TSTP Solution File: MGT036+3 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : MGT036+3 : 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 22:07:05 EDT 2022
% Result : Theorem 1.88s 1.13s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 07:44:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.62 ____ _
% 0.56/0.62 ___ / __ \_____(_)___ ________ __________
% 0.56/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.62
% 0.56/0.62 A Theorem Prover for First-Order Logic
% 0.56/0.62 (ePrincess v.1.0)
% 0.56/0.62
% 0.56/0.62 (c) Philipp Rümmer, 2009-2015
% 0.56/0.62 (c) Peter Backeman, 2014-2015
% 0.56/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.62 Bug reports to peter@backeman.se
% 0.56/0.62
% 0.56/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.62
% 0.56/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.90 Prover 0: Preprocessing ...
% 1.68/1.02 Prover 0: Constructing countermodel ...
% 1.88/1.13 Prover 0: proved (455ms)
% 1.88/1.13
% 1.88/1.13 No countermodel exists, formula is valid
% 1.88/1.13 % SZS status Theorem for theBenchmark
% 1.88/1.13
% 1.88/1.13 Generating proof ... found it (size 6)
% 2.48/1.28
% 2.48/1.28 % SZS output start Proof for theBenchmark
% 2.48/1.28 Assumed formulas after preprocessing and simplification:
% 2.48/1.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (growth_rate(efficient_producers, v1) = v3 & growth_rate(first_movers, v1) = v2 & greater(zero, v3) & greater_or_equal(v2, zero) & subpopulations(first_movers, efficient_producers, v0, v1) & environment(v0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (growth_rate(v6, v7) = v8) | ~ (growth_rate(v5, v7) = v9) | ~ outcompetes(v6, v5, v7) | ~ subpopulations(v5, v6, v4, v7) | ~ environment(v4) | greater(zero, v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (growth_rate(v6, v7) = v8) | ~ (growth_rate(v5, v7) = v9) | ~ outcompetes(v6, v5, v7) | ~ subpopulations(v5, v6, v4, v7) | ~ environment(v4) | greater_or_equal(v8, zero)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (growth_rate(v6, v7) = v8) | ~ (growth_rate(v5, v7) = v9) | ~ greater(zero, v9) | ~ greater_or_equal(v8, zero) | ~ subpopulations(v5, v6, v4, v7) | ~ environment(v4) | outcompetes(v6, v5, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (growth_rate(v7, v6) = v5) | ~ (growth_rate(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ subpopulations(v5, v6, v4, v7) | ~ environment(v4) | subpopulations(v6, v5, v4, v7)) & ! [v4] : ! [v5] : ( ~ outcompetes(first_movers, efficient_producers, v5) | ~ subpopulations(first_movers, efficient_producers, v4, v5) | ~ environment(v4)))
% 2.66/1.32 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.66/1.32 | (1) growth_rate(efficient_producers, all_0_2_2) = all_0_0_0 & growth_rate(first_movers, all_0_2_2) = all_0_1_1 & greater(zero, all_0_0_0) & greater_or_equal(all_0_1_1, zero) & subpopulations(first_movers, efficient_producers, all_0_3_3, all_0_2_2) & environment(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ outcompetes(v2, v1, v3) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater(zero, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ outcompetes(v2, v1, v3) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater_or_equal(v4, zero)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | outcompetes(v2, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | subpopulations(v2, v1, v0, v3)) & ! [v0] : ! [v1] : ( ~ outcompetes(first_movers, efficient_producers, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0))
% 2.66/1.32 |
% 2.66/1.32 | Applying alpha-rule on (1) yields:
% 2.66/1.32 | (2) ! [v0] : ! [v1] : ( ~ outcompetes(first_movers, efficient_producers, v1) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0))
% 2.66/1.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ greater(zero, v5) | ~ greater_or_equal(v4, zero) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | outcompetes(v2, v1, v3))
% 2.66/1.33 | (4) greater(zero, all_0_0_0)
% 2.66/1.33 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | subpopulations(v2, v1, v0, v3))
% 2.66/1.33 | (6) subpopulations(first_movers, efficient_producers, all_0_3_3, all_0_2_2)
% 2.66/1.33 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 2.66/1.33 | (8) growth_rate(efficient_producers, all_0_2_2) = all_0_0_0
% 2.66/1.33 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ outcompetes(v2, v1, v3) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater_or_equal(v4, zero))
% 2.66/1.33 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (growth_rate(v2, v3) = v4) | ~ (growth_rate(v1, v3) = v5) | ~ outcompetes(v2, v1, v3) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | greater(zero, v5))
% 2.66/1.33 | (11) greater_or_equal(all_0_1_1, zero)
% 2.66/1.33 | (12) environment(all_0_3_3)
% 2.66/1.33 | (13) growth_rate(first_movers, all_0_2_2) = all_0_1_1
% 2.66/1.33 |
% 2.66/1.33 | Instantiating formula (5) with all_0_2_2, efficient_producers, first_movers, all_0_3_3 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_3_3, all_0_2_2), environment(all_0_3_3), yields:
% 2.66/1.33 | (14) subpopulations(efficient_producers, first_movers, all_0_3_3, all_0_2_2)
% 2.66/1.33 |
% 2.66/1.33 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_2_2, first_movers, efficient_producers, all_0_3_3 and discharging atoms growth_rate(efficient_producers, all_0_2_2) = all_0_0_0, growth_rate(first_movers, all_0_2_2) = all_0_1_1, greater(zero, all_0_0_0), greater_or_equal(all_0_1_1, zero), subpopulations(efficient_producers, first_movers, all_0_3_3, all_0_2_2), environment(all_0_3_3), yields:
% 2.66/1.33 | (15) outcompetes(first_movers, efficient_producers, all_0_2_2)
% 2.66/1.33 |
% 2.66/1.33 | Instantiating formula (2) with all_0_2_2, all_0_3_3 and discharging atoms outcompetes(first_movers, efficient_producers, all_0_2_2), subpopulations(first_movers, efficient_producers, all_0_3_3, all_0_2_2), environment(all_0_3_3), yields:
% 2.66/1.33 | (16) $false
% 2.66/1.33 |
% 2.66/1.34 |-The branch is then unsatisfiable
% 2.66/1.34 % SZS output end Proof for theBenchmark
% 2.66/1.34
% 2.66/1.34 701ms
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