TSTP Solution File: SEU160+3 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 : Tue Jul 19 08:47:08 EDT 2022
% Result : Theorem 1.56s 0.97s
% Output : Proof 1.96s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 19 07:51:02 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.49 ____ _
% 0.14/0.49 ___ / __ \_____(_)___ ________ __________
% 0.14/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.49
% 0.14/0.49 A Theorem Prover for First-Order Logic
% 0.14/0.49 (ePrincess v.1.0)
% 0.14/0.49
% 0.14/0.49 (c) Philipp Rümmer, 2009-2015
% 0.14/0.49 (c) Peter Backeman, 2014-2015
% 0.14/0.49 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.49 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.49 Bug reports to peter@backeman.se
% 0.14/0.49
% 0.14/0.49 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.49
% 0.14/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.01/0.76 Prover 0: Preprocessing ...
% 1.26/0.85 Prover 0: Warning: ignoring some quantifiers
% 1.26/0.87 Prover 0: Constructing countermodel ...
% 1.56/0.97 Prover 0: proved (431ms)
% 1.56/0.97
% 1.56/0.97 No countermodel exists, formula is valid
% 1.56/0.97 % SZS status Theorem for theBenchmark
% 1.56/0.97
% 1.56/0.97 Generating proof ... Warning: ignoring some quantifiers
% 1.96/1.10 found it (size 21)
% 1.96/1.10
% 1.96/1.10 % SZS output start Proof for theBenchmark
% 1.96/1.10 Assumed formulas after preprocessing and simplification:
% 1.96/1.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (singleton(v1) = v2 & empty(v4) & empty(empty_set) & ~ empty(v3) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | v5 = empty_set | ~ (singleton(v6) = v7) | ~ subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ( ~ (singleton(v6) = v5) | subset(v5, v5)) & ! [v5] : ! [v6] : ( ~ (singleton(v5) = v6) | subset(empty_set, v6)) & ? [v5] : subset(v5, v5) & (( ~ (v2 = v0) & ~ (v0 = empty_set) & subset(v0, v2)) | ( ~ subset(v0, v2) & (v2 = v0 | v0 = empty_set))))
% 1.96/1.14 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 1.96/1.14 | (1) singleton(all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ? [v0] : subset(v0, v0) & (( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set)))
% 1.96/1.14 |
% 1.96/1.14 | Applying alpha-rule on (1) yields:
% 1.96/1.14 | (2) singleton(all_0_3_3) = all_0_2_2
% 1.96/1.14 | (3) ( ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set))
% 1.96/1.14 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 1.96/1.14 | (5) ? [v0] : subset(v0, v0)
% 1.96/1.14 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 1.96/1.14 | (7) ~ empty(all_0_1_1)
% 1.96/1.14 | (8) empty(all_0_0_0)
% 1.96/1.14 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 1.96/1.14 | (10) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 1.96/1.14 | (11) empty(empty_set)
% 1.96/1.14 |
% 1.96/1.14 | Instantiating formula (6) with all_0_3_3, all_0_2_2 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields:
% 1.96/1.15 | (12) subset(all_0_2_2, all_0_2_2)
% 1.96/1.15 |
% 1.96/1.15 | Instantiating formula (10) with all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields:
% 1.96/1.15 | (13) subset(empty_set, all_0_2_2)
% 1.96/1.15 |
% 1.96/1.15 +-Applying beta-rule and splitting (3), into two cases.
% 1.96/1.15 |-Branch one:
% 1.96/1.15 | (14) ~ (all_0_2_2 = all_0_4_4) & ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)
% 1.96/1.15 |
% 1.96/1.15 | Applying alpha-rule on (14) yields:
% 1.96/1.15 | (15) ~ (all_0_2_2 = all_0_4_4)
% 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set)
% 1.96/1.15 | (17) subset(all_0_4_4, all_0_2_2)
% 1.96/1.15 |
% 1.96/1.15 | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_3_3) = all_0_2_2, subset(all_0_4_4, all_0_2_2), yields:
% 1.96/1.15 | (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 1.96/1.15 |
% 1.96/1.15 +-Applying beta-rule and splitting (18), into two cases.
% 1.96/1.15 |-Branch one:
% 1.96/1.15 | (19) all_0_4_4 = empty_set
% 1.96/1.15 |
% 1.96/1.15 | Equations (19) can reduce 16 to:
% 1.96/1.15 | (20) $false
% 1.96/1.15 |
% 1.96/1.15 |-The branch is then unsatisfiable
% 1.96/1.15 |-Branch two:
% 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set)
% 1.96/1.15 | (22) all_0_2_2 = all_0_4_4
% 1.96/1.15 |
% 1.96/1.15 | Equations (22) can reduce 15 to:
% 1.96/1.15 | (20) $false
% 1.96/1.15 |
% 1.96/1.15 |-The branch is then unsatisfiable
% 1.96/1.15 |-Branch two:
% 1.96/1.15 | (24) ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set)
% 1.96/1.15 |
% 1.96/1.15 | Applying alpha-rule on (24) yields:
% 1.96/1.15 | (25) ~ subset(all_0_4_4, all_0_2_2)
% 1.96/1.15 | (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 1.96/1.15 |
% 1.96/1.15 +-Applying beta-rule and splitting (18), into two cases.
% 1.96/1.15 |-Branch one:
% 1.96/1.15 | (19) all_0_4_4 = empty_set
% 1.96/1.15 |
% 1.96/1.15 | From (19) and (25) follows:
% 1.96/1.15 | (28) ~ subset(empty_set, all_0_2_2)
% 1.96/1.15 |
% 1.96/1.15 | Using (13) and (28) yields:
% 1.96/1.15 | (29) $false
% 1.96/1.15 |
% 1.96/1.15 |-The branch is then unsatisfiable
% 1.96/1.15 |-Branch two:
% 1.96/1.15 | (16) ~ (all_0_4_4 = empty_set)
% 1.96/1.15 | (22) all_0_2_2 = all_0_4_4
% 1.96/1.15 |
% 1.96/1.15 | From (22)(22) and (12) follows:
% 1.96/1.15 | (32) subset(all_0_4_4, all_0_4_4)
% 1.96/1.15 |
% 1.96/1.15 | From (22) and (25) follows:
% 1.96/1.15 | (33) ~ subset(all_0_4_4, all_0_4_4)
% 1.96/1.15 |
% 1.96/1.15 | Using (32) and (33) yields:
% 1.96/1.15 | (29) $false
% 1.96/1.15 |
% 1.96/1.15 |-The branch is then unsatisfiable
% 1.96/1.15 % SZS output end Proof for theBenchmark
% 1.96/1.15
% 1.96/1.15 657ms
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