TSTP Solution File: SYN376+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 05:01:55 EDT 2022
% Result : Theorem 1.93s 1.14s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jul 11 19:19:44 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.54/0.55 ____ _
% 0.54/0.55 ___ / __ \_____(_)___ ________ __________
% 0.54/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.55
% 0.54/0.55 A Theorem Prover for First-Order Logic
% 0.54/0.56 (ePrincess v.1.0)
% 0.54/0.56
% 0.54/0.56 (c) Philipp Rümmer, 2009-2015
% 0.54/0.56 (c) Peter Backeman, 2014-2015
% 0.54/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.56 Bug reports to peter@backeman.se
% 0.54/0.56
% 0.54/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.56
% 0.54/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.23/0.86 Prover 0: Preprocessing ...
% 1.29/0.90 Prover 0: Warning: ignoring some quantifiers
% 1.29/0.92 Prover 0: Constructing countermodel ...
% 1.48/1.01 Prover 0: gave up
% 1.48/1.01 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.73/1.03 Prover 1: Preprocessing ...
% 1.93/1.09 Prover 1: Constructing countermodel ...
% 1.93/1.14 Prover 1: proved (125ms)
% 1.93/1.14
% 1.93/1.14 No countermodel exists, formula is valid
% 1.93/1.14 % SZS status Theorem for theBenchmark
% 1.93/1.14
% 1.93/1.14 Generating proof ... found it (size 14)
% 2.44/1.27
% 2.44/1.27 % SZS output start Proof for theBenchmark
% 2.44/1.27 Assumed formulas after preprocessing and simplification:
% 2.44/1.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = 0) & big_p(v3) = v4 & big_p(v1) = v2 & big_p(v0) = 0 & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_p(v7) = v6) | ~ (big_p(v7) = v5)) & ! [v5] : ! [v6] : ( ~ (v4 = 0) | v6 = 0 | ~ (big_p(v5) = v6)) & ! [v5] : (v4 = 0 | ~ (big_p(v5) = 0)))
% 2.44/1.29 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.44/1.29 | (1) ~ (all_0_2_2 = 0) & big_p(all_0_1_1) = all_0_0_0 & big_p(all_0_3_3) = all_0_2_2 & big_p(all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1)) & ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0))
% 2.44/1.30 |
% 2.44/1.30 | Applying alpha-rule on (1) yields:
% 2.44/1.30 | (2) big_p(all_0_1_1) = all_0_0_0
% 2.44/1.30 | (3) ! [v0] : ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 | ~ (big_p(v0) = v1))
% 2.44/1.30 | (4) ! [v0] : (all_0_0_0 = 0 | ~ (big_p(v0) = 0))
% 2.44/1.30 | (5) ~ (all_0_2_2 = 0)
% 2.44/1.30 | (6) big_p(all_0_4_4) = 0
% 2.44/1.30 | (7) big_p(all_0_3_3) = all_0_2_2
% 2.44/1.30 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.44/1.30 |
% 2.44/1.30 | Instantiating formula (8) with all_0_4_4, 0, all_0_0_0 and discharging atoms big_p(all_0_4_4) = 0, yields:
% 2.44/1.30 | (9) all_0_0_0 = 0 | ~ (big_p(all_0_4_4) = all_0_0_0)
% 2.44/1.30 |
% 2.44/1.30 | Instantiating formula (4) with all_0_4_4 and discharging atoms big_p(all_0_4_4) = 0, yields:
% 2.44/1.30 | (10) all_0_0_0 = 0
% 2.44/1.30 |
% 2.44/1.30 +-Applying beta-rule and splitting (9), into two cases.
% 2.44/1.30 |-Branch one:
% 2.44/1.30 | (11) ~ (big_p(all_0_4_4) = all_0_0_0)
% 2.44/1.30 |
% 2.44/1.30 | From (10) and (11) follows:
% 2.44/1.30 | (12) ~ (big_p(all_0_4_4) = 0)
% 2.44/1.30 |
% 2.44/1.30 | Using (6) and (12) yields:
% 2.44/1.30 | (13) $false
% 2.44/1.30 |
% 2.44/1.30 |-The branch is then unsatisfiable
% 2.44/1.30 |-Branch two:
% 2.44/1.30 | (14) big_p(all_0_4_4) = all_0_0_0
% 2.44/1.30 | (10) all_0_0_0 = 0
% 2.44/1.30 |
% 2.44/1.30 | Instantiating formula (3) with all_0_2_2, all_0_3_3 and discharging atoms big_p(all_0_3_3) = all_0_2_2, yields:
% 2.44/1.31 | (16) ~ (all_0_0_0 = 0) | all_0_2_2 = 0
% 2.44/1.31 |
% 2.44/1.31 +-Applying beta-rule and splitting (16), into two cases.
% 2.44/1.31 |-Branch one:
% 2.44/1.31 | (17) ~ (all_0_0_0 = 0)
% 2.44/1.31 |
% 2.44/1.31 | Equations (10) can reduce 17 to:
% 2.44/1.31 | (18) $false
% 2.44/1.31 |
% 2.44/1.31 |-The branch is then unsatisfiable
% 2.44/1.31 |-Branch two:
% 2.44/1.31 | (10) all_0_0_0 = 0
% 2.44/1.31 | (20) all_0_2_2 = 0
% 2.44/1.31 |
% 2.44/1.31 | Equations (20) can reduce 5 to:
% 2.44/1.31 | (18) $false
% 2.44/1.31 |
% 2.44/1.31 |-The branch is then unsatisfiable
% 2.44/1.31 % SZS output end Proof for theBenchmark
% 2.44/1.31
% 2.44/1.31 743ms
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