TSTP Solution File: MGT026+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 22:07:01 EDT 2022
% Result : Theorem 64.86s 31.77s
% Output : Proof 82.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:35:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.93 Prover 0: Preprocessing ...
% 1.97/1.14 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.16 Prover 0: Constructing countermodel ...
% 3.08/1.38 Prover 0: gave up
% 3.08/1.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.08/1.41 Prover 1: Preprocessing ...
% 3.53/1.50 Prover 1: Constructing countermodel ...
% 3.74/1.54 Prover 1: gave up
% 3.74/1.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.74/1.56 Prover 2: Preprocessing ...
% 4.50/1.70 Prover 2: Warning: ignoring some quantifiers
% 4.50/1.71 Prover 2: Constructing countermodel ...
% 10.93/3.24 Prover 2: gave up
% 10.93/3.26 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.93/3.27 Prover 3: Preprocessing ...
% 10.93/3.29 Prover 3: Warning: ignoring some quantifiers
% 10.93/3.29 Prover 3: Constructing countermodel ...
% 11.34/3.31 Prover 3: gave up
% 11.34/3.31 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 11.34/3.33 Prover 4: Preprocessing ...
% 11.77/3.41 Prover 4: Warning: ignoring some quantifiers
% 11.77/3.41 Prover 4: Constructing countermodel ...
% 15.91/4.39 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.91/4.42 Prover 5: Preprocessing ...
% 16.35/4.50 Prover 5: Constructing countermodel ...
% 39.96/19.67 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 40.16/19.70 Prover 6: Preprocessing ...
% 40.25/19.77 Prover 6: Warning: ignoring some quantifiers
% 40.25/19.78 Prover 6: Constructing countermodel ...
% 41.75/20.47 Prover 6: gave up
% 41.75/20.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 41.75/20.48 Prover 7: Preprocessing ...
% 41.75/20.49 Prover 7: Proving ...
% 54.21/27.54 Prover 5: stopped
% 54.56/27.74 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 54.56/27.77 Prover 8: Preprocessing ...
% 54.86/27.80 Prover 8: Constructing countermodel ...
% 54.99/27.81 Prover 8: gave up
% 54.99/27.81 Prover 9: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 55.08/27.82 Prover 9: Preprocessing ...
% 55.08/27.84 Prover 9: Proving ...
% 64.86/31.76 Prover 9: proved (3952ms)
% 64.86/31.76 Prover 4: stopped
% 64.86/31.77 Prover 7: stopped
% 64.86/31.77
% 64.86/31.77 % SZS status Theorem for theBenchmark
% 64.86/31.77
% 64.86/31.77 Generating proof ... found it (size 80)
% 81.72/42.99
% 81.72/42.99 % SZS output start Proof for theBenchmark
% 81.72/42.99 Assumed formulas after preprocessing and simplification:
% 81.72/42.99 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (critical_point(v3) = v5 & in_environment(v3, v4) & greater(v4, v5) & environment(v3) & ~ selection_favors(v0, v1, v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (appear(v9, v8) = v7) | ~ (appear(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (cardinality_at_time(v9, v8) = v7) | ~ (cardinality_at_time(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (growth_rate(v9, v8) = v7) | ~ (growth_rate(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ subpopulation(v8, v6, v9) | ~ subpopulation(v7, v6, v9) | ~ environment(v6) | selection_favors(v7, v8, v9) | ? [v10] : ? [v11] : (cardinality_at_time(v8, v9) = v11 & cardinality_at_time(v7, v9) = v10 & ( ~ (v11 = v2) | ~ greater(v10, v2)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ subpopulations(v7, v8, v6, v9) | ~ environment(v6) | selection_favors(v8, v7, v9) | ? [v10] : ? [v11] : (growth_rate(v8, v9) = v10 & growth_rate(v7, v9) = v11 & ~ greater(v10, v11))) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (critical_point(v8) = v7) | ~ (critical_point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ greater(v7, v8) | ~ greater(v6, v7) | greater(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ greater_or_equal(v6, v7) | greater(v6, v7)) & ! [v6] : ! [v7] : ( ~ in_environment(v6, v7) | ~ environment(v6) | subpopulation(v1, v6, v7)) & ! [v6] : ! [v7] : ( ~ in_environment(v6, v7) | ~ environment(v6) | subpopulation(v0, v6, v7)) & ! [v6] : ! [v7] : ( ~ in_environment(v6, v7) | ~ environment(v6) | subpopulations(v1, v0, v6, v7) | ? [v8] : ? [v9] : (cardinality_at_time(v1, v7) = v8 & cardinality_at_time(v0, v7) = v9 & ( ~ greater(v9, v2) | ~ greater(v8, v2)))) & ! [v6] : ! [v7] : ( ~ in_environment(v6, v7) | ~ environment(v6) | ? [v8] : ? [v9] : (appear(v0, v6) = v8 & cardinality_at_time(v0, v7) = v9 & ( ~ greater_or_equal(v7, v8) | greater(v9, v2)))) & ! [v6] : ! [v7] : ( ~ in_environment(v6, v7) | ~ environment(v6) | ? [v8] : (cardinality_at_time(v1, v7) = v8 & greater_or_equal(v8, v2))) & ! [v6] : ! [v7] : ( ~ greater(v6, v7) | greater_or_equal(v6, v7)) & ! [v6] : ( ~ environment(v6) | ! [v7] : ? [v8] : ? [v9] : ? [v10] : (critical_point(v6) = v8 & growth_rate(v1, v7) = v10 & growth_rate(v0, v7) = v9 & ( ~ (v8 = v7) | ( ~ greater(v9, v10) & ! [v11] : ( ~ greater(v11, v7) | ~ subpopulations(v1, v0, v6, v11) | ? [v12] : ? [v13] : (growth_rate(v1, v11) = v13 & growth_rate(v0, v11) = v12 & greater(v12, v13))))))) & ! [v6] : ( ~ environment(v6) | ? [v7] : ? [v8] : (critical_point(v6) = v7 & appear(v0, v6) = v8 & greater_or_equal(v7, v8))) & ! [v6] : greater_or_equal(v6, v6))
% 81.72/43.02 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 81.72/43.02 | (1) critical_point(all_0_2_2) = all_0_0_0 & in_environment(all_0_2_2, all_0_1_1) & greater(all_0_1_1, all_0_0_0) & environment(all_0_2_2) & ~ selection_favors(all_0_5_5, all_0_4_4, 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] : ( ~ subpopulation(v2, v0, v3) | ~ subpopulation(v1, v0, v3) | ~ environment(v0) | selection_favors(v1, v2, v3) | ? [v4] : ? [v5] : (cardinality_at_time(v2, v3) = v5 & cardinality_at_time(v1, v3) = v4 & ( ~ (v5 = all_0_3_3) | ~ greater(v4, all_0_3_3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | selection_favors(v2, v1, v3) | ? [v4] : ? [v5] : (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & ~ greater(v4, v5))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0)) & ! [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] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(all_0_4_4, v0, v1)) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(all_0_5_5, v0, v1)) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(all_0_4_4, all_0_5_5, v0, v1) | ? [v2] : ? [v3] : (cardinality_at_time(all_0_4_4, v1) = v2 & cardinality_at_time(all_0_5_5, v1) = v3 & ( ~ greater(v3, all_0_3_3) | ~ greater(v2, all_0_3_3)))) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : ? [v3] : (appear(all_0_5_5, v0) = v2 & cardinality_at_time(all_0_5_5, v1) = v3 & ( ~ greater_or_equal(v1, v2) | greater(v3, all_0_3_3)))) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : (cardinality_at_time(all_0_4_4, v1) = v2 & greater_or_equal(v2, all_0_3_3))) & ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ! [v0] : ( ~ environment(v0) | ! [v1] : ? [v2] : ? [v3] : ? [v4] : (critical_point(v0) = v2 & growth_rate(all_0_4_4, v1) = v4 & growth_rate(all_0_5_5, v1) = v3 & ( ~ (v2 = v1) | ( ~ greater(v3, v4) & ! [v5] : ( ~ greater(v5, v1) | ~ subpopulations(all_0_4_4, all_0_5_5, v0, v5) | ? [v6] : ? [v7] : (growth_rate(all_0_4_4, v5) = v7 & growth_rate(all_0_5_5, v5) = v6 & greater(v6, v7))))))) & ! [v0] : ( ~ environment(v0) | ? [v1] : ? [v2] : (critical_point(v0) = v1 & appear(all_0_5_5, v0) = v2 & greater_or_equal(v1, v2))) & ! [v0] : greater_or_equal(v0, v0)
% 82.01/43.03 |
% 82.01/43.03 | Applying alpha-rule on (1) yields:
% 82.01/43.03 | (2) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulations(all_0_4_4, all_0_5_5, v0, v1) | ? [v2] : ? [v3] : (cardinality_at_time(all_0_4_4, v1) = v2 & cardinality_at_time(all_0_5_5, v1) = v3 & ( ~ greater(v3, all_0_3_3) | ~ greater(v2, all_0_3_3))))
% 82.01/43.03 | (3) environment(all_0_2_2)
% 82.01/43.03 | (4) ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1))
% 82.01/43.03 | (5) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : ? [v3] : (appear(all_0_5_5, v0) = v2 & cardinality_at_time(all_0_5_5, v1) = v3 & ( ~ greater_or_equal(v1, v2) | greater(v3, all_0_3_3))))
% 82.01/43.03 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ subpopulation(v2, v0, v3) | ~ subpopulation(v1, v0, v3) | ~ environment(v0) | selection_favors(v1, v2, v3) | ? [v4] : ? [v5] : (cardinality_at_time(v2, v3) = v5 & cardinality_at_time(v1, v3) = v4 & ( ~ (v5 = all_0_3_3) | ~ greater(v4, all_0_3_3))))
% 82.01/43.03 | (7) in_environment(all_0_2_2, all_0_1_1)
% 82.01/43.03 | (8) greater(all_0_1_1, all_0_0_0)
% 82.01/43.03 | (9) ! [v0] : ( ~ environment(v0) | ? [v1] : ? [v2] : (critical_point(v0) = v1 & appear(all_0_5_5, v0) = v2 & greater_or_equal(v1, v2)))
% 82.01/43.03 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (appear(v3, v2) = v1) | ~ (appear(v3, v2) = v0))
% 82.01/43.03 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 82.01/43.03 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0))
% 82.01/43.03 | (13) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(all_0_5_5, v0, v1))
% 82.01/43.03 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | selection_favors(v2, v1, v3) | ? [v4] : ? [v5] : (growth_rate(v2, v3) = v4 & growth_rate(v1, v3) = v5 & ~ greater(v4, v5)))
% 82.01/43.03 | (15) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2] : (cardinality_at_time(all_0_4_4, v1) = v2 & greater_or_equal(v2, all_0_3_3)))
% 82.01/43.03 | (16) ! [v0] : ( ~ environment(v0) | ! [v1] : ? [v2] : ? [v3] : ? [v4] : (critical_point(v0) = v2 & growth_rate(all_0_4_4, v1) = v4 & growth_rate(all_0_5_5, v1) = v3 & ( ~ (v2 = v1) | ( ~ greater(v3, v4) & ! [v5] : ( ~ greater(v5, v1) | ~ subpopulations(all_0_4_4, all_0_5_5, v0, v5) | ? [v6] : ? [v7] : (growth_rate(all_0_4_4, v5) = v7 & growth_rate(all_0_5_5, v5) = v6 & greater(v6, v7)))))))
% 82.01/43.03 | (17) critical_point(all_0_2_2) = all_0_0_0
% 82.01/43.03 | (18) ! [v0] : greater_or_equal(v0, v0)
% 82.01/43.03 | (19) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(all_0_4_4, v0, v1))
% 82.01/43.03 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cardinality_at_time(v3, v2) = v1) | ~ (cardinality_at_time(v3, v2) = v0))
% 82.01/43.03 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ greater_or_equal(v0, v1) | greater(v0, v1))
% 82.01/43.03 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 82.01/43.03 | (23) ~ selection_favors(all_0_5_5, all_0_4_4, all_0_1_1)
% 82.01/43.03 |
% 82.01/43.03 | Instantiating formula (4) with all_0_0_0, all_0_1_1 and discharging atoms greater(all_0_1_1, all_0_0_0), yields:
% 82.01/43.03 | (24) greater_or_equal(all_0_1_1, all_0_0_0)
% 82.01/43.03 |
% 82.01/43.03 | Instantiating formula (19) with all_0_1_1, all_0_2_2 and discharging atoms in_environment(all_0_2_2, all_0_1_1), environment(all_0_2_2), yields:
% 82.01/43.03 | (25) subpopulation(all_0_4_4, all_0_2_2, all_0_1_1)
% 82.01/43.03 |
% 82.01/43.03 | Instantiating formula (13) with all_0_1_1, all_0_2_2 and discharging atoms in_environment(all_0_2_2, all_0_1_1), environment(all_0_2_2), yields:
% 82.01/43.03 | (26) subpopulation(all_0_5_5, all_0_2_2, all_0_1_1)
% 82.01/43.03 |
% 82.01/43.03 | Instantiating formula (2) with all_0_1_1, all_0_2_2 and discharging atoms in_environment(all_0_2_2, all_0_1_1), environment(all_0_2_2), yields:
% 82.01/43.03 | (27) subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1) | ? [v0] : ? [v1] : (cardinality_at_time(all_0_4_4, all_0_1_1) = v0 & cardinality_at_time(all_0_5_5, all_0_1_1) = v1 & ( ~ greater(v1, all_0_3_3) | ~ greater(v0, all_0_3_3)))
% 82.01/43.03 |
% 82.01/43.03 | Instantiating formula (5) with all_0_1_1, all_0_2_2 and discharging atoms in_environment(all_0_2_2, all_0_1_1), environment(all_0_2_2), yields:
% 82.01/43.03 | (28) ? [v0] : ? [v1] : (appear(all_0_5_5, all_0_2_2) = v0 & cardinality_at_time(all_0_5_5, all_0_1_1) = v1 & ( ~ greater_or_equal(all_0_1_1, v0) | greater(v1, all_0_3_3)))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (15) with all_0_1_1, all_0_2_2 and discharging atoms in_environment(all_0_2_2, all_0_1_1), environment(all_0_2_2), yields:
% 82.01/43.04 | (29) ? [v0] : (cardinality_at_time(all_0_4_4, all_0_1_1) = v0 & greater_or_equal(v0, all_0_3_3))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (16) with all_0_2_2 and discharging atoms environment(all_0_2_2), yields:
% 82.01/43.04 | (30) ! [v0] : ? [v1] : ? [v2] : ? [v3] : (critical_point(all_0_2_2) = v1 & growth_rate(all_0_4_4, v0) = v3 & growth_rate(all_0_5_5, v0) = v2 & ( ~ (v1 = v0) | ( ~ greater(v2, v3) & ! [v4] : ( ~ greater(v4, v0) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v4) | ? [v5] : ? [v6] : (growth_rate(all_0_4_4, v4) = v6 & growth_rate(all_0_5_5, v4) = v5 & greater(v5, v6))))))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (9) with all_0_2_2 and discharging atoms environment(all_0_2_2), yields:
% 82.01/43.04 | (31) ? [v0] : ? [v1] : (critical_point(all_0_2_2) = v0 & appear(all_0_5_5, all_0_2_2) = v1 & greater_or_equal(v0, v1))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (29) with all_9_0_6 yields:
% 82.01/43.04 | (32) cardinality_at_time(all_0_4_4, all_0_1_1) = all_9_0_6 & greater_or_equal(all_9_0_6, all_0_3_3)
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (32) yields:
% 82.01/43.04 | (33) cardinality_at_time(all_0_4_4, all_0_1_1) = all_9_0_6
% 82.01/43.04 | (34) greater_or_equal(all_9_0_6, all_0_3_3)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (28) with all_11_0_7, all_11_1_8 yields:
% 82.01/43.04 | (35) appear(all_0_5_5, all_0_2_2) = all_11_1_8 & cardinality_at_time(all_0_5_5, all_0_1_1) = all_11_0_7 & ( ~ greater_or_equal(all_0_1_1, all_11_1_8) | greater(all_11_0_7, all_0_3_3))
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (35) yields:
% 82.01/43.04 | (36) appear(all_0_5_5, all_0_2_2) = all_11_1_8
% 82.01/43.04 | (37) cardinality_at_time(all_0_5_5, all_0_1_1) = all_11_0_7
% 82.01/43.04 | (38) ~ greater_or_equal(all_0_1_1, all_11_1_8) | greater(all_11_0_7, all_0_3_3)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (31) with all_13_0_9, all_13_1_10 yields:
% 82.01/43.04 | (39) critical_point(all_0_2_2) = all_13_1_10 & appear(all_0_5_5, all_0_2_2) = all_13_0_9 & greater_or_equal(all_13_1_10, all_13_0_9)
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (39) yields:
% 82.01/43.04 | (40) critical_point(all_0_2_2) = all_13_1_10
% 82.01/43.04 | (41) appear(all_0_5_5, all_0_2_2) = all_13_0_9
% 82.01/43.04 | (42) greater_or_equal(all_13_1_10, all_13_0_9)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (12) with all_0_2_2, all_13_1_10, all_0_0_0 and discharging atoms critical_point(all_0_2_2) = all_13_1_10, critical_point(all_0_2_2) = all_0_0_0, yields:
% 82.01/43.04 | (43) all_13_1_10 = all_0_0_0
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (10) with all_0_5_5, all_0_2_2, all_11_1_8, all_13_0_9 and discharging atoms appear(all_0_5_5, all_0_2_2) = all_13_0_9, appear(all_0_5_5, all_0_2_2) = all_11_1_8, yields:
% 82.01/43.04 | (44) all_13_0_9 = all_11_1_8
% 82.01/43.04 |
% 82.01/43.04 | From (43)(44) and (42) follows:
% 82.01/43.04 | (45) greater_or_equal(all_0_0_0, all_11_1_8)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (21) with all_0_3_3, all_9_0_6 and discharging atoms greater_or_equal(all_9_0_6, all_0_3_3), yields:
% 82.01/43.04 | (46) all_9_0_6 = all_0_3_3 | greater(all_9_0_6, all_0_3_3)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (21) with all_11_1_8, all_0_0_0 and discharging atoms greater_or_equal(all_0_0_0, all_11_1_8), yields:
% 82.01/43.04 | (47) all_11_1_8 = all_0_0_0 | greater(all_0_0_0, all_11_1_8)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (6) with all_0_1_1, all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms subpopulation(all_0_4_4, all_0_2_2, all_0_1_1), subpopulation(all_0_5_5, all_0_2_2, all_0_1_1), environment(all_0_2_2), ~ selection_favors(all_0_5_5, all_0_4_4, all_0_1_1), yields:
% 82.01/43.04 | (48) ? [v0] : ? [v1] : (cardinality_at_time(all_0_4_4, all_0_1_1) = v1 & cardinality_at_time(all_0_5_5, all_0_1_1) = v0 & ( ~ (v1 = all_0_3_3) | ~ greater(v0, all_0_3_3)))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (48) with all_24_0_11, all_24_1_12 yields:
% 82.01/43.04 | (49) cardinality_at_time(all_0_4_4, all_0_1_1) = all_24_0_11 & cardinality_at_time(all_0_5_5, all_0_1_1) = all_24_1_12 & ( ~ (all_24_0_11 = all_0_3_3) | ~ greater(all_24_1_12, all_0_3_3))
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (49) yields:
% 82.01/43.04 | (50) cardinality_at_time(all_0_4_4, all_0_1_1) = all_24_0_11
% 82.01/43.04 | (51) cardinality_at_time(all_0_5_5, all_0_1_1) = all_24_1_12
% 82.01/43.04 | (52) ~ (all_24_0_11 = all_0_3_3) | ~ greater(all_24_1_12, all_0_3_3)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (20) with all_0_4_4, all_0_1_1, all_24_0_11, all_9_0_6 and discharging atoms cardinality_at_time(all_0_4_4, all_0_1_1) = all_24_0_11, cardinality_at_time(all_0_4_4, all_0_1_1) = all_9_0_6, yields:
% 82.01/43.04 | (53) all_24_0_11 = all_9_0_6
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (20) with all_0_5_5, all_0_1_1, all_24_1_12, all_11_0_7 and discharging atoms cardinality_at_time(all_0_5_5, all_0_1_1) = all_24_1_12, cardinality_at_time(all_0_5_5, all_0_1_1) = all_11_0_7, yields:
% 82.01/43.04 | (54) all_24_1_12 = all_11_0_7
% 82.01/43.04 |
% 82.01/43.04 +-Applying beta-rule and splitting (27), into two cases.
% 82.01/43.04 |-Branch one:
% 82.01/43.04 | (55) subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1)
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (14) with all_0_1_1, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1), environment(all_0_2_2), ~ selection_favors(all_0_5_5, all_0_4_4, all_0_1_1), yields:
% 82.01/43.04 | (56) ? [v0] : ? [v1] : (growth_rate(all_0_4_4, all_0_1_1) = v1 & growth_rate(all_0_5_5, all_0_1_1) = v0 & ~ greater(v0, v1))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (56) with all_42_0_15, all_42_1_16 yields:
% 82.01/43.04 | (57) growth_rate(all_0_4_4, all_0_1_1) = all_42_0_15 & growth_rate(all_0_5_5, all_0_1_1) = all_42_1_16 & ~ greater(all_42_1_16, all_42_0_15)
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (57) yields:
% 82.01/43.04 | (58) growth_rate(all_0_4_4, all_0_1_1) = all_42_0_15
% 82.01/43.04 | (59) growth_rate(all_0_5_5, all_0_1_1) = all_42_1_16
% 82.01/43.04 | (60) ~ greater(all_42_1_16, all_42_0_15)
% 82.01/43.04 |
% 82.01/43.04 | Introducing new symbol ex_112_0_22 defined by:
% 82.01/43.04 | (61) ex_112_0_22 = all_0_0_0
% 82.01/43.04 |
% 82.01/43.04 | Instantiating formula (30) with ex_112_0_22 yields:
% 82.01/43.04 | (62) ? [v0] : ? [v1] : ? [v2] : (critical_point(all_0_2_2) = v0 & growth_rate(all_0_4_4, ex_112_0_22) = v2 & growth_rate(all_0_5_5, ex_112_0_22) = v1 & ( ~ (v0 = ex_112_0_22) | ( ~ greater(v1, v2) & ! [v3] : ( ~ greater(v3, ex_112_0_22) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v3) | ? [v4] : ? [v5] : (growth_rate(all_0_4_4, v3) = v5 & growth_rate(all_0_5_5, v3) = v4 & greater(v4, v5))))))
% 82.01/43.04 |
% 82.01/43.04 | Instantiating (62) with all_113_0_23, all_113_1_24, all_113_2_25 yields:
% 82.01/43.04 | (63) critical_point(all_0_2_2) = all_113_2_25 & growth_rate(all_0_4_4, ex_112_0_22) = all_113_0_23 & growth_rate(all_0_5_5, ex_112_0_22) = all_113_1_24 & ( ~ (all_113_2_25 = ex_112_0_22) | ( ~ greater(all_113_1_24, all_113_0_23) & ! [v0] : ( ~ greater(v0, ex_112_0_22) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v0) | ? [v1] : ? [v2] : (growth_rate(all_0_4_4, v0) = v2 & growth_rate(all_0_5_5, v0) = v1 & greater(v1, v2)))))
% 82.01/43.04 |
% 82.01/43.04 | Applying alpha-rule on (63) yields:
% 82.01/43.05 | (64) critical_point(all_0_2_2) = all_113_2_25
% 82.01/43.05 | (65) growth_rate(all_0_4_4, ex_112_0_22) = all_113_0_23
% 82.01/43.05 | (66) growth_rate(all_0_5_5, ex_112_0_22) = all_113_1_24
% 82.01/43.05 | (67) ~ (all_113_2_25 = ex_112_0_22) | ( ~ greater(all_113_1_24, all_113_0_23) & ! [v0] : ( ~ greater(v0, ex_112_0_22) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v0) | ? [v1] : ? [v2] : (growth_rate(all_0_4_4, v0) = v2 & growth_rate(all_0_5_5, v0) = v1 & greater(v1, v2))))
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (12) with all_0_2_2, all_113_2_25, all_0_0_0 and discharging atoms critical_point(all_0_2_2) = all_113_2_25, critical_point(all_0_2_2) = all_0_0_0, yields:
% 82.01/43.05 | (68) all_113_2_25 = all_0_0_0
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (67), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (69) ~ (all_113_2_25 = ex_112_0_22)
% 82.01/43.05 |
% 82.01/43.05 | Equations (68) can reduce 69 to:
% 82.01/43.05 | (70) ~ (ex_112_0_22 = all_0_0_0)
% 82.01/43.05 |
% 82.01/43.05 | Simplifying 70 yields:
% 82.01/43.05 | (71) ~ (ex_112_0_22 = all_0_0_0)
% 82.01/43.05 |
% 82.01/43.05 | Equations (61) can reduce 71 to:
% 82.01/43.05 | (72) $false
% 82.01/43.05 |
% 82.01/43.05 |-The branch is then unsatisfiable
% 82.01/43.05 |-Branch two:
% 82.01/43.05 | (73) ~ greater(all_113_1_24, all_113_0_23) & ! [v0] : ( ~ greater(v0, ex_112_0_22) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v0) | ? [v1] : ? [v2] : (growth_rate(all_0_4_4, v0) = v2 & growth_rate(all_0_5_5, v0) = v1 & greater(v1, v2)))
% 82.01/43.05 |
% 82.01/43.05 | Applying alpha-rule on (73) yields:
% 82.01/43.05 | (74) ~ greater(all_113_1_24, all_113_0_23)
% 82.01/43.05 | (75) ! [v0] : ( ~ greater(v0, ex_112_0_22) | ~ subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, v0) | ? [v1] : ? [v2] : (growth_rate(all_0_4_4, v0) = v2 & growth_rate(all_0_5_5, v0) = v1 & greater(v1, v2)))
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (75) with all_0_1_1 and discharging atoms subpopulations(all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1), yields:
% 82.01/43.05 | (76) ~ greater(all_0_1_1, ex_112_0_22) | ? [v0] : ? [v1] : (growth_rate(all_0_4_4, all_0_1_1) = v1 & growth_rate(all_0_5_5, all_0_1_1) = v0 & greater(v0, v1))
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (76), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (77) ~ greater(all_0_1_1, ex_112_0_22)
% 82.01/43.05 |
% 82.01/43.05 | From (61) and (77) follows:
% 82.01/43.05 | (78) ~ greater(all_0_1_1, all_0_0_0)
% 82.01/43.05 |
% 82.01/43.05 | Using (8) and (78) yields:
% 82.01/43.05 | (79) $false
% 82.01/43.05 |
% 82.01/43.05 |-The branch is then unsatisfiable
% 82.01/43.05 |-Branch two:
% 82.01/43.05 | (80) ? [v0] : ? [v1] : (growth_rate(all_0_4_4, all_0_1_1) = v1 & growth_rate(all_0_5_5, all_0_1_1) = v0 & greater(v0, v1))
% 82.01/43.05 |
% 82.01/43.05 | Instantiating (80) with all_130_0_26, all_130_1_27 yields:
% 82.01/43.05 | (81) growth_rate(all_0_4_4, all_0_1_1) = all_130_0_26 & growth_rate(all_0_5_5, all_0_1_1) = all_130_1_27 & greater(all_130_1_27, all_130_0_26)
% 82.01/43.05 |
% 82.01/43.05 | Applying alpha-rule on (81) yields:
% 82.01/43.05 | (82) growth_rate(all_0_4_4, all_0_1_1) = all_130_0_26
% 82.01/43.05 | (83) growth_rate(all_0_5_5, all_0_1_1) = all_130_1_27
% 82.01/43.05 | (84) greater(all_130_1_27, all_130_0_26)
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (22) with all_0_4_4, all_0_1_1, all_130_0_26, all_42_0_15 and discharging atoms growth_rate(all_0_4_4, all_0_1_1) = all_130_0_26, growth_rate(all_0_4_4, all_0_1_1) = all_42_0_15, yields:
% 82.01/43.05 | (85) all_130_0_26 = all_42_0_15
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (22) with all_0_5_5, all_0_1_1, all_130_1_27, all_42_1_16 and discharging atoms growth_rate(all_0_5_5, all_0_1_1) = all_130_1_27, growth_rate(all_0_5_5, all_0_1_1) = all_42_1_16, yields:
% 82.01/43.05 | (86) all_130_1_27 = all_42_1_16
% 82.01/43.05 |
% 82.01/43.05 | From (86)(85) and (84) follows:
% 82.01/43.05 | (87) greater(all_42_1_16, all_42_0_15)
% 82.01/43.05 |
% 82.01/43.05 | Using (87) and (60) yields:
% 82.01/43.05 | (79) $false
% 82.01/43.05 |
% 82.01/43.05 |-The branch is then unsatisfiable
% 82.01/43.05 |-Branch two:
% 82.01/43.05 | (89) ? [v0] : ? [v1] : (cardinality_at_time(all_0_4_4, all_0_1_1) = v0 & cardinality_at_time(all_0_5_5, all_0_1_1) = v1 & ( ~ greater(v1, all_0_3_3) | ~ greater(v0, all_0_3_3)))
% 82.01/43.05 |
% 82.01/43.05 | Instantiating (89) with all_37_0_13, all_37_1_14 yields:
% 82.01/43.05 | (90) cardinality_at_time(all_0_4_4, all_0_1_1) = all_37_1_14 & cardinality_at_time(all_0_5_5, all_0_1_1) = all_37_0_13 & ( ~ greater(all_37_0_13, all_0_3_3) | ~ greater(all_37_1_14, all_0_3_3))
% 82.01/43.05 |
% 82.01/43.05 | Applying alpha-rule on (90) yields:
% 82.01/43.05 | (91) cardinality_at_time(all_0_4_4, all_0_1_1) = all_37_1_14
% 82.01/43.05 | (92) cardinality_at_time(all_0_5_5, all_0_1_1) = all_37_0_13
% 82.01/43.05 | (93) ~ greater(all_37_0_13, all_0_3_3) | ~ greater(all_37_1_14, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (20) with all_0_4_4, all_0_1_1, all_37_1_14, all_9_0_6 and discharging atoms cardinality_at_time(all_0_4_4, all_0_1_1) = all_37_1_14, cardinality_at_time(all_0_4_4, all_0_1_1) = all_9_0_6, yields:
% 82.01/43.05 | (94) all_37_1_14 = all_9_0_6
% 82.01/43.05 |
% 82.01/43.05 | Instantiating formula (20) with all_0_5_5, all_0_1_1, all_37_0_13, all_11_0_7 and discharging atoms cardinality_at_time(all_0_5_5, all_0_1_1) = all_37_0_13, cardinality_at_time(all_0_5_5, all_0_1_1) = all_11_0_7, yields:
% 82.01/43.05 | (95) all_37_0_13 = all_11_0_7
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (38), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (96) greater(all_11_0_7, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (93), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (97) ~ greater(all_37_0_13, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | From (95) and (97) follows:
% 82.01/43.05 | (98) ~ greater(all_11_0_7, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | Using (96) and (98) yields:
% 82.01/43.05 | (79) $false
% 82.01/43.05 |
% 82.01/43.05 |-The branch is then unsatisfiable
% 82.01/43.05 |-Branch two:
% 82.01/43.05 | (100) ~ greater(all_37_1_14, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | From (94) and (100) follows:
% 82.01/43.05 | (101) ~ greater(all_9_0_6, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (46), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (102) greater(all_9_0_6, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | Using (102) and (101) yields:
% 82.01/43.05 | (79) $false
% 82.01/43.05 |
% 82.01/43.05 |-The branch is then unsatisfiable
% 82.01/43.05 |-Branch two:
% 82.01/43.05 | (104) all_9_0_6 = all_0_3_3
% 82.01/43.05 |
% 82.01/43.05 | Combining equations (104,53) yields a new equation:
% 82.01/43.05 | (105) all_24_0_11 = all_0_3_3
% 82.01/43.05 |
% 82.01/43.05 +-Applying beta-rule and splitting (52), into two cases.
% 82.01/43.05 |-Branch one:
% 82.01/43.05 | (106) ~ greater(all_24_1_12, all_0_3_3)
% 82.01/43.05 |
% 82.01/43.05 | From (54) and (106) follows:
% 82.01/43.06 | (98) ~ greater(all_11_0_7, all_0_3_3)
% 82.01/43.06 |
% 82.01/43.06 | Using (96) and (98) yields:
% 82.01/43.06 | (79) $false
% 82.01/43.06 |
% 82.01/43.06 |-The branch is then unsatisfiable
% 82.01/43.06 |-Branch two:
% 82.01/43.06 | (109) ~ (all_24_0_11 = all_0_3_3)
% 82.01/43.06 |
% 82.01/43.06 | Equations (105) can reduce 109 to:
% 82.01/43.06 | (72) $false
% 82.01/43.06 |
% 82.01/43.06 |-The branch is then unsatisfiable
% 82.01/43.06 |-Branch two:
% 82.01/43.06 | (111) ~ greater_or_equal(all_0_1_1, all_11_1_8)
% 82.01/43.06 |
% 82.01/43.06 +-Applying beta-rule and splitting (47), into two cases.
% 82.01/43.06 |-Branch one:
% 82.01/43.06 | (112) greater(all_0_0_0, all_11_1_8)
% 82.01/43.06 |
% 82.01/43.06 | Instantiating formula (11) with all_11_1_8, all_0_0_0, all_0_1_1 and discharging atoms greater(all_0_0_0, all_11_1_8), greater(all_0_1_1, all_0_0_0), yields:
% 82.01/43.06 | (113) greater(all_0_1_1, all_11_1_8)
% 82.01/43.06 |
% 82.01/43.06 | Instantiating formula (4) with all_11_1_8, all_0_1_1 and discharging atoms greater(all_0_1_1, all_11_1_8), ~ greater_or_equal(all_0_1_1, all_11_1_8), yields:
% 82.01/43.06 | (79) $false
% 82.01/43.06 |
% 82.01/43.06 |-The branch is then unsatisfiable
% 82.01/43.06 |-Branch two:
% 82.01/43.06 | (115) all_11_1_8 = all_0_0_0
% 82.01/43.06 |
% 82.01/43.06 | From (115) and (111) follows:
% 82.01/43.06 | (116) ~ greater_or_equal(all_0_1_1, all_0_0_0)
% 82.01/43.06 |
% 82.01/43.06 | Using (24) and (116) yields:
% 82.01/43.06 | (79) $false
% 82.01/43.06 |
% 82.01/43.06 |-The branch is then unsatisfiable
% 82.01/43.06 % SZS output end Proof for theBenchmark
% 82.01/43.06
% 82.01/43.06 42467ms
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