TSTP Solution File: SET924+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET924+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 00:23:12 EDT 2022
% Result : Theorem 1.77s 1.12s
% Output : Proof 2.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET924+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 15:34:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.59 (ePrincess v.1.0)
% 0.51/0.59
% 0.51/0.59 (c) Philipp Rümmer, 2009-2015
% 0.51/0.59 (c) Peter Backeman, 2014-2015
% 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.59 Bug reports to peter@backeman.se
% 0.51/0.59
% 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.59
% 0.51/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.24/0.91 Prover 0: Preprocessing ...
% 1.53/1.02 Prover 0: Constructing countermodel ...
% 1.77/1.12 Prover 0: proved (478ms)
% 1.77/1.12
% 1.77/1.12 No countermodel exists, formula is valid
% 1.77/1.12 % SZS status Theorem for theBenchmark
% 1.77/1.12
% 1.77/1.12 Generating proof ... found it (size 14)
% 2.32/1.26
% 2.32/1.26 % SZS output start Proof for theBenchmark
% 2.32/1.26 Assumed formulas after preprocessing and simplification:
% 2.32/1.26 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (singleton(v0) = v2 & set_difference(v2, v1) = v3 & empty(v5) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = v9) | in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_difference(v9, v8) = v7) | ~ (set_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (singleton(v6) = v8) | ~ (set_difference(v8, v7) = v8) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)) & ((v3 = v2 & in(v0, v1)) | ( ~ (v3 = v2) & ~ in(v0, v1))))
% 2.38/1.30 | 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:
% 2.38/1.30 | (1) singleton(all_0_5_5) = all_0_3_3 & set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ((all_0_2_2 = all_0_3_3 & in(all_0_5_5, all_0_4_4)) | ( ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_5_5, all_0_4_4)))
% 2.38/1.30 |
% 2.38/1.30 | Applying alpha-rule on (1) yields:
% 2.38/1.30 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | in(v0, v1))
% 2.38/1.31 | (3) singleton(all_0_5_5) = all_0_3_3
% 2.38/1.31 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.38/1.31 | (5) (all_0_2_2 = all_0_3_3 & in(all_0_5_5, all_0_4_4)) | ( ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_5_5, all_0_4_4))
% 2.38/1.31 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.38/1.31 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ in(v0, v1))
% 2.38/1.31 | (8) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.38/1.31 | (9) ~ empty(all_0_1_1)
% 2.38/1.31 | (10) empty(all_0_0_0)
% 2.38/1.31 | (11) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 2.38/1.31 |
% 2.38/1.31 | Instantiating formula (2) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 2.38/1.31 | (12) all_0_2_2 = all_0_3_3 | in(all_0_5_5, all_0_4_4)
% 2.38/1.31 |
% 2.38/1.31 +-Applying beta-rule and splitting (5), into two cases.
% 2.38/1.31 |-Branch one:
% 2.38/1.31 | (13) all_0_2_2 = all_0_3_3 & in(all_0_5_5, all_0_4_4)
% 2.38/1.31 |
% 2.38/1.31 | Applying alpha-rule on (13) yields:
% 2.38/1.31 | (14) all_0_2_2 = all_0_3_3
% 2.38/1.31 | (15) in(all_0_5_5, all_0_4_4)
% 2.38/1.31 |
% 2.38/1.31 | From (14) and (11) follows:
% 2.38/1.31 | (16) set_difference(all_0_3_3, all_0_4_4) = all_0_3_3
% 2.38/1.31 |
% 2.38/1.31 | Instantiating formula (7) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, set_difference(all_0_3_3, all_0_4_4) = all_0_3_3, in(all_0_5_5, all_0_4_4), yields:
% 2.38/1.31 | (17) $false
% 2.38/1.31 |
% 2.38/1.31 |-The branch is then unsatisfiable
% 2.38/1.31 |-Branch two:
% 2.38/1.31 | (18) ~ (all_0_2_2 = all_0_3_3) & ~ in(all_0_5_5, all_0_4_4)
% 2.38/1.31 |
% 2.38/1.31 | Applying alpha-rule on (18) yields:
% 2.38/1.31 | (19) ~ (all_0_2_2 = all_0_3_3)
% 2.38/1.31 | (20) ~ in(all_0_5_5, all_0_4_4)
% 2.38/1.31 |
% 2.38/1.32 +-Applying beta-rule and splitting (12), into two cases.
% 2.38/1.32 |-Branch one:
% 2.38/1.32 | (15) in(all_0_5_5, all_0_4_4)
% 2.38/1.32 |
% 2.38/1.32 | Using (15) and (20) yields:
% 2.38/1.32 | (17) $false
% 2.38/1.32 |
% 2.38/1.32 |-The branch is then unsatisfiable
% 2.38/1.32 |-Branch two:
% 2.38/1.32 | (20) ~ in(all_0_5_5, all_0_4_4)
% 2.38/1.32 | (14) all_0_2_2 = all_0_3_3
% 2.38/1.32 |
% 2.38/1.32 | Equations (14) can reduce 19 to:
% 2.38/1.32 | (25) $false
% 2.38/1.32 |
% 2.38/1.32 |-The branch is then unsatisfiable
% 2.38/1.32 % SZS output end Proof for theBenchmark
% 2.38/1.32
% 2.38/1.32 719ms
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