TSTP Solution File: MGT022+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT022+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 22:07:00 EDT 2022
% Result : Theorem 2.24s 1.18s
% Output : Proof 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MGT022+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 9 11:31:21 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.56 ____ _
% 0.18/0.56 ___ / __ \_____(_)___ ________ __________
% 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic
% 0.18/0.56 (ePrincess v.1.0)
% 0.18/0.56
% 0.18/0.56 (c) Philipp Rümmer, 2009-2015
% 0.18/0.56 (c) Peter Backeman, 2014-2015
% 0.18/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.56 Bug reports to peter@backeman.se
% 0.18/0.56
% 0.18/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.56
% 0.18/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.89 Prover 0: Preprocessing ...
% 1.69/1.05 Prover 0: Constructing countermodel ...
% 2.24/1.18 Prover 0: proved (564ms)
% 2.24/1.18
% 2.24/1.18 No countermodel exists, formula is valid
% 2.24/1.18 % SZS status Theorem for theBenchmark
% 2.24/1.18
% 2.24/1.18 Generating proof ... found it (size 33)
% 2.78/1.39
% 2.78/1.39 % SZS output start Proof for theBenchmark
% 2.78/1.39 Assumed formulas after preprocessing and simplification:
% 2.78/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (resources(v2, v3) = v4 & disbanding_rate(first_movers, v3) = v5 & disbanding_rate(efficient_producers, v3) = v6 & difference(v5, v6) = v7 & resilience(first_movers) = v1 & resilience(efficient_producers) = v0 & greater(v0, v1) & subpopulations(first_movers, efficient_producers, v2, v3) & environment(v2) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (resources(v8, v11) = v12) | ~ (disbanding_rate(v10, v11) = v14) | ~ (disbanding_rate(v9, v11) = v13) | ~ (difference(v13, v14) = v15) | ~ subpopulations(v9, v10, v8, v11) | ~ environment(v8) | ~ decreases(v12) | increases(v15) | ? [v16] : ? [v17] : (resilience(v10) = v16 & resilience(v9) = v17 & ~ greater(v16, v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (resources(v8, v11) = v12) | ~ (disbanding_rate(v10, v11) = v14) | ~ (disbanding_rate(v9, v11) = v13) | ~ (difference(v13, v14) = v15) | ~ subpopulations(v9, v10, v8, v11) | ~ environment(v8) | ~ constant(v12) | constant(v15) | ? [v16] : ? [v17] : (resilience(v10) = v16 & resilience(v9) = v17 & ~ greater(v16, v17))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (resources(v8, v11) = v14) | ~ (resilience(v10) = v12) | ~ (resilience(v9) = v13) | ~ greater(v12, v13) | ~ subpopulations(v9, v10, v8, v11) | ~ environment(v8) | ? [v15] : ? [v16] : ? [v17] : (disbanding_rate(v10, v11) = v16 & disbanding_rate(v9, v11) = v15 & difference(v15, v16) = v17 & ( ~ decreases(v14) | increases(v17)) & ( ~ constant(v14) | constant(v17)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (resources(v11, v10) = v9) | ~ (resources(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disbanding_rate(v11, v10) = v9) | ~ (disbanding_rate(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (resilience(v10) = v9) | ~ (resilience(v10) = v8)) & ! [v8] : ( ~ decreases(v8) | ~ constant(v8)) & ((decreases(v7) & constant(v4)) | (decreases(v4) & ~ increases(v7))))
% 3.07/1.43 | 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 yields:
% 3.07/1.43 | (1) resources(all_0_5_5, all_0_4_4) = all_0_3_3 & disbanding_rate(first_movers, all_0_4_4) = all_0_2_2 & disbanding_rate(efficient_producers, all_0_4_4) = all_0_1_1 & difference(all_0_2_2, all_0_1_1) = all_0_0_0 & resilience(first_movers) = all_0_6_6 & resilience(efficient_producers) = all_0_7_7 & greater(all_0_7_7, all_0_6_6) & subpopulations(first_movers, efficient_producers, all_0_5_5, all_0_4_4) & environment(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (resources(v0, v3) = v4) | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ (difference(v5, v6) = v7) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ decreases(v4) | increases(v7) | ? [v8] : ? [v9] : (resilience(v2) = v8 & resilience(v1) = v9 & ~ greater(v8, v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (resources(v0, v3) = v4) | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ (difference(v5, v6) = v7) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ constant(v4) | constant(v7) | ? [v8] : ? [v9] : (resilience(v2) = v8 & resilience(v1) = v9 & ~ greater(v8, v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (resources(v0, v3) = v6) | ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ greater(v4, v5) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ? [v7] : ? [v8] : ? [v9] : (disbanding_rate(v2, v3) = v8 & disbanding_rate(v1, v3) = v7 & difference(v7, v8) = v9 & ( ~ decreases(v6) | increases(v9)) & ( ~ constant(v6) | constant(v9)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ (resilience(v2) = v0)) & ! [v0] : ( ~ decreases(v0) | ~ constant(v0)) & ((decreases(all_0_0_0) & constant(all_0_3_3)) | (decreases(all_0_3_3) & ~ increases(all_0_0_0)))
% 3.07/1.44 |
% 3.07/1.44 | Applying alpha-rule on (1) yields:
% 3.07/1.44 | (2) disbanding_rate(efficient_producers, all_0_4_4) = all_0_1_1
% 3.07/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (resources(v3, v2) = v1) | ~ (resources(v3, v2) = v0))
% 3.07/1.44 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (resources(v0, v3) = v4) | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ (difference(v5, v6) = v7) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ decreases(v4) | increases(v7) | ? [v8] : ? [v9] : (resilience(v2) = v8 & resilience(v1) = v9 & ~ greater(v8, v9)))
% 3.07/1.44 | (5) ! [v0] : ( ~ decreases(v0) | ~ constant(v0))
% 3.07/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.07/1.44 | (7) greater(all_0_7_7, all_0_6_6)
% 3.07/1.44 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (resources(v0, v3) = v4) | ~ (disbanding_rate(v2, v3) = v6) | ~ (disbanding_rate(v1, v3) = v5) | ~ (difference(v5, v6) = v7) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ~ constant(v4) | constant(v7) | ? [v8] : ? [v9] : (resilience(v2) = v8 & resilience(v1) = v9 & ~ greater(v8, v9)))
% 3.07/1.44 | (9) resources(all_0_5_5, all_0_4_4) = all_0_3_3
% 3.07/1.45 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disbanding_rate(v3, v2) = v1) | ~ (disbanding_rate(v3, v2) = v0))
% 3.07/1.45 | (11) (decreases(all_0_0_0) & constant(all_0_3_3)) | (decreases(all_0_3_3) & ~ increases(all_0_0_0))
% 3.07/1.45 | (12) disbanding_rate(first_movers, all_0_4_4) = all_0_2_2
% 3.07/1.45 | (13) difference(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.07/1.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (resources(v0, v3) = v6) | ~ (resilience(v2) = v4) | ~ (resilience(v1) = v5) | ~ greater(v4, v5) | ~ subpopulations(v1, v2, v0, v3) | ~ environment(v0) | ? [v7] : ? [v8] : ? [v9] : (disbanding_rate(v2, v3) = v8 & disbanding_rate(v1, v3) = v7 & difference(v7, v8) = v9 & ( ~ decreases(v6) | increases(v9)) & ( ~ constant(v6) | constant(v9))))
% 3.07/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (resilience(v2) = v1) | ~ (resilience(v2) = v0))
% 3.07/1.45 | (16) subpopulations(first_movers, efficient_producers, all_0_5_5, all_0_4_4)
% 3.07/1.45 | (17) environment(all_0_5_5)
% 3.07/1.45 | (18) resilience(efficient_producers) = all_0_7_7
% 3.07/1.45 | (19) resilience(first_movers) = all_0_6_6
% 3.07/1.45 |
% 3.07/1.45 | Instantiating formula (14) with all_0_3_3, all_0_6_6, all_0_7_7, all_0_4_4, efficient_producers, first_movers, all_0_5_5 and discharging atoms resources(all_0_5_5, all_0_4_4) = all_0_3_3, resilience(first_movers) = all_0_6_6, resilience(efficient_producers) = all_0_7_7, greater(all_0_7_7, all_0_6_6), subpopulations(first_movers, efficient_producers, all_0_5_5, all_0_4_4), environment(all_0_5_5), yields:
% 3.07/1.45 | (20) ? [v0] : ? [v1] : ? [v2] : (disbanding_rate(first_movers, all_0_4_4) = v0 & disbanding_rate(efficient_producers, all_0_4_4) = v1 & difference(v0, v1) = v2 & ( ~ decreases(all_0_3_3) | increases(v2)) & ( ~ constant(all_0_3_3) | constant(v2)))
% 3.07/1.45 |
% 3.07/1.45 | Instantiating (20) with all_8_0_8, all_8_1_9, all_8_2_10 yields:
% 3.07/1.45 | (21) disbanding_rate(first_movers, all_0_4_4) = all_8_2_10 & disbanding_rate(efficient_producers, all_0_4_4) = all_8_1_9 & difference(all_8_2_10, all_8_1_9) = all_8_0_8 & ( ~ decreases(all_0_3_3) | increases(all_8_0_8)) & ( ~ constant(all_0_3_3) | constant(all_8_0_8))
% 3.07/1.45 |
% 3.07/1.45 | Applying alpha-rule on (21) yields:
% 3.07/1.45 | (22) difference(all_8_2_10, all_8_1_9) = all_8_0_8
% 3.07/1.45 | (23) ~ decreases(all_0_3_3) | increases(all_8_0_8)
% 3.07/1.45 | (24) ~ constant(all_0_3_3) | constant(all_8_0_8)
% 3.07/1.45 | (25) disbanding_rate(efficient_producers, all_0_4_4) = all_8_1_9
% 3.07/1.45 | (26) disbanding_rate(first_movers, all_0_4_4) = all_8_2_10
% 3.07/1.45 |
% 3.07/1.45 | Instantiating formula (10) with first_movers, all_0_4_4, all_8_2_10, all_0_2_2 and discharging atoms disbanding_rate(first_movers, all_0_4_4) = all_8_2_10, disbanding_rate(first_movers, all_0_4_4) = all_0_2_2, yields:
% 3.07/1.45 | (27) all_8_2_10 = all_0_2_2
% 3.07/1.45 |
% 3.07/1.45 | Instantiating formula (10) with efficient_producers, all_0_4_4, all_8_1_9, all_0_1_1 and discharging atoms disbanding_rate(efficient_producers, all_0_4_4) = all_8_1_9, disbanding_rate(efficient_producers, all_0_4_4) = all_0_1_1, yields:
% 3.07/1.45 | (28) all_8_1_9 = all_0_1_1
% 3.07/1.45 |
% 3.07/1.46 | From (27)(28) and (22) follows:
% 3.07/1.46 | (29) difference(all_0_2_2, all_0_1_1) = all_8_0_8
% 3.07/1.46 |
% 3.07/1.46 | Instantiating formula (6) with all_0_2_2, all_0_1_1, all_8_0_8, all_0_0_0 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_8_0_8, difference(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 3.07/1.46 | (30) all_8_0_8 = all_0_0_0
% 3.07/1.46 |
% 3.07/1.46 +-Applying beta-rule and splitting (24), into two cases.
% 3.07/1.46 |-Branch one:
% 3.07/1.46 | (31) ~ constant(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 +-Applying beta-rule and splitting (11), into two cases.
% 3.07/1.46 |-Branch one:
% 3.07/1.46 | (32) decreases(all_0_0_0) & constant(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Applying alpha-rule on (32) yields:
% 3.07/1.46 | (33) decreases(all_0_0_0)
% 3.07/1.46 | (34) constant(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Using (34) and (31) yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 |-Branch two:
% 3.07/1.46 | (36) decreases(all_0_3_3) & ~ increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 | Applying alpha-rule on (36) yields:
% 3.07/1.46 | (37) decreases(all_0_3_3)
% 3.07/1.46 | (38) ~ increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 +-Applying beta-rule and splitting (23), into two cases.
% 3.07/1.46 |-Branch one:
% 3.07/1.46 | (39) ~ decreases(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Using (37) and (39) yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 |-Branch two:
% 3.07/1.46 | (37) decreases(all_0_3_3)
% 3.07/1.46 | (42) increases(all_8_0_8)
% 3.07/1.46 |
% 3.07/1.46 | From (30) and (42) follows:
% 3.07/1.46 | (43) increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 | Using (43) and (38) yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 |-Branch two:
% 3.07/1.46 | (34) constant(all_0_3_3)
% 3.07/1.46 | (46) constant(all_8_0_8)
% 3.07/1.46 |
% 3.07/1.46 | From (30) and (46) follows:
% 3.07/1.46 | (47) constant(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 +-Applying beta-rule and splitting (11), into two cases.
% 3.07/1.46 |-Branch one:
% 3.07/1.46 | (32) decreases(all_0_0_0) & constant(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Applying alpha-rule on (32) yields:
% 3.07/1.46 | (33) decreases(all_0_0_0)
% 3.07/1.46 | (34) constant(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Instantiating formula (5) with all_0_0_0 and discharging atoms decreases(all_0_0_0), constant(all_0_0_0), yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 |-Branch two:
% 3.07/1.46 | (36) decreases(all_0_3_3) & ~ increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 | Applying alpha-rule on (36) yields:
% 3.07/1.46 | (37) decreases(all_0_3_3)
% 3.07/1.46 | (38) ~ increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 +-Applying beta-rule and splitting (23), into two cases.
% 3.07/1.46 |-Branch one:
% 3.07/1.46 | (39) ~ decreases(all_0_3_3)
% 3.07/1.46 |
% 3.07/1.46 | Using (37) and (39) yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 |-Branch two:
% 3.07/1.46 | (37) decreases(all_0_3_3)
% 3.07/1.46 | (42) increases(all_8_0_8)
% 3.07/1.46 |
% 3.07/1.46 | From (30) and (42) follows:
% 3.07/1.46 | (43) increases(all_0_0_0)
% 3.07/1.46 |
% 3.07/1.46 | Using (43) and (38) yields:
% 3.07/1.46 | (35) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 % SZS output end Proof for theBenchmark
% 3.07/1.46
% 3.07/1.46 895ms
%------------------------------------------------------------------------------