TSTP Solution File: SET910+1 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SET910+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 00:23:05 EDT 2022
% Result : Theorem 1.80s 1.08s
% 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 : SET910+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 02:05:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.57 ____ _
% 0.49/0.57 ___ / __ \_____(_)___ ________ __________
% 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.57
% 0.49/0.57 A Theorem Prover for First-Order Logic
% 0.49/0.57 (ePrincess v.1.0)
% 0.49/0.57
% 0.49/0.57 (c) Philipp Rümmer, 2009-2015
% 0.49/0.57 (c) Peter Backeman, 2014-2015
% 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57 Bug reports to peter@backeman.se
% 0.49/0.57
% 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57
% 0.49/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.22/0.87 Prover 0: Preprocessing ...
% 1.52/1.00 Prover 0: Constructing countermodel ...
% 1.80/1.08 Prover 0: proved (457ms)
% 1.80/1.08
% 1.80/1.08 No countermodel exists, formula is valid
% 1.80/1.08 % SZS status Theorem for theBenchmark
% 1.80/1.08
% 1.80/1.08 Generating proof ... found it (size 4)
% 2.14/1.23
% 2.14/1.23 % SZS output start Proof for theBenchmark
% 2.14/1.23 Assumed formulas after preprocessing and simplification:
% 2.30/1.23 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (singleton(v1) = v2 & set_intersection2(v0, v2) = v2 & empty(v4) & ~ empty(v3) & ~ in(v1, v0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_intersection2(v8, v7) = v6) | ~ (set_intersection2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | ~ (set_intersection2(v5, v7) = v7) | in(v6, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v6, v5) = v7) | set_intersection2(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_intersection2(v5, v6) = v7) | set_intersection2(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_intersection2(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ in(v6, v5) | ~ in(v5, v6)))
% 2.30/1.27 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.30/1.27 | (1) singleton(all_0_3_3) = all_0_2_2 & set_intersection2(all_0_4_4, all_0_2_2) = all_0_2_2 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ in(all_0_3_3, all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_intersection2(v0, v2) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.30/1.27 |
% 2.30/1.27 | Applying alpha-rule on (1) yields:
% 2.30/1.27 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 2.30/1.27 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 2.38/1.27 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 2.38/1.27 | (5) ~ in(all_0_3_3, all_0_4_4)
% 2.38/1.27 | (6) empty(all_0_0_0)
% 2.38/1.27 | (7) set_intersection2(all_0_4_4, all_0_2_2) = all_0_2_2
% 2.38/1.27 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_intersection2(v0, v2) = v2) | in(v1, v0))
% 2.38/1.27 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 2.38/1.28 | (10) ~ empty(all_0_1_1)
% 2.38/1.28 | (11) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.38/1.28 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.38/1.28 | (13) singleton(all_0_3_3) = all_0_2_2
% 2.38/1.28 |
% 2.38/1.28 | Instantiating formula (8) 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, set_intersection2(all_0_4_4, all_0_2_2) = all_0_2_2, ~ in(all_0_3_3, all_0_4_4), yields:
% 2.38/1.28 | (14) $false
% 2.38/1.28 |
% 2.38/1.28 |-The branch is then unsatisfiable
% 2.38/1.28 % SZS output end Proof for theBenchmark
% 2.38/1.28
% 2.38/1.28 694ms
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