TSTP Solution File: PUZ132+1 by ePrincess---1.0
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% File : ePrincess---1.0
% Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 : Mon Jul 18 18:08:59 EDT 2022
% Result : Theorem 1.71s 1.01s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ132+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 02:26:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.10/0.85 Prover 0: Preprocessing ...
% 1.48/0.94 Prover 0: Constructing countermodel ...
% 1.71/1.01 Prover 0: proved (378ms)
% 1.71/1.01
% 1.71/1.01 No countermodel exists, formula is valid
% 1.71/1.01 % SZS status Theorem for theBenchmark
% 1.71/1.01
% 1.71/1.01 Generating proof ... found it (size 9)
% 2.06/1.17
% 2.06/1.17 % SZS output start Proof for theBenchmark
% 2.06/1.17 Assumed formulas after preprocessing and simplification:
% 2.06/1.17 | (0) ? [v0] : ? [v1] : ? [v2] : (capital_city(usa) = washington & country(v0) & country(usa) & city(v1) & capital(v2) & capital(washington) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (capital_city(v5) = v4) | ~ (capital_city(v5) = v3)) & ! [v3] : ! [v4] : ( ~ (capital_city(v3) = v4) | ~ country(v3) | beautiful(v4)) & ! [v3] : ! [v4] : ( ~ (capital_city(v3) = v4) | ~ country(v3) | capital(v4)) & ! [v3] : ( ~ city(v3) | has_crime(v3)) & ! [v3] : ( ~ capital(v3) | city(v3)) & ( ~ beautiful(washington) | ~ has_crime(washington)))
% 2.33/1.21 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.33/1.21 | (1) capital_city(usa) = washington & country(all_0_2_2) & country(usa) & city(all_0_1_1) & capital(all_0_0_0) & capital(washington) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (capital_city(v2) = v1) | ~ (capital_city(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (capital_city(v0) = v1) | ~ country(v0) | beautiful(v1)) & ! [v0] : ! [v1] : ( ~ (capital_city(v0) = v1) | ~ country(v0) | capital(v1)) & ! [v0] : ( ~ city(v0) | has_crime(v0)) & ! [v0] : ( ~ capital(v0) | city(v0)) & ( ~ beautiful(washington) | ~ has_crime(washington))
% 2.33/1.21 |
% 2.33/1.21 | Applying alpha-rule on (1) yields:
% 2.33/1.21 | (2) city(all_0_1_1)
% 2.33/1.21 | (3) capital(all_0_0_0)
% 2.33/1.21 | (4) ! [v0] : ! [v1] : ( ~ (capital_city(v0) = v1) | ~ country(v0) | beautiful(v1))
% 2.33/1.21 | (5) ~ beautiful(washington) | ~ has_crime(washington)
% 2.33/1.21 | (6) country(usa)
% 2.33/1.21 | (7) country(all_0_2_2)
% 2.33/1.21 | (8) ! [v0] : ! [v1] : ( ~ (capital_city(v0) = v1) | ~ country(v0) | capital(v1))
% 2.33/1.21 | (9) ! [v0] : ( ~ city(v0) | has_crime(v0))
% 2.33/1.21 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (capital_city(v2) = v1) | ~ (capital_city(v2) = v0))
% 2.33/1.21 | (11) capital(washington)
% 2.33/1.21 | (12) ! [v0] : ( ~ capital(v0) | city(v0))
% 2.33/1.21 | (13) capital_city(usa) = washington
% 2.33/1.21 |
% 2.33/1.21 | Instantiating formula (4) with washington, usa and discharging atoms capital_city(usa) = washington, country(usa), yields:
% 2.33/1.22 | (14) beautiful(washington)
% 2.33/1.22 |
% 2.33/1.22 | Instantiating formula (12) with washington and discharging atoms capital(washington), yields:
% 2.33/1.22 | (15) city(washington)
% 2.33/1.22 |
% 2.33/1.22 +-Applying beta-rule and splitting (5), into two cases.
% 2.33/1.22 |-Branch one:
% 2.33/1.22 | (16) ~ beautiful(washington)
% 2.33/1.22 |
% 2.33/1.22 | Using (14) and (16) yields:
% 2.33/1.22 | (17) $false
% 2.33/1.22 |
% 2.33/1.22 |-The branch is then unsatisfiable
% 2.33/1.22 |-Branch two:
% 2.33/1.22 | (14) beautiful(washington)
% 2.33/1.22 | (19) ~ has_crime(washington)
% 2.33/1.22 |
% 2.33/1.22 | Instantiating formula (9) with washington and discharging atoms city(washington), ~ has_crime(washington), yields:
% 2.33/1.22 | (17) $false
% 2.33/1.22 |
% 2.33/1.22 |-The branch is then unsatisfiable
% 2.33/1.22 % SZS output end Proof for theBenchmark
% 2.33/1.22
% 2.33/1.22 626ms
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