TSTP Solution File: SEU148+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 08:46:59 EDT 2022
% Result : Theorem 2.14s 1.19s
% Output : Proof 2.84s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 12:48:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.55/0.60 ____ _
% 0.55/0.60 ___ / __ \_____(_)___ ________ __________
% 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.60
% 0.55/0.60 A Theorem Prover for First-Order Logic
% 0.55/0.60 (ePrincess v.1.0)
% 0.55/0.60
% 0.55/0.60 (c) Philipp Rümmer, 2009-2015
% 0.55/0.60 (c) Peter Backeman, 2014-2015
% 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.60 Bug reports to peter@backeman.se
% 0.55/0.60
% 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.60
% 0.55/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.92 Prover 0: Preprocessing ...
% 1.63/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.63/1.06 Prover 0: Constructing countermodel ...
% 2.14/1.19 Prover 0: proved (543ms)
% 2.14/1.19
% 2.14/1.19 No countermodel exists, formula is valid
% 2.14/1.19 % SZS status Theorem for theBenchmark
% 2.14/1.19
% 2.14/1.19 Generating proof ... Warning: ignoring some quantifiers
% 2.65/1.33 found it (size 12)
% 2.65/1.33
% 2.65/1.33 % SZS output start Proof for theBenchmark
% 2.65/1.33 Assumed formulas after preprocessing and simplification:
% 2.65/1.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v1 = v0) & singleton(v1) = v3 & singleton(v0) = v2 & subset(v2, v3) & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | v6 = empty_set | ~ (singleton(v7) = v8) | ~ subset(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v6) = v7) | ~ in(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ? [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v7) = v8) | ? [v9] : (( ~ (v9 = v7) | ~ in(v7, v6)) & (v9 = v7 | in(v9, v6)))) & ! [v6] : ! [v7] : ( ~ (singleton(v7) = v6) | subset(v6, v6)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | subset(empty_set, v7)) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)) & ! [v6] : ~ (singleton(v6) = empty_set) & ? [v6] : subset(v6, v6))
% 2.65/1.37 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 2.65/1.37 | (1) ~ (all_0_4_4 = all_0_5_5) & singleton(all_0_4_4) = all_0_2_2 & singleton(all_0_5_5) = all_0_3_3 & subset(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] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ~ (singleton(v0) = empty_set) & ? [v0] : subset(v0, v0)
% 2.65/1.37 |
% 2.65/1.37 | Applying alpha-rule on (1) yields:
% 2.65/1.37 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.65/1.37 | (3) singleton(all_0_5_5) = all_0_3_3
% 2.65/1.37 | (4) singleton(all_0_4_4) = all_0_2_2
% 2.65/1.37 | (5) ~ (all_0_4_4 = all_0_5_5)
% 2.65/1.37 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.65/1.38 | (7) subset(all_0_3_3, all_0_2_2)
% 2.65/1.38 | (8) ~ empty(all_0_1_1)
% 2.65/1.38 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.65/1.38 | (10) ? [v0] : subset(v0, v0)
% 2.65/1.38 | (11) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 2.65/1.38 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 2.84/1.38 | (13) ! [v0] : ~ (singleton(v0) = empty_set)
% 2.84/1.38 | (14) empty(all_0_0_0)
% 2.84/1.38 | (15) empty(empty_set)
% 2.84/1.38 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 2.84/1.38 | (17) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.84/1.38 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.84/1.38 |
% 2.84/1.38 | Instantiating formula (12) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms singleton(all_0_4_4) = all_0_2_2, subset(all_0_3_3, all_0_2_2), yields:
% 2.84/1.38 | (19) all_0_2_2 = all_0_3_3 | all_0_3_3 = empty_set
% 2.84/1.38 |
% 2.84/1.38 | Instantiating formula (6) with all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, yields:
% 2.84/1.38 | (20) in(all_0_4_4, all_0_2_2)
% 2.84/1.38 |
% 2.84/1.38 +-Applying beta-rule and splitting (19), into two cases.
% 2.84/1.38 |-Branch one:
% 2.84/1.38 | (21) all_0_3_3 = empty_set
% 2.84/1.38 |
% 2.84/1.38 | From (21) and (3) follows:
% 2.84/1.38 | (22) singleton(all_0_5_5) = empty_set
% 2.84/1.38 |
% 2.84/1.38 | Instantiating formula (13) with all_0_5_5 and discharging atoms singleton(all_0_5_5) = empty_set, yields:
% 2.84/1.38 | (23) $false
% 2.84/1.38 |
% 2.84/1.38 |-The branch is then unsatisfiable
% 2.84/1.38 |-Branch two:
% 2.84/1.38 | (24) ~ (all_0_3_3 = empty_set)
% 2.84/1.38 | (25) all_0_2_2 = all_0_3_3
% 2.84/1.38 |
% 2.84/1.38 | From (25) and (20) follows:
% 2.84/1.38 | (26) in(all_0_4_4, all_0_3_3)
% 2.84/1.38 |
% 2.84/1.39 | Instantiating formula (18) with all_0_4_4, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, in(all_0_4_4, all_0_3_3), yields:
% 2.84/1.39 | (27) all_0_4_4 = all_0_5_5
% 2.84/1.39 |
% 2.84/1.39 | Equations (27) can reduce 5 to:
% 2.84/1.39 | (28) $false
% 2.84/1.39 |
% 2.84/1.39 |-The branch is then unsatisfiable
% 2.84/1.39 % SZS output end Proof for theBenchmark
% 2.84/1.39
% 2.84/1.39 778ms
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