TSTP Solution File: SEU161+1 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 1.88s 1.27s
% Output : Proof 2.64s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n029.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 Jun 19 12:47:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.63/0.63 ____ _
% 0.63/0.63 ___ / __ \_____(_)___ ________ __________
% 0.63/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.63
% 0.63/0.63 A Theorem Prover for First-Order Logic
% 0.63/0.63 (ePrincess v.1.0)
% 0.63/0.63
% 0.63/0.63 (c) Philipp Rümmer, 2009-2015
% 0.63/0.63 (c) Peter Backeman, 2014-2015
% 0.63/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.63 Bug reports to peter@backeman.se
% 0.63/0.63
% 0.63/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.63
% 0.63/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/1.00 Prover 0: Preprocessing ...
% 1.56/1.16 Prover 0: Constructing countermodel ...
% 1.88/1.27 Prover 0: proved (567ms)
% 1.88/1.27
% 1.88/1.27 No countermodel exists, formula is valid
% 1.88/1.27 % SZS status Theorem for theBenchmark
% 1.88/1.27
% 1.88/1.27 Generating proof ... found it (size 5)
% 2.49/1.41
% 2.49/1.41 % SZS output start Proof for theBenchmark
% 2.49/1.41 Assumed formulas after preprocessing and simplification:
% 2.49/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v1) & singleton(v0) = v2 & set_union2(v2, v1) = v3 & in(v0, v1) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v4) = v6) | ~ (set_union2(v6, v5) = v7) | ~ in(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (set_union2(v7, v6) = v5) | ~ (set_union2(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v6) = v5) | ~ (singleton(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v5, v4) = v6) | set_union2(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (set_union2(v4, v5) = v6) | set_union2(v5, v4) = v6) & ! [v4] : ! [v5] : (v5 = v4 | ~ (set_union2(v4, v4) = v5)) & ! [v4] : ! [v5] : ( ~ in(v5, v4) | ~ in(v4, v5)))
% 2.64/1.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.64/1.47 | (1) ~ (all_0_0_0 = all_0_2_2) & singleton(all_0_3_3) = all_0_1_1 & set_union2(all_0_1_1, all_0_2_2) = all_0_0_0 & in(all_0_3_3, all_0_2_2) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.64/1.47 |
% 2.64/1.47 | Applying alpha-rule on (1) yields:
% 2.64/1.47 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.64/1.47 | (3) singleton(all_0_3_3) = all_0_1_1
% 2.64/1.47 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.64/1.47 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 2.64/1.48 | (6) ~ (all_0_0_0 = all_0_2_2)
% 2.64/1.48 | (7) in(all_0_3_3, all_0_2_2)
% 2.64/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.64/1.48 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.64/1.48 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.64/1.48 | (11) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.64/1.48 | (12) set_union2(all_0_1_1, all_0_2_2) = all_0_0_0
% 2.64/1.48 |
% 2.64/1.48 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_1_1, set_union2(all_0_1_1, all_0_2_2) = all_0_0_0, in(all_0_3_3, all_0_2_2), yields:
% 2.64/1.48 | (13) all_0_0_0 = all_0_2_2
% 2.64/1.48 |
% 2.64/1.48 | Equations (13) can reduce 6 to:
% 2.64/1.48 | (14) $false
% 2.64/1.48 |
% 2.64/1.48 |-The branch is then unsatisfiable
% 2.64/1.48 % SZS output end Proof for theBenchmark
% 2.64/1.48
% 2.64/1.48 834ms
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