TSTP Solution File: SYN051+1 by ePrincess---1.0
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% File : ePrincess---1.0
% Problem : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 04:59:24 EDT 2022
% Result : Theorem 1.98s 1.14s
% Output : Proof 2.50s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jul 12 03:02:45 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.47/0.62 ____ _
% 0.47/0.62 ___ / __ \_____(_)___ ________ __________
% 0.47/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.62
% 0.47/0.62 A Theorem Prover for First-Order Logic
% 0.47/0.62 (ePrincess v.1.0)
% 0.47/0.62
% 0.47/0.62 (c) Philipp Rümmer, 2009-2015
% 0.47/0.62 (c) Peter Backeman, 2014-2015
% 0.47/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.62 Bug reports to peter@backeman.se
% 0.47/0.62
% 0.47/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.62
% 0.47/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.89 Prover 0: Preprocessing ...
% 1.40/0.94 Prover 0: Warning: ignoring some quantifiers
% 1.40/0.95 Prover 0: Constructing countermodel ...
% 1.63/1.04 Prover 0: gave up
% 1.63/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.63/1.05 Prover 1: Preprocessing ...
% 1.80/1.09 Prover 1: Constructing countermodel ...
% 1.98/1.14 Prover 1: proved (101ms)
% 1.98/1.14
% 1.98/1.14 No countermodel exists, formula is valid
% 1.98/1.14 % SZS status Theorem for theBenchmark
% 1.98/1.14
% 1.98/1.14 Generating proof ... found it (size 15)
% 2.34/1.28
% 2.34/1.28 % SZS output start Proof for theBenchmark
% 2.34/1.28 Assumed formulas after preprocessing and simplification:
% 2.34/1.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (big_f(v2) = v3 & big_f(v0) = v1 & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (big_f(v6) = v5) | ~ (big_f(v6) = v4)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (big_f(v4) = v5) | p) & ! [v4] : ( ~ (big_f(v4) = 0) | ~ p) & ( ~ (v1 = 0) | p) & (v3 = 0 | ~ p))
% 2.34/1.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.34/1.31 | (1) big_f(all_0_1_1) = all_0_0_0 & big_f(all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | p) & ! [v0] : ( ~ (big_f(v0) = 0) | ~ p) & ( ~ (all_0_2_2 = 0) | p) & (all_0_0_0 = 0 | ~ p)
% 2.34/1.31 |
% 2.34/1.31 | Applying alpha-rule on (1) yields:
% 2.34/1.32 | (2) big_f(all_0_1_1) = all_0_0_0
% 2.34/1.32 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 2.34/1.32 | (4) ! [v0] : ( ~ (big_f(v0) = 0) | ~ p)
% 2.34/1.32 | (5) big_f(all_0_3_3) = all_0_2_2
% 2.34/1.32 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_f(v0) = v1) | p)
% 2.34/1.32 | (7) ~ (all_0_2_2 = 0) | p
% 2.34/1.32 | (8) all_0_0_0 = 0 | ~ p
% 2.34/1.32 |
% 2.34/1.32 | Instantiating formula (6) with all_0_2_2, all_0_3_3 and discharging atoms big_f(all_0_3_3) = all_0_2_2, yields:
% 2.34/1.32 | (9) all_0_2_2 = 0 | p
% 2.34/1.32 |
% 2.34/1.32 +-Applying beta-rule and splitting (8), into two cases.
% 2.34/1.32 |-Branch one:
% 2.34/1.32 | (10) ~ p
% 2.34/1.32 |
% 2.34/1.32 +-Applying beta-rule and splitting (7), into two cases.
% 2.34/1.32 |-Branch one:
% 2.34/1.32 | (11) p
% 2.34/1.32 |
% 2.34/1.32 | Using (11) and (10) yields:
% 2.34/1.32 | (12) $false
% 2.34/1.32 |
% 2.50/1.32 |-The branch is then unsatisfiable
% 2.50/1.32 |-Branch two:
% 2.50/1.32 | (10) ~ p
% 2.50/1.32 | (14) ~ (all_0_2_2 = 0)
% 2.50/1.32 |
% 2.50/1.32 +-Applying beta-rule and splitting (9), into two cases.
% 2.50/1.32 |-Branch one:
% 2.50/1.32 | (11) p
% 2.50/1.32 |
% 2.50/1.32 | Using (11) and (10) yields:
% 2.50/1.32 | (12) $false
% 2.50/1.32 |
% 2.50/1.32 |-The branch is then unsatisfiable
% 2.50/1.32 |-Branch two:
% 2.50/1.32 | (10) ~ p
% 2.50/1.32 | (18) all_0_2_2 = 0
% 2.50/1.32 |
% 2.50/1.32 | Equations (18) can reduce 14 to:
% 2.50/1.32 | (19) $false
% 2.50/1.32 |
% 2.50/1.32 |-The branch is then unsatisfiable
% 2.50/1.32 |-Branch two:
% 2.50/1.32 | (11) p
% 2.50/1.32 | (21) all_0_0_0 = 0
% 2.50/1.32 |
% 2.50/1.32 | From (21) and (2) follows:
% 2.50/1.32 | (22) big_f(all_0_1_1) = 0
% 2.50/1.32 |
% 2.50/1.32 | Instantiating formula (4) with all_0_1_1 and discharging atoms big_f(all_0_1_1) = 0, p, yields:
% 2.50/1.32 | (12) $false
% 2.50/1.32 |
% 2.50/1.32 |-The branch is then unsatisfiable
% 2.50/1.32 % SZS output end Proof for theBenchmark
% 2.50/1.33
% 2.50/1.33 692ms
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