TSTP Solution File: MGT032+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT032+2 : 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 22:07:03 EDT 2022
% Result : Theorem 3.29s 1.46s
% Output : Proof 5.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 12:15:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.91 Prover 0: Preprocessing ...
% 1.61/1.02 Prover 0: Constructing countermodel ...
% 2.12/1.14 Prover 0: gave up
% 2.12/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.12/1.16 Prover 1: Preprocessing ...
% 2.27/1.23 Prover 1: Constructing countermodel ...
% 2.53/1.30 Prover 1: gave up
% 2.53/1.30 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.53/1.31 Prover 2: Preprocessing ...
% 2.96/1.39 Prover 2: Warning: ignoring some quantifiers
% 2.96/1.39 Prover 2: Constructing countermodel ...
% 3.29/1.46 Prover 2: proved (164ms)
% 3.29/1.46
% 3.29/1.46 No countermodel exists, formula is valid
% 3.29/1.46 % SZS status Theorem for theBenchmark
% 3.29/1.46
% 3.29/1.46 Generating proof ... Warning: ignoring some quantifiers
% 5.30/1.96 found it (size 53)
% 5.30/1.96
% 5.30/1.96 % SZS output start Proof for theBenchmark
% 5.30/1.96 Assumed formulas after preprocessing and simplification:
% 5.30/1.96 | (0) ? [v0] : (stable(v0) = 0 & environment(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (subpopulations(v6, v5, v4, v3) = v2) | ~ (subpopulations(v6, v5, v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (selection_favors(v5, v4, v3) = v2) | ~ (selection_favors(v5, v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (in_environment(v4, v3) = v2) | ~ (in_environment(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (greater_or_equal(v4, v3) = v2) | ~ (greater_or_equal(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (growth_rate(v4, v3) = v2) | ~ (growth_rate(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (greater(v4, v3) = v2) | ~ (greater(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subpopulations(v2, v3, v1, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v5 = 0 & selection_favors(v3, v2, v4) = 0) | ( ~ (v7 = 0) & growth_rate(v3, v4) = v5 & growth_rate(v2, v4) = v6 & greater(v5, v6) = v7) | ( ~ (v5 = 0) & environment(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (stable(v3) = v2) | ~ (stable(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (environment(v3) = v2) | ~ (environment(v3) = v1)) & ! [v1] : ( ~ (stable(v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & in_environment(v1, v2) = 0 & ! [v4] : ! [v5] : ( ~ (growth_rate(efficient_producers, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v6 = 0) & greater_or_equal(v4, v2) = v6) | ( ~ (v6 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v6))) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v6 & greater(v6, v5) = 0) | ( ~ (v6 = 0) & greater_or_equal(v4, v2) = v6) | ( ~ (v6 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v6))) & ! [v4] : ( ~ (greater_or_equal(v4, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v5))) & ! [v4] : ( ~ (subpopulations(first_movers, efficient_producers, v1, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v5 = 0) & greater_or_equal(v4, v2) = v5)))) | ( ~ (v2 = 0) & environment(v1) = v2))) & ! [v1] : ( ~ (in_environment(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & greater_or_equal(v2, v1) = 0 & subpopulations(first_movers, efficient_producers, v0, v2) = 0 & selection_favors(efficient_producers, first_movers, v2) = v3)) & ! [v1] : ( ~ (environment(v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & in_environment(v1, v2) = 0 & ! [v4] : ! [v5] : ( ~ (growth_rate(efficient_producers, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v6 = 0) & greater_or_equal(v4, v2) = v6) | ( ~ (v6 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v6))) & ! [v4] : ! [v5] : ( ~ (growth_rate(first_movers, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v6 & greater(v6, v5) = 0) | ( ~ (v6 = 0) & greater_or_equal(v4, v2) = v6) | ( ~ (v6 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v6))) & ! [v4] : ( ~ (greater_or_equal(v4, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v1, v4) = v5))) & ! [v4] : ( ~ (subpopulations(first_movers, efficient_producers, v1, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & growth_rate(efficient_producers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater(v5, v6) = 0) | ( ~ (v5 = 0) & greater_or_equal(v4, v2) = v5)))) | ( ~ (v2 = 0) & stable(v1) = v2))) & ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : subpopulations(v4, v3, v2, v1) = v5 & ? [v1] : ? [v2] : ? [v3] : ? [v4] : selection_favors(v3, v2, v1) = v4 & ? [v1] : ? [v2] : ? [v3] : in_environment(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : greater_or_equal(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : growth_rate(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : greater(v2, v1) = v3 & ? [v1] : ? [v2] : stable(v1) = v2 & ? [v1] : ? [v2] : environment(v1) = v2)
% 5.54/2.00 | Instantiating (0) with all_0_0_0 yields:
% 5.54/2.00 | (1) stable(all_0_0_0) = 0 & environment(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] : (v1 = v0 | ~ (selection_favors(v4, v3, v2) = v1) | ~ (selection_favors(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(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 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & selection_favors(v2, v1, v3) = 0) | ( ~ (v6 = 0) & growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & greater(v4, v5) = v6) | ( ~ (v4 = 0) & environment(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (stable(v2) = v1) | ~ (stable(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & ! [v0] : ( ~ (stable(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & in_environment(v0, v1) = 0 & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v5 & greater(v5, v4) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ( ~ (greater_or_equal(v3, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v4))) & ! [v3] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & greater_or_equal(v3, v1) = v4)))) | ( ~ (v1 = 0) & environment(v0) = v1))) & ! [v0] : ( ~ (in_environment(all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & greater_or_equal(v1, v0) = 0 & subpopulations(first_movers, efficient_producers, all_0_0_0, v1) = 0 & selection_favors(efficient_producers, first_movers, v1) = v2)) & ! [v0] : ( ~ (environment(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & in_environment(v0, v1) = 0 & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v5 & greater(v5, v4) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ( ~ (greater_or_equal(v3, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v4))) & ! [v3] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & greater_or_equal(v3, v1) = v4)))) | ( ~ (v1 = 0) & stable(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : subpopulations(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : selection_favors(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : in_environment(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : greater_or_equal(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : growth_rate(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : greater(v1, v0) = v2 & ? [v0] : ? [v1] : stable(v0) = v1 & ? [v0] : ? [v1] : environment(v0) = v1
% 5.54/2.01 |
% 5.54/2.01 | Applying alpha-rule on (1) yields:
% 5.54/2.01 | (2) ? [v0] : ? [v1] : ? [v2] : greater_or_equal(v1, v0) = v2
% 5.54/2.01 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (selection_favors(v4, v3, v2) = v1) | ~ (selection_favors(v4, v3, v2) = v0))
% 5.54/2.01 | (4) ? [v0] : ? [v1] : ? [v2] : in_environment(v1, v0) = v2
% 5.54/2.01 | (5) ? [v0] : ? [v1] : ? [v2] : ? [v3] : selection_favors(v2, v1, v0) = v3
% 5.54/2.01 | (6) ! [v0] : ( ~ (environment(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & in_environment(v0, v1) = 0 & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v5 & greater(v5, v4) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ( ~ (greater_or_equal(v3, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v4))) & ! [v3] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & greater_or_equal(v3, v1) = v4)))) | ( ~ (v1 = 0) & stable(v0) = v1)))
% 5.54/2.01 | (7) ! [v0] : ( ~ (stable(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & in_environment(v0, v1) = 0 & ! [v3] : ! [v4] : ( ~ (growth_rate(efficient_producers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v5 & greater(v5, v4) = 0) | ( ~ (v5 = 0) & greater_or_equal(v3, v1) = v5) | ( ~ (v5 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v5))) & ! [v3] : ( ~ (greater_or_equal(v3, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, v0, v3) = v4))) & ! [v3] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & growth_rate(efficient_producers, v3) = v4 & growth_rate(first_movers, v3) = v5 & greater(v4, v5) = 0) | ( ~ (v4 = 0) & greater_or_equal(v3, v1) = v4)))) | ( ~ (v1 = 0) & environment(v0) = v1)))
% 5.54/2.01 | (8) environment(all_0_0_0) = 0
% 5.54/2.02 | (9) ? [v0] : ? [v1] : ? [v2] : growth_rate(v1, v0) = v2
% 5.54/2.02 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 5.54/2.02 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0))
% 5.54/2.02 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0))
% 5.54/2.02 | (13) ? [v0] : ? [v1] : ? [v2] : greater(v1, v0) = v2
% 5.54/2.02 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0))
% 5.54/2.02 | (15) ? [v0] : ? [v1] : environment(v0) = v1
% 5.54/2.02 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 5.54/2.02 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : subpopulations(v3, v2, v1, v0) = v4
% 5.54/2.02 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subpopulations(v1, v2, v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v4 = 0 & selection_favors(v2, v1, v3) = 0) | ( ~ (v6 = 0) & growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & greater(v4, v5) = v6) | ( ~ (v4 = 0) & environment(v0) = v4)))
% 5.54/2.02 | (19) ? [v0] : ? [v1] : stable(v0) = v1
% 5.54/2.02 | (20) stable(all_0_0_0) = 0
% 5.54/2.02 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 5.54/2.02 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (stable(v2) = v1) | ~ (stable(v2) = v0))
% 5.54/2.02 | (23) ! [v0] : ( ~ (in_environment(all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = 0) & greater_or_equal(v1, v0) = 0 & subpopulations(first_movers, efficient_producers, all_0_0_0, v1) = 0 & selection_favors(efficient_producers, first_movers, v1) = v2))
% 5.54/2.02 |
% 5.54/2.02 | Instantiating formula (6) with all_0_0_0 and discharging atoms environment(all_0_0_0) = 0, yields:
% 5.54/2.02 | (24) ? [v0] : ? [v1] : ((v1 = 0 & in_environment(all_0_0_0, v0) = 0 & ! [v2] : ! [v3] : ( ~ (growth_rate(efficient_producers, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & growth_rate(first_movers, v2) = v4 & greater(v3, v4) = 0) | ( ~ (v4 = 0) & greater_or_equal(v2, v0) = v4) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v2) = v4))) & ! [v2] : ! [v3] : ( ~ (growth_rate(first_movers, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & growth_rate(efficient_producers, v2) = v4 & greater(v4, v3) = 0) | ( ~ (v4 = 0) & greater_or_equal(v2, v0) = v4) | ( ~ (v4 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v2) = v4))) & ! [v2] : ( ~ (greater_or_equal(v2, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater(v3, v4) = 0) | ( ~ (v3 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v2) = v3))) & ! [v2] : ( ~ (subpopulations(first_movers, efficient_producers, all_0_0_0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & growth_rate(efficient_producers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater(v3, v4) = 0) | ( ~ (v3 = 0) & greater_or_equal(v2, v0) = v3)))) | ( ~ (v0 = 0) & stable(all_0_0_0) = v0))
% 5.54/2.02 |
% 5.54/2.02 | Instantiating (24) with all_24_0_26, all_24_1_27 yields:
% 5.54/2.02 | (25) (all_24_0_26 = 0 & in_environment(all_0_0_0, all_24_1_27) = 0 & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v2 & greater(v2, v1) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2))) & ! [v0] : ( ~ (greater_or_equal(v0, all_24_1_27) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v1))) & ! [v0] : ( ~ (subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & greater_or_equal(v0, all_24_1_27) = v1)))) | ( ~ (all_24_1_27 = 0) & stable(all_0_0_0) = all_24_1_27)
% 5.54/2.03 |
% 5.54/2.03 +-Applying beta-rule and splitting (25), into two cases.
% 5.54/2.03 |-Branch one:
% 5.54/2.03 | (26) all_24_0_26 = 0 & in_environment(all_0_0_0, all_24_1_27) = 0 & ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v2 & greater(v2, v1) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2))) & ! [v0] : ( ~ (greater_or_equal(v0, all_24_1_27) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v1))) & ! [v0] : ( ~ (subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & greater_or_equal(v0, all_24_1_27) = v1)))
% 5.54/2.03 |
% 5.54/2.03 | Applying alpha-rule on (26) yields:
% 5.54/2.03 | (27) ! [v0] : ! [v1] : ( ~ (growth_rate(efficient_producers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2)))
% 5.54/2.03 | (28) in_environment(all_0_0_0, all_24_1_27) = 0
% 5.54/2.03 | (29) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v2 & greater(v2, v1) = 0) | ( ~ (v2 = 0) & greater_or_equal(v0, all_24_1_27) = v2) | ( ~ (v2 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v2)))
% 5.54/2.03 | (30) all_24_0_26 = 0
% 5.54/2.03 | (31) ! [v0] : ( ~ (subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & greater_or_equal(v0, all_24_1_27) = v1)))
% 5.54/2.03 | (32) ! [v0] : ( ~ (greater_or_equal(v0, all_24_1_27) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & growth_rate(efficient_producers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater(v1, v2) = 0) | ( ~ (v1 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = v1)))
% 5.54/2.03 |
% 5.54/2.03 | Instantiating formula (23) with all_24_1_27 and discharging atoms in_environment(all_0_0_0, all_24_1_27) = 0, yields:
% 5.54/2.03 | (33) ? [v0] : ? [v1] : ( ~ (v1 = 0) & greater_or_equal(v0, all_24_1_27) = 0 & subpopulations(first_movers, efficient_producers, all_0_0_0, v0) = 0 & selection_favors(efficient_producers, first_movers, v0) = v1)
% 5.54/2.03 |
% 5.54/2.03 | Instantiating (33) with all_39_0_30, all_39_1_31 yields:
% 5.54/2.03 | (34) ~ (all_39_0_30 = 0) & greater_or_equal(all_39_1_31, all_24_1_27) = 0 & subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = 0 & selection_favors(efficient_producers, first_movers, all_39_1_31) = all_39_0_30
% 5.54/2.03 |
% 5.54/2.03 | Applying alpha-rule on (34) yields:
% 5.54/2.03 | (35) ~ (all_39_0_30 = 0)
% 5.54/2.03 | (36) greater_or_equal(all_39_1_31, all_24_1_27) = 0
% 5.54/2.03 | (37) subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = 0
% 5.54/2.03 | (38) selection_favors(efficient_producers, first_movers, all_39_1_31) = all_39_0_30
% 5.54/2.03 |
% 5.54/2.03 | Instantiating formula (32) with all_39_1_31 and discharging atoms greater_or_equal(all_39_1_31, all_24_1_27) = 0, yields:
% 5.54/2.03 | (39) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & growth_rate(efficient_producers, all_39_1_31) = v0 & growth_rate(first_movers, all_39_1_31) = v1 & greater(v0, v1) = 0) | ( ~ (v0 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = v0))
% 5.54/2.03 |
% 5.54/2.03 | Instantiating formula (31) with all_39_1_31 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = 0, yields:
% 5.54/2.03 | (40) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & growth_rate(efficient_producers, all_39_1_31) = v0 & growth_rate(first_movers, all_39_1_31) = v1 & greater(v0, v1) = 0) | ( ~ (v0 = 0) & greater_or_equal(all_39_1_31, all_24_1_27) = v0))
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (18) with all_39_1_31, efficient_producers, first_movers, all_0_0_0 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = 0, yields:
% 5.54/2.04 | (41) ? [v0] : ? [v1] : ? [v2] : ((v0 = 0 & selection_favors(efficient_producers, first_movers, all_39_1_31) = 0) | ( ~ (v2 = 0) & growth_rate(efficient_producers, all_39_1_31) = v0 & growth_rate(first_movers, all_39_1_31) = v1 & greater(v0, v1) = v2) | ( ~ (v0 = 0) & environment(all_0_0_0) = v0))
% 5.54/2.04 |
% 5.54/2.04 | Instantiating (41) with all_48_0_34, all_48_1_35, all_48_2_36 yields:
% 5.54/2.04 | (42) (all_48_2_36 = 0 & selection_favors(efficient_producers, first_movers, all_39_1_31) = 0) | ( ~ (all_48_0_34 = 0) & growth_rate(efficient_producers, all_39_1_31) = all_48_2_36 & growth_rate(first_movers, all_39_1_31) = all_48_1_35 & greater(all_48_2_36, all_48_1_35) = all_48_0_34) | ( ~ (all_48_2_36 = 0) & environment(all_0_0_0) = all_48_2_36)
% 5.54/2.04 |
% 5.54/2.04 | Instantiating (40) with all_49_0_37, all_49_1_38, all_49_2_39 yields:
% 5.54/2.04 | (43) (all_49_0_37 = 0 & growth_rate(efficient_producers, all_39_1_31) = all_49_2_39 & growth_rate(first_movers, all_39_1_31) = all_49_1_38 & greater(all_49_2_39, all_49_1_38) = 0) | ( ~ (all_49_2_39 = 0) & greater_or_equal(all_39_1_31, all_24_1_27) = all_49_2_39)
% 5.54/2.04 |
% 5.54/2.04 | Instantiating (39) with all_53_0_49, all_53_1_50, all_53_2_51 yields:
% 5.54/2.04 | (44) (all_53_0_49 = 0 & growth_rate(efficient_producers, all_39_1_31) = all_53_2_51 & growth_rate(first_movers, all_39_1_31) = all_53_1_50 & greater(all_53_2_51, all_53_1_50) = 0) | ( ~ (all_53_2_51 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = all_53_2_51)
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (43), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (45) all_49_0_37 = 0 & growth_rate(efficient_producers, all_39_1_31) = all_49_2_39 & growth_rate(first_movers, all_39_1_31) = all_49_1_38 & greater(all_49_2_39, all_49_1_38) = 0
% 5.54/2.04 |
% 5.54/2.04 | Applying alpha-rule on (45) yields:
% 5.54/2.04 | (46) all_49_0_37 = 0
% 5.54/2.04 | (47) growth_rate(efficient_producers, all_39_1_31) = all_49_2_39
% 5.54/2.04 | (48) growth_rate(first_movers, all_39_1_31) = all_49_1_38
% 5.54/2.04 | (49) greater(all_49_2_39, all_49_1_38) = 0
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (44), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (50) all_53_0_49 = 0 & growth_rate(efficient_producers, all_39_1_31) = all_53_2_51 & growth_rate(first_movers, all_39_1_31) = all_53_1_50 & greater(all_53_2_51, all_53_1_50) = 0
% 5.54/2.04 |
% 5.54/2.04 | Applying alpha-rule on (50) yields:
% 5.54/2.04 | (51) all_53_0_49 = 0
% 5.54/2.04 | (52) growth_rate(efficient_producers, all_39_1_31) = all_53_2_51
% 5.54/2.04 | (53) growth_rate(first_movers, all_39_1_31) = all_53_1_50
% 5.54/2.04 | (54) greater(all_53_2_51, all_53_1_50) = 0
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (42), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (55) (all_48_2_36 = 0 & selection_favors(efficient_producers, first_movers, all_39_1_31) = 0) | ( ~ (all_48_0_34 = 0) & growth_rate(efficient_producers, all_39_1_31) = all_48_2_36 & growth_rate(first_movers, all_39_1_31) = all_48_1_35 & greater(all_48_2_36, all_48_1_35) = all_48_0_34)
% 5.54/2.04 |
% 5.54/2.04 +-Applying beta-rule and splitting (55), into two cases.
% 5.54/2.04 |-Branch one:
% 5.54/2.04 | (56) all_48_2_36 = 0 & selection_favors(efficient_producers, first_movers, all_39_1_31) = 0
% 5.54/2.04 |
% 5.54/2.04 | Applying alpha-rule on (56) yields:
% 5.54/2.04 | (57) all_48_2_36 = 0
% 5.54/2.04 | (58) selection_favors(efficient_producers, first_movers, all_39_1_31) = 0
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (3) with efficient_producers, first_movers, all_39_1_31, 0, all_39_0_30 and discharging atoms selection_favors(efficient_producers, first_movers, all_39_1_31) = all_39_0_30, selection_favors(efficient_producers, first_movers, all_39_1_31) = 0, yields:
% 5.54/2.04 | (59) all_39_0_30 = 0
% 5.54/2.04 |
% 5.54/2.04 | Equations (59) can reduce 35 to:
% 5.54/2.04 | (60) $false
% 5.54/2.04 |
% 5.54/2.04 |-The branch is then unsatisfiable
% 5.54/2.04 |-Branch two:
% 5.54/2.04 | (61) ~ (all_48_0_34 = 0) & growth_rate(efficient_producers, all_39_1_31) = all_48_2_36 & growth_rate(first_movers, all_39_1_31) = all_48_1_35 & greater(all_48_2_36, all_48_1_35) = all_48_0_34
% 5.54/2.04 |
% 5.54/2.04 | Applying alpha-rule on (61) yields:
% 5.54/2.04 | (62) ~ (all_48_0_34 = 0)
% 5.54/2.04 | (63) growth_rate(efficient_producers, all_39_1_31) = all_48_2_36
% 5.54/2.04 | (64) growth_rate(first_movers, all_39_1_31) = all_48_1_35
% 5.54/2.04 | (65) greater(all_48_2_36, all_48_1_35) = all_48_0_34
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (16) with efficient_producers, all_39_1_31, all_49_2_39, all_53_2_51 and discharging atoms growth_rate(efficient_producers, all_39_1_31) = all_53_2_51, growth_rate(efficient_producers, all_39_1_31) = all_49_2_39, yields:
% 5.54/2.04 | (66) all_53_2_51 = all_49_2_39
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (16) with efficient_producers, all_39_1_31, all_48_2_36, all_53_2_51 and discharging atoms growth_rate(efficient_producers, all_39_1_31) = all_53_2_51, growth_rate(efficient_producers, all_39_1_31) = all_48_2_36, yields:
% 5.54/2.04 | (67) all_53_2_51 = all_48_2_36
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (16) with first_movers, all_39_1_31, all_49_1_38, all_53_1_50 and discharging atoms growth_rate(first_movers, all_39_1_31) = all_53_1_50, growth_rate(first_movers, all_39_1_31) = all_49_1_38, yields:
% 5.54/2.04 | (68) all_53_1_50 = all_49_1_38
% 5.54/2.04 |
% 5.54/2.04 | Instantiating formula (16) with first_movers, all_39_1_31, all_48_1_35, all_53_1_50 and discharging atoms growth_rate(first_movers, all_39_1_31) = all_53_1_50, growth_rate(first_movers, all_39_1_31) = all_48_1_35, yields:
% 5.54/2.04 | (69) all_53_1_50 = all_48_1_35
% 5.54/2.04 |
% 5.54/2.04 | Combining equations (69,68) yields a new equation:
% 5.54/2.05 | (70) all_49_1_38 = all_48_1_35
% 5.54/2.05 |
% 5.54/2.05 | Combining equations (66,67) yields a new equation:
% 5.54/2.05 | (71) all_49_2_39 = all_48_2_36
% 5.54/2.05 |
% 5.54/2.05 | Simplifying 71 yields:
% 5.54/2.05 | (72) all_49_2_39 = all_48_2_36
% 5.54/2.05 |
% 5.54/2.05 | From (72)(70) and (49) follows:
% 5.54/2.05 | (73) greater(all_48_2_36, all_48_1_35) = 0
% 5.54/2.05 |
% 5.54/2.05 | Instantiating formula (21) with all_48_2_36, all_48_1_35, 0, all_48_0_34 and discharging atoms greater(all_48_2_36, all_48_1_35) = all_48_0_34, greater(all_48_2_36, all_48_1_35) = 0, yields:
% 5.54/2.05 | (74) all_48_0_34 = 0
% 5.54/2.05 |
% 5.54/2.05 | Equations (74) can reduce 62 to:
% 5.54/2.05 | (60) $false
% 5.54/2.05 |
% 5.54/2.05 |-The branch is then unsatisfiable
% 5.54/2.05 |-Branch two:
% 5.54/2.05 | (76) ~ (all_48_2_36 = 0) & environment(all_0_0_0) = all_48_2_36
% 5.54/2.05 |
% 5.54/2.05 | Applying alpha-rule on (76) yields:
% 5.54/2.05 | (77) ~ (all_48_2_36 = 0)
% 5.54/2.05 | (78) environment(all_0_0_0) = all_48_2_36
% 5.54/2.05 |
% 5.54/2.05 | Instantiating formula (10) with all_0_0_0, all_48_2_36, 0 and discharging atoms environment(all_0_0_0) = all_48_2_36, environment(all_0_0_0) = 0, yields:
% 5.54/2.05 | (57) all_48_2_36 = 0
% 5.54/2.05 |
% 5.54/2.05 | Equations (57) can reduce 77 to:
% 5.54/2.05 | (60) $false
% 5.54/2.05 |
% 5.54/2.05 |-The branch is then unsatisfiable
% 5.54/2.05 |-Branch two:
% 5.54/2.05 | (81) ~ (all_53_2_51 = 0) & subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = all_53_2_51
% 5.54/2.05 |
% 5.54/2.05 | Applying alpha-rule on (81) yields:
% 5.54/2.05 | (82) ~ (all_53_2_51 = 0)
% 5.54/2.05 | (83) subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = all_53_2_51
% 5.54/2.05 |
% 5.54/2.05 | Instantiating formula (11) with first_movers, efficient_producers, all_0_0_0, all_39_1_31, all_53_2_51, 0 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = all_53_2_51, subpopulations(first_movers, efficient_producers, all_0_0_0, all_39_1_31) = 0, yields:
% 5.54/2.05 | (84) all_53_2_51 = 0
% 5.54/2.05 |
% 5.54/2.05 | Equations (84) can reduce 82 to:
% 5.54/2.05 | (60) $false
% 5.54/2.05 |
% 5.54/2.05 |-The branch is then unsatisfiable
% 5.54/2.05 |-Branch two:
% 5.54/2.05 | (86) ~ (all_49_2_39 = 0) & greater_or_equal(all_39_1_31, all_24_1_27) = all_49_2_39
% 5.54/2.05 |
% 5.54/2.05 | Applying alpha-rule on (86) yields:
% 5.54/2.05 | (87) ~ (all_49_2_39 = 0)
% 5.54/2.05 | (88) greater_or_equal(all_39_1_31, all_24_1_27) = all_49_2_39
% 5.54/2.05 |
% 5.54/2.05 | Instantiating formula (12) with all_39_1_31, all_24_1_27, all_49_2_39, 0 and discharging atoms greater_or_equal(all_39_1_31, all_24_1_27) = all_49_2_39, greater_or_equal(all_39_1_31, all_24_1_27) = 0, yields:
% 5.54/2.05 | (89) all_49_2_39 = 0
% 5.54/2.05 |
% 5.54/2.05 | Equations (89) can reduce 87 to:
% 5.54/2.05 | (60) $false
% 5.54/2.05 |
% 5.54/2.05 |-The branch is then unsatisfiable
% 5.54/2.05 |-Branch two:
% 5.89/2.05 | (91) ~ (all_24_1_27 = 0) & stable(all_0_0_0) = all_24_1_27
% 5.89/2.05 |
% 5.89/2.05 | Applying alpha-rule on (91) yields:
% 5.89/2.05 | (92) ~ (all_24_1_27 = 0)
% 5.89/2.05 | (93) stable(all_0_0_0) = all_24_1_27
% 5.89/2.05 |
% 5.89/2.05 | Instantiating formula (22) with all_0_0_0, all_24_1_27, 0 and discharging atoms stable(all_0_0_0) = all_24_1_27, stable(all_0_0_0) = 0, yields:
% 5.89/2.05 | (94) all_24_1_27 = 0
% 5.89/2.05 |
% 5.89/2.05 | Equations (94) can reduce 92 to:
% 5.89/2.05 | (60) $false
% 5.89/2.05 |
% 5.89/2.05 |-The branch is then unsatisfiable
% 5.89/2.05 % SZS output end Proof for theBenchmark
% 5.89/2.05
% 5.89/2.05 1445ms
%------------------------------------------------------------------------------