TSTP Solution File: PUZ005+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : PUZ005+1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Mon Jul 18 18:08:49 EDT 2022
% Result : Theorem 14.51s 4.57s
% Output : Proof 17.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ005+1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 22:05:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.63/0.62 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/1.03 Prover 0: Preprocessing ...
% 2.27/1.22 Prover 0: Constructing countermodel ...
% 14.51/4.56 Prover 0: proved (3867ms)
% 14.51/4.57
% 14.51/4.57 No countermodel exists, formula is valid
% 14.51/4.57 % SZS status Theorem for theBenchmark
% 14.51/4.57
% 14.51/4.57 Generating proof ... found it (size 22)
% 17.00/5.19
% 17.00/5.19 % SZS output start Proof for theBenchmark
% 17.00/5.19 Assumed formulas after preprocessing and simplification:
% 17.00/5.19 | (0) sunday(a_sunday) & saturday(a_saturday) & friday(a_friday) & thursday(a_thursday) & wednesday(a_wednesday) & tuesday(a_tuesday) & monday(a_monday) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (yesterday(v2) = v1) | ~ (yesterday(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ sunday(v0) | saturday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ saturday(v0) | friday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ friday(v0) | thursday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ thursday(v0) | wednesday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ wednesday(v0) | tuesday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ tuesday(v0) | monday(v1)) & ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ monday(v0) | sunday(v1)) & ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ unicorn_lies(v1) | ~ unicorn_lies(v0) | ~ day(v1) | ~ day(v0)) & ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ day(v1) | ~ day(v0) | unicorn_lies(v1) | unicorn_lies(v0)) & ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_lion, v0, v1) | ~ lion_lies(v1) | ~ lion_lies(v0) | ~ day(v1) | ~ day(v0)) & ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_lion, v0, v1) | ~ day(v1) | ~ day(v0) | lion_lies(v1) | lion_lies(v0)) & ! [v0] : ! [v1] : ( ~ unicorn_lies(v1) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_unicorn, v0, v1) | unicorn_lies(v0)) & ! [v0] : ! [v1] : ( ~ unicorn_lies(v0) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_unicorn, v0, v1) | unicorn_lies(v1)) & ! [v0] : ! [v1] : ( ~ lion_lies(v1) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_lion, v0, v1) | lion_lies(v0)) & ! [v0] : ! [v1] : ( ~ lion_lies(v0) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_lion, v0, v1) | lion_lies(v1)) & ! [v0] : ( ~ unicorn_lies(v0) | ~ sunday(v0)) & ! [v0] : ( ~ unicorn_lies(v0) | ~ wednesday(v0)) & ! [v0] : ( ~ unicorn_lies(v0) | ~ tuesday(v0)) & ! [v0] : ( ~ unicorn_lies(v0) | ~ monday(v0)) & ! [v0] : ( ~ unicorn_lies(v0) | day(v0)) & ! [v0] : ( ~ lion_lies(v0) | ~ sunday(v0)) & ! [v0] : ( ~ lion_lies(v0) | ~ saturday(v0)) & ! [v0] : ( ~ lion_lies(v0) | ~ friday(v0)) & ! [v0] : ( ~ lion_lies(v0) | ~ thursday(v0)) & ! [v0] : ( ~ lion_lies(v0) | day(v0)) & ! [v0] : ( ~ day(v0) | ? [v1] : (yesterday(v0) = v1 & ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ lies_on_one_of(a_lion, v0, v1)))) & ! [v0] : ( ~ sunday(v0) | day(v0)) & ! [v0] : ( ~ saturday(v0) | unicorn_lies(v0)) & ! [v0] : ( ~ saturday(v0) | day(v0)) & ! [v0] : ( ~ friday(v0) | unicorn_lies(v0)) & ! [v0] : ( ~ friday(v0) | day(v0)) & ! [v0] : ( ~ thursday(v0) | unicorn_lies(v0)) & ! [v0] : ( ~ thursday(v0) | day(v0)) & ! [v0] : ( ~ wednesday(v0) | lion_lies(v0)) & ! [v0] : ( ~ wednesday(v0) | day(v0)) & ! [v0] : ( ~ tuesday(v0) | lion_lies(v0)) & ! [v0] : ( ~ tuesday(v0) | day(v0)) & ! [v0] : ( ~ monday(v0) | lion_lies(v0)) & ! [v0] : ( ~ monday(v0) | day(v0))
% 17.21/5.24 | Applying alpha-rule on (0) yields:
% 17.21/5.24 | (1) ! [v0] : ! [v1] : ( ~ lion_lies(v1) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_lion, v0, v1) | lion_lies(v0))
% 17.21/5.24 | (2) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ monday(v0) | sunday(v1))
% 17.21/5.24 | (3) saturday(a_saturday)
% 17.21/5.24 | (4) thursday(a_thursday)
% 17.21/5.24 | (5) ! [v0] : ( ~ lion_lies(v0) | ~ sunday(v0))
% 17.21/5.24 | (6) ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_lion, v0, v1) | ~ day(v1) | ~ day(v0) | lion_lies(v1) | lion_lies(v0))
% 17.21/5.24 | (7) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ saturday(v0) | friday(v1))
% 17.21/5.24 | (8) ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_lion, v0, v1) | ~ lion_lies(v1) | ~ lion_lies(v0) | ~ day(v1) | ~ day(v0))
% 17.21/5.24 | (9) ! [v0] : ( ~ wednesday(v0) | day(v0))
% 17.21/5.24 | (10) ! [v0] : ( ~ saturday(v0) | day(v0))
% 17.21/5.24 | (11) ! [v0] : ( ~ unicorn_lies(v0) | ~ monday(v0))
% 17.21/5.24 | (12) ! [v0] : ( ~ day(v0) | ? [v1] : (yesterday(v0) = v1 & ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ lies_on_one_of(a_lion, v0, v1))))
% 17.21/5.24 | (13) ! [v0] : ( ~ monday(v0) | day(v0))
% 17.21/5.24 | (14) friday(a_friday)
% 17.21/5.24 | (15) sunday(a_sunday)
% 17.21/5.24 | (16) ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ day(v1) | ~ day(v0) | unicorn_lies(v1) | unicorn_lies(v0))
% 17.21/5.24 | (17) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ tuesday(v0) | monday(v1))
% 17.21/5.24 | (18) monday(a_monday)
% 17.21/5.24 | (19) ! [v0] : ( ~ sunday(v0) | day(v0))
% 17.21/5.24 | (20) ! [v0] : ( ~ tuesday(v0) | day(v0))
% 17.21/5.24 | (21) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ friday(v0) | thursday(v1))
% 17.21/5.25 | (22) ! [v0] : ( ~ lion_lies(v0) | ~ saturday(v0))
% 17.21/5.25 | (23) ! [v0] : ( ~ unicorn_lies(v0) | ~ wednesday(v0))
% 17.21/5.25 | (24) ! [v0] : ( ~ lion_lies(v0) | day(v0))
% 17.21/5.25 | (25) wednesday(a_wednesday)
% 17.21/5.25 | (26) ! [v0] : ( ~ saturday(v0) | unicorn_lies(v0))
% 17.21/5.25 | (27) ! [v0] : ! [v1] : ( ~ unicorn_lies(v0) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_unicorn, v0, v1) | unicorn_lies(v1))
% 17.21/5.25 | (28) ! [v0] : ( ~ thursday(v0) | unicorn_lies(v0))
% 17.21/5.25 | (29) ! [v0] : ! [v1] : ( ~ unicorn_lies(v1) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_unicorn, v0, v1) | unicorn_lies(v0))
% 17.21/5.25 | (30) ! [v0] : ( ~ friday(v0) | unicorn_lies(v0))
% 17.21/5.25 | (31) ! [v0] : ! [v1] : ( ~ lies_on_one_of(a_unicorn, v0, v1) | ~ unicorn_lies(v1) | ~ unicorn_lies(v0) | ~ day(v1) | ~ day(v0))
% 17.21/5.25 | (32) ! [v0] : ( ~ lion_lies(v0) | ~ thursday(v0))
% 17.21/5.25 | (33) ! [v0] : ( ~ wednesday(v0) | lion_lies(v0))
% 17.21/5.25 | (34) ! [v0] : ( ~ monday(v0) | lion_lies(v0))
% 17.21/5.25 | (35) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ wednesday(v0) | tuesday(v1))
% 17.21/5.25 | (36) ! [v0] : ( ~ unicorn_lies(v0) | day(v0))
% 17.21/5.25 | (37) ! [v0] : ( ~ unicorn_lies(v0) | ~ sunday(v0))
% 17.21/5.25 | (38) ! [v0] : ( ~ unicorn_lies(v0) | ~ tuesday(v0))
% 17.21/5.25 | (39) ! [v0] : ! [v1] : ( ~ lion_lies(v0) | ~ day(v1) | ~ day(v0) | lies_on_one_of(a_lion, v0, v1) | lion_lies(v1))
% 17.21/5.25 | (40) ! [v0] : ( ~ thursday(v0) | day(v0))
% 17.21/5.25 | (41) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ thursday(v0) | wednesday(v1))
% 17.21/5.25 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (yesterday(v2) = v1) | ~ (yesterday(v2) = v0))
% 17.21/5.25 | (43) ! [v0] : ( ~ friday(v0) | day(v0))
% 17.21/5.25 | (44) ! [v0] : ( ~ lion_lies(v0) | ~ friday(v0))
% 17.21/5.25 | (45) ! [v0] : ( ~ tuesday(v0) | lion_lies(v0))
% 17.21/5.25 | (46) tuesday(a_tuesday)
% 17.21/5.25 | (47) ! [v0] : ! [v1] : ( ~ (yesterday(v0) = v1) | ~ sunday(v0) | saturday(v1))
% 17.21/5.25 |
% 17.21/5.25 | Instantiating formula (28) with a_thursday and discharging atoms thursday(a_thursday), yields:
% 17.21/5.25 | (48) unicorn_lies(a_thursday)
% 17.21/5.25 |
% 17.21/5.25 | Instantiating formula (40) with a_thursday and discharging atoms thursday(a_thursday), yields:
% 17.21/5.25 | (49) day(a_thursday)
% 17.21/5.25 |
% 17.21/5.25 | Instantiating formula (12) with a_thursday and discharging atoms day(a_thursday), yields:
% 17.21/5.25 | (50) ? [v0] : (yesterday(a_thursday) = v0 & ( ~ lies_on_one_of(a_unicorn, a_thursday, v0) | ~ lies_on_one_of(a_lion, a_thursday, v0)))
% 17.21/5.25 |
% 17.21/5.25 | Instantiating (50) with all_17_0_2 yields:
% 17.21/5.25 | (51) yesterday(a_thursday) = all_17_0_2 & ( ~ lies_on_one_of(a_unicorn, a_thursday, all_17_0_2) | ~ lies_on_one_of(a_lion, a_thursday, all_17_0_2))
% 17.21/5.25 |
% 17.21/5.25 | Applying alpha-rule on (51) yields:
% 17.21/5.25 | (52) yesterday(a_thursday) = all_17_0_2
% 17.21/5.25 | (53) ~ lies_on_one_of(a_unicorn, a_thursday, all_17_0_2) | ~ lies_on_one_of(a_lion, a_thursday, all_17_0_2)
% 17.21/5.25 |
% 17.21/5.25 | Instantiating formula (41) with all_17_0_2, a_thursday and discharging atoms yesterday(a_thursday) = all_17_0_2, thursday(a_thursday), yields:
% 17.21/5.25 | (54) wednesday(all_17_0_2)
% 17.21/5.25 |
% 17.21/5.25 | Instantiating formula (33) with all_17_0_2 and discharging atoms wednesday(all_17_0_2), yields:
% 17.21/5.25 | (55) lion_lies(all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Instantiating formula (9) with all_17_0_2 and discharging atoms wednesday(all_17_0_2), yields:
% 17.21/5.26 | (56) day(all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Instantiating formula (27) with all_17_0_2, a_thursday and discharging atoms unicorn_lies(a_thursday), day(all_17_0_2), day(a_thursday), yields:
% 17.21/5.26 | (57) lies_on_one_of(a_unicorn, a_thursday, all_17_0_2) | unicorn_lies(all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Instantiating formula (1) with all_17_0_2, a_thursday and discharging atoms lion_lies(all_17_0_2), day(all_17_0_2), day(a_thursday), yields:
% 17.21/5.26 | (58) lies_on_one_of(a_lion, a_thursday, all_17_0_2) | lion_lies(a_thursday)
% 17.21/5.26 |
% 17.21/5.26 +-Applying beta-rule and splitting (53), into two cases.
% 17.21/5.26 |-Branch one:
% 17.21/5.26 | (59) ~ lies_on_one_of(a_unicorn, a_thursday, all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 +-Applying beta-rule and splitting (57), into two cases.
% 17.21/5.26 |-Branch one:
% 17.21/5.26 | (60) lies_on_one_of(a_unicorn, a_thursday, all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Using (60) and (59) yields:
% 17.21/5.26 | (61) $false
% 17.21/5.26 |
% 17.21/5.26 |-The branch is then unsatisfiable
% 17.21/5.26 |-Branch two:
% 17.21/5.26 | (59) ~ lies_on_one_of(a_unicorn, a_thursday, all_17_0_2)
% 17.21/5.26 | (63) unicorn_lies(all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Instantiating formula (23) with all_17_0_2 and discharging atoms unicorn_lies(all_17_0_2), wednesday(all_17_0_2), yields:
% 17.21/5.26 | (61) $false
% 17.21/5.26 |
% 17.21/5.26 |-The branch is then unsatisfiable
% 17.21/5.26 |-Branch two:
% 17.21/5.26 | (60) lies_on_one_of(a_unicorn, a_thursday, all_17_0_2)
% 17.21/5.26 | (66) ~ lies_on_one_of(a_lion, a_thursday, all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 +-Applying beta-rule and splitting (58), into two cases.
% 17.21/5.26 |-Branch one:
% 17.21/5.26 | (67) lies_on_one_of(a_lion, a_thursday, all_17_0_2)
% 17.21/5.26 |
% 17.21/5.26 | Using (67) and (66) yields:
% 17.21/5.26 | (61) $false
% 17.21/5.26 |
% 17.21/5.26 |-The branch is then unsatisfiable
% 17.21/5.26 |-Branch two:
% 17.21/5.26 | (66) ~ lies_on_one_of(a_lion, a_thursday, all_17_0_2)
% 17.21/5.26 | (70) lion_lies(a_thursday)
% 17.21/5.26 |
% 17.21/5.26 | Instantiating formula (32) with a_thursday and discharging atoms lion_lies(a_thursday), thursday(a_thursday), yields:
% 17.21/5.26 | (61) $false
% 17.21/5.26 |
% 17.21/5.26 |-The branch is then unsatisfiable
% 17.21/5.26 % SZS output end Proof for theBenchmark
% 17.21/5.26
% 17.21/5.26 4624ms
%------------------------------------------------------------------------------