TSTP Solution File: MGT025+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 2.95s 1.42s
% Output : Proof 5.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 9 08:53:19 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.64/0.64 ____ _
% 0.64/0.64 ___ / __ \_____(_)___ ________ __________
% 0.64/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.64
% 0.64/0.64 A Theorem Prover for First-Order Logic
% 0.64/0.64 (ePrincess v.1.0)
% 0.64/0.64
% 0.64/0.64 (c) Philipp Rümmer, 2009-2015
% 0.64/0.64 (c) Peter Backeman, 2014-2015
% 0.64/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.64 Bug reports to peter@backeman.se
% 0.64/0.64
% 0.64/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.64
% 0.64/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.98 Prover 0: Preprocessing ...
% 2.11/1.21 Prover 0: Constructing countermodel ...
% 2.95/1.41 Prover 0: proved (716ms)
% 2.95/1.42
% 2.95/1.42 No countermodel exists, formula is valid
% 2.95/1.42 % SZS status Theorem for theBenchmark
% 2.95/1.42
% 2.95/1.42 Generating proof ... found it (size 217)
% 4.59/1.89
% 4.59/1.89 % SZS output start Proof for theBenchmark
% 4.59/1.89 Assumed formulas after preprocessing and simplification:
% 4.59/1.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (growth_rate(first_movers, v1) = v3 & growth_rate(efficient_producers, v1) = v4 & number_of_organizations(v0, v1) = v2 & subpopulations(first_movers, efficient_producers, v0, v1) & constant(v2) & environment(v0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (number_of_organizations(v5, v7) = v9) | ~ (cardinality_at_time(v6, v7) = v8) | ~ subpopulation(v6, v5, v7) | ~ environment(v5) | greater(v8, zero) | ? [v10] : ? [v11] : (cardinality_at_time(first_movers, v7) = v10 & cardinality_at_time(efficient_producers, v7) = v11 & sum(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (growth_rate(v8, v7) = v6) | ~ (growth_rate(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (number_of_organizations(v8, v7) = v6) | ~ (number_of_organizations(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cardinality_at_time(v8, v7) = v6) | ~ (cardinality_at_time(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sum(v8, v7) = v6) | ~ (sum(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = first_movers | v6 = efficient_producers | ~ (cardinality_at_time(v6, v7) = v8) | ~ greater(v8, zero) | ~ subpopulation(v6, v5, v7) | ~ environment(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (growth_rate(v5, v7) = v8) | ~ in_environment(v6, v7) | ~ subpopulation(v5, v6, v7) | ~ environment(v6) | ? [v9] : (cardinality_at_time(v5, v7) = v9 & ( ~ greater(v9, zero) | ((v8 = zero | ~ constant(v9)) & ( ~ decreases(v9) | greater(zero, v8)) & ( ~ increases(v9) | greater(v8, zero)))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (number_of_organizations(v5, v6) = v8) | ~ (cardinality_at_time(first_movers, v6) = v7) | ~ subpopulation(first_movers, v5, v6) | ~ environment(v5) | ? [v9] : (cardinality_at_time(efficient_producers, v6) = v9 & sum(v7, v9) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (number_of_organizations(v5, v6) = v8) | ~ (cardinality_at_time(efficient_producers, v6) = v7) | ~ subpopulation(efficient_producers, v5, v6) | ~ environment(v5) | ? [v9] : (cardinality_at_time(first_movers, v6) = v9 & sum(v9, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cardinality_at_time(v5, v7) = v8) | ~ in_environment(v6, v7) | ~ greater(v8, zero) | ~ subpopulation(v5, v6, v7) | ~ environment(v6) | ? [v9] : (growth_rate(v5, v7) = v9 & (v9 = zero | ~ constant(v8)) & ( ~ decreases(v8) | greater(zero, v9)) & ( ~ increases(v8) | greater(v9, zero)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cardinality_at_time(first_movers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v5, v6) | ~ environment(v5) | greater(v7, zero)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cardinality_at_time(first_movers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v5, v6) | ~ environment(v5) | ? [v8] : (cardinality_at_time(efficient_producers, v6) = v8 & greater(v8, zero))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cardinality_at_time(efficient_producers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v5, v6) | ~ environment(v5) | greater(v7, zero)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cardinality_at_time(efficient_producers, v6) = v7) | ~ subpopulations(first_movers, efficient_producers, v5, v6) | ~ environment(v5) | ? [v8] : (cardinality_at_time(first_movers, v6) = v8 & greater(v8, zero))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v7) | decreases(v6) | constant(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v7) | decreases(v6) | constant(v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v7) | increases(v7) | constant(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v7) | increases(v7) | constant(v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v6) | increases(v6) | constant(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | decreases(v6) | increases(v6) | constant(v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | increases(v7) | increases(v6) | constant(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6, v7) = v5) | ~ constant(v5) | increases(v7) | increases(v6) | constant(v6)) & ! [v5] : ! [v6] : ( ~ subpopulations(first_movers, efficient_producers, v5, v6) | ~ environment(v5) | in_environment(v5, v6)) & ! [v5] : ! [v6] : ( ~ in_environment(v5, v6) | ~ environment(v5) | subpopulation(first_movers, v5, v6)) & ! [v5] : ! [v6] : ( ~ in_environment(v5, v6) | ~ environment(v5) | subpopulation(efficient_producers, v5, v6)) & ( ~ (v4 = zero) | ~ (v3 = zero)) & ( ~ greater(v4, zero) | ~ greater(zero, v3)) & ( ~ greater(v3, zero) | ~ greater(zero, v4)))
% 4.59/1.93 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.59/1.93 | (1) growth_rate(first_movers, all_0_3_3) = all_0_1_1 & growth_rate(efficient_producers, all_0_3_3) = all_0_0_0 & number_of_organizations(all_0_4_4, all_0_3_3) = all_0_2_2 & subpopulations(first_movers, efficient_producers, all_0_4_4, all_0_3_3) & constant(all_0_2_2) & environment(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_of_organizations(v0, v2) = v4) | ~ (cardinality_at_time(v1, v2) = v3) | ~ subpopulation(v1, v0, v2) | ~ environment(v0) | greater(v3, zero) | ? [v5] : ? [v6] : (cardinality_at_time(first_movers, v2) = v5 & cardinality_at_time(efficient_producers, v2) = v6 & sum(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(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 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = first_movers | v1 = efficient_producers | ~ (cardinality_at_time(v1, v2) = v3) | ~ greater(v3, zero) | ~ subpopulation(v1, v0, v2) | ~ environment(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (growth_rate(v0, v2) = v3) | ~ in_environment(v1, v2) | ~ subpopulation(v0, v1, v2) | ~ environment(v1) | ? [v4] : (cardinality_at_time(v0, v2) = v4 & ( ~ greater(v4, zero) | ((v3 = zero | ~ constant(v4)) & ( ~ decreases(v4) | greater(zero, v3)) & ( ~ increases(v4) | greater(v3, zero)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_of_organizations(v0, v1) = v3) | ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulation(first_movers, v0, v1) | ~ environment(v0) | ? [v4] : (cardinality_at_time(efficient_producers, v1) = v4 & sum(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_of_organizations(v0, v1) = v3) | ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulation(efficient_producers, v0, v1) | ~ environment(v0) | ? [v4] : (cardinality_at_time(first_movers, v1) = v4 & sum(v4, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cardinality_at_time(v0, v2) = v3) | ~ in_environment(v1, v2) | ~ greater(v3, zero) | ~ subpopulation(v0, v1, v2) | ~ environment(v1) | ? [v4] : (growth_rate(v0, v2) = v4 & (v4 = zero | ~ constant(v3)) & ( ~ decreases(v3) | greater(zero, v4)) & ( ~ increases(v3) | greater(v4, zero)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | greater(v2, zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | ? [v3] : (cardinality_at_time(efficient_producers, v1) = v3 & greater(v3, zero))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | greater(v2, zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | ? [v3] : (cardinality_at_time(first_movers, v1) = v3 & greater(v3, zero))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | decreases(v1) | constant(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | decreases(v1) | constant(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | increases(v2) | constant(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | increases(v2) | constant(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v1) | increases(v1) | constant(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v1) | increases(v1) | constant(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | increases(v2) | increases(v1) | constant(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | increases(v2) | increases(v1) | constant(v1)) & ! [v0] : ! [v1] : ( ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | in_environment(v0, v1)) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(first_movers, v0, v1)) & ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(efficient_producers, v0, v1)) & ( ~ (all_0_0_0 = zero) | ~ (all_0_1_1 = zero)) & ( ~ greater(all_0_0_0, zero) | ~ greater(zero, all_0_1_1)) & ( ~ greater(all_0_1_1, zero) | ~ greater(zero, all_0_0_0))
% 4.90/1.94 |
% 4.90/1.94 | Applying alpha-rule on (1) yields:
% 4.90/1.94 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | increases(v2) | constant(v2))
% 4.90/1.94 | (3) environment(all_0_4_4)
% 4.90/1.94 | (4) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(first_movers, v0, v1))
% 4.90/1.94 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | ? [v3] : (cardinality_at_time(efficient_producers, v1) = v3 & greater(v3, zero)))
% 4.90/1.94 | (6) constant(all_0_2_2)
% 4.90/1.94 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(v3, v2) = v0))
% 4.90/1.94 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | decreases(v1) | constant(v2))
% 4.90/1.94 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cardinality_at_time(v3, v2) = v1) | ~ (cardinality_at_time(v3, v2) = v0))
% 4.90/1.94 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | decreases(v1) | constant(v1))
% 4.90/1.94 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | greater(v2, zero))
% 4.90/1.94 | (12) ~ (all_0_0_0 = zero) | ~ (all_0_1_1 = zero)
% 4.90/1.94 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) = v0))
% 4.90/1.94 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cardinality_at_time(v0, v2) = v3) | ~ in_environment(v1, v2) | ~ greater(v3, zero) | ~ subpopulation(v0, v1, v2) | ~ environment(v1) | ? [v4] : (growth_rate(v0, v2) = v4 & (v4 = zero | ~ constant(v3)) & ( ~ decreases(v3) | greater(zero, v4)) & ( ~ increases(v3) | greater(v4, zero))))
% 4.90/1.94 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_of_organizations(v0, v1) = v3) | ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulation(efficient_producers, v0, v1) | ~ environment(v0) | ? [v4] : (cardinality_at_time(first_movers, v1) = v4 & sum(v4, v2) = v3))
% 4.90/1.94 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | increases(v2) | increases(v1) | constant(v2))
% 4.90/1.94 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = first_movers | v1 = efficient_producers | ~ (cardinality_at_time(v1, v2) = v3) | ~ greater(v3, zero) | ~ subpopulation(v1, v0, v2) | ~ environment(v0))
% 4.90/1.95 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_of_organizations(v0, v1) = v3) | ~ (cardinality_at_time(first_movers, v1) = v2) | ~ subpopulation(first_movers, v0, v1) | ~ environment(v0) | ? [v4] : (cardinality_at_time(efficient_producers, v1) = v4 & sum(v2, v4) = v3))
% 4.90/1.95 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v1) | increases(v1) | constant(v1))
% 4.90/1.95 | (20) ! [v0] : ! [v1] : ( ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | in_environment(v0, v1))
% 4.90/1.95 | (21) subpopulations(first_movers, efficient_producers, all_0_4_4, all_0_3_3)
% 4.90/1.95 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v2) | increases(v2) | constant(v1))
% 4.90/1.95 | (23) number_of_organizations(all_0_4_4, all_0_3_3) = all_0_2_2
% 4.90/1.95 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | greater(v2, zero))
% 4.90/1.95 | (25) ~ greater(all_0_1_1, zero) | ~ greater(zero, all_0_0_0)
% 4.90/1.95 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 4.90/1.95 | (27) ! [v0] : ! [v1] : ( ~ in_environment(v0, v1) | ~ environment(v0) | subpopulation(efficient_producers, v0, v1))
% 4.90/1.95 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | decreases(v1) | increases(v1) | constant(v2))
% 4.90/1.95 | (29) growth_rate(first_movers, all_0_3_3) = all_0_1_1
% 4.90/1.95 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_of_organizations(v0, v2) = v4) | ~ (cardinality_at_time(v1, v2) = v3) | ~ subpopulation(v1, v0, v2) | ~ environment(v0) | greater(v3, zero) | ? [v5] : ? [v6] : (cardinality_at_time(first_movers, v2) = v5 & cardinality_at_time(efficient_producers, v2) = v6 & sum(v5, v6) = v4))
% 4.90/1.95 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (growth_rate(v0, v2) = v3) | ~ in_environment(v1, v2) | ~ subpopulation(v0, v1, v2) | ~ environment(v1) | ? [v4] : (cardinality_at_time(v0, v2) = v4 & ( ~ greater(v4, zero) | ((v3 = zero | ~ constant(v4)) & ( ~ decreases(v4) | greater(zero, v3)) & ( ~ increases(v4) | greater(v3, zero))))))
% 4.90/1.95 | (32) growth_rate(efficient_producers, all_0_3_3) = all_0_0_0
% 4.90/1.95 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1, v2) = v0) | ~ constant(v0) | increases(v2) | increases(v1) | constant(v1))
% 4.90/1.95 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (cardinality_at_time(efficient_producers, v1) = v2) | ~ subpopulations(first_movers, efficient_producers, v0, v1) | ~ environment(v0) | ? [v3] : (cardinality_at_time(first_movers, v1) = v3 & greater(v3, zero)))
% 4.90/1.95 | (35) ~ greater(all_0_0_0, zero) | ~ greater(zero, all_0_1_1)
% 4.90/1.95 |
% 4.90/1.95 | Instantiating formula (20) with all_0_3_3, all_0_4_4 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.95 | (36) in_environment(all_0_4_4, all_0_3_3)
% 4.90/1.95 |
% 4.90/1.95 | Instantiating formula (4) with all_0_3_3, all_0_4_4 and discharging atoms in_environment(all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.95 | (37) subpopulation(first_movers, all_0_4_4, all_0_3_3)
% 4.90/1.95 |
% 4.90/1.95 | Instantiating formula (27) with all_0_3_3, all_0_4_4 and discharging atoms in_environment(all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.95 | (38) subpopulation(efficient_producers, all_0_4_4, all_0_3_3)
% 4.90/1.95 |
% 4.90/1.95 | Instantiating formula (31) with all_0_1_1, all_0_3_3, all_0_4_4, first_movers and discharging atoms growth_rate(first_movers, all_0_3_3) = all_0_1_1, in_environment(all_0_4_4, all_0_3_3), subpopulation(first_movers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.95 | (39) ? [v0] : (cardinality_at_time(first_movers, all_0_3_3) = v0 & ( ~ greater(v0, zero) | ((all_0_1_1 = zero | ~ constant(v0)) & ( ~ decreases(v0) | greater(zero, all_0_1_1)) & ( ~ increases(v0) | greater(all_0_1_1, zero)))))
% 4.90/1.95 |
% 4.90/1.95 | Instantiating formula (31) with all_0_0_0, all_0_3_3, all_0_4_4, efficient_producers and discharging atoms growth_rate(efficient_producers, all_0_3_3) = all_0_0_0, in_environment(all_0_4_4, all_0_3_3), subpopulation(efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.96 | (40) ? [v0] : (cardinality_at_time(efficient_producers, all_0_3_3) = v0 & ( ~ greater(v0, zero) | ((all_0_0_0 = zero | ~ constant(v0)) & ( ~ decreases(v0) | greater(zero, all_0_0_0)) & ( ~ increases(v0) | greater(all_0_0_0, zero)))))
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (40) with all_20_0_5 yields:
% 4.90/1.96 | (41) cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5 & ( ~ greater(all_20_0_5, zero) | ((all_0_0_0 = zero | ~ constant(all_20_0_5)) & ( ~ decreases(all_20_0_5) | greater(zero, all_0_0_0)) & ( ~ increases(all_20_0_5) | greater(all_0_0_0, zero))))
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (41) yields:
% 4.90/1.96 | (42) cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5
% 4.90/1.96 | (43) ~ greater(all_20_0_5, zero) | ((all_0_0_0 = zero | ~ constant(all_20_0_5)) & ( ~ decreases(all_20_0_5) | greater(zero, all_0_0_0)) & ( ~ increases(all_20_0_5) | greater(all_0_0_0, zero)))
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (39) with all_22_0_6 yields:
% 4.90/1.96 | (44) cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6 & ( ~ greater(all_22_0_6, zero) | ((all_0_1_1 = zero | ~ constant(all_22_0_6)) & ( ~ decreases(all_22_0_6) | greater(zero, all_0_1_1)) & ( ~ increases(all_22_0_6) | greater(all_0_1_1, zero))))
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (44) yields:
% 4.90/1.96 | (45) cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6
% 4.90/1.96 | (46) ~ greater(all_22_0_6, zero) | ((all_0_1_1 = zero | ~ constant(all_22_0_6)) & ( ~ decreases(all_22_0_6) | greater(zero, all_0_1_1)) & ( ~ increases(all_22_0_6) | greater(all_0_1_1, zero)))
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (18) with all_0_2_2, all_22_0_6, all_0_3_3, all_0_4_4 and discharging atoms number_of_organizations(all_0_4_4, all_0_3_3) = all_0_2_2, cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6, subpopulation(first_movers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.96 | (47) ? [v0] : (cardinality_at_time(efficient_producers, all_0_3_3) = v0 & sum(all_22_0_6, v0) = all_0_2_2)
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (5) with all_22_0_6, all_0_3_3, all_0_4_4 and discharging atoms cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6, subpopulations(first_movers, efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.96 | (48) ? [v0] : (cardinality_at_time(efficient_producers, all_0_3_3) = v0 & greater(v0, zero))
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (15) with all_0_2_2, all_20_0_5, all_0_3_3, all_0_4_4 and discharging atoms number_of_organizations(all_0_4_4, all_0_3_3) = all_0_2_2, cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5, subpopulation(efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.96 | (49) ? [v0] : (cardinality_at_time(first_movers, all_0_3_3) = v0 & sum(v0, all_20_0_5) = all_0_2_2)
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (34) with all_20_0_5, all_0_3_3, all_0_4_4 and discharging atoms cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5, subpopulations(first_movers, efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.96 | (50) ? [v0] : (cardinality_at_time(first_movers, all_0_3_3) = v0 & greater(v0, zero))
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (49) with all_30_0_7 yields:
% 4.90/1.96 | (51) cardinality_at_time(first_movers, all_0_3_3) = all_30_0_7 & sum(all_30_0_7, all_20_0_5) = all_0_2_2
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (51) yields:
% 4.90/1.96 | (52) cardinality_at_time(first_movers, all_0_3_3) = all_30_0_7
% 4.90/1.96 | (53) sum(all_30_0_7, all_20_0_5) = all_0_2_2
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (47) with all_32_0_8 yields:
% 4.90/1.96 | (54) cardinality_at_time(efficient_producers, all_0_3_3) = all_32_0_8 & sum(all_22_0_6, all_32_0_8) = all_0_2_2
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (54) yields:
% 4.90/1.96 | (55) cardinality_at_time(efficient_producers, all_0_3_3) = all_32_0_8
% 4.90/1.96 | (56) sum(all_22_0_6, all_32_0_8) = all_0_2_2
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (50) with all_34_0_9 yields:
% 4.90/1.96 | (57) cardinality_at_time(first_movers, all_0_3_3) = all_34_0_9 & greater(all_34_0_9, zero)
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (57) yields:
% 4.90/1.96 | (58) cardinality_at_time(first_movers, all_0_3_3) = all_34_0_9
% 4.90/1.96 | (59) greater(all_34_0_9, zero)
% 4.90/1.96 |
% 4.90/1.96 | Instantiating (48) with all_36_0_10 yields:
% 4.90/1.96 | (60) cardinality_at_time(efficient_producers, all_0_3_3) = all_36_0_10 & greater(all_36_0_10, zero)
% 4.90/1.96 |
% 4.90/1.96 | Applying alpha-rule on (60) yields:
% 4.90/1.96 | (61) cardinality_at_time(efficient_producers, all_0_3_3) = all_36_0_10
% 4.90/1.96 | (62) greater(all_36_0_10, zero)
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (9) with first_movers, all_0_3_3, all_34_0_9, all_22_0_6 and discharging atoms cardinality_at_time(first_movers, all_0_3_3) = all_34_0_9, cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6, yields:
% 4.90/1.96 | (63) all_34_0_9 = all_22_0_6
% 4.90/1.96 |
% 4.90/1.96 | Instantiating formula (9) with first_movers, all_0_3_3, all_30_0_7, all_34_0_9 and discharging atoms cardinality_at_time(first_movers, all_0_3_3) = all_34_0_9, cardinality_at_time(first_movers, all_0_3_3) = all_30_0_7, yields:
% 4.90/1.96 | (64) all_34_0_9 = all_30_0_7
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (9) with efficient_producers, all_0_3_3, all_36_0_10, all_20_0_5 and discharging atoms cardinality_at_time(efficient_producers, all_0_3_3) = all_36_0_10, cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5, yields:
% 4.90/1.97 | (65) all_36_0_10 = all_20_0_5
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (9) with efficient_producers, all_0_3_3, all_32_0_8, all_36_0_10 and discharging atoms cardinality_at_time(efficient_producers, all_0_3_3) = all_36_0_10, cardinality_at_time(efficient_producers, all_0_3_3) = all_32_0_8, yields:
% 4.90/1.97 | (66) all_36_0_10 = all_32_0_8
% 4.90/1.97 |
% 4.90/1.97 | Combining equations (65,66) yields a new equation:
% 4.90/1.97 | (67) all_32_0_8 = all_20_0_5
% 4.90/1.97 |
% 4.90/1.97 | Combining equations (64,63) yields a new equation:
% 4.90/1.97 | (68) all_30_0_7 = all_22_0_6
% 4.90/1.97 |
% 4.90/1.97 | Simplifying 68 yields:
% 4.90/1.97 | (69) all_30_0_7 = all_22_0_6
% 4.90/1.97 |
% 4.90/1.97 | Combining equations (67,66) yields a new equation:
% 4.90/1.97 | (65) all_36_0_10 = all_20_0_5
% 4.90/1.97 |
% 4.90/1.97 | From (69) and (52) follows:
% 4.90/1.97 | (45) cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6
% 4.90/1.97 |
% 4.90/1.97 | From (67) and (55) follows:
% 4.90/1.97 | (42) cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5
% 4.90/1.97 |
% 4.90/1.97 | From (67) and (56) follows:
% 4.90/1.97 | (73) sum(all_22_0_6, all_20_0_5) = all_0_2_2
% 4.90/1.97 |
% 4.90/1.97 | From (65) and (62) follows:
% 4.90/1.97 | (74) greater(all_20_0_5, zero)
% 4.90/1.97 |
% 4.90/1.97 | From (63) and (59) follows:
% 4.90/1.97 | (75) greater(all_22_0_6, zero)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (8) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (76) decreases(all_22_0_6) | decreases(all_20_0_5) | constant(all_20_0_5)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (10) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (77) decreases(all_22_0_6) | decreases(all_20_0_5) | constant(all_22_0_6)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (2) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (78) decreases(all_20_0_5) | increases(all_20_0_5) | constant(all_20_0_5)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (22) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (79) decreases(all_20_0_5) | increases(all_20_0_5) | constant(all_22_0_6)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (28) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (80) decreases(all_22_0_6) | increases(all_22_0_6) | constant(all_20_0_5)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (19) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (81) decreases(all_22_0_6) | increases(all_22_0_6) | constant(all_22_0_6)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (16) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (82) increases(all_22_0_6) | increases(all_20_0_5) | constant(all_20_0_5)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (33) with all_20_0_5, all_22_0_6, all_0_2_2 and discharging atoms sum(all_22_0_6, all_20_0_5) = all_0_2_2, constant(all_0_2_2), yields:
% 4.90/1.97 | (83) increases(all_22_0_6) | increases(all_20_0_5) | constant(all_22_0_6)
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (14) with all_22_0_6, all_0_3_3, all_0_4_4, first_movers and discharging atoms cardinality_at_time(first_movers, all_0_3_3) = all_22_0_6, in_environment(all_0_4_4, all_0_3_3), greater(all_22_0_6, zero), subpopulation(first_movers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.97 | (84) ? [v0] : (growth_rate(first_movers, all_0_3_3) = v0 & (v0 = zero | ~ constant(all_22_0_6)) & ( ~ decreases(all_22_0_6) | greater(zero, v0)) & ( ~ increases(all_22_0_6) | greater(v0, zero)))
% 4.90/1.97 |
% 4.90/1.97 | Instantiating formula (14) with all_20_0_5, all_0_3_3, all_0_4_4, efficient_producers and discharging atoms cardinality_at_time(efficient_producers, all_0_3_3) = all_20_0_5, in_environment(all_0_4_4, all_0_3_3), greater(all_20_0_5, zero), subpopulation(efficient_producers, all_0_4_4, all_0_3_3), environment(all_0_4_4), yields:
% 4.90/1.97 | (85) ? [v0] : (growth_rate(efficient_producers, all_0_3_3) = v0 & (v0 = zero | ~ constant(all_20_0_5)) & ( ~ decreases(all_20_0_5) | greater(zero, v0)) & ( ~ increases(all_20_0_5) | greater(v0, zero)))
% 4.90/1.97 |
% 4.90/1.97 | Instantiating (85) with all_47_0_11 yields:
% 4.90/1.97 | (86) growth_rate(efficient_producers, all_0_3_3) = all_47_0_11 & (all_47_0_11 = zero | ~ constant(all_20_0_5)) & ( ~ decreases(all_20_0_5) | greater(zero, all_47_0_11)) & ( ~ increases(all_20_0_5) | greater(all_47_0_11, zero))
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (86) yields:
% 4.90/1.98 | (87) growth_rate(efficient_producers, all_0_3_3) = all_47_0_11
% 4.90/1.98 | (88) all_47_0_11 = zero | ~ constant(all_20_0_5)
% 4.90/1.98 | (89) ~ decreases(all_20_0_5) | greater(zero, all_47_0_11)
% 4.90/1.98 | (90) ~ increases(all_20_0_5) | greater(all_47_0_11, zero)
% 4.90/1.98 |
% 4.90/1.98 | Instantiating (84) with all_49_0_12 yields:
% 4.90/1.98 | (91) growth_rate(first_movers, all_0_3_3) = all_49_0_12 & (all_49_0_12 = zero | ~ constant(all_22_0_6)) & ( ~ decreases(all_22_0_6) | greater(zero, all_49_0_12)) & ( ~ increases(all_22_0_6) | greater(all_49_0_12, zero))
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (91) yields:
% 4.90/1.98 | (92) growth_rate(first_movers, all_0_3_3) = all_49_0_12
% 4.90/1.98 | (93) all_49_0_12 = zero | ~ constant(all_22_0_6)
% 4.90/1.98 | (94) ~ decreases(all_22_0_6) | greater(zero, all_49_0_12)
% 4.90/1.98 | (95) ~ increases(all_22_0_6) | greater(all_49_0_12, zero)
% 4.90/1.98 |
% 4.90/1.98 | Instantiating formula (26) with first_movers, all_0_3_3, all_49_0_12, all_0_1_1 and discharging atoms growth_rate(first_movers, all_0_3_3) = all_49_0_12, growth_rate(first_movers, all_0_3_3) = all_0_1_1, yields:
% 4.90/1.98 | (96) all_49_0_12 = all_0_1_1
% 4.90/1.98 |
% 4.90/1.98 | Instantiating formula (26) with efficient_producers, all_0_3_3, all_47_0_11, all_0_0_0 and discharging atoms growth_rate(efficient_producers, all_0_3_3) = all_47_0_11, growth_rate(efficient_producers, all_0_3_3) = all_0_0_0, yields:
% 4.90/1.98 | (97) all_47_0_11 = all_0_0_0
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (35), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (98) ~ greater(all_0_0_0, zero)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (43), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (99) ~ greater(all_20_0_5, zero)
% 4.90/1.98 |
% 4.90/1.98 | Using (74) and (99) yields:
% 4.90/1.98 | (100) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (74) greater(all_20_0_5, zero)
% 4.90/1.98 | (102) (all_0_0_0 = zero | ~ constant(all_20_0_5)) & ( ~ decreases(all_20_0_5) | greater(zero, all_0_0_0)) & ( ~ increases(all_20_0_5) | greater(all_0_0_0, zero))
% 4.90/1.98 |
% 4.90/1.98 | Applying alpha-rule on (102) yields:
% 4.90/1.98 | (103) all_0_0_0 = zero | ~ constant(all_20_0_5)
% 4.90/1.98 | (104) ~ decreases(all_20_0_5) | greater(zero, all_0_0_0)
% 4.90/1.98 | (105) ~ increases(all_20_0_5) | greater(all_0_0_0, zero)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (105), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (106) greater(all_0_0_0, zero)
% 4.90/1.98 |
% 4.90/1.98 | Using (106) and (98) yields:
% 4.90/1.98 | (100) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (98) ~ greater(all_0_0_0, zero)
% 4.90/1.98 | (109) ~ increases(all_20_0_5)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (25), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (110) ~ greater(all_0_1_1, zero)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (95), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (111) greater(all_49_0_12, zero)
% 4.90/1.98 |
% 4.90/1.98 | From (96) and (111) follows:
% 4.90/1.98 | (112) greater(all_0_1_1, zero)
% 4.90/1.98 |
% 4.90/1.98 | Using (112) and (110) yields:
% 4.90/1.98 | (100) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (114) ~ greater(all_49_0_12, zero)
% 4.90/1.98 | (115) ~ increases(all_22_0_6)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (83), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (116) constant(all_22_0_6)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (82), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (117) constant(all_20_0_5)
% 4.90/1.98 |
% 4.90/1.98 +-Applying beta-rule and splitting (88), into two cases.
% 4.90/1.98 |-Branch one:
% 4.90/1.98 | (118) ~ constant(all_20_0_5)
% 4.90/1.98 |
% 4.90/1.98 | Using (117) and (118) yields:
% 4.90/1.98 | (100) $false
% 4.90/1.98 |
% 4.90/1.98 |-The branch is then unsatisfiable
% 4.90/1.98 |-Branch two:
% 4.90/1.98 | (117) constant(all_20_0_5)
% 4.90/1.98 | (121) all_47_0_11 = zero
% 4.90/1.99 |
% 4.90/1.99 | Combining equations (97,121) yields a new equation:
% 4.90/1.99 | (122) all_0_0_0 = zero
% 4.90/1.99 |
% 4.90/1.99 | Simplifying 122 yields:
% 4.90/1.99 | (123) all_0_0_0 = zero
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (12), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (124) ~ (all_0_0_0 = zero)
% 5.12/1.99 |
% 5.12/1.99 | Equations (123) can reduce 124 to:
% 5.12/1.99 | (125) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (123) all_0_0_0 = zero
% 5.12/1.99 | (127) ~ (all_0_1_1 = zero)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (93), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (128) ~ constant(all_22_0_6)
% 5.12/1.99 |
% 5.12/1.99 | Using (116) and (128) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (116) constant(all_22_0_6)
% 5.12/1.99 | (131) all_49_0_12 = zero
% 5.12/1.99 |
% 5.12/1.99 | Combining equations (131,96) yields a new equation:
% 5.12/1.99 | (132) all_0_1_1 = zero
% 5.12/1.99 |
% 5.12/1.99 | Equations (132) can reduce 127 to:
% 5.12/1.99 | (125) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (118) ~ constant(all_20_0_5)
% 5.12/1.99 | (135) increases(all_22_0_6) | increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (135), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (136) increases(all_22_0_6)
% 5.12/1.99 |
% 5.12/1.99 | Using (136) and (115) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (115) ~ increases(all_22_0_6)
% 5.12/1.99 | (139) increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 | Using (139) and (109) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (128) ~ constant(all_22_0_6)
% 5.12/1.99 | (135) increases(all_22_0_6) | increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (82), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (117) constant(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (79), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (116) constant(all_22_0_6)
% 5.12/1.99 |
% 5.12/1.99 | Using (116) and (128) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (128) ~ constant(all_22_0_6)
% 5.12/1.99 | (147) decreases(all_20_0_5) | increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (88), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (118) ~ constant(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 | Using (117) and (118) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (117) constant(all_20_0_5)
% 5.12/1.99 | (121) all_47_0_11 = zero
% 5.12/1.99 |
% 5.12/1.99 | Combining equations (97,121) yields a new equation:
% 5.12/1.99 | (122) all_0_0_0 = zero
% 5.12/1.99 |
% 5.12/1.99 | Simplifying 122 yields:
% 5.12/1.99 | (123) all_0_0_0 = zero
% 5.12/1.99 |
% 5.12/1.99 | From (123) and (98) follows:
% 5.12/1.99 | (154) ~ greater(zero, zero)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (147), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (155) decreases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (89), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (156) greater(zero, all_47_0_11)
% 5.12/1.99 |
% 5.12/1.99 | From (121) and (156) follows:
% 5.12/1.99 | (157) greater(zero, zero)
% 5.12/1.99 |
% 5.12/1.99 | Using (157) and (154) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (159) ~ greater(zero, all_47_0_11)
% 5.12/1.99 | (160) ~ decreases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 | Using (155) and (160) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (160) ~ decreases(all_20_0_5)
% 5.12/1.99 | (139) increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 | Using (139) and (109) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (118) ~ constant(all_20_0_5)
% 5.12/1.99 | (135) increases(all_22_0_6) | increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 +-Applying beta-rule and splitting (135), into two cases.
% 5.12/1.99 |-Branch one:
% 5.12/1.99 | (136) increases(all_22_0_6)
% 5.12/1.99 |
% 5.12/1.99 | Using (136) and (115) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (115) ~ increases(all_22_0_6)
% 5.12/1.99 | (139) increases(all_20_0_5)
% 5.12/1.99 |
% 5.12/1.99 | Using (139) and (109) yields:
% 5.12/1.99 | (100) $false
% 5.12/1.99 |
% 5.12/1.99 |-The branch is then unsatisfiable
% 5.12/1.99 |-Branch two:
% 5.12/1.99 | (112) greater(all_0_1_1, zero)
% 5.12/1.99 | (173) ~ greater(zero, all_0_0_0)
% 5.12/1.99 |
% 5.12/2.00 +-Applying beta-rule and splitting (89), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (156) greater(zero, all_47_0_11)
% 5.12/2.00 |
% 5.12/2.00 | From (97) and (156) follows:
% 5.12/2.00 | (175) greater(zero, all_0_0_0)
% 5.12/2.00 |
% 5.12/2.00 | Using (175) and (173) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (159) ~ greater(zero, all_47_0_11)
% 5.12/2.00 | (160) ~ decreases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (79), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (116) constant(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (78), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (117) constant(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (93), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (128) ~ constant(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (116) and (128) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (116) constant(all_22_0_6)
% 5.12/2.00 | (131) all_49_0_12 = zero
% 5.12/2.00 |
% 5.12/2.00 | Combining equations (131,96) yields a new equation:
% 5.12/2.00 | (132) all_0_1_1 = zero
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (12), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (124) ~ (all_0_0_0 = zero)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (88), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (118) ~ constant(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (117) and (118) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (117) constant(all_20_0_5)
% 5.12/2.00 | (121) all_47_0_11 = zero
% 5.12/2.00 |
% 5.12/2.00 | Combining equations (97,121) yields a new equation:
% 5.12/2.00 | (122) all_0_0_0 = zero
% 5.12/2.00 |
% 5.12/2.00 | Simplifying 122 yields:
% 5.12/2.00 | (123) all_0_0_0 = zero
% 5.12/2.00 |
% 5.12/2.00 | Equations (123) can reduce 124 to:
% 5.12/2.00 | (125) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (123) all_0_0_0 = zero
% 5.12/2.00 | (127) ~ (all_0_1_1 = zero)
% 5.12/2.00 |
% 5.12/2.00 | Equations (132) can reduce 127 to:
% 5.12/2.00 | (125) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (118) ~ constant(all_20_0_5)
% 5.12/2.00 | (147) decreases(all_20_0_5) | increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (147), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (155) decreases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (155) and (160) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (160) ~ decreases(all_20_0_5)
% 5.12/2.00 | (139) increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (139) and (109) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (128) ~ constant(all_22_0_6)
% 5.12/2.00 | (147) decreases(all_20_0_5) | increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (147), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (155) decreases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (155) and (160) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (160) ~ decreases(all_20_0_5)
% 5.12/2.00 | (139) increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (139) and (109) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (106) greater(all_0_0_0, zero)
% 5.12/2.00 | (212) ~ greater(zero, all_0_1_1)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (46), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (213) ~ greater(all_22_0_6, zero)
% 5.12/2.00 |
% 5.12/2.00 | Using (75) and (213) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (75) greater(all_22_0_6, zero)
% 5.12/2.00 | (216) (all_0_1_1 = zero | ~ constant(all_22_0_6)) & ( ~ decreases(all_22_0_6) | greater(zero, all_0_1_1)) & ( ~ increases(all_22_0_6) | greater(all_0_1_1, zero))
% 5.12/2.00 |
% 5.12/2.00 | Applying alpha-rule on (216) yields:
% 5.12/2.00 | (217) all_0_1_1 = zero | ~ constant(all_22_0_6)
% 5.12/2.00 | (218) ~ decreases(all_22_0_6) | greater(zero, all_0_1_1)
% 5.12/2.00 | (219) ~ increases(all_22_0_6) | greater(all_0_1_1, zero)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (218), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (220) greater(zero, all_0_1_1)
% 5.12/2.00 |
% 5.12/2.00 | Using (220) and (212) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (212) ~ greater(zero, all_0_1_1)
% 5.12/2.00 | (223) ~ decreases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (25), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (110) ~ greater(all_0_1_1, zero)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (219), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (112) greater(all_0_1_1, zero)
% 5.12/2.00 |
% 5.12/2.00 | Using (112) and (110) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (110) ~ greater(all_0_1_1, zero)
% 5.12/2.00 | (115) ~ increases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (80), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (117) constant(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (88), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (118) ~ constant(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 | Using (117) and (118) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (117) constant(all_20_0_5)
% 5.12/2.00 | (121) all_47_0_11 = zero
% 5.12/2.00 |
% 5.12/2.00 | Combining equations (97,121) yields a new equation:
% 5.12/2.00 | (122) all_0_0_0 = zero
% 5.12/2.00 |
% 5.12/2.00 | Simplifying 122 yields:
% 5.12/2.00 | (123) all_0_0_0 = zero
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (12), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (124) ~ (all_0_0_0 = zero)
% 5.12/2.00 |
% 5.12/2.00 | Equations (123) can reduce 124 to:
% 5.12/2.00 | (125) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (123) all_0_0_0 = zero
% 5.12/2.00 | (127) ~ (all_0_1_1 = zero)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (93), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (128) ~ constant(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (83), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (116) constant(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (116) and (128) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (128) ~ constant(all_22_0_6)
% 5.12/2.00 | (135) increases(all_22_0_6) | increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (135), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (136) increases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (136) and (115) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (115) ~ increases(all_22_0_6)
% 5.12/2.00 | (139) increases(all_20_0_5)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (81), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (116) constant(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (116) and (128) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (128) ~ constant(all_22_0_6)
% 5.12/2.00 | (252) decreases(all_22_0_6) | increases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 +-Applying beta-rule and splitting (252), into two cases.
% 5.12/2.00 |-Branch one:
% 5.12/2.00 | (253) decreases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (253) and (223) yields:
% 5.12/2.00 | (100) $false
% 5.12/2.00 |
% 5.12/2.00 |-The branch is then unsatisfiable
% 5.12/2.00 |-Branch two:
% 5.12/2.00 | (223) ~ decreases(all_22_0_6)
% 5.12/2.00 | (136) increases(all_22_0_6)
% 5.12/2.00 |
% 5.12/2.00 | Using (136) and (115) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (116) constant(all_22_0_6)
% 5.12/2.01 | (131) all_49_0_12 = zero
% 5.12/2.01 |
% 5.12/2.01 | Combining equations (131,96) yields a new equation:
% 5.12/2.01 | (132) all_0_1_1 = zero
% 5.12/2.01 |
% 5.12/2.01 | Equations (132) can reduce 127 to:
% 5.12/2.01 | (125) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (118) ~ constant(all_20_0_5)
% 5.12/2.01 | (252) decreases(all_22_0_6) | increases(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (252), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (253) decreases(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 | Using (253) and (223) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (223) ~ decreases(all_22_0_6)
% 5.12/2.01 | (136) increases(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 | Using (136) and (115) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (112) greater(all_0_1_1, zero)
% 5.12/2.01 | (173) ~ greater(zero, all_0_0_0)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (89), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (156) greater(zero, all_47_0_11)
% 5.12/2.01 |
% 5.12/2.01 | From (97) and (156) follows:
% 5.12/2.01 | (175) greater(zero, all_0_0_0)
% 5.12/2.01 |
% 5.12/2.01 | Using (175) and (173) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (159) ~ greater(zero, all_47_0_11)
% 5.12/2.01 | (160) ~ decreases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 | From (97) and (159) follows:
% 5.12/2.01 | (173) ~ greater(zero, all_0_0_0)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (76), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (117) constant(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (88), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (118) ~ constant(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 | Using (117) and (118) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (117) constant(all_20_0_5)
% 5.12/2.01 | (121) all_47_0_11 = zero
% 5.12/2.01 |
% 5.12/2.01 | Combining equations (97,121) yields a new equation:
% 5.12/2.01 | (122) all_0_0_0 = zero
% 5.12/2.01 |
% 5.12/2.01 | Simplifying 122 yields:
% 5.12/2.01 | (123) all_0_0_0 = zero
% 5.12/2.01 |
% 5.12/2.01 | From (123) and (106) follows:
% 5.12/2.01 | (157) greater(zero, zero)
% 5.12/2.01 |
% 5.12/2.01 | From (123) and (173) follows:
% 5.12/2.01 | (154) ~ greater(zero, zero)
% 5.12/2.01 |
% 5.12/2.01 | Using (157) and (154) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (118) ~ constant(all_20_0_5)
% 5.12/2.01 | (288) decreases(all_22_0_6) | decreases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (78), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (117) constant(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 | Using (117) and (118) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (118) ~ constant(all_20_0_5)
% 5.12/2.01 | (147) decreases(all_20_0_5) | increases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (77), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (116) constant(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (217), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (128) ~ constant(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 | Using (116) and (128) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (116) constant(all_22_0_6)
% 5.12/2.01 | (132) all_0_1_1 = zero
% 5.12/2.01 |
% 5.12/2.01 | From (132) and (112) follows:
% 5.12/2.01 | (157) greater(zero, zero)
% 5.12/2.01 |
% 5.12/2.01 | From (132) and (212) follows:
% 5.12/2.01 | (154) ~ greater(zero, zero)
% 5.12/2.01 |
% 5.12/2.01 | Using (157) and (154) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (128) ~ constant(all_22_0_6)
% 5.12/2.01 | (288) decreases(all_22_0_6) | decreases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (147), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (155) decreases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 | Using (155) and (160) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (160) ~ decreases(all_20_0_5)
% 5.12/2.01 | (139) increases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 +-Applying beta-rule and splitting (288), into two cases.
% 5.12/2.01 |-Branch one:
% 5.12/2.01 | (253) decreases(all_22_0_6)
% 5.12/2.01 |
% 5.12/2.01 | Using (253) and (223) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 |-Branch two:
% 5.12/2.01 | (223) ~ decreases(all_22_0_6)
% 5.12/2.01 | (155) decreases(all_20_0_5)
% 5.12/2.01 |
% 5.12/2.01 | Using (155) and (160) yields:
% 5.12/2.01 | (100) $false
% 5.12/2.01 |
% 5.12/2.01 |-The branch is then unsatisfiable
% 5.12/2.01 % SZS output end Proof for theBenchmark
% 5.12/2.01
% 5.12/2.01 1358ms
%------------------------------------------------------------------------------