TSTP Solution File: SYN922+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 05:05:52 EDT 2022
% Result : Theorem 1.86s 1.11s
% Output : Proof 2.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN922+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n017.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
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 01:30:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.87 Prover 0: Preprocessing ...
% 1.24/0.91 Prover 0: Warning: ignoring some quantifiers
% 1.24/0.93 Prover 0: Constructing countermodel ...
% 1.46/1.01 Prover 0: gave up
% 1.46/1.01 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.46/1.03 Prover 1: Preprocessing ...
% 1.70/1.07 Prover 1: Constructing countermodel ...
% 1.86/1.11 Prover 1: proved (96ms)
% 1.86/1.11
% 1.86/1.11 No countermodel exists, formula is valid
% 1.86/1.11 % SZS status Theorem for theBenchmark
% 1.86/1.11
% 1.86/1.11 Generating proof ... found it (size 20)
% 2.31/1.23
% 2.31/1.23 % SZS output start Proof for theBenchmark
% 2.31/1.23 Assumed formulas after preprocessing and simplification:
% 2.31/1.23 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (q(v5) = v4) | ~ (q(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (p(v5) = v4) | ~ (p(v5) = v3)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (q(v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (p(v3) = v4)) & (( ~ (v1 = 0) & q(v0) = v1) | ( ~ (v1 = 0) & p(v0) = v1) | (q(v0) = v2 & p(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 2.35/1.27 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.35/1.27 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1)) & (( ~ (all_0_1_1 = 0) & q(all_0_2_2) = all_0_1_1) | ( ~ (all_0_1_1 = 0) & p(all_0_2_2) = all_0_1_1) | (q(all_0_2_2) = all_0_0_0 & p(all_0_2_2) = all_0_1_1 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))
% 2.35/1.27 |
% 2.35/1.27 | Applying alpha-rule on (1) yields:
% 2.35/1.27 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (q(v0) = v1))
% 2.35/1.27 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 2.35/1.27 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 2.35/1.27 | (5) ( ~ (all_0_1_1 = 0) & q(all_0_2_2) = all_0_1_1) | ( ~ (all_0_1_1 = 0) & p(all_0_2_2) = all_0_1_1) | (q(all_0_2_2) = all_0_0_0 & p(all_0_2_2) = all_0_1_1 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))
% 2.35/1.27 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (p(v0) = v1))
% 2.35/1.27 |
% 2.35/1.27 +-Applying beta-rule and splitting (5), into two cases.
% 2.35/1.27 |-Branch one:
% 2.35/1.27 | (7) ( ~ (all_0_1_1 = 0) & q(all_0_2_2) = all_0_1_1) | ( ~ (all_0_1_1 = 0) & p(all_0_2_2) = all_0_1_1)
% 2.35/1.27 |
% 2.35/1.27 +-Applying beta-rule and splitting (7), into two cases.
% 2.35/1.27 |-Branch one:
% 2.35/1.27 | (8) ~ (all_0_1_1 = 0) & q(all_0_2_2) = all_0_1_1
% 2.35/1.27 |
% 2.35/1.27 | Applying alpha-rule on (8) yields:
% 2.35/1.27 | (9) ~ (all_0_1_1 = 0)
% 2.35/1.27 | (10) q(all_0_2_2) = all_0_1_1
% 2.35/1.28 |
% 2.35/1.28 | Instantiating formula (2) with all_0_1_1, all_0_2_2 and discharging atoms q(all_0_2_2) = all_0_1_1, yields:
% 2.35/1.28 | (11) all_0_1_1 = 0
% 2.35/1.28 |
% 2.35/1.28 | Equations (11) can reduce 9 to:
% 2.35/1.28 | (12) $false
% 2.35/1.28 |
% 2.35/1.28 |-The branch is then unsatisfiable
% 2.35/1.28 |-Branch two:
% 2.35/1.28 | (13) ~ (all_0_1_1 = 0) & p(all_0_2_2) = all_0_1_1
% 2.35/1.28 |
% 2.35/1.28 | Applying alpha-rule on (13) yields:
% 2.35/1.28 | (9) ~ (all_0_1_1 = 0)
% 2.35/1.28 | (15) p(all_0_2_2) = all_0_1_1
% 2.35/1.28 |
% 2.35/1.28 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_1_1, yields:
% 2.35/1.28 | (11) all_0_1_1 = 0
% 2.35/1.28 |
% 2.35/1.28 | Equations (11) can reduce 9 to:
% 2.35/1.28 | (12) $false
% 2.35/1.28 |
% 2.35/1.28 |-The branch is then unsatisfiable
% 2.35/1.28 |-Branch two:
% 2.35/1.28 | (18) q(all_0_2_2) = all_0_0_0 & p(all_0_2_2) = all_0_1_1 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))
% 2.35/1.28 |
% 2.35/1.28 | Applying alpha-rule on (18) yields:
% 2.35/1.28 | (19) q(all_0_2_2) = all_0_0_0
% 2.35/1.28 | (15) p(all_0_2_2) = all_0_1_1
% 2.35/1.28 | (21) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)
% 2.35/1.28 |
% 2.35/1.28 | Instantiating formula (2) with all_0_0_0, all_0_2_2 and discharging atoms q(all_0_2_2) = all_0_0_0, yields:
% 2.35/1.28 | (22) all_0_0_0 = 0
% 2.35/1.28 |
% 2.35/1.28 | Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_1_1, yields:
% 2.35/1.28 | (11) all_0_1_1 = 0
% 2.35/1.28 |
% 2.35/1.28 +-Applying beta-rule and splitting (21), into two cases.
% 2.35/1.28 |-Branch one:
% 2.35/1.28 | (24) ~ (all_0_0_0 = 0)
% 2.35/1.28 |
% 2.35/1.28 | Equations (22) can reduce 24 to:
% 2.35/1.28 | (12) $false
% 2.35/1.28 |
% 2.35/1.28 |-The branch is then unsatisfiable
% 2.35/1.28 |-Branch two:
% 2.35/1.28 | (22) all_0_0_0 = 0
% 2.35/1.28 | (9) ~ (all_0_1_1 = 0)
% 2.35/1.28 |
% 2.35/1.28 | Equations (11) can reduce 9 to:
% 2.35/1.28 | (12) $false
% 2.35/1.28 |
% 2.35/1.28 |-The branch is then unsatisfiable
% 2.35/1.28 % SZS output end Proof for theBenchmark
% 2.35/1.28
% 2.35/1.28 687ms
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