TSTP Solution File: MGT027+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 3.37s 1.50s
% Output : Proof 4.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 11:52:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.68/0.66 ____ _
% 0.68/0.66 ___ / __ \_____(_)___ ________ __________
% 0.68/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.68/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.68/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.68/0.66
% 0.68/0.66 A Theorem Prover for First-Order Logic
% 0.68/0.66 (ePrincess v.1.0)
% 0.68/0.66
% 0.68/0.66 (c) Philipp Rümmer, 2009-2015
% 0.68/0.66 (c) Peter Backeman, 2014-2015
% 0.68/0.66 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.68/0.66 Free software under GNU Lesser General Public License (LGPL).
% 0.68/0.66 Bug reports to peter@backeman.se
% 0.68/0.66
% 0.68/0.66 For more information, visit http://user.uu.se/~petba168/breu/
% 0.68/0.66
% 0.68/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.78/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.99 Prover 0: Preprocessing ...
% 2.00/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.00/1.15 Prover 0: Constructing countermodel ...
% 3.37/1.50 Prover 0: proved (778ms)
% 3.37/1.50
% 3.37/1.50 No countermodel exists, formula is valid
% 3.37/1.50 % SZS status Theorem for theBenchmark
% 3.37/1.50
% 3.37/1.50 Generating proof ... Warning: ignoring some quantifiers
% 4.14/1.76 found it (size 38)
% 4.14/1.76
% 4.14/1.76 % SZS output start Proof for theBenchmark
% 4.14/1.76 Assumed formulas after preprocessing and simplification:
% 4.14/1.76 | (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 | ~ (cardinality_at_time(v5, v4) = v3) | ~ (cardinality_at_time(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (growth_rate(v5, v4) = v3) | ~ (growth_rate(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (appear(efficient_producers, v2) = v4) | ~ (cardinality_at_time(efficient_producers, v3) = v5) | ~ greater_or_equal(v3, v4) | ~ in_environment(v2, v3) | ~ environment(v2) | greater(v5, zero)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (cardinality_at_time(efficient_producers, v3) = v4) | ~ greater(v4, zero) | ~ in_environment(v2, v3) | ~ environment(v2) | subpopulations(first_movers, efficient_producers, v2, v3) | ? [v5] : (cardinality_at_time(first_movers, v3) = v5 & ~ greater(v5, zero))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (cardinality_at_time(first_movers, v3) = v4) | ~ greater(v4, zero) | ~ in_environment(v2, v3) | ~ environment(v2) | subpopulations(first_movers, efficient_producers, v2, v3) | ? [v5] : (cardinality_at_time(efficient_producers, v3) = v5 & ~ greater(v5, zero))) & ! [v2] : ! [v3] : ! [v4] : ( ~ greater(v4, v3) | ~ in_environment(v2, v3) | ~ stable(v2) | ~ environment(v2) | in_environment(v2, v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ greater(v3, v4) | ~ greater(v2, v3) | greater(v2, v4)) & ! [v2] : ! [v3] : (v3 = v2 | ~ greater_or_equal(v2, v3) | greater(v2, v3)) & ! [v2] : ! [v3] : ( ~ (appear(efficient_producers, v2) = v3) | ~ stable(v2) | ~ environment(v2) | in_environment(v2, v3)) & ! [v2] : ! [v3] : ( ~ (appear(efficient_producers, v2) = v3) | ~ stable(v2) | ~ environment(v2) | ? [v4] : (greater(v4, v3) & ! [v5] : ! [v6] : ( ~ (growth_rate(first_movers, v5) = v6) | ~ subpopulations(first_movers, efficient_producers, v2, v5) | ~ greater_or_equal(v5, v4) | greater(zero, v6)))) & ! [v2] : ! [v3] : ( ~ greater(v2, v3) | greater_or_equal(v2, v3)) & ! [v2] : ! [v3] : ( ~ in_environment(v2, v3) | ~ stable(v2) | ~ environment(v2) | contracts_from(v3, first_movers) | ? [v4] : ? [v5] : ? [v6] : (cardinality_at_time(first_movers, v4) = v5 & growth_rate(first_movers, v4) = v6 & greater_or_equal(v4, v3) & greater(v5, zero) & ~ greater(zero, v6))) & ! [v2] : ( ~ contracts_from(v2, first_movers) | ~ greater(v2, v1)) & ? [v2] : greater_or_equal(v2, v2))
% 4.27/1.80 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 4.27/1.80 | (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 | ~ (cardinality_at_time(v3, v2) = v1) | ~ (cardinality_at_time(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (appear(efficient_producers, v0) = v2) | ~ (cardinality_at_time(efficient_producers, v1) = v3) | ~ greater_or_equal(v1, v2) | ~ in_environment(v0, v1) | ~ environment(v0) | greater(v3, zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(first_movers, efficient_producers, v0, v1) | ? [v3] : (cardinality_at_time(first_movers, v1) = v3 & ~ greater(v3, zero))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(first_movers, efficient_producers, v0, v1) | ? [v3] : (cardinality_at_time(efficient_producers, v1) = v3 & ~ greater(v3, zero))) & ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v2, v1) | ~ in_environment(v0, v1) | ~ stable(v0) | ~ environment(v0) | in_environment(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0] : ! [v1] : ( ~ (appear(efficient_producers, v0) = v1) | ~ stable(v0) | ~ environment(v0) | in_environment(v0, v1)) & ! [v0] : ! [v1] : ( ~ (appear(efficient_producers, v0) = v1) | ~ stable(v0) | ~ environment(v0) | ? [v2] : (greater(v2, v1) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ~ subpopulations(first_movers, efficient_producers, v0, v3) | ~ greater_or_equal(v3, v2) | greater(zero, v4)))) & ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ stable(v0) | ~ environment(v0) | contracts_from(v1, first_movers) | ? [v2] : ? [v3] : ? [v4] : (cardinality_at_time(first_movers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater_or_equal(v2, v1) & greater(v3, zero) & ~ greater(zero, v4))) & ! [v0] : ( ~ contracts_from(v0, first_movers) | ~ greater(v0, all_0_0_0)) & ? [v0] : greater_or_equal(v0, v0)
% 4.27/1.81 |
% 4.27/1.81 | Applying alpha-rule on (1) yields:
% 4.27/1.81 | (2) stable(all_0_1_1)
% 4.27/1.81 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 4.27/1.81 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cardinality_at_time(v3, v2) = v1) | ~ (cardinality_at_time(v3, v2) = v0))
% 4.27/1.81 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (appear(v3, v2) = v1) | ~ (appear(v3, v2) = v0))
% 4.27/1.81 | (6) ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1))
% 4.27/1.81 | (7) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ stable(v0) | ~ environment(v0) | contracts_from(v1, first_movers) | ? [v2] : ? [v3] : ? [v4] : (cardinality_at_time(first_movers, v2) = v3 & growth_rate(first_movers, v2) = v4 & greater_or_equal(v2, v1) & greater(v3, zero) & ~ greater(zero, v4)))
% 4.27/1.81 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(first_movers, efficient_producers, v0, v1) | ? [v3] : (cardinality_at_time(efficient_producers, v1) = v3 & ~ greater(v3, zero)))
% 4.27/1.81 | (9) ! [v0] : ! [v1] : ( ~ (appear(efficient_producers, v0) = v1) | ~ stable(v0) | ~ environment(v0) | in_environment(v0, v1))
% 4.27/1.81 | (10) appear(efficient_producers, all_0_1_1) = all_0_0_0
% 4.27/1.81 | (11) ! [v0] : ! [v1] : ( ~ (appear(efficient_producers, v0) = v1) | ~ stable(v0) | ~ environment(v0) | ? [v2] : (greater(v2, v1) & ! [v3] : ! [v4] : ( ~ (growth_rate(first_movers, v3) = v4) | ~ subpopulations(first_movers, efficient_producers, v0, v3) | ~ greater_or_equal(v3, v2) | greater(zero, v4))))
% 4.27/1.81 | (12) ? [v0] : greater_or_equal(v0, v0)
% 4.27/1.81 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (appear(efficient_producers, v0) = v2) | ~ (cardinality_at_time(efficient_producers, v1) = v3) | ~ greater_or_equal(v1, v2) | ~ in_environment(v0, v1) | ~ environment(v0) | greater(v3, zero))
% 4.27/1.81 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ greater(v2, zero) | ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(first_movers, efficient_producers, v0, v1) | ? [v3] : (cardinality_at_time(first_movers, v1) = v3 & ~ greater(v3, zero)))
% 4.27/1.81 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v2, v1) | ~ in_environment(v0, v1) | ~ stable(v0) | ~ environment(v0) | in_environment(v0, v2))
% 4.27/1.82 | (16) ! [v0] : ( ~ contracts_from(v0, first_movers) | ~ greater(v0, all_0_0_0))
% 4.27/1.82 | (17) environment(all_0_1_1)
% 4.27/1.82 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 4.27/1.82 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ greater_or_equal(v0, v1) | greater(v0, v1))
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (9) with all_0_0_0, all_0_1_1 and discharging atoms appear(efficient_producers, all_0_1_1) = all_0_0_0, stable(all_0_1_1), environment(all_0_1_1), yields:
% 4.27/1.82 | (20) in_environment(all_0_1_1, all_0_0_0)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (11) with all_0_0_0, all_0_1_1 and discharging atoms appear(efficient_producers, all_0_1_1) = all_0_0_0, stable(all_0_1_1), environment(all_0_1_1), yields:
% 4.27/1.82 | (21) ? [v0] : (greater(v0, all_0_0_0) & ! [v1] : ! [v2] : ( ~ (growth_rate(first_movers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v1) | ~ greater_or_equal(v1, v0) | greater(zero, v2)))
% 4.27/1.82 |
% 4.27/1.82 | Instantiating (21) with all_11_0_3 yields:
% 4.27/1.82 | (22) greater(all_11_0_3, all_0_0_0) & ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater_or_equal(v0, all_11_0_3) | greater(zero, v1))
% 4.27/1.82 |
% 4.27/1.82 | Applying alpha-rule on (22) yields:
% 4.27/1.82 | (23) greater(all_11_0_3, all_0_0_0)
% 4.27/1.82 | (24) ! [v0] : ! [v1] : ( ~ (growth_rate(first_movers, v0) = v1) | ~ subpopulations(first_movers, efficient_producers, all_0_1_1, v0) | ~ greater_or_equal(v0, all_11_0_3) | greater(zero, v1))
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (6) with all_0_0_0, all_11_0_3 and discharging atoms greater(all_11_0_3, all_0_0_0), yields:
% 4.27/1.82 | (25) greater_or_equal(all_11_0_3, all_0_0_0)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (15) with all_11_0_3, all_0_0_0, all_0_1_1 and discharging atoms greater(all_11_0_3, all_0_0_0), in_environment(all_0_1_1, all_0_0_0), stable(all_0_1_1), environment(all_0_1_1), yields:
% 4.27/1.82 | (26) in_environment(all_0_1_1, all_11_0_3)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (7) with all_11_0_3, all_0_1_1 and discharging atoms in_environment(all_0_1_1, all_11_0_3), stable(all_0_1_1), environment(all_0_1_1), yields:
% 4.27/1.82 | (27) contracts_from(all_11_0_3, first_movers) | ? [v0] : ? [v1] : ? [v2] : (cardinality_at_time(first_movers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater_or_equal(v0, all_11_0_3) & greater(v1, zero) & ~ greater(zero, v2))
% 4.27/1.82 |
% 4.27/1.82 +-Applying beta-rule and splitting (27), into two cases.
% 4.27/1.82 |-Branch one:
% 4.27/1.82 | (28) contracts_from(all_11_0_3, first_movers)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (16) with all_11_0_3 and discharging atoms contracts_from(all_11_0_3, first_movers), greater(all_11_0_3, all_0_0_0), yields:
% 4.27/1.82 | (29) $false
% 4.27/1.82 |
% 4.27/1.82 |-The branch is then unsatisfiable
% 4.27/1.82 |-Branch two:
% 4.27/1.82 | (30) ~ contracts_from(all_11_0_3, first_movers)
% 4.27/1.82 | (31) ? [v0] : ? [v1] : ? [v2] : (cardinality_at_time(first_movers, v0) = v1 & growth_rate(first_movers, v0) = v2 & greater_or_equal(v0, all_11_0_3) & greater(v1, zero) & ~ greater(zero, v2))
% 4.27/1.82 |
% 4.27/1.82 | Instantiating (31) with all_34_0_4, all_34_1_5, all_34_2_6 yields:
% 4.27/1.82 | (32) cardinality_at_time(first_movers, all_34_2_6) = all_34_1_5 & growth_rate(first_movers, all_34_2_6) = all_34_0_4 & greater_or_equal(all_34_2_6, all_11_0_3) & greater(all_34_1_5, zero) & ~ greater(zero, all_34_0_4)
% 4.27/1.82 |
% 4.27/1.82 | Applying alpha-rule on (32) yields:
% 4.27/1.82 | (33) greater(all_34_1_5, zero)
% 4.27/1.82 | (34) growth_rate(first_movers, all_34_2_6) = all_34_0_4
% 4.27/1.82 | (35) greater_or_equal(all_34_2_6, all_11_0_3)
% 4.27/1.82 | (36) cardinality_at_time(first_movers, all_34_2_6) = all_34_1_5
% 4.27/1.82 | (37) ~ greater(zero, all_34_0_4)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (19) with all_11_0_3, all_34_2_6 and discharging atoms greater_or_equal(all_34_2_6, all_11_0_3), yields:
% 4.27/1.82 | (38) all_34_2_6 = all_11_0_3 | greater(all_34_2_6, all_11_0_3)
% 4.27/1.82 |
% 4.27/1.82 +-Applying beta-rule and splitting (38), into two cases.
% 4.27/1.82 |-Branch one:
% 4.27/1.82 | (39) greater(all_34_2_6, all_11_0_3)
% 4.27/1.82 |
% 4.27/1.82 | Instantiating formula (15) with all_34_2_6, all_11_0_3, all_0_1_1 and discharging atoms greater(all_34_2_6, all_11_0_3), in_environment(all_0_1_1, all_11_0_3), stable(all_0_1_1), environment(all_0_1_1), yields:
% 4.27/1.83 | (40) in_environment(all_0_1_1, all_34_2_6)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (18) with all_0_0_0, all_11_0_3, all_34_2_6 and discharging atoms greater(all_34_2_6, all_11_0_3), greater(all_11_0_3, all_0_0_0), yields:
% 4.27/1.83 | (41) greater(all_34_2_6, all_0_0_0)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (6) with all_0_0_0, all_34_2_6 and discharging atoms greater(all_34_2_6, all_0_0_0), yields:
% 4.27/1.83 | (42) greater_or_equal(all_34_2_6, all_0_0_0)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (8) with all_34_1_5, all_34_2_6, all_0_1_1 and discharging atoms cardinality_at_time(first_movers, all_34_2_6) = all_34_1_5, greater(all_34_1_5, zero), in_environment(all_0_1_1, all_34_2_6), environment(all_0_1_1), yields:
% 4.27/1.83 | (43) subpopulations(first_movers, efficient_producers, all_0_1_1, all_34_2_6) | ? [v0] : (cardinality_at_time(efficient_producers, all_34_2_6) = v0 & ~ greater(v0, zero))
% 4.27/1.83 |
% 4.27/1.83 +-Applying beta-rule and splitting (43), into two cases.
% 4.27/1.83 |-Branch one:
% 4.27/1.83 | (44) subpopulations(first_movers, efficient_producers, all_0_1_1, all_34_2_6)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (24) with all_34_0_4, all_34_2_6 and discharging atoms growth_rate(first_movers, all_34_2_6) = all_34_0_4, subpopulations(first_movers, efficient_producers, all_0_1_1, all_34_2_6), greater_or_equal(all_34_2_6, all_11_0_3), ~ greater(zero, all_34_0_4), yields:
% 4.27/1.83 | (29) $false
% 4.27/1.83 |
% 4.27/1.83 |-The branch is then unsatisfiable
% 4.27/1.83 |-Branch two:
% 4.27/1.83 | (46) ~ subpopulations(first_movers, efficient_producers, all_0_1_1, all_34_2_6)
% 4.27/1.83 | (47) ? [v0] : (cardinality_at_time(efficient_producers, all_34_2_6) = v0 & ~ greater(v0, zero))
% 4.27/1.83 |
% 4.27/1.83 | Instantiating (47) with all_68_0_7 yields:
% 4.27/1.83 | (48) cardinality_at_time(efficient_producers, all_34_2_6) = all_68_0_7 & ~ greater(all_68_0_7, zero)
% 4.27/1.83 |
% 4.27/1.83 | Applying alpha-rule on (48) yields:
% 4.27/1.83 | (49) cardinality_at_time(efficient_producers, all_34_2_6) = all_68_0_7
% 4.27/1.83 | (50) ~ greater(all_68_0_7, zero)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (13) with all_68_0_7, all_0_0_0, all_34_2_6, all_0_1_1 and discharging atoms appear(efficient_producers, all_0_1_1) = all_0_0_0, cardinality_at_time(efficient_producers, all_34_2_6) = all_68_0_7, greater_or_equal(all_34_2_6, all_0_0_0), in_environment(all_0_1_1, all_34_2_6), environment(all_0_1_1), ~ greater(all_68_0_7, zero), yields:
% 4.27/1.83 | (29) $false
% 4.27/1.83 |
% 4.27/1.83 |-The branch is then unsatisfiable
% 4.27/1.83 |-Branch two:
% 4.27/1.83 | (52) ~ greater(all_34_2_6, all_11_0_3)
% 4.27/1.83 | (53) all_34_2_6 = all_11_0_3
% 4.27/1.83 |
% 4.27/1.83 | From (53) and (36) follows:
% 4.27/1.83 | (54) cardinality_at_time(first_movers, all_11_0_3) = all_34_1_5
% 4.27/1.83 |
% 4.27/1.83 | From (53) and (34) follows:
% 4.27/1.83 | (55) growth_rate(first_movers, all_11_0_3) = all_34_0_4
% 4.27/1.83 |
% 4.27/1.83 | From (53) and (35) follows:
% 4.27/1.83 | (56) greater_or_equal(all_11_0_3, all_11_0_3)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (8) with all_34_1_5, all_11_0_3, all_0_1_1 and discharging atoms cardinality_at_time(first_movers, all_11_0_3) = all_34_1_5, greater(all_34_1_5, zero), in_environment(all_0_1_1, all_11_0_3), environment(all_0_1_1), yields:
% 4.27/1.83 | (57) subpopulations(first_movers, efficient_producers, all_0_1_1, all_11_0_3) | ? [v0] : (cardinality_at_time(efficient_producers, all_11_0_3) = v0 & ~ greater(v0, zero))
% 4.27/1.83 |
% 4.27/1.83 +-Applying beta-rule and splitting (57), into two cases.
% 4.27/1.83 |-Branch one:
% 4.27/1.83 | (58) subpopulations(first_movers, efficient_producers, all_0_1_1, all_11_0_3)
% 4.27/1.83 |
% 4.27/1.83 | Instantiating formula (24) with all_34_0_4, all_11_0_3 and discharging atoms growth_rate(first_movers, all_11_0_3) = all_34_0_4, subpopulations(first_movers, efficient_producers, all_0_1_1, all_11_0_3), greater_or_equal(all_11_0_3, all_11_0_3), ~ greater(zero, all_34_0_4), yields:
% 4.27/1.83 | (29) $false
% 4.27/1.83 |
% 4.27/1.83 |-The branch is then unsatisfiable
% 4.27/1.83 |-Branch two:
% 4.27/1.83 | (60) ~ subpopulations(first_movers, efficient_producers, all_0_1_1, all_11_0_3)
% 4.27/1.83 | (61) ? [v0] : (cardinality_at_time(efficient_producers, all_11_0_3) = v0 & ~ greater(v0, zero))
% 4.27/1.83 |
% 4.27/1.83 | Instantiating (61) with all_56_0_8 yields:
% 4.27/1.83 | (62) cardinality_at_time(efficient_producers, all_11_0_3) = all_56_0_8 & ~ greater(all_56_0_8, zero)
% 4.27/1.83 |
% 4.27/1.83 | Applying alpha-rule on (62) yields:
% 4.27/1.84 | (63) cardinality_at_time(efficient_producers, all_11_0_3) = all_56_0_8
% 4.47/1.84 | (64) ~ greater(all_56_0_8, zero)
% 4.47/1.84 |
% 4.47/1.84 | Instantiating formula (13) with all_56_0_8, all_0_0_0, all_11_0_3, all_0_1_1 and discharging atoms appear(efficient_producers, all_0_1_1) = all_0_0_0, cardinality_at_time(efficient_producers, all_11_0_3) = all_56_0_8, greater_or_equal(all_11_0_3, all_0_0_0), in_environment(all_0_1_1, all_11_0_3), environment(all_0_1_1), ~ greater(all_56_0_8, zero), yields:
% 4.47/1.84 | (29) $false
% 4.47/1.84 |
% 4.47/1.84 |-The branch is then unsatisfiable
% 4.47/1.84 % SZS output end Proof for theBenchmark
% 4.47/1.84
% 4.47/1.84 1164ms
%------------------------------------------------------------------------------