TSTP Solution File: MGT036+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT036+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 22:07:04 EDT 2022
% Result : Theorem 2.91s 1.45s
% Output : Proof 4.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 09:55:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.91 Prover 0: Preprocessing ...
% 1.68/1.08 Prover 0: Warning: ignoring some quantifiers
% 1.86/1.10 Prover 0: Constructing countermodel ...
% 2.42/1.29 Prover 0: gave up
% 2.42/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.42/1.31 Prover 1: Preprocessing ...
% 2.71/1.38 Prover 1: Constructing countermodel ...
% 2.91/1.45 Prover 1: proved (166ms)
% 2.91/1.45
% 2.91/1.45 No countermodel exists, formula is valid
% 2.91/1.45 % SZS status Theorem for theBenchmark
% 2.91/1.45
% 2.91/1.45 Generating proof ... found it (size 126)
% 4.36/1.75
% 4.36/1.75 % SZS output start Proof for theBenchmark
% 4.36/1.75 Assumed formulas after preprocessing and simplification:
% 4.36/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (resilience(efficient_producers) = v0 & resilience(first_movers) = v1 & outcompetes(first_movers, efficient_producers, v3) = 0 & greater(v0, v1) = 0 & environment(v2) = 0 & subpopulations(first_movers, efficient_producers, v2, v3) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (subpopulations(v9, v8, v7, v6) = v5) | ~ (subpopulations(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (resilience(v6) = v8) | ~ (resilience(v5) = v9) | ~ (greater(v8, v9) = 0) | ~ (in_environment(v4, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (growth_rate(v6, v7) = v13 & growth_rate(v5, v7) = v11 & greater(zero, v13) = v14 & greater(zero, v11) = v12 & environment(v4) = v10 & ( ~ (v14 = 0) | ~ (v10 = 0) | v12 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (outcompetes(v8, v7, v6) = v5) | ~ (outcompetes(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (outcompetes(v6, v5, v7) = v8) | ~ (environment(v4) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (growth_rate(v6, v7) = v10 & growth_rate(v5, v7) = v12 & greater_or_equal(v10, zero) = v11 & greater(zero, v12) = v13 & subpopulations(v5, v6, v4, v7) = v9 & ( ~ (v9 = 0) | (( ~ (v13 = 0) | ~ (v11 = 0) | v8 = 0) & ( ~ (v8 = 0) | (v13 = 0 & v11 = 0)))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (subpopulations(v5, v6, v4, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (growth_rate(v5, v7) = v10 & greater_or_equal(v10, zero) = v11 & greater(zero, v10) = v12 & environment(v4) = v9 & ( ~ (v12 = 0) | (v9 = 0 & v8 = 0 & ~ (v11 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (growth_rate(v7, v6) = v5) | ~ (growth_rate(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (greater_or_equal(v7, v6) = v5) | ~ (greater_or_equal(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (greater(v7, v6) = v5) | ~ (greater(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (in_environment(v7, v6) = v5) | ~ (in_environment(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subpopulations(v5, v6, v4, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (growth_rate(v5, v7) = v8 & greater_or_equal(v8, zero) = v11 & greater(zero, v8) = v9 & environment(v4) = v10 & ( ~ (v10 = 0) | v11 = 0 | v9 = 0))) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (resilience(v6) = v5) | ~ (resilience(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (environment(v6) = v5) | ~ (environment(v6) = v4)) & ! [v4] : ! [v5] : ( ~ (subpopulations(first_movers, efficient_producers, v4, v5) = 0) | ? [v6] : ? [v7] : (in_environment(v4, v5) = v7 & environment(v4) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4] : ! [v5] : ( ~ (subpopulations(first_movers, efficient_producers, v4, v5) = 0) | ? [v6] : ? [v7] : (environment(v4) = v6 & subpopulations(efficient_producers, first_movers, v4, v5) = v7 & ( ~ (v6 = 0) | v7 = 0))))
% 4.75/1.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.75/1.78 | (1) resilience(efficient_producers) = all_0_3_3 & resilience(first_movers) = all_0_2_2 & outcompetes(first_movers, efficient_producers, all_0_0_0) = 0 & greater(all_0_3_3, all_0_2_2) = 0 & environment(all_0_1_1) = 0 & subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (growth_rate(v2, v3) = v9 & growth_rate(v1, v3) = v7 & greater(zero, v9) = v10 & greater(zero, v7) = v8 & environment(v0) = v6 & ( ~ (v10 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (outcompetes(v4, v3, v2) = v1) | ~ (outcompetes(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (growth_rate(v2, v3) = v6 & growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) = v7 & greater(zero, v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = v7 & greater(zero, v6) = v8 & environment(v0) = v5 & ( ~ (v8 = 0) | (v5 = 0 & v4 = 0 & ~ (v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = v7 & greater(zero, v4) = v5 & environment(v0) = v6 & ( ~ (v6 = 0) | v7 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ (resilience(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (in_environment(v0, v1) = v3 & environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (environment(v0) = v2 & subpopulations(efficient_producers, first_movers, v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 4.75/1.79 |
% 4.75/1.79 | Applying alpha-rule on (1) yields:
% 4.75/1.79 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 4.75/1.79 | (3) resilience(efficient_producers) = all_0_3_3
% 4.75/1.79 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (growth_rate(v1, v3) = v4 & greater_or_equal(v4, zero) = v7 & greater(zero, v4) = v5 & environment(v0) = v6 & ( ~ (v6 = 0) | v7 = 0 | v5 = 0)))
% 4.75/1.79 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subpopulations(v1, v2, v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (growth_rate(v1, v3) = v6 & greater_or_equal(v6, zero) = v7 & greater(zero, v6) = v8 & environment(v0) = v5 & ( ~ (v8 = 0) | (v5 = 0 & v4 = 0 & ~ (v7 = 0)))))
% 4.75/1.79 | (6) ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (in_environment(v0, v1) = v3 & environment(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 4.83/1.79 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ (resilience(v2) = v0))
% 4.83/1.80 | (8) subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0
% 4.83/1.80 | (9) ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (environment(v0) = v2 & subpopulations(efficient_producers, first_movers, v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 4.83/1.80 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ (greater(v4, v5) = 0) | ~ (in_environment(v0, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (growth_rate(v2, v3) = v9 & growth_rate(v1, v3) = v7 & greater(zero, v9) = v10 & greater(zero, v7) = v8 & environment(v0) = v6 & ( ~ (v10 = 0) | ~ (v6 = 0) | v8 = 0)))
% 4.83/1.80 | (11) environment(all_0_1_1) = 0
% 4.83/1.80 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0))
% 4.83/1.80 | (13) outcompetes(first_movers, efficient_producers, all_0_0_0) = 0
% 4.83/1.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (outcompetes(v4, v3, v2) = v1) | ~ (outcompetes(v4, v3, v2) = v0))
% 4.83/1.80 | (15) resilience(first_movers) = all_0_2_2
% 4.83/1.80 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 4.83/1.80 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (outcompetes(v2, v1, v3) = v4) | ~ (environment(v0) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (growth_rate(v2, v3) = v6 & growth_rate(v1, v3) = v8 & greater_or_equal(v6, zero) = v7 & greater(zero, v8) = v9 & subpopulations(v1, v2, v0, v3) = v5 & ( ~ (v5 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = 0 & v7 = 0))))))
% 4.83/1.80 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0))
% 4.83/1.80 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 4.83/1.80 | (20) greater(all_0_3_3, all_0_2_2) = 0
% 4.83/1.80 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0))
% 4.83/1.80 |
% 4.83/1.80 | Instantiating formula (17) with 0, all_0_0_0, first_movers, efficient_producers, all_0_1_1 and discharging atoms outcompetes(first_movers, efficient_producers, all_0_0_0) = 0, environment(all_0_1_1) = 0, yields:
% 4.83/1.80 | (22) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (growth_rate(efficient_producers, all_0_0_0) = v3 & growth_rate(first_movers, all_0_0_0) = v1 & greater_or_equal(v1, zero) = v2 & greater(zero, v3) = v4 & subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 4.83/1.80 |
% 4.83/1.80 | Instantiating formula (6) with all_0_0_0, all_0_1_1 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.83/1.80 | (23) ? [v0] : ? [v1] : (in_environment(all_0_1_1, all_0_0_0) = v1 & environment(all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 4.83/1.80 |
% 4.83/1.80 | Instantiating formula (9) with all_0_0_0, all_0_1_1 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.83/1.80 | (24) ? [v0] : ? [v1] : (environment(all_0_1_1) = v0 & subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 4.83/1.80 |
% 4.83/1.81 | Instantiating formula (4) with all_0_0_0, efficient_producers, first_movers, all_0_1_1 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.83/1.81 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (growth_rate(first_movers, all_0_0_0) = v0 & greater_or_equal(v0, zero) = v3 & greater(zero, v0) = v1 & environment(all_0_1_1) = v2 & ( ~ (v2 = 0) | v3 = 0 | v1 = 0))
% 4.83/1.81 |
% 4.83/1.81 | Instantiating formula (5) with 0, all_0_0_0, efficient_producers, first_movers, all_0_1_1 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.83/1.81 | (26) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (growth_rate(first_movers, all_0_0_0) = v1 & greater_or_equal(v1, zero) = v2 & greater(zero, v1) = v3 & environment(all_0_1_1) = v0 & ( ~ (v3 = 0) | (v0 = 0 & ~ (v2 = 0))))
% 4.83/1.81 |
% 4.83/1.81 | Instantiating (26) with all_8_0_4, all_8_1_5, all_8_2_6, all_8_3_7 yields:
% 4.83/1.81 | (27) growth_rate(first_movers, all_0_0_0) = all_8_2_6 & greater_or_equal(all_8_2_6, zero) = all_8_1_5 & greater(zero, all_8_2_6) = all_8_0_4 & environment(all_0_1_1) = all_8_3_7 & ( ~ (all_8_0_4 = 0) | (all_8_3_7 = 0 & ~ (all_8_1_5 = 0)))
% 4.83/1.81 |
% 4.83/1.81 | Applying alpha-rule on (27) yields:
% 4.83/1.81 | (28) greater_or_equal(all_8_2_6, zero) = all_8_1_5
% 4.83/1.81 | (29) growth_rate(first_movers, all_0_0_0) = all_8_2_6
% 4.83/1.81 | (30) ~ (all_8_0_4 = 0) | (all_8_3_7 = 0 & ~ (all_8_1_5 = 0))
% 4.83/1.81 | (31) environment(all_0_1_1) = all_8_3_7
% 4.83/1.81 | (32) greater(zero, all_8_2_6) = all_8_0_4
% 4.83/1.81 |
% 4.83/1.81 | Instantiating (24) with all_10_0_8, all_10_1_9 yields:
% 4.83/1.81 | (33) environment(all_0_1_1) = all_10_1_9 & subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_10_0_8 & ( ~ (all_10_1_9 = 0) | all_10_0_8 = 0)
% 4.83/1.81 |
% 4.83/1.81 | Applying alpha-rule on (33) yields:
% 4.83/1.81 | (34) environment(all_0_1_1) = all_10_1_9
% 4.83/1.81 | (35) subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_10_0_8
% 4.83/1.81 | (36) ~ (all_10_1_9 = 0) | all_10_0_8 = 0
% 4.83/1.81 |
% 4.83/1.81 | Instantiating (23) with all_12_0_10, all_12_1_11 yields:
% 4.83/1.81 | (37) in_environment(all_0_1_1, all_0_0_0) = all_12_0_10 & environment(all_0_1_1) = all_12_1_11 & ( ~ (all_12_1_11 = 0) | all_12_0_10 = 0)
% 4.83/1.81 |
% 4.83/1.81 | Applying alpha-rule on (37) yields:
% 4.83/1.81 | (38) in_environment(all_0_1_1, all_0_0_0) = all_12_0_10
% 4.83/1.81 | (39) environment(all_0_1_1) = all_12_1_11
% 4.83/1.81 | (40) ~ (all_12_1_11 = 0) | all_12_0_10 = 0
% 4.83/1.81 |
% 4.83/1.81 | Instantiating (25) with all_14_0_12, all_14_1_13, all_14_2_14, all_14_3_15 yields:
% 4.83/1.81 | (41) growth_rate(first_movers, all_0_0_0) = all_14_3_15 & greater_or_equal(all_14_3_15, zero) = all_14_0_12 & greater(zero, all_14_3_15) = all_14_2_14 & environment(all_0_1_1) = all_14_1_13 & ( ~ (all_14_1_13 = 0) | all_14_0_12 = 0 | all_14_2_14 = 0)
% 4.83/1.81 |
% 4.83/1.81 | Applying alpha-rule on (41) yields:
% 4.83/1.81 | (42) ~ (all_14_1_13 = 0) | all_14_0_12 = 0 | all_14_2_14 = 0
% 4.83/1.81 | (43) environment(all_0_1_1) = all_14_1_13
% 4.83/1.81 | (44) growth_rate(first_movers, all_0_0_0) = all_14_3_15
% 4.91/1.81 | (45) greater_or_equal(all_14_3_15, zero) = all_14_0_12
% 4.91/1.81 | (46) greater(zero, all_14_3_15) = all_14_2_14
% 4.91/1.81 |
% 4.91/1.81 | Instantiating (22) with all_16_0_16, all_16_1_17, all_16_2_18, all_16_3_19, all_16_4_20 yields:
% 4.91/1.81 | (47) growth_rate(efficient_producers, all_0_0_0) = all_16_1_17 & growth_rate(first_movers, all_0_0_0) = all_16_3_19 & greater_or_equal(all_16_3_19, zero) = all_16_2_18 & greater(zero, all_16_1_17) = all_16_0_16 & subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_16_4_20 & ( ~ (all_16_4_20 = 0) | (all_16_0_16 = 0 & all_16_2_18 = 0))
% 4.91/1.81 |
% 4.91/1.81 | Applying alpha-rule on (47) yields:
% 4.91/1.81 | (48) subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_16_4_20
% 4.91/1.81 | (49) growth_rate(first_movers, all_0_0_0) = all_16_3_19
% 4.91/1.81 | (50) greater_or_equal(all_16_3_19, zero) = all_16_2_18
% 4.91/1.81 | (51) ~ (all_16_4_20 = 0) | (all_16_0_16 = 0 & all_16_2_18 = 0)
% 4.91/1.81 | (52) greater(zero, all_16_1_17) = all_16_0_16
% 4.91/1.81 | (53) growth_rate(efficient_producers, all_0_0_0) = all_16_1_17
% 4.91/1.81 |
% 4.91/1.81 | Instantiating formula (19) with first_movers, all_0_0_0, all_14_3_15, all_16_3_19 and discharging atoms growth_rate(first_movers, all_0_0_0) = all_16_3_19, growth_rate(first_movers, all_0_0_0) = all_14_3_15, yields:
% 4.91/1.81 | (54) all_16_3_19 = all_14_3_15
% 4.91/1.82 |
% 4.91/1.82 | Instantiating formula (19) with first_movers, all_0_0_0, all_8_2_6, all_16_3_19 and discharging atoms growth_rate(first_movers, all_0_0_0) = all_16_3_19, growth_rate(first_movers, all_0_0_0) = all_8_2_6, yields:
% 4.91/1.82 | (55) all_16_3_19 = all_8_2_6
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (18) with all_8_2_6, zero, all_8_1_5, all_16_2_18 and discharging atoms greater_or_equal(all_8_2_6, zero) = all_8_1_5, yields:
% 4.92/1.82 | (56) all_16_2_18 = all_8_1_5 | ~ (greater_or_equal(all_8_2_6, zero) = all_16_2_18)
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (2) with zero, all_8_2_6, all_8_0_4, all_14_2_14 and discharging atoms greater(zero, all_8_2_6) = all_8_0_4, yields:
% 4.92/1.82 | (57) all_14_2_14 = all_8_0_4 | ~ (greater(zero, all_8_2_6) = all_14_2_14)
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (16) with all_0_1_1, all_12_1_11, all_14_1_13 and discharging atoms environment(all_0_1_1) = all_14_1_13, environment(all_0_1_1) = all_12_1_11, yields:
% 4.92/1.82 | (58) all_14_1_13 = all_12_1_11
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (16) with all_0_1_1, all_10_1_9, 0 and discharging atoms environment(all_0_1_1) = all_10_1_9, environment(all_0_1_1) = 0, yields:
% 4.92/1.82 | (59) all_10_1_9 = 0
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (16) with all_0_1_1, all_10_1_9, all_12_1_11 and discharging atoms environment(all_0_1_1) = all_12_1_11, environment(all_0_1_1) = all_10_1_9, yields:
% 4.92/1.82 | (60) all_12_1_11 = all_10_1_9
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (16) with all_0_1_1, all_8_3_7, all_14_1_13 and discharging atoms environment(all_0_1_1) = all_14_1_13, environment(all_0_1_1) = all_8_3_7, yields:
% 4.92/1.82 | (61) all_14_1_13 = all_8_3_7
% 4.92/1.82 |
% 4.92/1.82 | Instantiating formula (12) with efficient_producers, first_movers, all_0_1_1, all_0_0_0, all_10_0_8, all_16_4_20 and discharging atoms subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_16_4_20, subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_10_0_8, yields:
% 4.92/1.82 | (62) all_16_4_20 = all_10_0_8
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (54,55) yields a new equation:
% 4.92/1.82 | (63) all_14_3_15 = all_8_2_6
% 4.92/1.82 |
% 4.92/1.82 | Simplifying 63 yields:
% 4.92/1.82 | (64) all_14_3_15 = all_8_2_6
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (58,61) yields a new equation:
% 4.92/1.82 | (65) all_12_1_11 = all_8_3_7
% 4.92/1.82 |
% 4.92/1.82 | Simplifying 65 yields:
% 4.92/1.82 | (66) all_12_1_11 = all_8_3_7
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (60,66) yields a new equation:
% 4.92/1.82 | (67) all_10_1_9 = all_8_3_7
% 4.92/1.82 |
% 4.92/1.82 | Simplifying 67 yields:
% 4.92/1.82 | (68) all_10_1_9 = all_8_3_7
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (59,68) yields a new equation:
% 4.92/1.82 | (69) all_8_3_7 = 0
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (69,68) yields a new equation:
% 4.92/1.82 | (59) all_10_1_9 = 0
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (69,66) yields a new equation:
% 4.92/1.82 | (71) all_12_1_11 = 0
% 4.92/1.82 |
% 4.92/1.82 | From (64) and (44) follows:
% 4.92/1.82 | (29) growth_rate(first_movers, all_0_0_0) = all_8_2_6
% 4.92/1.82 |
% 4.92/1.82 | From (55) and (50) follows:
% 4.92/1.82 | (73) greater_or_equal(all_8_2_6, zero) = all_16_2_18
% 4.92/1.82 |
% 4.92/1.82 | From (64) and (46) follows:
% 4.92/1.82 | (74) greater(zero, all_8_2_6) = all_14_2_14
% 4.92/1.82 |
% 4.92/1.82 | From (69) and (31) follows:
% 4.92/1.82 | (11) environment(all_0_1_1) = 0
% 4.92/1.82 |
% 4.92/1.82 | From (62) and (48) follows:
% 4.92/1.82 | (35) subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = all_10_0_8
% 4.92/1.82 |
% 4.92/1.82 +-Applying beta-rule and splitting (36), into two cases.
% 4.92/1.82 |-Branch one:
% 4.92/1.82 | (77) ~ (all_10_1_9 = 0)
% 4.92/1.82 |
% 4.92/1.82 | Equations (59) can reduce 77 to:
% 4.92/1.82 | (78) $false
% 4.92/1.82 |
% 4.92/1.82 |-The branch is then unsatisfiable
% 4.92/1.82 |-Branch two:
% 4.92/1.82 | (59) all_10_1_9 = 0
% 4.92/1.82 | (80) all_10_0_8 = 0
% 4.92/1.82 |
% 4.92/1.82 | Combining equations (80,62) yields a new equation:
% 4.92/1.82 | (81) all_16_4_20 = 0
% 4.92/1.82 |
% 4.92/1.82 | From (80) and (35) follows:
% 4.92/1.82 | (82) subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = 0
% 4.92/1.82 |
% 4.92/1.82 +-Applying beta-rule and splitting (56), into two cases.
% 4.92/1.82 |-Branch one:
% 4.92/1.82 | (83) ~ (greater_or_equal(all_8_2_6, zero) = all_16_2_18)
% 4.92/1.83 |
% 4.92/1.83 | Using (73) and (83) yields:
% 4.92/1.83 | (84) $false
% 4.92/1.83 |
% 4.92/1.83 |-The branch is then unsatisfiable
% 4.92/1.83 |-Branch two:
% 4.92/1.83 | (73) greater_or_equal(all_8_2_6, zero) = all_16_2_18
% 4.92/1.83 | (86) all_16_2_18 = all_8_1_5
% 4.92/1.83 |
% 4.92/1.83 +-Applying beta-rule and splitting (51), into two cases.
% 4.92/1.83 |-Branch one:
% 4.92/1.83 | (87) ~ (all_16_4_20 = 0)
% 4.92/1.83 |
% 4.92/1.83 | Equations (81) can reduce 87 to:
% 4.92/1.83 | (78) $false
% 4.92/1.83 |
% 4.92/1.83 |-The branch is then unsatisfiable
% 4.92/1.83 |-Branch two:
% 4.92/1.83 | (81) all_16_4_20 = 0
% 4.92/1.83 | (90) all_16_0_16 = 0 & all_16_2_18 = 0
% 4.92/1.83 |
% 4.92/1.83 | Applying alpha-rule on (90) yields:
% 4.92/1.83 | (91) all_16_0_16 = 0
% 4.92/1.83 | (92) all_16_2_18 = 0
% 4.92/1.83 |
% 4.92/1.83 | Combining equations (92,86) yields a new equation:
% 4.92/1.83 | (93) all_8_1_5 = 0
% 4.92/1.83 |
% 4.92/1.83 | From (91) and (52) follows:
% 4.92/1.83 | (94) greater(zero, all_16_1_17) = 0
% 4.92/1.83 |
% 4.92/1.83 +-Applying beta-rule and splitting (30), into two cases.
% 4.92/1.83 |-Branch one:
% 4.92/1.83 | (95) ~ (all_8_0_4 = 0)
% 4.92/1.83 |
% 4.92/1.83 +-Applying beta-rule and splitting (40), into two cases.
% 4.92/1.83 |-Branch one:
% 4.92/1.83 | (96) ~ (all_12_1_11 = 0)
% 4.92/1.83 |
% 4.92/1.83 | Equations (71) can reduce 96 to:
% 4.92/1.83 | (78) $false
% 4.92/1.83 |
% 4.92/1.83 |-The branch is then unsatisfiable
% 4.92/1.83 |-Branch two:
% 4.92/1.83 | (71) all_12_1_11 = 0
% 4.92/1.83 | (99) all_12_0_10 = 0
% 4.92/1.83 |
% 4.92/1.83 | From (99) and (38) follows:
% 4.92/1.83 | (100) in_environment(all_0_1_1, all_0_0_0) = 0
% 4.92/1.83 |
% 4.92/1.83 +-Applying beta-rule and splitting (57), into two cases.
% 4.92/1.83 |-Branch one:
% 4.92/1.83 | (101) ~ (greater(zero, all_8_2_6) = all_14_2_14)
% 4.92/1.83 |
% 4.92/1.83 | Using (74) and (101) yields:
% 4.92/1.83 | (84) $false
% 4.92/1.83 |
% 4.92/1.83 |-The branch is then unsatisfiable
% 4.92/1.83 |-Branch two:
% 4.92/1.83 | (74) greater(zero, all_8_2_6) = all_14_2_14
% 4.92/1.83 | (104) all_14_2_14 = all_8_0_4
% 4.92/1.83 |
% 4.92/1.83 | From (104) and (74) follows:
% 4.92/1.83 | (32) greater(zero, all_8_2_6) = all_8_0_4
% 4.92/1.83 |
% 4.92/1.83 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_0_0, efficient_producers, first_movers, all_0_1_1 and discharging atoms resilience(efficient_producers) = all_0_3_3, resilience(first_movers) = all_0_2_2, greater(all_0_3_3, all_0_2_2) = 0, in_environment(all_0_1_1, all_0_0_0) = 0, yields:
% 4.92/1.83 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (growth_rate(efficient_producers, all_0_0_0) = v3 & growth_rate(first_movers, all_0_0_0) = v1 & greater(zero, v3) = v4 & greater(zero, v1) = v2 & environment(all_0_1_1) = v0 & ( ~ (v4 = 0) | ~ (v0 = 0) | v2 = 0))
% 4.92/1.83 |
% 4.92/1.83 | Instantiating formula (4) with all_0_0_0, first_movers, efficient_producers, all_0_1_1 and discharging atoms subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.92/1.83 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (growth_rate(efficient_producers, all_0_0_0) = v0 & greater_or_equal(v0, zero) = v3 & greater(zero, v0) = v1 & environment(all_0_1_1) = v2 & ( ~ (v2 = 0) | v3 = 0 | v1 = 0))
% 4.92/1.83 |
% 4.92/1.83 | Instantiating formula (5) with 0, all_0_0_0, first_movers, efficient_producers, all_0_1_1 and discharging atoms subpopulations(efficient_producers, first_movers, all_0_1_1, all_0_0_0) = 0, yields:
% 4.92/1.83 | (108) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (growth_rate(efficient_producers, all_0_0_0) = v1 & greater_or_equal(v1, zero) = v2 & greater(zero, v1) = v3 & environment(all_0_1_1) = v0 & ( ~ (v3 = 0) | (v0 = 0 & ~ (v2 = 0))))
% 4.92/1.83 |
% 4.92/1.83 | Instantiating (108) with all_55_0_21, all_55_1_22, all_55_2_23, all_55_3_24 yields:
% 4.92/1.83 | (109) growth_rate(efficient_producers, all_0_0_0) = all_55_2_23 & greater_or_equal(all_55_2_23, zero) = all_55_1_22 & greater(zero, all_55_2_23) = all_55_0_21 & environment(all_0_1_1) = all_55_3_24 & ( ~ (all_55_0_21 = 0) | (all_55_3_24 = 0 & ~ (all_55_1_22 = 0)))
% 4.92/1.83 |
% 4.92/1.83 | Applying alpha-rule on (109) yields:
% 4.92/1.83 | (110) growth_rate(efficient_producers, all_0_0_0) = all_55_2_23
% 4.92/1.83 | (111) ~ (all_55_0_21 = 0) | (all_55_3_24 = 0 & ~ (all_55_1_22 = 0))
% 4.92/1.83 | (112) greater(zero, all_55_2_23) = all_55_0_21
% 4.92/1.83 | (113) greater_or_equal(all_55_2_23, zero) = all_55_1_22
% 4.92/1.83 | (114) environment(all_0_1_1) = all_55_3_24
% 4.92/1.83 |
% 4.92/1.84 | Instantiating (107) with all_57_0_25, all_57_1_26, all_57_2_27, all_57_3_28 yields:
% 4.92/1.84 | (115) growth_rate(efficient_producers, all_0_0_0) = all_57_3_28 & greater_or_equal(all_57_3_28, zero) = all_57_0_25 & greater(zero, all_57_3_28) = all_57_2_27 & environment(all_0_1_1) = all_57_1_26 & ( ~ (all_57_1_26 = 0) | all_57_0_25 = 0 | all_57_2_27 = 0)
% 4.92/1.84 |
% 4.92/1.84 | Applying alpha-rule on (115) yields:
% 4.92/1.84 | (116) ~ (all_57_1_26 = 0) | all_57_0_25 = 0 | all_57_2_27 = 0
% 4.92/1.84 | (117) growth_rate(efficient_producers, all_0_0_0) = all_57_3_28
% 4.92/1.84 | (118) environment(all_0_1_1) = all_57_1_26
% 4.92/1.84 | (119) greater(zero, all_57_3_28) = all_57_2_27
% 4.92/1.84 | (120) greater_or_equal(all_57_3_28, zero) = all_57_0_25
% 4.92/1.84 |
% 4.92/1.84 | Instantiating (106) with all_59_0_29, all_59_1_30, all_59_2_31, all_59_3_32, all_59_4_33 yields:
% 4.92/1.84 | (121) growth_rate(efficient_producers, all_0_0_0) = all_59_1_30 & growth_rate(first_movers, all_0_0_0) = all_59_3_32 & greater(zero, all_59_1_30) = all_59_0_29 & greater(zero, all_59_3_32) = all_59_2_31 & environment(all_0_1_1) = all_59_4_33 & ( ~ (all_59_0_29 = 0) | ~ (all_59_4_33 = 0) | all_59_2_31 = 0)
% 4.92/1.84 |
% 4.92/1.84 | Applying alpha-rule on (121) yields:
% 4.92/1.84 | (122) greater(zero, all_59_1_30) = all_59_0_29
% 4.92/1.84 | (123) environment(all_0_1_1) = all_59_4_33
% 4.92/1.84 | (124) growth_rate(first_movers, all_0_0_0) = all_59_3_32
% 4.92/1.84 | (125) greater(zero, all_59_3_32) = all_59_2_31
% 4.92/1.84 | (126) ~ (all_59_0_29 = 0) | ~ (all_59_4_33 = 0) | all_59_2_31 = 0
% 4.92/1.84 | (127) growth_rate(efficient_producers, all_0_0_0) = all_59_1_30
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (19) with efficient_producers, all_0_0_0, all_57_3_28, all_16_1_17 and discharging atoms growth_rate(efficient_producers, all_0_0_0) = all_57_3_28, growth_rate(efficient_producers, all_0_0_0) = all_16_1_17, yields:
% 4.92/1.84 | (128) all_57_3_28 = all_16_1_17
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (19) with efficient_producers, all_0_0_0, all_57_3_28, all_59_1_30 and discharging atoms growth_rate(efficient_producers, all_0_0_0) = all_59_1_30, growth_rate(efficient_producers, all_0_0_0) = all_57_3_28, yields:
% 4.92/1.84 | (129) all_59_1_30 = all_57_3_28
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (19) with efficient_producers, all_0_0_0, all_55_2_23, all_59_1_30 and discharging atoms growth_rate(efficient_producers, all_0_0_0) = all_59_1_30, growth_rate(efficient_producers, all_0_0_0) = all_55_2_23, yields:
% 4.92/1.84 | (130) all_59_1_30 = all_55_2_23
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (19) with first_movers, all_0_0_0, all_59_3_32, all_8_2_6 and discharging atoms growth_rate(first_movers, all_0_0_0) = all_59_3_32, growth_rate(first_movers, all_0_0_0) = all_8_2_6, yields:
% 4.92/1.84 | (131) all_59_3_32 = all_8_2_6
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (2) with zero, all_8_2_6, all_59_2_31, all_8_0_4 and discharging atoms greater(zero, all_8_2_6) = all_8_0_4, yields:
% 4.92/1.84 | (132) all_59_2_31 = all_8_0_4 | ~ (greater(zero, all_8_2_6) = all_59_2_31)
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (2) with zero, all_16_1_17, all_57_2_27, 0 and discharging atoms greater(zero, all_16_1_17) = 0, yields:
% 4.92/1.84 | (133) all_57_2_27 = 0 | ~ (greater(zero, all_16_1_17) = all_57_2_27)
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (2) with zero, all_55_2_23, all_55_0_21, all_59_0_29 and discharging atoms greater(zero, all_55_2_23) = all_55_0_21, yields:
% 4.92/1.84 | (134) all_59_0_29 = all_55_0_21 | ~ (greater(zero, all_55_2_23) = all_59_0_29)
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (2) with zero, all_55_2_23, all_55_0_21, all_57_2_27 and discharging atoms greater(zero, all_55_2_23) = all_55_0_21, yields:
% 4.92/1.84 | (135) all_57_2_27 = all_55_0_21 | ~ (greater(zero, all_55_2_23) = all_57_2_27)
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (16) with all_0_1_1, all_59_4_33, 0 and discharging atoms environment(all_0_1_1) = all_59_4_33, environment(all_0_1_1) = 0, yields:
% 4.92/1.84 | (136) all_59_4_33 = 0
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (16) with all_0_1_1, all_57_1_26, all_59_4_33 and discharging atoms environment(all_0_1_1) = all_59_4_33, environment(all_0_1_1) = all_57_1_26, yields:
% 4.92/1.84 | (137) all_59_4_33 = all_57_1_26
% 4.92/1.84 |
% 4.92/1.84 | Instantiating formula (16) with all_0_1_1, all_55_3_24, all_59_4_33 and discharging atoms environment(all_0_1_1) = all_59_4_33, environment(all_0_1_1) = all_55_3_24, yields:
% 4.92/1.85 | (138) all_59_4_33 = all_55_3_24
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (129,130) yields a new equation:
% 4.92/1.85 | (139) all_57_3_28 = all_55_2_23
% 4.92/1.85 |
% 4.92/1.85 | Simplifying 139 yields:
% 4.92/1.85 | (140) all_57_3_28 = all_55_2_23
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (136,137) yields a new equation:
% 4.92/1.85 | (141) all_57_1_26 = 0
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (138,137) yields a new equation:
% 4.92/1.85 | (142) all_57_1_26 = all_55_3_24
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (141,142) yields a new equation:
% 4.92/1.85 | (143) all_55_3_24 = 0
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (140,128) yields a new equation:
% 4.92/1.85 | (144) all_55_2_23 = all_16_1_17
% 4.92/1.85 |
% 4.92/1.85 | Simplifying 144 yields:
% 4.92/1.85 | (145) all_55_2_23 = all_16_1_17
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (143,142) yields a new equation:
% 4.92/1.85 | (141) all_57_1_26 = 0
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (141,137) yields a new equation:
% 4.92/1.85 | (136) all_59_4_33 = 0
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (145,130) yields a new equation:
% 4.92/1.85 | (148) all_59_1_30 = all_16_1_17
% 4.92/1.85 |
% 4.92/1.85 | From (148) and (122) follows:
% 4.92/1.85 | (149) greater(zero, all_16_1_17) = all_59_0_29
% 4.92/1.85 |
% 4.92/1.85 | From (131) and (125) follows:
% 4.92/1.85 | (150) greater(zero, all_8_2_6) = all_59_2_31
% 4.92/1.85 |
% 4.92/1.85 | From (128) and (119) follows:
% 4.92/1.85 | (151) greater(zero, all_16_1_17) = all_57_2_27
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (132), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (152) ~ (greater(zero, all_8_2_6) = all_59_2_31)
% 4.92/1.85 |
% 4.92/1.85 | Using (150) and (152) yields:
% 4.92/1.85 | (84) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (150) greater(zero, all_8_2_6) = all_59_2_31
% 4.92/1.85 | (155) all_59_2_31 = all_8_0_4
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (126), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (156) ~ (all_59_0_29 = 0)
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (133), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (157) ~ (greater(zero, all_16_1_17) = all_57_2_27)
% 4.92/1.85 |
% 4.92/1.85 | Using (151) and (157) yields:
% 4.92/1.85 | (84) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (151) greater(zero, all_16_1_17) = all_57_2_27
% 4.92/1.85 | (160) all_57_2_27 = 0
% 4.92/1.85 |
% 4.92/1.85 | From (160) and (151) follows:
% 4.92/1.85 | (94) greater(zero, all_16_1_17) = 0
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (134), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (162) ~ (greater(zero, all_55_2_23) = all_59_0_29)
% 4.92/1.85 |
% 4.92/1.85 | From (145) and (162) follows:
% 4.92/1.85 | (163) ~ (greater(zero, all_16_1_17) = all_59_0_29)
% 4.92/1.85 |
% 4.92/1.85 | Using (149) and (163) yields:
% 4.92/1.85 | (84) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (165) greater(zero, all_55_2_23) = all_59_0_29
% 4.92/1.85 | (166) all_59_0_29 = all_55_0_21
% 4.92/1.85 |
% 4.92/1.85 | Equations (166) can reduce 156 to:
% 4.92/1.85 | (167) ~ (all_55_0_21 = 0)
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (135), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (168) ~ (greater(zero, all_55_2_23) = all_57_2_27)
% 4.92/1.85 |
% 4.92/1.85 | From (145)(160) and (168) follows:
% 4.92/1.85 | (169) ~ (greater(zero, all_16_1_17) = 0)
% 4.92/1.85 |
% 4.92/1.85 | Using (94) and (169) yields:
% 4.92/1.85 | (84) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (171) greater(zero, all_55_2_23) = all_57_2_27
% 4.92/1.85 | (172) all_57_2_27 = all_55_0_21
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (160,172) yields a new equation:
% 4.92/1.85 | (173) all_55_0_21 = 0
% 4.92/1.85 |
% 4.92/1.85 | Equations (173) can reduce 167 to:
% 4.92/1.85 | (78) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (175) all_59_0_29 = 0
% 4.92/1.85 | (176) ~ (all_59_4_33 = 0) | all_59_2_31 = 0
% 4.92/1.85 |
% 4.92/1.85 +-Applying beta-rule and splitting (176), into two cases.
% 4.92/1.85 |-Branch one:
% 4.92/1.85 | (177) ~ (all_59_4_33 = 0)
% 4.92/1.85 |
% 4.92/1.85 | Equations (136) can reduce 177 to:
% 4.92/1.85 | (78) $false
% 4.92/1.85 |
% 4.92/1.85 |-The branch is then unsatisfiable
% 4.92/1.85 |-Branch two:
% 4.92/1.85 | (136) all_59_4_33 = 0
% 4.92/1.85 | (180) all_59_2_31 = 0
% 4.92/1.85 |
% 4.92/1.85 | Combining equations (155,180) yields a new equation:
% 4.92/1.86 | (181) all_8_0_4 = 0
% 4.92/1.86 |
% 4.92/1.86 | Simplifying 181 yields:
% 4.92/1.86 | (182) all_8_0_4 = 0
% 4.92/1.86 |
% 4.92/1.86 | Equations (182) can reduce 95 to:
% 4.92/1.86 | (78) $false
% 4.92/1.86 |
% 4.92/1.86 |-The branch is then unsatisfiable
% 4.92/1.86 |-Branch two:
% 4.92/1.86 | (182) all_8_0_4 = 0
% 4.92/1.86 | (185) all_8_3_7 = 0 & ~ (all_8_1_5 = 0)
% 4.92/1.86 |
% 4.92/1.86 | Applying alpha-rule on (185) yields:
% 4.92/1.86 | (69) all_8_3_7 = 0
% 4.92/1.86 | (187) ~ (all_8_1_5 = 0)
% 4.92/1.86 |
% 4.92/1.86 | Equations (93) can reduce 187 to:
% 4.92/1.86 | (78) $false
% 4.92/1.86 |
% 4.92/1.86 |-The branch is then unsatisfiable
% 4.92/1.86 % SZS output end Proof for theBenchmark
% 4.92/1.86
% 4.92/1.86 1258ms
%------------------------------------------------------------------------------