TSTP Solution File: SET009+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:15:53 EDT 2022
% Result : Theorem 2.40s 1.30s
% Output : Proof 3.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 09:48:57 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.50/0.61 ____ _
% 0.50/0.61 ___ / __ \_____(_)___ ________ __________
% 0.50/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.61
% 0.50/0.61 A Theorem Prover for First-Order Logic
% 0.50/0.61 (ePrincess v.1.0)
% 0.50/0.61
% 0.50/0.61 (c) Philipp Rümmer, 2009-2015
% 0.50/0.61 (c) Peter Backeman, 2014-2015
% 0.50/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.61 Bug reports to peter@backeman.se
% 0.50/0.61
% 0.50/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.61
% 0.50/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.90 Prover 0: Preprocessing ...
% 1.58/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.58/1.02 Prover 0: Constructing countermodel ...
% 2.05/1.14 Prover 0: gave up
% 2.05/1.14 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.05/1.16 Prover 1: Preprocessing ...
% 2.18/1.22 Prover 1: Constructing countermodel ...
% 2.40/1.30 Prover 1: proved (151ms)
% 2.40/1.30
% 2.40/1.30 No countermodel exists, formula is valid
% 2.40/1.30 % SZS status Theorem for theBenchmark
% 2.40/1.30
% 2.40/1.30 Generating proof ... found it (size 29)
% 3.51/1.56
% 3.51/1.56 % SZS output start Proof for theBenchmark
% 3.51/1.56 Assumed formulas after preprocessing and simplification:
% 3.51/1.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & difference(v2, v1) = v3 & difference(v2, v0) = v4 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (difference(v6, v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : (member(v8, v7) = v12 & member(v8, v6) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10 & member(v8, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v6, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10 & member(v9, v6) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (subset(v6, v7) = 0) | ~ (member(v8, v6) = 0) | member(v8, v7) = 0) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)))
% 3.51/1.59 | 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 yields:
% 3.51/1.59 | (1) ~ (all_0_0_0 = 0) & subset(all_0_2_2, all_0_1_1) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & difference(all_0_3_3, all_0_4_4) = all_0_2_2 & difference(all_0_3_3, all_0_5_5) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) & ! [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))
% 3.51/1.60 |
% 3.51/1.60 | Applying alpha-rule on (1) yields:
% 3.51/1.60 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.51/1.60 | (3) subset(all_0_5_5, all_0_4_4) = 0
% 3.51/1.60 | (4) ~ (all_0_0_0 = 0)
% 3.51/1.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 3.51/1.60 | (6) subset(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.51/1.60 | (7) difference(all_0_3_3, all_0_5_5) = all_0_1_1
% 3.51/1.60 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.51/1.60 | (9) difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 3.51/1.60 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 3.51/1.60 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.51/1.60 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.51/1.60 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 3.51/1.60 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.51/1.60 |
% 3.51/1.61 | Instantiating formula (2) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 3.51/1.61 | (15) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.51/1.61 |
% 3.51/1.61 +-Applying beta-rule and splitting (15), into two cases.
% 3.51/1.61 |-Branch one:
% 3.51/1.61 | (16) all_0_0_0 = 0
% 3.51/1.61 |
% 3.51/1.61 | Equations (16) can reduce 4 to:
% 3.51/1.61 | (17) $false
% 3.51/1.61 |
% 3.51/1.61 |-The branch is then unsatisfiable
% 3.51/1.61 |-Branch two:
% 3.51/1.61 | (4) ~ (all_0_0_0 = 0)
% 3.51/1.61 | (19) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.51/1.61 |
% 3.51/1.61 | Instantiating (19) with all_18_0_6, all_18_1_7 yields:
% 3.51/1.61 | (20) ~ (all_18_0_6 = 0) & member(all_18_1_7, all_0_1_1) = all_18_0_6 & member(all_18_1_7, all_0_2_2) = 0
% 3.51/1.61 |
% 3.51/1.61 | Applying alpha-rule on (20) yields:
% 3.51/1.61 | (21) ~ (all_18_0_6 = 0)
% 3.51/1.61 | (22) member(all_18_1_7, all_0_1_1) = all_18_0_6
% 3.51/1.61 | (23) member(all_18_1_7, all_0_2_2) = 0
% 3.51/1.61 |
% 3.51/1.61 | Instantiating formula (5) with all_18_0_6, all_0_1_1, all_18_1_7, all_0_5_5, all_0_3_3 and discharging atoms difference(all_0_3_3, all_0_5_5) = all_0_1_1, member(all_18_1_7, all_0_1_1) = all_18_0_6, yields:
% 3.51/1.61 | (24) all_18_0_6 = 0 | ? [v0] : ? [v1] : (member(all_18_1_7, all_0_3_3) = v0 & member(all_18_1_7, all_0_5_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 3.51/1.61 |
% 3.51/1.61 | Instantiating formula (10) with all_0_2_2, all_18_1_7, all_0_4_4, all_0_3_3 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, member(all_18_1_7, all_0_2_2) = 0, yields:
% 3.51/1.61 | (25) ? [v0] : ( ~ (v0 = 0) & member(all_18_1_7, all_0_3_3) = 0 & member(all_18_1_7, all_0_4_4) = v0)
% 3.51/1.61 |
% 3.51/1.61 | Instantiating formula (13) with all_18_1_7, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields:
% 3.51/1.61 | (26) ~ (member(all_18_1_7, all_0_5_5) = 0) | member(all_18_1_7, all_0_4_4) = 0
% 3.51/1.61 |
% 3.51/1.61 | Instantiating (25) with all_29_0_8 yields:
% 3.51/1.61 | (27) ~ (all_29_0_8 = 0) & member(all_18_1_7, all_0_3_3) = 0 & member(all_18_1_7, all_0_4_4) = all_29_0_8
% 3.51/1.61 |
% 3.51/1.61 | Applying alpha-rule on (27) yields:
% 3.51/1.61 | (28) ~ (all_29_0_8 = 0)
% 3.51/1.61 | (29) member(all_18_1_7, all_0_3_3) = 0
% 3.51/1.61 | (30) member(all_18_1_7, all_0_4_4) = all_29_0_8
% 3.51/1.61 |
% 3.51/1.61 +-Applying beta-rule and splitting (24), into two cases.
% 3.51/1.61 |-Branch one:
% 3.51/1.61 | (31) all_18_0_6 = 0
% 3.51/1.61 |
% 3.51/1.61 | Equations (31) can reduce 21 to:
% 3.51/1.61 | (17) $false
% 3.51/1.61 |
% 3.51/1.61 |-The branch is then unsatisfiable
% 3.51/1.61 |-Branch two:
% 3.51/1.61 | (21) ~ (all_18_0_6 = 0)
% 3.51/1.61 | (34) ? [v0] : ? [v1] : (member(all_18_1_7, all_0_3_3) = v0 & member(all_18_1_7, all_0_5_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 3.51/1.61 |
% 3.51/1.61 | Instantiating (34) with all_35_0_9, all_35_1_10 yields:
% 3.51/1.61 | (35) member(all_18_1_7, all_0_3_3) = all_35_1_10 & member(all_18_1_7, all_0_5_5) = all_35_0_9 & ( ~ (all_35_1_10 = 0) | all_35_0_9 = 0)
% 3.51/1.61 |
% 3.51/1.61 | Applying alpha-rule on (35) yields:
% 3.51/1.61 | (36) member(all_18_1_7, all_0_3_3) = all_35_1_10
% 3.51/1.61 | (37) member(all_18_1_7, all_0_5_5) = all_35_0_9
% 3.51/1.61 | (38) ~ (all_35_1_10 = 0) | all_35_0_9 = 0
% 3.51/1.61 |
% 3.51/1.61 +-Applying beta-rule and splitting (26), into two cases.
% 3.51/1.61 |-Branch one:
% 3.51/1.61 | (39) ~ (member(all_18_1_7, all_0_5_5) = 0)
% 3.51/1.61 |
% 3.51/1.61 | Instantiating formula (11) with all_18_1_7, all_0_3_3, all_35_1_10, 0 and discharging atoms member(all_18_1_7, all_0_3_3) = all_35_1_10, member(all_18_1_7, all_0_3_3) = 0, yields:
% 3.51/1.61 | (40) all_35_1_10 = 0
% 3.51/1.61 |
% 3.51/1.62 | Using (37) and (39) yields:
% 3.51/1.62 | (41) ~ (all_35_0_9 = 0)
% 3.51/1.62 |
% 3.51/1.62 +-Applying beta-rule and splitting (38), into two cases.
% 3.51/1.62 |-Branch one:
% 3.51/1.62 | (42) ~ (all_35_1_10 = 0)
% 3.51/1.62 |
% 3.51/1.62 | Equations (40) can reduce 42 to:
% 3.51/1.62 | (17) $false
% 3.51/1.62 |
% 3.51/1.62 |-The branch is then unsatisfiable
% 3.51/1.62 |-Branch two:
% 3.51/1.62 | (40) all_35_1_10 = 0
% 3.51/1.62 | (45) all_35_0_9 = 0
% 3.51/1.62 |
% 3.51/1.62 | Equations (45) can reduce 41 to:
% 3.51/1.62 | (17) $false
% 3.51/1.62 |
% 3.51/1.62 |-The branch is then unsatisfiable
% 3.51/1.62 |-Branch two:
% 3.51/1.62 | (47) member(all_18_1_7, all_0_5_5) = 0
% 3.51/1.62 | (48) member(all_18_1_7, all_0_4_4) = 0
% 3.51/1.62 |
% 3.51/1.62 | Instantiating formula (11) with all_18_1_7, all_0_4_4, all_29_0_8, 0 and discharging atoms member(all_18_1_7, all_0_4_4) = all_29_0_8, member(all_18_1_7, all_0_4_4) = 0, yields:
% 3.51/1.62 | (49) all_29_0_8 = 0
% 3.51/1.62 |
% 3.51/1.62 | Equations (49) can reduce 28 to:
% 3.51/1.62 | (17) $false
% 3.51/1.62 |
% 3.51/1.62 |-The branch is then unsatisfiable
% 3.51/1.62 % SZS output end Proof for theBenchmark
% 3.51/1.62
% 3.51/1.62 994ms
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