TSTP Solution File: SEU122+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU122+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 08:46:43 EDT 2022
% Result : Theorem 2.33s 1.23s
% Output : Proof 3.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU122+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n007.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 : Mon Jun 20 04:35:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.59 ____ _
% 0.55/0.59 ___ / __ \_____(_)___ ________ __________
% 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.59
% 0.55/0.59 A Theorem Prover for First-Order Logic
% 0.55/0.59 (ePrincess v.1.0)
% 0.55/0.59
% 0.55/0.59 (c) Philipp Rümmer, 2009-2015
% 0.55/0.59 (c) Peter Backeman, 2014-2015
% 0.55/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.59 Bug reports to peter@backeman.se
% 0.55/0.59
% 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.59
% 0.55/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.88 Prover 0: Preprocessing ...
% 1.51/0.95 Prover 0: Warning: ignoring some quantifiers
% 1.57/0.96 Prover 0: Constructing countermodel ...
% 1.89/1.08 Prover 0: gave up
% 1.89/1.08 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.89/1.10 Prover 1: Preprocessing ...
% 2.24/1.18 Prover 1: Constructing countermodel ...
% 2.33/1.23 Prover 1: proved (141ms)
% 2.33/1.23
% 2.33/1.23 No countermodel exists, formula is valid
% 2.33/1.23 % SZS status Theorem for theBenchmark
% 2.33/1.23
% 2.33/1.23 Generating proof ... found it (size 16)
% 2.81/1.41
% 2.81/1.41 % SZS output start Proof for theBenchmark
% 2.81/1.41 Assumed formulas after preprocessing and simplification:
% 2.81/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = 0) & ~ (v1 = 0) & empty(v4) = 0 & empty(v2) = v3 & empty(empty_set) = 0 & subset(empty_set, v0) = v1 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (in(v8, v7) = v6) | ~ (in(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & in(v8, v6) = v9 & in(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (empty(v7) = v6) | ~ (empty(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (in(v7, v5) = 0) | in(v7, v6) = 0) & ! [v5] : ! [v6] : (v6 = v5 | ~ (empty(v6) = 0) | ~ (empty(v5) = 0)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (in(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & empty(v6) = v7)) & ! [v5] : ! [v6] : ( ~ (in(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & in(v6, v5) = v7)) & ! [v5] : (v5 = empty_set | ~ (empty(v5) = 0)))
% 2.81/1.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.81/1.44 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(empty_set, all_0_4_4) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 2.81/1.44 |
% 2.81/1.44 | Applying alpha-rule on (1) yields:
% 2.81/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 2.81/1.45 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 2.81/1.45 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 2.81/1.45 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 2.81/1.45 | (6) ~ (all_0_3_3 = 0)
% 2.81/1.45 | (7) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 2.81/1.45 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 2.81/1.45 | (9) subset(empty_set, all_0_4_4) = all_0_3_3
% 2.81/1.45 | (10) empty(all_0_2_2) = all_0_1_1
% 2.81/1.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 2.81/1.45 | (12) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 2.81/1.45 | (13) empty(empty_set) = 0
% 2.81/1.45 | (14) empty(all_0_0_0) = 0
% 2.81/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 2.81/1.45 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 2.81/1.45 | (17) ~ (all_0_1_1 = 0)
% 2.81/1.45 |
% 2.81/1.45 | Instantiating formula (8) with empty_set, all_0_0_0 and discharging atoms empty(all_0_0_0) = 0, empty(empty_set) = 0, yields:
% 2.81/1.45 | (18) all_0_0_0 = empty_set
% 2.81/1.45 |
% 2.81/1.45 | From (18) and (14) follows:
% 2.81/1.45 | (13) empty(empty_set) = 0
% 2.81/1.45 |
% 2.81/1.45 | Instantiating formula (16) with all_0_3_3, all_0_4_4, empty_set and discharging atoms subset(empty_set, all_0_4_4) = all_0_3_3, yields:
% 2.81/1.45 | (20) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, empty_set) = 0)
% 2.81/1.45 |
% 2.81/1.45 +-Applying beta-rule and splitting (20), into two cases.
% 2.81/1.45 |-Branch one:
% 2.81/1.45 | (21) all_0_3_3 = 0
% 2.81/1.45 |
% 2.81/1.45 | Equations (21) can reduce 6 to:
% 2.81/1.45 | (22) $false
% 2.81/1.45 |
% 2.81/1.46 |-The branch is then unsatisfiable
% 2.81/1.46 |-Branch two:
% 2.81/1.46 | (6) ~ (all_0_3_3 = 0)
% 2.81/1.46 | (24) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, empty_set) = 0)
% 2.81/1.46 |
% 2.81/1.46 | Instantiating (24) with all_26_0_5, all_26_1_6 yields:
% 2.81/1.46 | (25) ~ (all_26_0_5 = 0) & in(all_26_1_6, all_0_4_4) = all_26_0_5 & in(all_26_1_6, empty_set) = 0
% 2.81/1.46 |
% 2.81/1.46 | Applying alpha-rule on (25) yields:
% 2.81/1.46 | (26) ~ (all_26_0_5 = 0)
% 2.81/1.46 | (27) in(all_26_1_6, all_0_4_4) = all_26_0_5
% 3.15/1.46 | (28) in(all_26_1_6, empty_set) = 0
% 3.15/1.46 |
% 3.15/1.46 | Instantiating formula (12) with empty_set, all_26_1_6 and discharging atoms in(all_26_1_6, empty_set) = 0, yields:
% 3.15/1.46 | (29) ? [v0] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 3.15/1.46 |
% 3.15/1.46 | Instantiating (29) with all_39_0_8 yields:
% 3.15/1.46 | (30) ~ (all_39_0_8 = 0) & empty(empty_set) = all_39_0_8
% 3.15/1.46 |
% 3.15/1.46 | Applying alpha-rule on (30) yields:
% 3.15/1.46 | (31) ~ (all_39_0_8 = 0)
% 3.15/1.46 | (32) empty(empty_set) = all_39_0_8
% 3.15/1.46 |
% 3.15/1.46 | Instantiating formula (4) with empty_set, all_39_0_8, 0 and discharging atoms empty(empty_set) = all_39_0_8, empty(empty_set) = 0, yields:
% 3.15/1.46 | (33) all_39_0_8 = 0
% 3.15/1.46 |
% 3.15/1.46 | Equations (33) can reduce 31 to:
% 3.15/1.46 | (22) $false
% 3.15/1.46 |
% 3.15/1.46 |-The branch is then unsatisfiable
% 3.15/1.46 % SZS output end Proof for theBenchmark
% 3.15/1.46
% 3.15/1.46 855ms
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