TSTP Solution File: SET027+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 00:16:22 EDT 2022
% Result : Theorem 1.92s 1.16s
% Output : Proof 2.55s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.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 : Sun Jul 10 04:45:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.47/0.57 ____ _
% 0.47/0.57 ___ / __ \_____(_)___ ________ __________
% 0.47/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.47/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.47/0.57
% 0.47/0.57 A Theorem Prover for First-Order Logic
% 0.47/0.57 (ePrincess v.1.0)
% 0.47/0.57
% 0.47/0.57 (c) Philipp Rümmer, 2009-2015
% 0.47/0.57 (c) Peter Backeman, 2014-2015
% 0.47/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.57 Bug reports to peter@backeman.se
% 0.47/0.57
% 0.47/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.57
% 0.47/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.47/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.03/0.86 Prover 0: Preprocessing ...
% 1.33/0.92 Prover 0: Warning: ignoring some quantifiers
% 1.40/0.93 Prover 0: Constructing countermodel ...
% 1.68/1.03 Prover 0: gave up
% 1.68/1.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.68/1.05 Prover 1: Preprocessing ...
% 1.92/1.11 Prover 1: Constructing countermodel ...
% 1.92/1.16 Prover 1: proved (126ms)
% 1.92/1.16
% 1.92/1.16 No countermodel exists, formula is valid
% 1.92/1.16 % SZS status Theorem for theBenchmark
% 1.92/1.16
% 1.92/1.16 Generating proof ... found it (size 13)
% 2.48/1.33
% 2.48/1.33 % SZS output start Proof for theBenchmark
% 2.48/1.33 Assumed formulas after preprocessing and simplification:
% 2.48/1.33 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v4, v4) = v5)))
% 2.55/1.36 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.55/1.36 | (1) ~ (all_0_0_0 = 0) & subset(all_0_2_2, all_0_1_1) = 0 & subset(all_0_3_3, all_0_1_1) = all_0_0_0 & subset(all_0_3_3, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 2.55/1.36 |
% 2.55/1.36 | Applying alpha-rule on (1) yields:
% 2.55/1.36 | (2) subset(all_0_3_3, all_0_2_2) = 0
% 2.55/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 2.55/1.36 | (4) ~ (all_0_0_0 = 0)
% 2.55/1.36 | (5) subset(all_0_2_2, all_0_1_1) = 0
% 2.55/1.36 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 2.55/1.36 | (7) subset(all_0_3_3, all_0_1_1) = all_0_0_0
% 2.55/1.36 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 2.55/1.36 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 2.55/1.36 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 2.55/1.36 |
% 2.55/1.36 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 2.55/1.37 | (11) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 2.55/1.37 |
% 2.55/1.37 +-Applying beta-rule and splitting (11), into two cases.
% 2.55/1.37 |-Branch one:
% 2.55/1.37 | (12) all_0_0_0 = 0
% 2.55/1.37 |
% 2.55/1.37 | Equations (12) can reduce 4 to:
% 2.55/1.37 | (13) $false
% 2.55/1.37 |
% 2.55/1.37 |-The branch is then unsatisfiable
% 2.55/1.37 |-Branch two:
% 2.55/1.37 | (4) ~ (all_0_0_0 = 0)
% 2.55/1.37 | (15) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 2.55/1.37 |
% 2.55/1.37 | Instantiating (15) with all_18_0_4, all_18_1_5 yields:
% 2.55/1.37 | (16) ~ (all_18_0_4 = 0) & member(all_18_1_5, all_0_1_1) = all_18_0_4 & member(all_18_1_5, all_0_3_3) = 0
% 2.55/1.37 |
% 2.55/1.37 | Applying alpha-rule on (16) yields:
% 2.55/1.37 | (17) ~ (all_18_0_4 = 0)
% 2.55/1.37 | (18) member(all_18_1_5, all_0_1_1) = all_18_0_4
% 2.55/1.37 | (19) member(all_18_1_5, all_0_3_3) = 0
% 2.55/1.37 |
% 2.55/1.37 | Instantiating formula (8) with all_18_1_5, all_0_2_2, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_2_2) = 0, member(all_18_1_5, all_0_3_3) = 0, yields:
% 2.55/1.37 | (20) member(all_18_1_5, all_0_2_2) = 0
% 2.55/1.37 |
% 2.55/1.37 | Instantiating formula (8) with all_18_1_5, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = 0, member(all_18_1_5, all_0_2_2) = 0, yields:
% 2.55/1.37 | (21) member(all_18_1_5, all_0_1_1) = 0
% 2.55/1.37 |
% 2.55/1.37 | Instantiating formula (9) with all_18_1_5, all_0_1_1, 0, all_18_0_4 and discharging atoms member(all_18_1_5, all_0_1_1) = all_18_0_4, member(all_18_1_5, all_0_1_1) = 0, yields:
% 2.55/1.37 | (22) all_18_0_4 = 0
% 2.55/1.37 |
% 2.55/1.37 | Equations (22) can reduce 17 to:
% 2.55/1.37 | (13) $false
% 2.55/1.37 |
% 2.55/1.37 |-The branch is then unsatisfiable
% 2.55/1.37 % SZS output end Proof for theBenchmark
% 2.55/1.37
% 2.55/1.37 789ms
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