TSTP Solution File: SYN393+1.003 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN393+1.003 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 : Thu Jul 21 05:02:05 EDT 2022
% Result : Theorem 1.46s 0.98s
% Output : Proof 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN393+1.003 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 21:31:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.59/0.60 ____ _
% 0.59/0.60 ___ / __ \_____(_)___ ________ __________
% 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic
% 0.59/0.60 (ePrincess v.1.0)
% 0.59/0.60
% 0.59/0.60 (c) Philipp Rümmer, 2009-2015
% 0.59/0.60 (c) Peter Backeman, 2014-2015
% 0.59/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60 Bug reports to peter@backeman.se
% 0.59/0.60
% 0.59/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60
% 0.59/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.14/0.84 Prover 0: Preprocessing ...
% 1.41/0.91 Prover 0: Constructing countermodel ...
% 1.46/0.97 Prover 0: proved (326ms)
% 1.46/0.98
% 1.46/0.98 No countermodel exists, formula is valid
% 1.46/0.98 % SZS status Theorem for theBenchmark
% 1.46/0.98
% 1.46/0.98 Generating proof ... found it (size 117)
% 1.86/1.13
% 1.86/1.13 % SZS output start Proof for theBenchmark
% 1.86/1.13 Assumed formulas after preprocessing and simplification:
% 1.86/1.13 | (0) (((p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2)))) & ((p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 & ((p3 & p2) | ( ~ p3 & ~ p2))))) | (((p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1)))) & ((p1 & ((p3 & p2) | ( ~ p3 & ~ p2))) | ( ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3)))))
% 1.86/1.14 +-Applying beta-rule and splitting (0), into two cases.
% 1.86/1.14 |-Branch one:
% 1.86/1.14 | (1) ((p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2)))) & ((p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 & ((p3 & p2) | ( ~ p3 & ~ p2))))
% 1.86/1.14 |
% 1.86/1.14 | Applying alpha-rule on (1) yields:
% 1.86/1.14 | (2) (p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2)))
% 1.86/1.14 | (3) (p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 & ((p3 & p2) | ( ~ p3 & ~ p2)))
% 1.86/1.15 |
% 1.86/1.15 +-Applying beta-rule and splitting (3), into two cases.
% 1.86/1.15 |-Branch one:
% 1.86/1.15 | (4) p1 & ((p3 & ~ p2) | (p2 & ~ p3))
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (4) yields:
% 1.86/1.15 | (5) p1
% 1.86/1.15 | (6) (p3 & ~ p2) | (p2 & ~ p3)
% 1.86/1.15 |
% 1.86/1.15 +-Applying beta-rule and splitting (2), into two cases.
% 1.86/1.15 |-Branch one:
% 1.86/1.15 | (7) p3 & ((p2 & p1) | ( ~ p2 & ~ p1))
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (7) yields:
% 1.86/1.15 | (8) p3
% 1.86/1.15 | (9) (p2 & p1) | ( ~ p2 & ~ p1)
% 1.86/1.15 |
% 1.86/1.15 +-Applying beta-rule and splitting (6), into two cases.
% 1.86/1.15 |-Branch one:
% 1.86/1.15 | (10) p3 & ~ p2
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (10) yields:
% 1.86/1.15 | (8) p3
% 1.86/1.15 | (12) ~ p2
% 1.86/1.15 |
% 1.86/1.15 +-Applying beta-rule and splitting (9), into two cases.
% 1.86/1.15 |-Branch one:
% 1.86/1.15 | (13) p2 & p1
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (13) yields:
% 1.86/1.15 | (14) p2
% 1.86/1.15 | (5) p1
% 1.86/1.15 |
% 1.86/1.15 | Using (14) and (12) yields:
% 1.86/1.15 | (16) $false
% 1.86/1.15 |
% 1.86/1.15 |-The branch is then unsatisfiable
% 1.86/1.15 |-Branch two:
% 1.86/1.15 | (17) ~ p2 & ~ p1
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (17) yields:
% 1.86/1.15 | (12) ~ p2
% 1.86/1.15 | (19) ~ p1
% 1.86/1.15 |
% 1.86/1.15 | Using (5) and (19) yields:
% 1.86/1.15 | (16) $false
% 1.86/1.15 |
% 1.86/1.15 |-The branch is then unsatisfiable
% 1.86/1.15 |-Branch two:
% 1.86/1.15 | (21) p2 & ~ p3
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (21) yields:
% 1.86/1.15 | (14) p2
% 1.86/1.15 | (23) ~ p3
% 1.86/1.15 |
% 1.86/1.15 | Using (8) and (23) yields:
% 1.86/1.15 | (16) $false
% 1.86/1.15 |
% 1.86/1.15 |-The branch is then unsatisfiable
% 1.86/1.15 |-Branch two:
% 1.86/1.15 | (25) ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2))
% 1.86/1.15 |
% 1.86/1.15 | Applying alpha-rule on (25) yields:
% 1.86/1.15 | (23) ~ p3
% 1.86/1.15 | (27) (p2 & ~ p1) | (p1 & ~ p2)
% 1.86/1.16 |
% 1.86/1.16 +-Applying beta-rule and splitting (6), into two cases.
% 1.86/1.16 |-Branch one:
% 1.86/1.16 | (10) p3 & ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (10) yields:
% 1.86/1.16 | (8) p3
% 1.86/1.16 | (12) ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Using (8) and (23) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (21) p2 & ~ p3
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (21) yields:
% 1.86/1.16 | (14) p2
% 1.86/1.16 | (23) ~ p3
% 1.86/1.16 |
% 1.86/1.16 +-Applying beta-rule and splitting (27), into two cases.
% 1.86/1.16 |-Branch one:
% 1.86/1.16 | (35) p2 & ~ p1
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (35) yields:
% 1.86/1.16 | (14) p2
% 1.86/1.16 | (19) ~ p1
% 1.86/1.16 |
% 1.86/1.16 | Using (5) and (19) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (39) p1 & ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (39) yields:
% 1.86/1.16 | (5) p1
% 1.86/1.16 | (12) ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Using (14) and (12) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (43) ~ p1 & ((p3 & p2) | ( ~ p3 & ~ p2))
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (43) yields:
% 1.86/1.16 | (19) ~ p1
% 1.86/1.16 | (45) (p3 & p2) | ( ~ p3 & ~ p2)
% 1.86/1.16 |
% 1.86/1.16 +-Applying beta-rule and splitting (2), into two cases.
% 1.86/1.16 |-Branch one:
% 1.86/1.16 | (7) p3 & ((p2 & p1) | ( ~ p2 & ~ p1))
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (7) yields:
% 1.86/1.16 | (8) p3
% 1.86/1.16 | (9) (p2 & p1) | ( ~ p2 & ~ p1)
% 1.86/1.16 |
% 1.86/1.16 +-Applying beta-rule and splitting (45), into two cases.
% 1.86/1.16 |-Branch one:
% 1.86/1.16 | (49) p3 & p2
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (49) yields:
% 1.86/1.16 | (8) p3
% 1.86/1.16 | (14) p2
% 1.86/1.16 |
% 1.86/1.16 +-Applying beta-rule and splitting (9), into two cases.
% 1.86/1.16 |-Branch one:
% 1.86/1.16 | (13) p2 & p1
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (13) yields:
% 1.86/1.16 | (14) p2
% 1.86/1.16 | (5) p1
% 1.86/1.16 |
% 1.86/1.16 | Using (5) and (19) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (17) ~ p2 & ~ p1
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (17) yields:
% 1.86/1.16 | (12) ~ p2
% 1.86/1.16 | (19) ~ p1
% 1.86/1.16 |
% 1.86/1.16 | Using (14) and (12) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (60) ~ p3 & ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (60) yields:
% 1.86/1.16 | (23) ~ p3
% 1.86/1.16 | (12) ~ p2
% 1.86/1.16 |
% 1.86/1.16 | Using (8) and (23) yields:
% 1.86/1.16 | (16) $false
% 1.86/1.16 |
% 1.86/1.16 |-The branch is then unsatisfiable
% 1.86/1.16 |-Branch two:
% 1.86/1.16 | (25) ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2))
% 1.86/1.16 |
% 1.86/1.16 | Applying alpha-rule on (25) yields:
% 1.86/1.16 | (23) ~ p3
% 1.86/1.17 | (27) (p2 & ~ p1) | (p1 & ~ p2)
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (45), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (49) p3 & p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (49) yields:
% 1.86/1.17 | (8) p3
% 1.86/1.17 | (14) p2
% 1.86/1.17 |
% 1.86/1.17 | Using (8) and (23) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (60) ~ p3 & ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (60) yields:
% 1.86/1.17 | (23) ~ p3
% 1.86/1.17 | (12) ~ p2
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (27), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (35) p2 & ~ p1
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (35) yields:
% 1.86/1.17 | (14) p2
% 1.86/1.17 | (19) ~ p1
% 1.86/1.17 |
% 1.86/1.17 | Using (14) and (12) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (39) p1 & ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (39) yields:
% 1.86/1.17 | (5) p1
% 1.86/1.17 | (12) ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Using (5) and (19) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (82) ((p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1)))) & ((p1 & ((p3 & p2) | ( ~ p3 & ~ p2))) | ( ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3))))
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (82) yields:
% 1.86/1.17 | (83) (p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1)))
% 1.86/1.17 | (84) (p1 & ((p3 & p2) | ( ~ p3 & ~ p2))) | ( ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3)))
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (84), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (85) p1 & ((p3 & p2) | ( ~ p3 & ~ p2))
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (85) yields:
% 1.86/1.17 | (5) p1
% 1.86/1.17 | (45) (p3 & p2) | ( ~ p3 & ~ p2)
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (83), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (88) p3 & ((p2 & ~ p1) | (p1 & ~ p2))
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (88) yields:
% 1.86/1.17 | (8) p3
% 1.86/1.17 | (27) (p2 & ~ p1) | (p1 & ~ p2)
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (45), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (49) p3 & p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (49) yields:
% 1.86/1.17 | (8) p3
% 1.86/1.17 | (14) p2
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (27), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (35) p2 & ~ p1
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (35) yields:
% 1.86/1.17 | (14) p2
% 1.86/1.17 | (19) ~ p1
% 1.86/1.17 |
% 1.86/1.17 | Using (5) and (19) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (39) p1 & ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (39) yields:
% 1.86/1.17 | (5) p1
% 1.86/1.17 | (12) ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Using (14) and (12) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (60) ~ p3 & ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (60) yields:
% 1.86/1.17 | (23) ~ p3
% 1.86/1.17 | (12) ~ p2
% 1.86/1.17 |
% 1.86/1.17 | Using (8) and (23) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.17 | (106) ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1))
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (106) yields:
% 1.86/1.17 | (23) ~ p3
% 1.86/1.17 | (9) (p2 & p1) | ( ~ p2 & ~ p1)
% 1.86/1.17 |
% 1.86/1.17 +-Applying beta-rule and splitting (45), into two cases.
% 1.86/1.17 |-Branch one:
% 1.86/1.17 | (49) p3 & p2
% 1.86/1.17 |
% 1.86/1.17 | Applying alpha-rule on (49) yields:
% 1.86/1.17 | (8) p3
% 1.86/1.17 | (14) p2
% 1.86/1.17 |
% 1.86/1.17 | Using (8) and (23) yields:
% 1.86/1.17 | (16) $false
% 1.86/1.17 |
% 1.86/1.17 |-The branch is then unsatisfiable
% 1.86/1.17 |-Branch two:
% 1.86/1.18 | (60) ~ p3 & ~ p2
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (60) yields:
% 1.86/1.18 | (23) ~ p3
% 1.86/1.18 | (12) ~ p2
% 1.86/1.18 |
% 1.86/1.18 +-Applying beta-rule and splitting (9), into two cases.
% 1.86/1.18 |-Branch one:
% 1.86/1.18 | (13) p2 & p1
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (13) yields:
% 1.86/1.18 | (14) p2
% 1.86/1.18 | (5) p1
% 1.86/1.18 |
% 1.86/1.18 | Using (14) and (12) yields:
% 1.86/1.18 | (16) $false
% 1.86/1.18 |
% 1.86/1.18 |-The branch is then unsatisfiable
% 1.86/1.18 |-Branch two:
% 1.86/1.18 | (17) ~ p2 & ~ p1
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (17) yields:
% 1.86/1.18 | (12) ~ p2
% 1.86/1.18 | (19) ~ p1
% 1.86/1.18 |
% 1.86/1.18 | Using (5) and (19) yields:
% 1.86/1.18 | (16) $false
% 1.86/1.18 |
% 1.86/1.18 |-The branch is then unsatisfiable
% 1.86/1.18 |-Branch two:
% 1.86/1.18 | (124) ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3))
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (124) yields:
% 1.86/1.18 | (19) ~ p1
% 1.86/1.18 | (6) (p3 & ~ p2) | (p2 & ~ p3)
% 1.86/1.18 |
% 1.86/1.18 +-Applying beta-rule and splitting (83), into two cases.
% 1.86/1.18 |-Branch one:
% 1.86/1.18 | (88) p3 & ((p2 & ~ p1) | (p1 & ~ p2))
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (88) yields:
% 1.86/1.18 | (8) p3
% 1.86/1.18 | (27) (p2 & ~ p1) | (p1 & ~ p2)
% 1.86/1.18 |
% 1.86/1.18 +-Applying beta-rule and splitting (6), into two cases.
% 1.86/1.18 |-Branch one:
% 1.86/1.18 | (10) p3 & ~ p2
% 1.86/1.18 |
% 1.86/1.18 | Applying alpha-rule on (10) yields:
% 1.86/1.18 | (8) p3
% 1.86/1.18 | (12) ~ p2
% 1.86/1.18 |
% 2.12/1.18 +-Applying beta-rule and splitting (27), into two cases.
% 2.12/1.18 |-Branch one:
% 2.12/1.18 | (35) p2 & ~ p1
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (35) yields:
% 2.12/1.18 | (14) p2
% 2.12/1.18 | (19) ~ p1
% 2.12/1.18 |
% 2.12/1.18 | Using (14) and (12) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 |-Branch two:
% 2.12/1.18 | (39) p1 & ~ p2
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (39) yields:
% 2.12/1.18 | (5) p1
% 2.12/1.18 | (12) ~ p2
% 2.12/1.18 |
% 2.12/1.18 | Using (5) and (19) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 |-Branch two:
% 2.12/1.18 | (21) p2 & ~ p3
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (21) yields:
% 2.12/1.18 | (14) p2
% 2.12/1.18 | (23) ~ p3
% 2.12/1.18 |
% 2.12/1.18 | Using (8) and (23) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 |-Branch two:
% 2.12/1.18 | (106) ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1))
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (106) yields:
% 2.12/1.18 | (23) ~ p3
% 2.12/1.18 | (9) (p2 & p1) | ( ~ p2 & ~ p1)
% 2.12/1.18 |
% 2.12/1.18 +-Applying beta-rule and splitting (6), into two cases.
% 2.12/1.18 |-Branch one:
% 2.12/1.18 | (10) p3 & ~ p2
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (10) yields:
% 2.12/1.18 | (8) p3
% 2.12/1.18 | (12) ~ p2
% 2.12/1.18 |
% 2.12/1.18 | Using (8) and (23) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 |-Branch two:
% 2.12/1.18 | (21) p2 & ~ p3
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (21) yields:
% 2.12/1.18 | (14) p2
% 2.12/1.18 | (23) ~ p3
% 2.12/1.18 |
% 2.12/1.18 +-Applying beta-rule and splitting (9), into two cases.
% 2.12/1.18 |-Branch one:
% 2.12/1.18 | (13) p2 & p1
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (13) yields:
% 2.12/1.18 | (14) p2
% 2.12/1.18 | (5) p1
% 2.12/1.18 |
% 2.12/1.18 | Using (5) and (19) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 |-Branch two:
% 2.12/1.18 | (17) ~ p2 & ~ p1
% 2.12/1.18 |
% 2.12/1.18 | Applying alpha-rule on (17) yields:
% 2.12/1.18 | (12) ~ p2
% 2.12/1.18 | (19) ~ p1
% 2.12/1.18 |
% 2.12/1.18 | Using (14) and (12) yields:
% 2.12/1.18 | (16) $false
% 2.12/1.18 |
% 2.12/1.18 |-The branch is then unsatisfiable
% 2.12/1.18 % SZS output end Proof for theBenchmark
% 2.12/1.18
% 2.12/1.18 573ms
%------------------------------------------------------------------------------