equal(v0, all_16_1_4) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | greater(zero, v1)))
% 3.26/1.56 |
% 3.26/1.56 +-Applying beta-rule and splitting (18), into two cases.
% 3.26/1.56 |-Branch one:
% 3.26/1.56 | (19) growth_rate(first_movers, all_16_1_4) = all_16_0_3 & greater_or_equal(all_16_1_4, all_8_0_2) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_1_4) & ~ greater(zero, all_16_0_3)
% 3.26/1.56 |
% 3.26/1.56 | Applying alpha-rule on (19) yields:
% 3.26/1.57 | (20) growth_rate(first_movers, all_16_1_4) = all_16_0_3
% 3.26/1.57 | (21) greater_or_equal(all_16_1_4, all_8_0_2)
% 3.26/1.57 | (22) subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_1_4)
% 3.26/1.57 | (23) ~ greater(zero, all_16_0_3)
% 3.26/1.57 |
% 3.26/1.57 | Instantiating formula (13) with all_16_0_3, all_16_1_4 and discharging atoms growth_rate(first_movers, all_16_1_4) = all_16_0_3, greater_or_equal(all_16_1_4, all_8_0_2), subpopulations(first_movers, efficient_producers, all_0_1_1, all_16_1_4), ~ greater(zero, all_16_0_3), yields:
% 3.26/1.57 | (24) $false
% 3.26/1.57 |
% 3.26/1.57 |-The branch is then unsatisfiable
% 3.26/1.57 |-Branch two:
% 3.26/1.57 | (25) greater(all_16_1_4, all_0_0_0) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater_or_equal(v0, all_16_1_4) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | greater(zero, v1))
% 3.26/1.57 |
% 3.26/1.57 | Applying alpha-rule on (25) yields:
% 3.26/1.57 | (26) greater(all_16_1_4, all_0_0_0)
% 3.26/1.57 | (27) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ greater_or_equal(v0, all_16_1_4) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | greater(zero, v1))
% 3.26/1.57 |
% 3.26/1.57 | Instantiating formula (6) with all_16_1_4 and discharging atoms greater(all_16_1_4, all_0_0_0), yields:
% 3.26/1.57 | (28) ? [v0] : ? [v1] : (growth_rate(first_movers, v0) = v1 & greater_or_equal(v0, all_16_1_4) & subpopulations(first_movers, efficient_producers, all_0_1_1, v0) & ~ greater(zero, v1))
% 3.26/1.57 |
% 3.26/1.57 | Instantiating (28) with all_25_0_5, all_25_1_6 yields:
% 3.26/1.57 | (29) growth_rate(first_movers, all_25_1_6) = all_25_0_5 & greater_or_equal(all_25_1_6, all_16_1_4) & subpopulations(first_movers, efficient_producers, all_0_1_1, all_25_1_6) & ~ greater(zero, all_25_0_5)
% 3.26/1.57 |
% 3.26/1.57 | Applying alpha-rule on (29) yields:
% 3.26/1.57 | (30) growth_rate(first_movers, all_25_1_6) = all_25_0_5
% 3.26/1.57 | (31) greater_or_equal(all_25_1_6, all_16_1_4)
% 3.26/1.57 | (32) subpopulations(first_movers, efficient_producers, all_0_1_1, all_25_1_6)
% 3.26/1.57 | (33) ~ greater(zero, all_25_0_5)
% 3.26/1.57 |
% 3.26/1.57 | Instantiating formula (27) with all_25_0_5, all_25_1_6 and discharging atoms growth_rate(first_movers, all_25_1_6) = all_25_0_5, greater_or_equal(all_25_1_6, all_16_1_4), subpopulations(first_movers, efficient_producers, all_0_1_1, all_25_1_6), ~ greater(zero, all_25_0_5), yields:
% 3.26/1.57 | (24) $false
% 3.26/1.57 |
% 3.26/1.57 |-The branch is then unsatisfiable
% 3.26/1.57 % SZS output end Proof for theBenchmark
% 3.26/1.57
% 3.26/1.57 946ms
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