TSTP Solution File: SEU121+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU121+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 08:46:42 EDT 2022
% Result : Theorem 2.42s 1.24s
% Output : Proof 3.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU121+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.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 Jun 20 06:51:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56 ____ _
% 0.18/0.56 ___ / __ \_____(_)___ ________ __________
% 0.18/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic
% 0.18/0.57 (ePrincess v.1.0)
% 0.18/0.57
% 0.18/0.57 (c) Philipp Rümmer, 2009-2015
% 0.18/0.57 (c) Peter Backeman, 2014-2015
% 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.57 Bug reports to peter@backeman.se
% 0.18/0.57
% 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.57
% 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.11/0.85 Prover 0: Preprocessing ...
% 1.43/0.93 Prover 0: Warning: ignoring some quantifiers
% 1.52/0.94 Prover 0: Constructing countermodel ...
% 1.65/1.07 Prover 0: gave up
% 1.65/1.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.94/1.08 Prover 1: Preprocessing ...
% 1.94/1.16 Prover 1: Constructing countermodel ...
% 2.42/1.24 Prover 1: proved (175ms)
% 2.42/1.24
% 2.42/1.24 No countermodel exists, formula is valid
% 2.42/1.24 % SZS status Theorem for theBenchmark
% 2.42/1.24
% 2.42/1.24 Generating proof ... found it (size 13)
% 3.20/1.47
% 3.20/1.47 % SZS output start Proof for theBenchmark
% 3.20/1.48 Assumed formulas after preprocessing and simplification:
% 3.20/1.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)))
% 3.26/1.51 | 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, all_0_6_6 yields:
% 3.26/1.51 | (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(all_0_5_5, all_0_4_4) = 0 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & subset(all_0_6_6, all_0_5_5) = 0 & ! [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))
% 3.40/1.51 |
% 3.40/1.51 | Applying alpha-rule on (1) yields:
% 3.40/1.51 | (2) subset(all_0_6_6, all_0_4_4) = all_0_3_3
% 3.40/1.51 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.40/1.51 | (4) ~ (all_0_1_1 = 0)
% 3.40/1.51 | (5) ~ (all_0_3_3 = 0)
% 3.40/1.51 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 3.40/1.52 | (7) empty(all_0_2_2) = all_0_1_1
% 3.40/1.52 | (8) empty(all_0_0_0) = 0
% 3.40/1.52 | (9) empty(empty_set) = 0
% 3.40/1.52 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 3.40/1.52 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 3.40/1.52 | (12) subset(all_0_6_6, all_0_5_5) = 0
% 3.40/1.52 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 3.40/1.52 | (14) subset(all_0_5_5, all_0_4_4) = 0
% 3.40/1.52 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 3.40/1.52 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 3.40/1.52 | (17) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 3.40/1.52 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.40/1.52 | (19) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 3.40/1.52 |
% 3.40/1.52 | Instantiating formula (13) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 3.40/1.52 | (20) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 3.40/1.52 |
% 3.40/1.52 +-Applying beta-rule and splitting (20), into two cases.
% 3.40/1.52 |-Branch one:
% 3.40/1.52 | (21) all_0_3_3 = 0
% 3.40/1.52 |
% 3.40/1.52 | Equations (21) can reduce 5 to:
% 3.40/1.52 | (22) $false
% 3.40/1.52 |
% 3.40/1.52 |-The branch is then unsatisfiable
% 3.40/1.52 |-Branch two:
% 3.40/1.52 | (5) ~ (all_0_3_3 = 0)
% 3.40/1.52 | (24) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 3.40/1.52 |
% 3.40/1.52 | Instantiating (24) with all_26_0_7, all_26_1_8 yields:
% 3.40/1.52 | (25) ~ (all_26_0_7 = 0) & in(all_26_1_8, all_0_4_4) = all_26_0_7 & in(all_26_1_8, all_0_6_6) = 0
% 3.40/1.52 |
% 3.40/1.52 | Applying alpha-rule on (25) yields:
% 3.40/1.52 | (26) ~ (all_26_0_7 = 0)
% 3.40/1.52 | (27) in(all_26_1_8, all_0_4_4) = all_26_0_7
% 3.40/1.52 | (28) in(all_26_1_8, all_0_6_6) = 0
% 3.40/1.52 |
% 3.40/1.52 | Instantiating formula (6) with all_26_1_8, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, in(all_26_1_8, all_0_6_6) = 0, yields:
% 3.40/1.52 | (29) in(all_26_1_8, all_0_5_5) = 0
% 3.40/1.52 |
% 3.40/1.52 | Instantiating formula (6) with all_26_1_8, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, in(all_26_1_8, all_0_5_5) = 0, yields:
% 3.40/1.52 | (30) in(all_26_1_8, all_0_4_4) = 0
% 3.40/1.52 |
% 3.40/1.52 | Instantiating formula (15) with all_26_1_8, all_0_4_4, 0, all_26_0_7 and discharging atoms in(all_26_1_8, all_0_4_4) = all_26_0_7, in(all_26_1_8, all_0_4_4) = 0, yields:
% 3.40/1.52 | (31) all_26_0_7 = 0
% 3.40/1.52 |
% 3.40/1.52 | Equations (31) can reduce 26 to:
% 3.40/1.53 | (22) $false
% 3.40/1.53 |
% 3.40/1.53 |-The branch is then unsatisfiable
% 3.40/1.53 % SZS output end Proof for theBenchmark
% 3.40/1.53
% 3.40/1.53 950ms
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