TSTP Solution File: MGT024+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 2.77s 1.35s
% Output : Proof 6.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 600
% 0.08/0.27 % DateTime : Thu Jun 9 07:43:52 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.12/0.48 ____ _
% 0.12/0.48 ___ / __ \_____(_)___ ________ __________
% 0.12/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.12/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.12/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.12/0.48
% 0.12/0.48 A Theorem Prover for First-Order Logic
% 0.12/0.48 (ePrincess v.1.0)
% 0.12/0.48
% 0.12/0.48 (c) Philipp Rümmer, 2009-2015
% 0.12/0.48 (c) Peter Backeman, 2014-2015
% 0.12/0.48 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.12/0.48 Free software under GNU Lesser General Public License (LGPL).
% 0.12/0.48 Bug reports to peter@backeman.se
% 0.12/0.48
% 0.12/0.48 For more information, visit http://user.uu.se/~petba168/breu/
% 0.12/0.48
% 0.12/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.12/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.10/0.79 Prover 0: Preprocessing ...
% 1.38/0.96 Prover 0: Constructing countermodel ...
% 2.12/1.14 Prover 0: gave up
% 2.12/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.12/1.17 Prover 1: Preprocessing ...
% 2.41/1.24 Prover 1: Constructing countermodel ...
% 2.77/1.34 Prover 1: proved (208ms)
% 2.77/1.35
% 2.77/1.35 No countermodel exists, formula is valid
% 2.77/1.35 % SZS status Theorem for theBenchmark
% 2.77/1.35
% 2.77/1.35 Generating proof ... found it (size 315)
% 5.77/2.07
% 5.77/2.07 % SZS output start Proof for theBenchmark
% 5.77/2.07 Assumed formulas after preprocessing and simplification:
% 5.77/2.07 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (growth_rate(efficient_producers, v1) = v4 & growth_rate(first_movers, v1) = v3 & equilibrium(v0) = v2 & greater_or_equal(v1, v2) = 0 & greater(v4, zero) = v7 & greater(v3, zero) = v5 & greater(zero, v4) = v6 & greater(zero, v3) = v8 & subpopulations(first_movers, efficient_producers, v0, v1) = 0 & environment(v0) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (subpopulations(v14, v13, v12, v11) = v10) | ~ (subpopulations(v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (growth_rate(v12, v11) = v10) | ~ (growth_rate(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (resources(v12, v11) = v10) | ~ (resources(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (greater_or_equal(v12, v11) = v10) | ~ (greater_or_equal(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (number_of_organizations(v12, v11) = v10) | ~ (number_of_organizations(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (greater(v12, v11) = v10) | ~ (greater(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in_environment(v12, v11) = v10) | ~ (in_environment(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (equilibrium(v9) = v11) | ~ (greater(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (resources(v9, v10) = v17 & decreases(v17) = v18 & constant(v17) = v19 & number_of_organizations(v9, v10) = v15 & greater(v15, zero) = v16 & environment(v9) = v13 & in_environment(v9, v10) = v14 & ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | (( ~ (v12 = 0) | v18 = 0) & (v19 = 0 | v12 = 0))))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (decreases(v11) = v10) | ~ (decreases(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (constant(v11) = v10) | ~ (constant(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (equilibrium(v11) = v10) | ~ (equilibrium(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (environment(v11) = v10) | ~ (environment(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (equilibrium(v9) = v11) | ~ (greater_or_equal(v10, v11) = 0) | ? [v12] : ? [v13] : (greater(v11, v10) = v13 & environment(v9) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v9] : ! [v10] : ( ~ (subpopulations(first_movers, efficient_producers, v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (growth_rate(efficient_producers, v10) = v15 & growth_rate(first_movers, v10) = v14 & constant(v12) = v13 & number_of_organizations(v9, v10) = v12 & greater(v15, zero) = v18 & greater(v14, zero) = v16 & greater(zero, v15) = v17 & greater(zero, v14) = v19 & environment(v9) = v11 & ( ~ (v13 = 0) | ~ (v11 = 0) | (v19 = 0 & v18 = 0) | (v17 = 0 & v16 = 0) | (v15 = zero & v14 = zero)))) & ! [v9] : ! [v10] : ( ~ (subpopulations(first_movers, efficient_producers, v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (number_of_organizations(v9, v10) = v12 & greater(v12, zero) = v13 & environment(v9) = v11 & ( ~ (v11 = 0) | v13 = 0))) & ! [v9] : ! [v10] : ( ~ (subpopulations(first_movers, efficient_producers, v9, v10) = 0) | ? [v11] : ? [v12] : (environment(v9) = v11 & in_environment(v9, v10) = v12 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (in_environment(v9, v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (resources(v9, v10) = v12 & decreases(v14) = v15 & decreases(v12) = v13 & constant(v14) = v17 & constant(v12) = v16 & number_of_organizations(v9, v10) = v14 & environment(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v16 = 0) | v17 = 0) & ( ~ (v15 = 0) | ~ (v13 = 0)))))) & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)) & ( ~ (v4 = zero) | ~ (v3 = zero)))
% 5.77/2.10 | 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, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 5.77/2.10 | (1) growth_rate(efficient_producers, all_0_7_7) = all_0_4_4 & growth_rate(first_movers, all_0_7_7) = all_0_5_5 & equilibrium(all_0_8_8) = all_0_6_6 & greater_or_equal(all_0_7_7, all_0_6_6) = 0 & greater(all_0_4_4, zero) = all_0_1_1 & greater(all_0_5_5, zero) = all_0_3_3 & greater(zero, all_0_4_4) = all_0_2_2 & greater(zero, all_0_5_5) = all_0_0_0 & subpopulations(first_movers, efficient_producers, all_0_8_8, all_0_7_7) = 0 & environment(all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (resources(v0, v1) = v8 & decreases(v8) = v9 & constant(v8) = v10 & number_of_organizations(v0, v1) = v6 & greater(v6, zero) = v7 & environment(v0) = v4 & in_environment(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | v9 = 0) & (v10 = 0 | v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (equilibrium(v0) = v2) | ~ (greater_or_equal(v1, v2) = 0) | ? [v3] : ? [v4] : (greater(v2, v1) = v4 & environment(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (growth_rate(efficient_producers, v1) = v6 & growth_rate(first_movers, v1) = v5 & constant(v3) = v4 & number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 & greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5) = v10 & environment(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6 = zero & v5 = zero)))) & ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (number_of_organizations(v0, v1) = v3 & greater(v3, zero) = v4 & environment(v0) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (environment(v0) = v2 & in_environment(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (in_environment(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (resources(v0, v1) = v3 & decreases(v5) = v6 & decreases(v3) = v4 & constant(v5) = v8 & constant(v3) = v7 & number_of_organizations(v0, v1) = v5 & environment(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v8 = 0) & ( ~ (v6 = 0) | ~ (v4 = 0)))))) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)) & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0)) & ( ~ (all_0_4_4 = zero) | ~ (all_0_5_5 = zero))
% 5.77/2.11 |
% 5.77/2.11 | Applying alpha-rule on (1) yields:
% 5.77/2.11 | (2) greater(zero, all_0_4_4) = all_0_2_2
% 5.77/2.11 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in_environment(v3, v2) = v1) | ~ (in_environment(v3, v2) = v0))
% 5.77/2.11 | (4) ~ (all_0_4_4 = zero) | ~ (all_0_5_5 = zero)
% 5.77/2.11 | (5) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 5.77/2.11 | (6) growth_rate(first_movers, all_0_7_7) = all_0_5_5
% 5.77/2.11 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (environment(v2) = v1) | ~ (environment(v2) = v0))
% 5.77/2.11 | (8) ! [v0] : ! [v1] : ( ~ (in_environment(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (resources(v0, v1) = v3 & decreases(v5) = v6 & decreases(v3) = v4 & constant(v5) = v8 & constant(v3) = v7 & number_of_organizations(v0, v1) = v5 & environment(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v7 = 0) | v8 = 0) & ( ~ (v6 = 0) | ~ (v4 = 0))))))
% 6.23/2.11 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater_or_equal(v3, v2) = v1) | ~ (greater_or_equal(v3, v2) = v0))
% 6.23/2.11 | (10) ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (number_of_organizations(v0, v1) = v3 & greater(v3, zero) = v4 & environment(v0) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 6.23/2.11 | (11) ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (growth_rate(efficient_producers, v1) = v6 & growth_rate(first_movers, v1) = v5 & constant(v3) = v4 & number_of_organizations(v0, v1) = v3 & greater(v6, zero) = v9 & greater(v5, zero) = v7 & greater(zero, v6) = v8 & greater(zero, v5) = v10 & environment(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | (v10 = 0 & v9 = 0) | (v8 = 0 & v7 = 0) | (v6 = zero & v5 = zero))))
% 6.23/2.12 | (12) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0)
% 6.23/2.12 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (subpopulations(v5, v4, v3, v2) = v1) | ~ (subpopulations(v5, v4, v3, v2) = v0))
% 6.23/2.12 | (14) subpopulations(first_movers, efficient_producers, all_0_8_8, all_0_7_7) = 0
% 6.23/2.12 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0))
% 6.23/2.12 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (decreases(v2) = v1) | ~ (decreases(v2) = v0))
% 6.23/2.12 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equilibrium(v2) = v1) | ~ (equilibrium(v2) = v0))
% 6.23/2.12 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equilibrium(v0) = v2) | ~ (greater(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (resources(v0, v1) = v8 & decreases(v8) = v9 & constant(v8) = v10 & number_of_organizations(v0, v1) = v6 & greater(v6, zero) = v7 & environment(v0) = v4 & in_environment(v0, v1) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v3 = 0) | v9 = 0) & (v10 = 0 | v3 = 0)))))
% 6.23/2.12 | (19) equilibrium(all_0_8_8) = all_0_6_6
% 6.23/2.12 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (constant(v2) = v1) | ~ (constant(v2) = v0))
% 6.23/2.12 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (growth_rate(v3, v2) = v1) | ~ (growth_rate(v3, v2) = v0))
% 6.23/2.12 | (22) greater(all_0_4_4, zero) = all_0_1_1
% 6.23/2.12 | (23) ! [v0] : ! [v1] : ( ~ (subpopulations(first_movers, efficient_producers, v0, v1) = 0) | ? [v2] : ? [v3] : (environment(v0) = v2 & in_environment(v0, v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 6.23/2.12 | (24) greater(zero, all_0_5_5) = all_0_0_0
% 6.23/2.12 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0))
% 6.23/2.12 | (26) greater_or_equal(all_0_7_7, all_0_6_6) = 0
% 6.23/2.12 | (27) environment(all_0_8_8) = 0
% 6.23/2.12 | (28) growth_rate(efficient_producers, all_0_7_7) = all_0_4_4
% 6.23/2.12 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (number_of_organizations(v3, v2) = v1) | ~ (number_of_organizations(v3, v2) = v0))
% 6.23/2.12 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (equilibrium(v0) = v2) | ~ (greater_or_equal(v1, v2) = 0) | ? [v3] : ? [v4] : (greater(v2, v1) = v4 & environment(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.23/2.12 | (31) greater(all_0_5_5, zero) = all_0_3_3
% 6.23/2.12 |
% 6.23/2.12 | Instantiating formula (25) with all_0_5_5, zero, all_0_3_3, all_0_1_1 and discharging atoms greater(all_0_5_5, zero) = all_0_3_3, yields:
% 6.23/2.12 | (32) all_0_1_1 = all_0_3_3 | ~ (greater(all_0_5_5, zero) = all_0_1_1)
% 6.23/2.12 |
% 6.23/2.12 | Instantiating formula (25) with zero, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms greater(zero, all_0_5_5) = all_0_0_0, yields:
% 6.23/2.12 | (33) all_0_0_0 = all_0_2_2 | ~ (greater(zero, all_0_5_5) = all_0_2_2)
% 6.23/2.12 |
% 6.23/2.12 | Instantiating formula (30) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms equilibrium(all_0_8_8) = all_0_6_6, greater_or_equal(all_0_7_7, all_0_6_6) = 0, yields:
% 6.23/2.12 | (34) ? [v0] : ? [v1] : (greater(all_0_6_6, all_0_7_7) = v1 & environment(all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.23/2.12 |
% 6.23/2.12 | Instantiating formula (11) with all_0_7_7, all_0_8_8 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_8_8, all_0_7_7) = 0, yields:
% 6.23/2.12 | (35) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (growth_rate(efficient_producers, all_0_7_7) = v4 & growth_rate(first_movers, all_0_7_7) = v3 & constant(v1) = v2 & number_of_organizations(all_0_8_8, all_0_7_7) = v1 & greater(v4, zero) = v7 & greater(v3, zero) = v5 & greater(zero, v4) = v6 & greater(zero, v3) = v8 & environment(all_0_8_8) = v0 & ( ~ (v2 = 0) | ~ (v0 = 0) | (v8 = 0 & v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = zero & v3 = zero)))
% 6.23/2.12 |
% 6.23/2.12 | Instantiating formula (10) with all_0_7_7, all_0_8_8 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_8_8, all_0_7_7) = 0, yields:
% 6.23/2.12 | (36) ? [v0] : ? [v1] : ? [v2] : (number_of_organizations(all_0_8_8, all_0_7_7) = v1 & greater(v1, zero) = v2 & environment(all_0_8_8) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (23) with all_0_7_7, all_0_8_8 and discharging atoms subpopulations(first_movers, efficient_producers, all_0_8_8, all_0_7_7) = 0, yields:
% 6.23/2.13 | (37) ? [v0] : ? [v1] : (environment(all_0_8_8) = v0 & in_environment(all_0_8_8, all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.23/2.13 |
% 6.23/2.13 | Instantiating (37) with all_8_0_9, all_8_1_10 yields:
% 6.23/2.13 | (38) environment(all_0_8_8) = all_8_1_10 & in_environment(all_0_8_8, all_0_7_7) = all_8_0_9 & ( ~ (all_8_1_10 = 0) | all_8_0_9 = 0)
% 6.23/2.13 |
% 6.23/2.13 | Applying alpha-rule on (38) yields:
% 6.23/2.13 | (39) environment(all_0_8_8) = all_8_1_10
% 6.23/2.13 | (40) in_environment(all_0_8_8, all_0_7_7) = all_8_0_9
% 6.23/2.13 | (41) ~ (all_8_1_10 = 0) | all_8_0_9 = 0
% 6.23/2.13 |
% 6.23/2.13 | Instantiating (35) with all_10_0_11, all_10_1_12, all_10_2_13, all_10_3_14, all_10_4_15, all_10_5_16, all_10_6_17, all_10_7_18, all_10_8_19 yields:
% 6.23/2.13 | (42) growth_rate(efficient_producers, all_0_7_7) = all_10_4_15 & growth_rate(first_movers, all_0_7_7) = all_10_5_16 & constant(all_10_7_18) = all_10_6_17 & number_of_organizations(all_0_8_8, all_0_7_7) = all_10_7_18 & greater(all_10_4_15, zero) = all_10_1_12 & greater(all_10_5_16, zero) = all_10_3_14 & greater(zero, all_10_4_15) = all_10_2_13 & greater(zero, all_10_5_16) = all_10_0_11 & environment(all_0_8_8) = all_10_8_19 & ( ~ (all_10_6_17 = 0) | ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero))
% 6.23/2.13 |
% 6.23/2.13 | Applying alpha-rule on (42) yields:
% 6.23/2.13 | (43) greater(all_10_4_15, zero) = all_10_1_12
% 6.23/2.13 | (44) greater(all_10_5_16, zero) = all_10_3_14
% 6.23/2.13 | (45) greater(zero, all_10_5_16) = all_10_0_11
% 6.23/2.13 | (46) ~ (all_10_6_17 = 0) | ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.13 | (47) greater(zero, all_10_4_15) = all_10_2_13
% 6.23/2.13 | (48) growth_rate(efficient_producers, all_0_7_7) = all_10_4_15
% 6.23/2.13 | (49) environment(all_0_8_8) = all_10_8_19
% 6.23/2.13 | (50) growth_rate(first_movers, all_0_7_7) = all_10_5_16
% 6.23/2.13 | (51) constant(all_10_7_18) = all_10_6_17
% 6.23/2.13 | (52) number_of_organizations(all_0_8_8, all_0_7_7) = all_10_7_18
% 6.23/2.13 |
% 6.23/2.13 | Instantiating (36) with all_12_0_20, all_12_1_21, all_12_2_22 yields:
% 6.23/2.13 | (53) number_of_organizations(all_0_8_8, all_0_7_7) = all_12_1_21 & greater(all_12_1_21, zero) = all_12_0_20 & environment(all_0_8_8) = all_12_2_22 & ( ~ (all_12_2_22 = 0) | all_12_0_20 = 0)
% 6.23/2.13 |
% 6.23/2.13 | Applying alpha-rule on (53) yields:
% 6.23/2.13 | (54) number_of_organizations(all_0_8_8, all_0_7_7) = all_12_1_21
% 6.23/2.13 | (55) greater(all_12_1_21, zero) = all_12_0_20
% 6.23/2.13 | (56) environment(all_0_8_8) = all_12_2_22
% 6.23/2.13 | (57) ~ (all_12_2_22 = 0) | all_12_0_20 = 0
% 6.23/2.13 |
% 6.23/2.13 | Instantiating (34) with all_14_0_23, all_14_1_24 yields:
% 6.23/2.13 | (58) greater(all_0_6_6, all_0_7_7) = all_14_0_23 & environment(all_0_8_8) = all_14_1_24 & ( ~ (all_14_0_23 = 0) | ~ (all_14_1_24 = 0))
% 6.23/2.13 |
% 6.23/2.13 | Applying alpha-rule on (58) yields:
% 6.23/2.13 | (59) greater(all_0_6_6, all_0_7_7) = all_14_0_23
% 6.23/2.13 | (60) environment(all_0_8_8) = all_14_1_24
% 6.23/2.13 | (61) ~ (all_14_0_23 = 0) | ~ (all_14_1_24 = 0)
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (21) with efficient_producers, all_0_7_7, all_10_4_15, all_0_4_4 and discharging atoms growth_rate(efficient_producers, all_0_7_7) = all_10_4_15, growth_rate(efficient_producers, all_0_7_7) = all_0_4_4, yields:
% 6.23/2.13 | (62) all_10_4_15 = all_0_4_4
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (21) with first_movers, all_0_7_7, all_10_5_16, all_0_5_5 and discharging atoms growth_rate(first_movers, all_0_7_7) = all_10_5_16, growth_rate(first_movers, all_0_7_7) = all_0_5_5, yields:
% 6.23/2.13 | (63) all_10_5_16 = all_0_5_5
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (29) with all_0_8_8, all_0_7_7, all_10_7_18, all_12_1_21 and discharging atoms number_of_organizations(all_0_8_8, all_0_7_7) = all_12_1_21, number_of_organizations(all_0_8_8, all_0_7_7) = all_10_7_18, yields:
% 6.23/2.13 | (64) all_12_1_21 = all_10_7_18
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (25) with all_0_4_4, zero, all_10_1_12, all_0_1_1 and discharging atoms greater(all_0_4_4, zero) = all_0_1_1, yields:
% 6.23/2.13 | (65) all_10_1_12 = all_0_1_1 | ~ (greater(all_0_4_4, zero) = all_10_1_12)
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (25) with all_0_5_5, zero, all_10_3_14, all_0_3_3 and discharging atoms greater(all_0_5_5, zero) = all_0_3_3, yields:
% 6.23/2.13 | (66) all_10_3_14 = all_0_3_3 | ~ (greater(all_0_5_5, zero) = all_10_3_14)
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (25) with zero, all_0_4_4, all_10_2_13, all_0_2_2 and discharging atoms greater(zero, all_0_4_4) = all_0_2_2, yields:
% 6.23/2.13 | (67) all_10_2_13 = all_0_2_2 | ~ (greater(zero, all_0_4_4) = all_10_2_13)
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (25) with zero, all_0_5_5, all_10_0_11, all_0_0_0 and discharging atoms greater(zero, all_0_5_5) = all_0_0_0, yields:
% 6.23/2.13 | (68) all_10_0_11 = all_0_0_0 | ~ (greater(zero, all_0_5_5) = all_10_0_11)
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (7) with all_0_8_8, all_14_1_24, 0 and discharging atoms environment(all_0_8_8) = all_14_1_24, environment(all_0_8_8) = 0, yields:
% 6.23/2.13 | (69) all_14_1_24 = 0
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (7) with all_0_8_8, all_12_2_22, all_14_1_24 and discharging atoms environment(all_0_8_8) = all_14_1_24, environment(all_0_8_8) = all_12_2_22, yields:
% 6.23/2.13 | (70) all_14_1_24 = all_12_2_22
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (7) with all_0_8_8, all_10_8_19, all_14_1_24 and discharging atoms environment(all_0_8_8) = all_14_1_24, environment(all_0_8_8) = all_10_8_19, yields:
% 6.23/2.13 | (71) all_14_1_24 = all_10_8_19
% 6.23/2.13 |
% 6.23/2.13 | Instantiating formula (7) with all_0_8_8, all_8_1_10, all_10_8_19 and discharging atoms environment(all_0_8_8) = all_10_8_19, environment(all_0_8_8) = all_8_1_10, yields:
% 6.23/2.13 | (72) all_10_8_19 = all_8_1_10
% 6.23/2.13 |
% 6.23/2.14 | Combining equations (69,70) yields a new equation:
% 6.23/2.14 | (73) all_12_2_22 = 0
% 6.23/2.14 |
% 6.23/2.14 | Combining equations (71,70) yields a new equation:
% 6.23/2.14 | (74) all_12_2_22 = all_10_8_19
% 6.23/2.14 |
% 6.23/2.14 | Combining equations (74,73) yields a new equation:
% 6.23/2.14 | (75) all_10_8_19 = 0
% 6.23/2.14 |
% 6.23/2.14 | Simplifying 75 yields:
% 6.23/2.14 | (76) all_10_8_19 = 0
% 6.23/2.14 |
% 6.23/2.14 | Combining equations (72,76) yields a new equation:
% 6.23/2.14 | (77) all_8_1_10 = 0
% 6.23/2.14 |
% 6.23/2.14 | Simplifying 77 yields:
% 6.23/2.14 | (78) all_8_1_10 = 0
% 6.23/2.14 |
% 6.23/2.14 | Combining equations (73,70) yields a new equation:
% 6.23/2.14 | (69) all_14_1_24 = 0
% 6.23/2.14 |
% 6.23/2.14 | From (64) and (54) follows:
% 6.23/2.14 | (52) number_of_organizations(all_0_8_8, all_0_7_7) = all_10_7_18
% 6.23/2.14 |
% 6.23/2.14 | From (64) and (55) follows:
% 6.23/2.14 | (81) greater(all_10_7_18, zero) = all_12_0_20
% 6.23/2.14 |
% 6.23/2.14 | From (62) and (43) follows:
% 6.23/2.14 | (82) greater(all_0_4_4, zero) = all_10_1_12
% 6.23/2.14 |
% 6.23/2.14 | From (63) and (44) follows:
% 6.23/2.14 | (83) greater(all_0_5_5, zero) = all_10_3_14
% 6.23/2.14 |
% 6.23/2.14 | From (62) and (47) follows:
% 6.23/2.14 | (84) greater(zero, all_0_4_4) = all_10_2_13
% 6.23/2.14 |
% 6.23/2.14 | From (63) and (45) follows:
% 6.23/2.14 | (85) greater(zero, all_0_5_5) = all_10_0_11
% 6.23/2.14 |
% 6.23/2.14 | From (78) and (39) follows:
% 6.23/2.14 | (27) environment(all_0_8_8) = 0
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (57), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (87) ~ (all_12_2_22 = 0)
% 6.23/2.14 |
% 6.23/2.14 | Equations (73) can reduce 87 to:
% 6.23/2.14 | (88) $false
% 6.23/2.14 |
% 6.23/2.14 |-The branch is then unsatisfiable
% 6.23/2.14 |-Branch two:
% 6.23/2.14 | (73) all_12_2_22 = 0
% 6.23/2.14 | (90) all_12_0_20 = 0
% 6.23/2.14 |
% 6.23/2.14 | From (90) and (81) follows:
% 6.23/2.14 | (91) greater(all_10_7_18, zero) = 0
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (61), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (92) ~ (all_14_0_23 = 0)
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (41), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (93) ~ (all_8_1_10 = 0)
% 6.23/2.14 |
% 6.23/2.14 | Equations (78) can reduce 93 to:
% 6.23/2.14 | (88) $false
% 6.23/2.14 |
% 6.23/2.14 |-The branch is then unsatisfiable
% 6.23/2.14 |-Branch two:
% 6.23/2.14 | (78) all_8_1_10 = 0
% 6.23/2.14 | (96) all_8_0_9 = 0
% 6.23/2.14 |
% 6.23/2.14 | From (96) and (40) follows:
% 6.23/2.14 | (97) in_environment(all_0_8_8, all_0_7_7) = 0
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (68), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (98) ~ (greater(zero, all_0_5_5) = all_10_0_11)
% 6.23/2.14 |
% 6.23/2.14 | Using (85) and (98) yields:
% 6.23/2.14 | (99) $false
% 6.23/2.14 |
% 6.23/2.14 |-The branch is then unsatisfiable
% 6.23/2.14 |-Branch two:
% 6.23/2.14 | (85) greater(zero, all_0_5_5) = all_10_0_11
% 6.23/2.14 | (101) all_10_0_11 = all_0_0_0
% 6.23/2.14 |
% 6.23/2.14 | From (101) and (85) follows:
% 6.23/2.14 | (24) greater(zero, all_0_5_5) = all_0_0_0
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (67), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (103) ~ (greater(zero, all_0_4_4) = all_10_2_13)
% 6.23/2.14 |
% 6.23/2.14 | Using (84) and (103) yields:
% 6.23/2.14 | (99) $false
% 6.23/2.14 |
% 6.23/2.14 |-The branch is then unsatisfiable
% 6.23/2.14 |-Branch two:
% 6.23/2.14 | (84) greater(zero, all_0_4_4) = all_10_2_13
% 6.23/2.14 | (106) all_10_2_13 = all_0_2_2
% 6.23/2.14 |
% 6.23/2.14 | From (106) and (84) follows:
% 6.23/2.14 | (2) greater(zero, all_0_4_4) = all_0_2_2
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (66), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (108) ~ (greater(all_0_5_5, zero) = all_10_3_14)
% 6.23/2.14 |
% 6.23/2.14 | Using (83) and (108) yields:
% 6.23/2.14 | (99) $false
% 6.23/2.14 |
% 6.23/2.14 |-The branch is then unsatisfiable
% 6.23/2.14 |-Branch two:
% 6.23/2.14 | (83) greater(all_0_5_5, zero) = all_10_3_14
% 6.23/2.14 | (111) all_10_3_14 = all_0_3_3
% 6.23/2.14 |
% 6.23/2.14 | From (111) and (83) follows:
% 6.23/2.14 | (31) greater(all_0_5_5, zero) = all_0_3_3
% 6.23/2.14 |
% 6.23/2.14 +-Applying beta-rule and splitting (65), into two cases.
% 6.23/2.14 |-Branch one:
% 6.23/2.14 | (113) ~ (greater(all_0_4_4, zero) = all_10_1_12)
% 6.23/2.14 |
% 6.23/2.14 | Using (82) and (113) yields:
% 6.23/2.15 | (99) $false
% 6.23/2.15 |
% 6.23/2.15 |-The branch is then unsatisfiable
% 6.23/2.15 |-Branch two:
% 6.23/2.15 | (82) greater(all_0_4_4, zero) = all_10_1_12
% 6.23/2.15 | (116) all_10_1_12 = all_0_1_1
% 6.23/2.15 |
% 6.23/2.15 | From (116) and (82) follows:
% 6.23/2.15 | (22) greater(all_0_4_4, zero) = all_0_1_1
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (18) with all_14_0_23, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms equilibrium(all_0_8_8) = all_0_6_6, greater(all_0_6_6, all_0_7_7) = all_14_0_23, yields:
% 6.23/2.15 | (118) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (resources(all_0_8_8, all_0_7_7) = v4 & decreases(v4) = v5 & constant(v4) = v6 & number_of_organizations(all_0_8_8, all_0_7_7) = v2 & greater(v2, zero) = v3 & environment(all_0_8_8) = v0 & in_environment(all_0_8_8, all_0_7_7) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (all_14_0_23 = 0) | v5 = 0) & (v6 = 0 | all_14_0_23 = 0))))
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (8) with all_0_7_7, all_0_8_8 and discharging atoms in_environment(all_0_8_8, all_0_7_7) = 0, yields:
% 6.23/2.15 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (resources(all_0_8_8, all_0_7_7) = v1 & decreases(v3) = v4 & decreases(v1) = v2 & constant(v3) = v6 & constant(v1) = v5 & number_of_organizations(all_0_8_8, all_0_7_7) = v3 & environment(all_0_8_8) = v0 & ( ~ (v0 = 0) | (( ~ (v5 = 0) | v6 = 0) & ( ~ (v4 = 0) | ~ (v2 = 0)))))
% 6.23/2.15 |
% 6.23/2.15 | Instantiating (119) with all_53_0_25, all_53_1_26, all_53_2_27, all_53_3_28, all_53_4_29, all_53_5_30, all_53_6_31 yields:
% 6.23/2.15 | (120) resources(all_0_8_8, all_0_7_7) = all_53_5_30 & decreases(all_53_3_28) = all_53_2_27 & decreases(all_53_5_30) = all_53_4_29 & constant(all_53_3_28) = all_53_0_25 & constant(all_53_5_30) = all_53_1_26 & number_of_organizations(all_0_8_8, all_0_7_7) = all_53_3_28 & environment(all_0_8_8) = all_53_6_31 & ( ~ (all_53_6_31 = 0) | (( ~ (all_53_1_26 = 0) | all_53_0_25 = 0) & ( ~ (all_53_2_27 = 0) | ~ (all_53_4_29 = 0))))
% 6.23/2.15 |
% 6.23/2.15 | Applying alpha-rule on (120) yields:
% 6.23/2.15 | (121) number_of_organizations(all_0_8_8, all_0_7_7) = all_53_3_28
% 6.23/2.15 | (122) decreases(all_53_3_28) = all_53_2_27
% 6.23/2.15 | (123) constant(all_53_5_30) = all_53_1_26
% 6.23/2.15 | (124) ~ (all_53_6_31 = 0) | (( ~ (all_53_1_26 = 0) | all_53_0_25 = 0) & ( ~ (all_53_2_27 = 0) | ~ (all_53_4_29 = 0)))
% 6.23/2.15 | (125) resources(all_0_8_8, all_0_7_7) = all_53_5_30
% 6.23/2.15 | (126) constant(all_53_3_28) = all_53_0_25
% 6.23/2.15 | (127) environment(all_0_8_8) = all_53_6_31
% 6.23/2.15 | (128) decreases(all_53_5_30) = all_53_4_29
% 6.23/2.15 |
% 6.23/2.15 | Instantiating (118) with all_55_0_32, all_55_1_33, all_55_2_34, all_55_3_35, all_55_4_36, all_55_5_37, all_55_6_38 yields:
% 6.23/2.15 | (129) resources(all_0_8_8, all_0_7_7) = all_55_2_34 & decreases(all_55_2_34) = all_55_1_33 & constant(all_55_2_34) = all_55_0_32 & number_of_organizations(all_0_8_8, all_0_7_7) = all_55_4_36 & greater(all_55_4_36, zero) = all_55_3_35 & environment(all_0_8_8) = all_55_6_38 & in_environment(all_0_8_8, all_0_7_7) = all_55_5_37 & ( ~ (all_55_3_35 = 0) | ~ (all_55_5_37 = 0) | ~ (all_55_6_38 = 0) | (( ~ (all_14_0_23 = 0) | all_55_1_33 = 0) & (all_55_0_32 = 0 | all_14_0_23 = 0)))
% 6.23/2.15 |
% 6.23/2.15 | Applying alpha-rule on (129) yields:
% 6.23/2.15 | (130) ~ (all_55_3_35 = 0) | ~ (all_55_5_37 = 0) | ~ (all_55_6_38 = 0) | (( ~ (all_14_0_23 = 0) | all_55_1_33 = 0) & (all_55_0_32 = 0 | all_14_0_23 = 0))
% 6.23/2.15 | (131) resources(all_0_8_8, all_0_7_7) = all_55_2_34
% 6.23/2.15 | (132) constant(all_55_2_34) = all_55_0_32
% 6.23/2.15 | (133) greater(all_55_4_36, zero) = all_55_3_35
% 6.23/2.15 | (134) number_of_organizations(all_0_8_8, all_0_7_7) = all_55_4_36
% 6.23/2.15 | (135) environment(all_0_8_8) = all_55_6_38
% 6.23/2.15 | (136) in_environment(all_0_8_8, all_0_7_7) = all_55_5_37
% 6.23/2.15 | (137) decreases(all_55_2_34) = all_55_1_33
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (15) with all_0_8_8, all_0_7_7, all_53_5_30, all_55_2_34 and discharging atoms resources(all_0_8_8, all_0_7_7) = all_55_2_34, resources(all_0_8_8, all_0_7_7) = all_53_5_30, yields:
% 6.23/2.15 | (138) all_55_2_34 = all_53_5_30
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (20) with all_10_7_18, all_53_0_25, all_10_6_17 and discharging atoms constant(all_10_7_18) = all_10_6_17, yields:
% 6.23/2.15 | (139) all_53_0_25 = all_10_6_17 | ~ (constant(all_10_7_18) = all_53_0_25)
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (20) with all_53_5_30, all_53_1_26, all_55_0_32 and discharging atoms constant(all_53_5_30) = all_53_1_26, yields:
% 6.23/2.15 | (140) all_55_0_32 = all_53_1_26 | ~ (constant(all_53_5_30) = all_55_0_32)
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (29) with all_0_8_8, all_0_7_7, all_55_4_36, all_10_7_18 and discharging atoms number_of_organizations(all_0_8_8, all_0_7_7) = all_55_4_36, number_of_organizations(all_0_8_8, all_0_7_7) = all_10_7_18, yields:
% 6.23/2.15 | (141) all_55_4_36 = all_10_7_18
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (29) with all_0_8_8, all_0_7_7, all_53_3_28, all_55_4_36 and discharging atoms number_of_organizations(all_0_8_8, all_0_7_7) = all_55_4_36, number_of_organizations(all_0_8_8, all_0_7_7) = all_53_3_28, yields:
% 6.23/2.15 | (142) all_55_4_36 = all_53_3_28
% 6.23/2.15 |
% 6.23/2.15 | Instantiating formula (25) with all_10_7_18, zero, all_55_3_35, 0 and discharging atoms greater(all_10_7_18, zero) = 0, yields:
% 6.23/2.16 | (143) all_55_3_35 = 0 | ~ (greater(all_10_7_18, zero) = all_55_3_35)
% 6.23/2.16 |
% 6.23/2.16 | Instantiating formula (7) with all_0_8_8, all_55_6_38, 0 and discharging atoms environment(all_0_8_8) = all_55_6_38, environment(all_0_8_8) = 0, yields:
% 6.23/2.16 | (144) all_55_6_38 = 0
% 6.23/2.16 |
% 6.23/2.16 | Instantiating formula (7) with all_0_8_8, all_53_6_31, all_55_6_38 and discharging atoms environment(all_0_8_8) = all_55_6_38, environment(all_0_8_8) = all_53_6_31, yields:
% 6.23/2.16 | (145) all_55_6_38 = all_53_6_31
% 6.23/2.16 |
% 6.23/2.16 | Instantiating formula (3) with all_0_8_8, all_0_7_7, all_55_5_37, 0 and discharging atoms in_environment(all_0_8_8, all_0_7_7) = all_55_5_37, in_environment(all_0_8_8, all_0_7_7) = 0, yields:
% 6.23/2.16 | (146) all_55_5_37 = 0
% 6.23/2.16 |
% 6.23/2.16 | Combining equations (142,141) yields a new equation:
% 6.23/2.16 | (147) all_53_3_28 = all_10_7_18
% 6.23/2.16 |
% 6.23/2.16 | Simplifying 147 yields:
% 6.23/2.16 | (148) all_53_3_28 = all_10_7_18
% 6.23/2.16 |
% 6.23/2.16 | Combining equations (145,144) yields a new equation:
% 6.23/2.16 | (149) all_53_6_31 = 0
% 6.23/2.16 |
% 6.23/2.16 | Simplifying 149 yields:
% 6.23/2.16 | (150) all_53_6_31 = 0
% 6.23/2.16 |
% 6.23/2.16 | From (138) and (132) follows:
% 6.23/2.16 | (151) constant(all_53_5_30) = all_55_0_32
% 6.23/2.16 |
% 6.23/2.16 | From (148) and (126) follows:
% 6.23/2.16 | (152) constant(all_10_7_18) = all_53_0_25
% 6.23/2.16 |
% 6.23/2.16 | From (141) and (133) follows:
% 6.23/2.16 | (153) greater(all_10_7_18, zero) = all_55_3_35
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (143), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (154) ~ (greater(all_10_7_18, zero) = all_55_3_35)
% 6.23/2.16 |
% 6.23/2.16 | Using (153) and (154) yields:
% 6.23/2.16 | (99) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (153) greater(all_10_7_18, zero) = all_55_3_35
% 6.23/2.16 | (157) all_55_3_35 = 0
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (140), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (158) ~ (constant(all_53_5_30) = all_55_0_32)
% 6.23/2.16 |
% 6.23/2.16 | Using (151) and (158) yields:
% 6.23/2.16 | (99) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (151) constant(all_53_5_30) = all_55_0_32
% 6.23/2.16 | (161) all_55_0_32 = all_53_1_26
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (130), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (162) ~ (all_55_3_35 = 0)
% 6.23/2.16 |
% 6.23/2.16 | Equations (157) can reduce 162 to:
% 6.23/2.16 | (88) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (157) all_55_3_35 = 0
% 6.23/2.16 | (165) ~ (all_55_5_37 = 0) | ~ (all_55_6_38 = 0) | (( ~ (all_14_0_23 = 0) | all_55_1_33 = 0) & (all_55_0_32 = 0 | all_14_0_23 = 0))
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (139), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (166) ~ (constant(all_10_7_18) = all_53_0_25)
% 6.23/2.16 |
% 6.23/2.16 | Using (152) and (166) yields:
% 6.23/2.16 | (99) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (152) constant(all_10_7_18) = all_53_0_25
% 6.23/2.16 | (169) all_53_0_25 = all_10_6_17
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (165), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (170) ~ (all_55_5_37 = 0)
% 6.23/2.16 |
% 6.23/2.16 | Equations (146) can reduce 170 to:
% 6.23/2.16 | (88) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (146) all_55_5_37 = 0
% 6.23/2.16 | (173) ~ (all_55_6_38 = 0) | (( ~ (all_14_0_23 = 0) | all_55_1_33 = 0) & (all_55_0_32 = 0 | all_14_0_23 = 0))
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (173), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (174) ~ (all_55_6_38 = 0)
% 6.23/2.16 |
% 6.23/2.16 | Equations (144) can reduce 174 to:
% 6.23/2.16 | (88) $false
% 6.23/2.16 |
% 6.23/2.16 |-The branch is then unsatisfiable
% 6.23/2.16 |-Branch two:
% 6.23/2.16 | (144) all_55_6_38 = 0
% 6.23/2.16 | (177) ( ~ (all_14_0_23 = 0) | all_55_1_33 = 0) & (all_55_0_32 = 0 | all_14_0_23 = 0)
% 6.23/2.16 |
% 6.23/2.16 | Applying alpha-rule on (177) yields:
% 6.23/2.16 | (178) ~ (all_14_0_23 = 0) | all_55_1_33 = 0
% 6.23/2.16 | (179) all_55_0_32 = 0 | all_14_0_23 = 0
% 6.23/2.16 |
% 6.23/2.16 +-Applying beta-rule and splitting (179), into two cases.
% 6.23/2.16 |-Branch one:
% 6.23/2.16 | (180) all_55_0_32 = 0
% 6.23/2.16 |
% 6.23/2.17 | Combining equations (180,161) yields a new equation:
% 6.23/2.17 | (181) all_53_1_26 = 0
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (124), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (182) ~ (all_53_6_31 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (150) can reduce 182 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (150) all_53_6_31 = 0
% 6.23/2.17 | (185) ( ~ (all_53_1_26 = 0) | all_53_0_25 = 0) & ( ~ (all_53_2_27 = 0) | ~ (all_53_4_29 = 0))
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (185) yields:
% 6.23/2.17 | (186) ~ (all_53_1_26 = 0) | all_53_0_25 = 0
% 6.23/2.17 | (187) ~ (all_53_2_27 = 0) | ~ (all_53_4_29 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (186), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (188) ~ (all_53_1_26 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (181) can reduce 188 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (181) all_53_1_26 = 0
% 6.23/2.17 | (191) all_53_0_25 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (191,169) yields a new equation:
% 6.23/2.17 | (192) all_10_6_17 = 0
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (4), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (193) ~ (all_0_4_4 = zero)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (33), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (194) ~ (greater(zero, all_0_5_5) = all_0_2_2)
% 6.23/2.17 |
% 6.23/2.17 | Using (24) and (194) yields:
% 6.23/2.17 | (195) ~ (all_0_0_0 = all_0_2_2)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (5), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (196) ~ (all_0_0_0 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (192) can reduce 197 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (192) all_10_6_17 = 0
% 6.23/2.17 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (76) can reduce 201 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (76) all_10_8_19 = 0
% 6.23/2.17 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (206) yields:
% 6.23/2.17 | (207) all_10_0_11 = 0
% 6.23/2.17 | (208) all_10_1_12 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (207,101) yields a new equation:
% 6.23/2.17 | (209) all_0_0_0 = 0
% 6.23/2.17 |
% 6.23/2.17 | Equations (209) can reduce 196 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (211) yields:
% 6.23/2.17 | (212) all_10_2_13 = 0
% 6.23/2.17 | (213) all_10_3_14 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (106,212) yields a new equation:
% 6.23/2.17 | (214) all_0_2_2 = 0
% 6.23/2.17 |
% 6.23/2.17 | Simplifying 214 yields:
% 6.23/2.17 | (215) all_0_2_2 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (213,111) yields a new equation:
% 6.23/2.17 | (216) all_0_3_3 = 0
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (12), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (215) can reduce 217 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (215) all_0_2_2 = 0
% 6.23/2.17 | (220) ~ (all_0_3_3 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (216) can reduce 220 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (222) yields:
% 6.23/2.17 | (223) all_10_4_15 = zero
% 6.23/2.17 | (224) all_10_5_16 = zero
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (62,223) yields a new equation:
% 6.23/2.17 | (225) all_0_4_4 = zero
% 6.23/2.17 |
% 6.23/2.17 | Simplifying 225 yields:
% 6.23/2.17 | (226) all_0_4_4 = zero
% 6.23/2.17 |
% 6.23/2.17 | Equations (226) can reduce 193 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (209) all_0_0_0 = 0
% 6.23/2.17 | (229) ~ (all_0_1_1 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (209) can reduce 195 to:
% 6.23/2.17 | (230) ~ (all_0_2_2 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Simplifying 230 yields:
% 6.23/2.17 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (192) can reduce 197 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (192) all_10_6_17 = 0
% 6.23/2.17 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (76) can reduce 201 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (76) all_10_8_19 = 0
% 6.23/2.17 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (206) yields:
% 6.23/2.17 | (207) all_10_0_11 = 0
% 6.23/2.17 | (208) all_10_1_12 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (208,116) yields a new equation:
% 6.23/2.17 | (244) all_0_1_1 = 0
% 6.23/2.17 |
% 6.23/2.17 | Equations (244) can reduce 229 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (211) yields:
% 6.23/2.17 | (212) all_10_2_13 = 0
% 6.23/2.17 | (213) all_10_3_14 = 0
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (106,212) yields a new equation:
% 6.23/2.17 | (214) all_0_2_2 = 0
% 6.23/2.17 |
% 6.23/2.17 | Simplifying 214 yields:
% 6.23/2.17 | (215) all_0_2_2 = 0
% 6.23/2.17 |
% 6.23/2.17 | Equations (215) can reduce 217 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.17 |
% 6.23/2.17 | Applying alpha-rule on (222) yields:
% 6.23/2.17 | (223) all_10_4_15 = zero
% 6.23/2.17 | (224) all_10_5_16 = zero
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (62,223) yields a new equation:
% 6.23/2.17 | (225) all_0_4_4 = zero
% 6.23/2.17 |
% 6.23/2.17 | Simplifying 225 yields:
% 6.23/2.17 | (226) all_0_4_4 = zero
% 6.23/2.17 |
% 6.23/2.17 | Equations (226) can reduce 193 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (258) greater(zero, all_0_5_5) = all_0_2_2
% 6.23/2.17 | (259) all_0_0_0 = all_0_2_2
% 6.23/2.17 |
% 6.23/2.17 | Combining equations (259,101) yields a new equation:
% 6.23/2.17 | (260) all_10_0_11 = all_0_2_2
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (5), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (196) ~ (all_0_0_0 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (259) can reduce 196 to:
% 6.23/2.17 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.17 |
% 6.23/2.17 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.17 |-Branch one:
% 6.23/2.17 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.17 |
% 6.23/2.17 | Equations (192) can reduce 197 to:
% 6.23/2.17 | (88) $false
% 6.23/2.17 |
% 6.23/2.17 |-The branch is then unsatisfiable
% 6.23/2.17 |-Branch two:
% 6.23/2.17 | (192) all_10_6_17 = 0
% 6.23/2.17 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (76) can reduce 201 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (76) all_10_8_19 = 0
% 6.23/2.18 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (206) yields:
% 6.23/2.18 | (207) all_10_0_11 = 0
% 6.23/2.18 | (208) all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (207,260) yields a new equation:
% 6.23/2.18 | (215) all_0_2_2 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (215) can reduce 217 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (211) yields:
% 6.23/2.18 | (212) all_10_2_13 = 0
% 6.23/2.18 | (213) all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (106,212) yields a new equation:
% 6.23/2.18 | (214) all_0_2_2 = 0
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 214 yields:
% 6.23/2.18 | (215) all_0_2_2 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (215) can reduce 217 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (222) yields:
% 6.23/2.18 | (223) all_10_4_15 = zero
% 6.23/2.18 | (224) all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (62,223) yields a new equation:
% 6.23/2.18 | (225) all_0_4_4 = zero
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 225 yields:
% 6.23/2.18 | (226) all_0_4_4 = zero
% 6.23/2.18 |
% 6.23/2.18 | Equations (226) can reduce 193 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (209) all_0_0_0 = 0
% 6.23/2.18 | (229) ~ (all_0_1_1 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (209,259) yields a new equation:
% 6.23/2.18 | (215) all_0_2_2 = 0
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (12), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (215) can reduce 217 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (215) all_0_2_2 = 0
% 6.23/2.18 | (220) ~ (all_0_3_3 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (192) can reduce 197 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (192) all_10_6_17 = 0
% 6.23/2.18 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (76) can reduce 201 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (76) all_10_8_19 = 0
% 6.23/2.18 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (206) yields:
% 6.23/2.18 | (207) all_10_0_11 = 0
% 6.23/2.18 | (208) all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (116,208) yields a new equation:
% 6.23/2.18 | (308) all_0_1_1 = 0
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 308 yields:
% 6.23/2.18 | (244) all_0_1_1 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (244) can reduce 229 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (211) yields:
% 6.23/2.18 | (212) all_10_2_13 = 0
% 6.23/2.18 | (213) all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (111,213) yields a new equation:
% 6.23/2.18 | (314) all_0_3_3 = 0
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 314 yields:
% 6.23/2.18 | (216) all_0_3_3 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (216) can reduce 220 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (222) yields:
% 6.23/2.18 | (223) all_10_4_15 = zero
% 6.23/2.18 | (224) all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (62,223) yields a new equation:
% 6.23/2.18 | (225) all_0_4_4 = zero
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 225 yields:
% 6.23/2.18 | (226) all_0_4_4 = zero
% 6.23/2.18 |
% 6.23/2.18 | Equations (226) can reduce 193 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (226) all_0_4_4 = zero
% 6.23/2.18 | (324) ~ (all_0_5_5 = zero)
% 6.23/2.18 |
% 6.23/2.18 | From (226) and (22) follows:
% 6.23/2.18 | (325) greater(zero, zero) = all_0_1_1
% 6.23/2.18 |
% 6.23/2.18 | From (226) and (2) follows:
% 6.23/2.18 | (326) greater(zero, zero) = all_0_2_2
% 6.23/2.18 |
% 6.23/2.18 | Instantiating formula (25) with zero, zero, all_0_2_2, all_0_1_1 and discharging atoms greater(zero, zero) = all_0_1_1, greater(zero, zero) = all_0_2_2, yields:
% 6.23/2.18 | (327) all_0_1_1 = all_0_2_2
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (327,116) yields a new equation:
% 6.23/2.18 | (328) all_10_1_12 = all_0_2_2
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (32), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (329) ~ (greater(all_0_5_5, zero) = all_0_1_1)
% 6.23/2.18 |
% 6.23/2.18 | From (327) and (329) follows:
% 6.23/2.18 | (330) ~ (greater(all_0_5_5, zero) = all_0_2_2)
% 6.23/2.18 |
% 6.23/2.18 | Using (31) and (330) yields:
% 6.23/2.18 | (331) ~ (all_0_2_2 = all_0_3_3)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (5), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (196) ~ (all_0_0_0 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (192) can reduce 197 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (192) all_10_6_17 = 0
% 6.23/2.18 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (76) can reduce 201 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (76) all_10_8_19 = 0
% 6.23/2.18 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (206) yields:
% 6.23/2.18 | (207) all_10_0_11 = 0
% 6.23/2.18 | (208) all_10_1_12 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (207,101) yields a new equation:
% 6.23/2.18 | (209) all_0_0_0 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (209) can reduce 196 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (211) yields:
% 6.23/2.18 | (212) all_10_2_13 = 0
% 6.23/2.18 | (213) all_10_3_14 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (212,106) yields a new equation:
% 6.23/2.18 | (215) all_0_2_2 = 0
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (111,213) yields a new equation:
% 6.23/2.18 | (314) all_0_3_3 = 0
% 6.23/2.18 |
% 6.23/2.18 | Simplifying 314 yields:
% 6.23/2.18 | (216) all_0_3_3 = 0
% 6.23/2.18 |
% 6.23/2.18 | Equations (215,216) can reduce 331 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Applying alpha-rule on (222) yields:
% 6.23/2.18 | (223) all_10_4_15 = zero
% 6.23/2.18 | (224) all_10_5_16 = zero
% 6.23/2.18 |
% 6.23/2.18 | Combining equations (224,63) yields a new equation:
% 6.23/2.18 | (357) all_0_5_5 = zero
% 6.23/2.18 |
% 6.23/2.18 | Equations (357) can reduce 324 to:
% 6.23/2.18 | (88) $false
% 6.23/2.18 |
% 6.23/2.18 |-The branch is then unsatisfiable
% 6.23/2.18 |-Branch two:
% 6.23/2.18 | (209) all_0_0_0 = 0
% 6.23/2.18 | (229) ~ (all_0_1_1 = 0)
% 6.23/2.18 |
% 6.23/2.18 | Equations (327) can reduce 229 to:
% 6.23/2.18 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.18 |
% 6.23/2.18 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.18 |-Branch one:
% 6.23/2.18 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.18 |
% 6.23/2.19 | Equations (192) can reduce 197 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (192) all_10_6_17 = 0
% 6.23/2.19 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (76) can reduce 201 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (76) all_10_8_19 = 0
% 6.23/2.19 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (206) yields:
% 6.23/2.19 | (207) all_10_0_11 = 0
% 6.23/2.19 | (208) all_10_1_12 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (328,208) yields a new equation:
% 6.23/2.19 | (214) all_0_2_2 = 0
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 214 yields:
% 6.23/2.19 | (215) all_0_2_2 = 0
% 6.23/2.19 |
% 6.23/2.19 | Equations (215) can reduce 217 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (211) yields:
% 6.23/2.19 | (212) all_10_2_13 = 0
% 6.23/2.19 | (213) all_10_3_14 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (212,106) yields a new equation:
% 6.23/2.19 | (215) all_0_2_2 = 0
% 6.23/2.19 |
% 6.23/2.19 | Equations (215) can reduce 217 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (222) yields:
% 6.23/2.19 | (223) all_10_4_15 = zero
% 6.23/2.19 | (224) all_10_5_16 = zero
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (63,224) yields a new equation:
% 6.23/2.19 | (385) all_0_5_5 = zero
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 385 yields:
% 6.23/2.19 | (357) all_0_5_5 = zero
% 6.23/2.19 |
% 6.23/2.19 | Equations (357) can reduce 324 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (388) greater(all_0_5_5, zero) = all_0_1_1
% 6.23/2.19 | (389) all_0_1_1 = all_0_3_3
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (327,389) yields a new equation:
% 6.23/2.19 | (390) all_0_2_2 = all_0_3_3
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 390 yields:
% 6.23/2.19 | (391) all_0_2_2 = all_0_3_3
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (391,328) yields a new equation:
% 6.23/2.19 | (392) all_10_1_12 = all_0_3_3
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (46), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (197) ~ (all_10_6_17 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (192) can reduce 197 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (192) all_10_6_17 = 0
% 6.23/2.19 | (200) ~ (all_10_8_19 = 0) | (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (200), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (201) ~ (all_10_8_19 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (76) can reduce 201 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (76) all_10_8_19 = 0
% 6.23/2.19 | (204) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0) | (all_10_4_15 = zero & all_10_5_16 = zero)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (204), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (205) (all_10_0_11 = 0 & all_10_1_12 = 0) | (all_10_2_13 = 0 & all_10_3_14 = 0)
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (205), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (206) all_10_0_11 = 0 & all_10_1_12 = 0
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (206) yields:
% 6.23/2.19 | (207) all_10_0_11 = 0
% 6.23/2.19 | (208) all_10_1_12 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (207,101) yields a new equation:
% 6.23/2.19 | (209) all_0_0_0 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (392,208) yields a new equation:
% 6.23/2.19 | (314) all_0_3_3 = 0
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 314 yields:
% 6.23/2.19 | (216) all_0_3_3 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (216,389) yields a new equation:
% 6.23/2.19 | (244) all_0_1_1 = 0
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (5), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (196) ~ (all_0_0_0 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (209) can reduce 196 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (209) all_0_0_0 = 0
% 6.23/2.19 | (229) ~ (all_0_1_1 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (244) can reduce 229 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (211) all_10_2_13 = 0 & all_10_3_14 = 0
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (211) yields:
% 6.23/2.19 | (212) all_10_2_13 = 0
% 6.23/2.19 | (213) all_10_3_14 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (111,213) yields a new equation:
% 6.23/2.19 | (314) all_0_3_3 = 0
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 314 yields:
% 6.23/2.19 | (216) all_0_3_3 = 0
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (216,391) yields a new equation:
% 6.23/2.19 | (215) all_0_2_2 = 0
% 6.23/2.19 |
% 6.23/2.19 +-Applying beta-rule and splitting (12), into two cases.
% 6.23/2.19 |-Branch one:
% 6.23/2.19 | (217) ~ (all_0_2_2 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (215) can reduce 217 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (215) all_0_2_2 = 0
% 6.23/2.19 | (220) ~ (all_0_3_3 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (216) can reduce 220 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (222) all_10_4_15 = zero & all_10_5_16 = zero
% 6.23/2.19 |
% 6.23/2.19 | Applying alpha-rule on (222) yields:
% 6.23/2.19 | (223) all_10_4_15 = zero
% 6.23/2.19 | (224) all_10_5_16 = zero
% 6.23/2.19 |
% 6.23/2.19 | Combining equations (63,224) yields a new equation:
% 6.23/2.19 | (385) all_0_5_5 = zero
% 6.23/2.19 |
% 6.23/2.19 | Simplifying 385 yields:
% 6.23/2.19 | (357) all_0_5_5 = zero
% 6.23/2.19 |
% 6.23/2.19 | Equations (357) can reduce 324 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (431) ~ (all_55_0_32 = 0)
% 6.23/2.19 | (432) all_14_0_23 = 0
% 6.23/2.19 |
% 6.23/2.19 | Equations (432) can reduce 92 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 |-Branch two:
% 6.23/2.19 | (432) all_14_0_23 = 0
% 6.23/2.19 | (435) ~ (all_14_1_24 = 0)
% 6.23/2.19 |
% 6.23/2.19 | Equations (69) can reduce 435 to:
% 6.23/2.19 | (88) $false
% 6.23/2.19 |
% 6.23/2.19 |-The branch is then unsatisfiable
% 6.23/2.19 % SZS output end Proof for theBenchmark
% 6.23/2.19
% 6.23/2.19 1703ms
%------------------------------------------------------------------------------