TSTP Solution File: SYN063+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN063+1 : 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 04:59:34 EDT 2022
% Result : Theorem 1.93s 1.14s
% Output : Proof 2.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Tue Jul 12 03:11:09 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.56/0.58 ____ _
% 0.56/0.58 ___ / __ \_____(_)___ ________ __________
% 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.58
% 0.56/0.58 A Theorem Prover for First-Order Logic
% 0.56/0.58 (ePrincess v.1.0)
% 0.56/0.58
% 0.56/0.58 (c) Philipp Rümmer, 2009-2015
% 0.56/0.58 (c) Peter Backeman, 2014-2015
% 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58 Bug reports to peter@backeman.se
% 0.56/0.58
% 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58
% 0.56/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.28/0.87 Prover 0: Preprocessing ...
% 1.36/0.93 Prover 0: Warning: ignoring some quantifiers
% 1.47/0.94 Prover 0: Constructing countermodel ...
% 1.60/1.03 Prover 0: gave up
% 1.60/1.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.60/1.04 Prover 1: Preprocessing ...
% 1.93/1.09 Prover 1: Constructing countermodel ...
% 1.93/1.13 Prover 1: proved (108ms)
% 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 11)
% 2.43/1.28
% 2.43/1.28 % SZS output start Proof for theBenchmark
% 2.43/1.28 Assumed formulas after preprocessing and simplification:
% 2.43/1.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (big_p(c) = v2 & big_p(b) = v1 & big_p(a) = v0 & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (big_p(v7) = v6) | ~ (big_p(v7) = v5)) & ((v0 = 0 & ~ (v4 = 0) & ~ (v2 = 0) & ~ (v1 = 0) & big_p(v3) = v4 & ! [v5] : ! [v6] : (v6 = 0 | ~ (big_p(v5) = v6))) | (v0 = 0 & ~ (v2 = 0) & big_p(v3) = v4 & ! [v5] : ! [v6] : ( ~ (v1 = 0) | ~ (big_p(v5) = v6)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (big_p(v5) = v6)) & ( ~ (v4 = 0) | v1 = 0))))
% 2.43/1.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.43/1.31 | (1) big_p(c) = all_0_2_2 & big_p(b) = all_0_3_3 & big_p(a) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ((all_0_4_4 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | (all_0_4_4 = 0 & ~ (all_0_2_2 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_3_3 = 0) | ~ (big_p(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ( ~ (all_0_0_0 = 0) | all_0_3_3 = 0)))
% 2.43/1.31 |
% 2.43/1.31 | Applying alpha-rule on (1) yields:
% 2.43/1.31 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0))
% 2.43/1.31 | (3) big_p(a) = all_0_4_4
% 2.43/1.31 | (4) big_p(b) = all_0_3_3
% 2.43/1.31 | (5) big_p(c) = all_0_2_2
% 2.43/1.31 | (6) (all_0_4_4 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))) | (all_0_4_4 = 0 & ~ (all_0_2_2 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_3_3 = 0) | ~ (big_p(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ( ~ (all_0_0_0 = 0) | all_0_3_3 = 0))
% 2.43/1.31 |
% 2.43/1.31 +-Applying beta-rule and splitting (6), into two cases.
% 2.43/1.31 |-Branch one:
% 2.43/1.31 | (7) all_0_4_4 = 0 & ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_3_3 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 2.43/1.32 |
% 2.43/1.32 | Applying alpha-rule on (7) yields:
% 2.43/1.32 | (8) ~ (all_0_3_3 = 0)
% 2.43/1.32 | (9) big_p(all_0_1_1) = all_0_0_0
% 2.43/1.32 | (10) ~ (all_0_2_2 = 0)
% 2.43/1.32 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 2.43/1.32 | (12) all_0_4_4 = 0
% 2.43/1.32 | (13) ~ (all_0_0_0 = 0)
% 2.43/1.32 |
% 2.43/1.32 | Instantiating formula (11) with all_0_3_3, b and discharging atoms big_p(b) = all_0_3_3, yields:
% 2.43/1.32 | (14) all_0_3_3 = 0
% 2.43/1.32 |
% 2.43/1.32 | Equations (14) can reduce 8 to:
% 2.43/1.32 | (15) $false
% 2.43/1.32 |
% 2.43/1.32 |-The branch is then unsatisfiable
% 2.43/1.32 |-Branch two:
% 2.43/1.32 | (16) all_0_4_4 = 0 & ~ (all_0_2_2 = 0) & big_p(all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ( ~ (all_0_3_3 = 0) | ~ (big_p(v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1)) & ( ~ (all_0_0_0 = 0) | all_0_3_3 = 0)
% 2.43/1.32 |
% 2.43/1.32 | Applying alpha-rule on (16) yields:
% 2.43/1.32 | (9) big_p(all_0_1_1) = all_0_0_0
% 2.43/1.32 | (18) ~ (all_0_0_0 = 0) | all_0_3_3 = 0
% 2.43/1.32 | (10) ~ (all_0_2_2 = 0)
% 2.43/1.32 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_p(v0) = v1))
% 2.43/1.32 | (21) ! [v0] : ! [v1] : ( ~ (all_0_3_3 = 0) | ~ (big_p(v0) = v1))
% 2.43/1.32 | (12) all_0_4_4 = 0
% 2.43/1.32 |
% 2.43/1.32 | Instantiating formula (11) with all_0_2_2, c and discharging atoms big_p(c) = all_0_2_2, yields:
% 2.43/1.32 | (23) all_0_2_2 = 0
% 2.43/1.32 |
% 2.43/1.32 | Equations (23) can reduce 10 to:
% 2.43/1.32 | (15) $false
% 2.43/1.32 |
% 2.43/1.32 |-The branch is then unsatisfiable
% 2.43/1.32 % SZS output end Proof for theBenchmark
% 2.43/1.32
% 2.43/1.32 728ms
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