TSTP Solution File: MGT056+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 22:07:13 EDT 2022
% Result : Theorem 3.85s 1.53s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT056+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 11:50:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.47/0.61 ____ _
% 0.47/0.61 ___ / __ \_____(_)___ ________ __________
% 0.47/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.61
% 0.47/0.61 A Theorem Prover for First-Order Logic
% 0.47/0.61 (ePrincess v.1.0)
% 0.47/0.61
% 0.47/0.61 (c) Philipp Rümmer, 2009-2015
% 0.47/0.61 (c) Peter Backeman, 2014-2015
% 0.47/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.61 Bug reports to peter@backeman.se
% 0.47/0.61
% 0.47/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.61
% 0.47/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.94 Prover 0: Preprocessing ...
% 2.02/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.12 Prover 0: Constructing countermodel ...
% 3.85/1.53 Prover 0: proved (866ms)
% 3.85/1.53
% 3.85/1.53 No countermodel exists, formula is valid
% 3.85/1.53 % SZS status Theorem for theBenchmark
% 3.85/1.53
% 3.85/1.53 Generating proof ... Warning: ignoring some quantifiers
% 4.65/1.76 found it (size 26)
% 4.65/1.76
% 4.65/1.76 % SZS output start Proof for theBenchmark
% 4.65/1.77 Assumed formulas after preprocessing and simplification:
% 4.65/1.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (hazard_of_mortality(v0, v3) = v6 & hazard_of_mortality(v0, v2) = v7 & hazard_of_mortality(v0, v1) = v8 & age(v0, v3) = v5 & age(v0, v2) = v4 & age(v0, v1) = zero & organization(v0) & has_endowment(v0) & greater(v5, eta) & greater(sigma, zero) & greater_or_equal(eta, sigma) & smaller_or_equal(v4, eta) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (hazard_of_mortality(v9, v11) = v13) | ~ (hazard_of_mortality(v9, v10) = v12) | ~ has_immunity(v9, v11) | ~ has_immunity(v9, v10) | ~ organization(v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (hazard_of_mortality(v9, v11) = v12) | ~ (hazard_of_mortality(v9, v10) = v13) | ~ has_immunity(v9, v10) | ~ organization(v9) | has_immunity(v9, v11) | greater(v12, v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (hazard_of_mortality(v12, v11) = v10) | ~ (hazard_of_mortality(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (age(v12, v11) = v10) | ~ (age(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (age(v9, v10) = v11) | ~ has_immunity(v9, v10) | ~ has_endowment(v9) | ~ greater(v11, eta)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (age(v9, v10) = v11) | ~ has_endowment(v9) | ~ smaller_or_equal(v11, eta) | has_immunity(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ greater(v10, v11) | ~ greater(v9, v10) | greater(v9, v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ greater_or_equal(v9, v10) | greater(v9, v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ smaller_or_equal(v9, v10) | smaller(v9, v10)) & ! [v9] : ! [v10] : ( ~ greater(v10, v9) | ~ greater(v9, v10)) & ! [v9] : ! [v10] : ( ~ greater(v10, v9) | smaller(v9, v10)) & ! [v9] : ! [v10] : ( ~ greater(v9, v10) | greater_or_equal(v9, v10)) & ! [v9] : ! [v10] : ( ~ smaller(v9, v10) | greater(v10, v9)) & ! [v9] : ! [v10] : ( ~ smaller(v9, v10) | smaller_or_equal(v9, v10)) & ! [v9] : ( ~ has_endowment(v9) | organization(v9)) & ? [v9] : ? [v10] : (v10 = v9 | greater(v9, v10) | smaller(v9, v10)) & ? [v9] : (has_endowment(v9) | ? [v10] : ? [v11] : (age(v9, v10) = v11 & ( ~ organization(v9) | (has_immunity(v9, v10) & greater(v11, eta)) | (smaller_or_equal(v11, eta) & ~ has_immunity(v9, v10))))) & ? [v9] : greater_or_equal(v9, v9) & ? [v9] : smaller_or_equal(v9, v9) & ( ~ (v8 = v7) | ~ greater(v6, v7)))
% 4.65/1.80 | 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:
% 4.65/1.80 | (1) hazard_of_mortality(all_0_8_8, all_0_5_5) = all_0_2_2 & hazard_of_mortality(all_0_8_8, all_0_6_6) = all_0_1_1 & hazard_of_mortality(all_0_8_8, all_0_7_7) = all_0_0_0 & age(all_0_8_8, all_0_5_5) = all_0_3_3 & age(all_0_8_8, all_0_6_6) = all_0_4_4 & age(all_0_8_8, all_0_7_7) = zero & organization(all_0_8_8) & has_endowment(all_0_8_8) & greater(all_0_3_3, eta) & greater(sigma, zero) & greater_or_equal(eta, sigma) & smaller_or_equal(all_0_4_4, eta) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (hazard_of_mortality(v0, v2) = v4) | ~ (hazard_of_mortality(v0, v1) = v3) | ~ has_immunity(v0, v2) | ~ has_immunity(v0, v1) | ~ organization(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hazard_of_mortality(v0, v2) = v3) | ~ (hazard_of_mortality(v0, v1) = v4) | ~ has_immunity(v0, v1) | ~ organization(v0) | has_immunity(v0, v2) | greater(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (hazard_of_mortality(v3, v2) = v1) | ~ (hazard_of_mortality(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (age(v3, v2) = v1) | ~ (age(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (age(v0, v1) = v2) | ~ has_immunity(v0, v1) | ~ has_endowment(v0) | ~ greater(v2, eta)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (age(v0, v1) = v2) | ~ has_endowment(v0) | ~ smaller_or_equal(v2, eta) | has_immunity(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ smaller_or_equal(v0, v1) | smaller(v0, v1)) & ! [v0] : ! [v1] : ( ~ greater(v1, v0) | ~ greater(v0, v1)) & ! [v0] : ! [v1] : ( ~ greater(v1, v0) | smaller(v0, v1)) & ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ! [v0] : ! [v1] : ( ~ smaller(v0, v1) | greater(v1, v0)) & ! [v0] : ! [v1] : ( ~ smaller(v0, v1) | smaller_or_equal(v0, v1)) & ! [v0] : ( ~ has_endowment(v0) | organization(v0)) & ? [v0] : ? [v1] : (v1 = v0 | greater(v0, v1) | smaller(v0, v1)) & ? [v0] : (has_endowment(v0) | ? [v1] : ? [v2] : (age(v0, v1) = v2 & ( ~ organization(v0) | (has_immunity(v0, v1) & greater(v2, eta)) | (smaller_or_equal(v2, eta) & ~ has_immunity(v0, v1))))) & ? [v0] : greater_or_equal(v0, v0) & ? [v0] : smaller_or_equal(v0, v0) & ( ~ (all_0_0_0 = all_0_1_1) | ~ greater(all_0_2_2, all_0_1_1))
% 4.82/1.81 |
% 4.82/1.81 | Applying alpha-rule on (1) yields:
% 4.82/1.81 | (2) age(all_0_8_8, all_0_7_7) = zero
% 4.82/1.81 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (hazard_of_mortality(v0, v2) = v4) | ~ (hazard_of_mortality(v0, v1) = v3) | ~ has_immunity(v0, v2) | ~ has_immunity(v0, v1) | ~ organization(v0))
% 4.82/1.81 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (age(v0, v1) = v2) | ~ has_immunity(v0, v1) | ~ has_endowment(v0) | ~ greater(v2, eta))
% 4.82/1.81 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 4.82/1.81 | (6) ? [v0] : (has_endowment(v0) | ? [v1] : ? [v2] : (age(v0, v1) = v2 & ( ~ organization(v0) | (has_immunity(v0, v1) & greater(v2, eta)) | (smaller_or_equal(v2, eta) & ~ has_immunity(v0, v1)))))
% 4.82/1.81 | (7) ? [v0] : ? [v1] : (v1 = v0 | greater(v0, v1) | smaller(v0, v1))
% 4.82/1.81 | (8) greater(sigma, zero)
% 4.82/1.81 | (9) ? [v0] : greater_or_equal(v0, v0)
% 4.82/1.81 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (hazard_of_mortality(v3, v2) = v1) | ~ (hazard_of_mortality(v3, v2) = v0))
% 4.82/1.81 | (11) age(all_0_8_8, all_0_5_5) = all_0_3_3
% 4.82/1.81 | (12) smaller_or_equal(all_0_4_4, eta)
% 4.82/1.81 | (13) ! [v0] : ! [v1] : ( ~ greater(v1, v0) | ~ greater(v0, v1))
% 4.82/1.82 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (age(v0, v1) = v2) | ~ has_endowment(v0) | ~ smaller_or_equal(v2, eta) | has_immunity(v0, v1))
% 4.82/1.82 | (15) has_endowment(all_0_8_8)
% 4.82/1.82 | (16) hazard_of_mortality(all_0_8_8, all_0_6_6) = all_0_1_1
% 4.82/1.82 | (17) greater_or_equal(eta, sigma)
% 4.82/1.82 | (18) age(all_0_8_8, all_0_6_6) = all_0_4_4
% 4.82/1.82 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ greater_or_equal(v0, v1) | greater(v0, v1))
% 4.82/1.82 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ smaller_or_equal(v0, v1) | smaller(v0, v1))
% 4.82/1.82 | (21) ! [v0] : ! [v1] : ( ~ smaller(v0, v1) | greater(v1, v0))
% 4.82/1.82 | (22) ! [v0] : ! [v1] : ( ~ greater(v1, v0) | smaller(v0, v1))
% 4.82/1.82 | (23) ? [v0] : smaller_or_equal(v0, v0)
% 4.82/1.82 | (24) hazard_of_mortality(all_0_8_8, all_0_5_5) = all_0_2_2
% 4.82/1.82 | (25) ! [v0] : ( ~ has_endowment(v0) | organization(v0))
% 4.82/1.82 | (26) greater(all_0_3_3, eta)
% 4.82/1.82 | (27) ! [v0] : ! [v1] : ( ~ smaller(v0, v1) | smaller_or_equal(v0, v1))
% 4.82/1.82 | (28) ~ (all_0_0_0 = all_0_1_1) | ~ greater(all_0_2_2, all_0_1_1)
% 4.82/1.82 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (age(v3, v2) = v1) | ~ (age(v3, v2) = v0))
% 4.82/1.82 | (30) organization(all_0_8_8)
% 4.82/1.82 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (hazard_of_mortality(v0, v2) = v3) | ~ (hazard_of_mortality(v0, v1) = v4) | ~ has_immunity(v0, v1) | ~ organization(v0) | has_immunity(v0, v2) | greater(v3, v4))
% 4.82/1.82 | (32) ! [v0] : ! [v1] : ( ~ greater(v0, v1) | greater_or_equal(v0, v1))
% 4.82/1.82 | (33) hazard_of_mortality(all_0_8_8, all_0_7_7) = all_0_0_0
% 4.82/1.82 |
% 4.82/1.82 | Instantiating formula (22) with sigma, zero and discharging atoms greater(sigma, zero), yields:
% 4.82/1.82 | (34) smaller(zero, sigma)
% 4.82/1.82 |
% 4.82/1.82 | Instantiating formula (19) with sigma, eta and discharging atoms greater_or_equal(eta, sigma), yields:
% 4.82/1.82 | (35) sigma = eta | greater(eta, sigma)
% 4.82/1.82 |
% 4.82/1.82 | Instantiating formula (14) with all_0_4_4, all_0_6_6, all_0_8_8 and discharging atoms age(all_0_8_8, all_0_6_6) = all_0_4_4, has_endowment(all_0_8_8), smaller_or_equal(all_0_4_4, eta), yields:
% 4.82/1.82 | (36) has_immunity(all_0_8_8, all_0_6_6)
% 4.82/1.82 |
% 4.82/1.82 | Instantiating formula (31) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms hazard_of_mortality(all_0_8_8, all_0_5_5) = all_0_2_2, hazard_of_mortality(all_0_8_8, all_0_6_6) = all_0_1_1, has_immunity(all_0_8_8, all_0_6_6), organization(all_0_8_8), yields:
% 4.82/1.82 | (37) has_immunity(all_0_8_8, all_0_5_5) | greater(all_0_2_2, all_0_1_1)
% 4.82/1.82 |
% 4.82/1.82 | Instantiating formula (27) with sigma, zero and discharging atoms smaller(zero, sigma), yields:
% 4.82/1.82 | (38) smaller_or_equal(zero, sigma)
% 4.82/1.82 |
% 4.82/1.82 +-Applying beta-rule and splitting (28), into two cases.
% 4.82/1.82 |-Branch one:
% 4.82/1.82 | (39) ~ greater(all_0_2_2, all_0_1_1)
% 4.82/1.82 |
% 4.82/1.82 +-Applying beta-rule and splitting (37), into two cases.
% 4.82/1.82 |-Branch one:
% 4.82/1.82 | (40) greater(all_0_2_2, all_0_1_1)
% 4.82/1.82 |
% 4.82/1.82 | Using (40) and (39) yields:
% 4.82/1.82 | (41) $false
% 4.82/1.82 |
% 4.82/1.82 |-The branch is then unsatisfiable
% 4.82/1.82 |-Branch two:
% 4.82/1.82 | (39) ~ greater(all_0_2_2, all_0_1_1)
% 4.82/1.82 | (43) has_immunity(all_0_8_8, all_0_5_5)
% 4.82/1.82 |
% 4.82/1.83 | Instantiating formula (4) with all_0_3_3, all_0_5_5, all_0_8_8 and discharging atoms age(all_0_8_8, all_0_5_5) = all_0_3_3, has_immunity(all_0_8_8, all_0_5_5), has_endowment(all_0_8_8), greater(all_0_3_3, eta), yields:
% 4.82/1.83 | (41) $false
% 4.82/1.83 |
% 4.82/1.83 |-The branch is then unsatisfiable
% 4.82/1.83 |-Branch two:
% 4.82/1.83 | (40) greater(all_0_2_2, all_0_1_1)
% 4.82/1.83 | (46) ~ (all_0_0_0 = all_0_1_1)
% 4.82/1.83 |
% 4.82/1.83 +-Applying beta-rule and splitting (35), into two cases.
% 4.82/1.83 |-Branch one:
% 4.82/1.83 | (47) greater(eta, sigma)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (5) with zero, sigma, eta and discharging atoms greater(sigma, zero), greater(eta, sigma), yields:
% 4.82/1.83 | (48) greater(eta, zero)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (22) with eta, zero and discharging atoms greater(eta, zero), yields:
% 4.82/1.83 | (49) smaller(zero, eta)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (27) with eta, zero and discharging atoms smaller(zero, eta), yields:
% 4.82/1.83 | (50) smaller_or_equal(zero, eta)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (14) with zero, all_0_7_7, all_0_8_8 and discharging atoms age(all_0_8_8, all_0_7_7) = zero, has_endowment(all_0_8_8), smaller_or_equal(zero, eta), yields:
% 4.82/1.83 | (51) has_immunity(all_0_8_8, all_0_7_7)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (3) with all_0_1_1, all_0_0_0, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms hazard_of_mortality(all_0_8_8, all_0_6_6) = all_0_1_1, hazard_of_mortality(all_0_8_8, all_0_7_7) = all_0_0_0, has_immunity(all_0_8_8, all_0_6_6), has_immunity(all_0_8_8, all_0_7_7), organization(all_0_8_8), yields:
% 4.82/1.83 | (52) all_0_0_0 = all_0_1_1
% 4.82/1.83 |
% 4.82/1.83 | Equations (52) can reduce 46 to:
% 4.82/1.83 | (53) $false
% 4.82/1.83 |
% 4.82/1.83 |-The branch is then unsatisfiable
% 4.82/1.83 |-Branch two:
% 4.82/1.83 | (54) ~ greater(eta, sigma)
% 4.82/1.83 | (55) sigma = eta
% 4.82/1.83 |
% 4.82/1.83 | From (55) and (38) follows:
% 4.82/1.83 | (50) smaller_or_equal(zero, eta)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (14) with zero, all_0_7_7, all_0_8_8 and discharging atoms age(all_0_8_8, all_0_7_7) = zero, has_endowment(all_0_8_8), smaller_or_equal(zero, eta), yields:
% 4.82/1.83 | (51) has_immunity(all_0_8_8, all_0_7_7)
% 4.82/1.83 |
% 4.82/1.83 | Instantiating formula (3) with all_0_1_1, all_0_0_0, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms hazard_of_mortality(all_0_8_8, all_0_6_6) = all_0_1_1, hazard_of_mortality(all_0_8_8, all_0_7_7) = all_0_0_0, has_immunity(all_0_8_8, all_0_6_6), has_immunity(all_0_8_8, all_0_7_7), organization(all_0_8_8), yields:
% 4.82/1.83 | (52) all_0_0_0 = all_0_1_1
% 4.82/1.83 |
% 4.82/1.83 | Equations (52) can reduce 46 to:
% 4.82/1.83 | (53) $false
% 4.82/1.83 |
% 4.82/1.83 |-The branch is then unsatisfiable
% 4.82/1.83 % SZS output end Proof for theBenchmark
% 4.82/1.83
% 4.82/1.83 1209ms
%------------------------------------------------------------------------------