TSTP Solution File: SET201+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 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 00:18:23 EDT 2022
% Result : Theorem 2.78s 1.37s
% Output : Proof 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sat Jul 9 18:38:59 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.59 (ePrincess v.1.0)
% 0.51/0.59
% 0.51/0.59 (c) Philipp Rümmer, 2009-2015
% 0.51/0.59 (c) Peter Backeman, 2014-2015
% 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.59 Bug reports to peter@backeman.se
% 0.51/0.59
% 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.59
% 0.51/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.88 Prover 0: Preprocessing ...
% 1.63/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.63/1.04 Prover 0: Constructing countermodel ...
% 2.12/1.20 Prover 0: gave up
% 2.12/1.20 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.12/1.22 Prover 1: Preprocessing ...
% 2.49/1.28 Prover 1: Warning: ignoring some quantifiers
% 2.49/1.28 Prover 1: Constructing countermodel ...
% 2.78/1.37 Prover 1: proved (171ms)
% 2.78/1.37
% 2.78/1.37 No countermodel exists, formula is valid
% 2.78/1.37 % SZS status Theorem for theBenchmark
% 2.78/1.37
% 2.78/1.37 Generating proof ... Warning: ignoring some quantifiers
% 3.49/1.61 found it (size 33)
% 3.49/1.61
% 3.49/1.61 % SZS output start Proof for theBenchmark
% 3.49/1.61 Assumed formulas after preprocessing and simplification:
% 3.49/1.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0 & subset(v0, v1) = 0 & intersection(v1, v3) = v5 & intersection(v0, v2) = v4 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : (member(v9, v8) = v13 & member(v9, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = 0) | (member(v9, v8) = 0 & member(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v7, v8) = v9) | intersection(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (member(v9, v8) = v11 & member(v9, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & (v11 = 0 | v10 = 0))))
% 3.49/1.64 | 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:
% 3.49/1.64 | (1) ~ (all_0_0_0 = 0) & subset(all_0_2_2, all_0_1_1) = all_0_0_0 & subset(all_0_4_4, all_0_3_3) = 0 & subset(all_0_6_6, all_0_5_5) = 0 & intersection(all_0_5_5, all_0_3_3) = all_0_1_1 & intersection(all_0_6_6, all_0_4_4) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & 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] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.49/1.65 |
% 3.49/1.65 | Applying alpha-rule on (1) yields:
% 3.49/1.65 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 3.49/1.65 | (3) ~ (all_0_0_0 = 0)
% 3.49/1.65 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.49/1.65 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.49/1.65 | (6) intersection(all_0_5_5, all_0_3_3) = all_0_1_1
% 3.49/1.65 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 3.49/1.65 | (8) subset(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.49/1.65 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.49/1.65 | (10) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.49/1.65 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 3.49/1.65 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.49/1.65 | (13) subset(all_0_4_4, all_0_3_3) = 0
% 3.49/1.65 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 3.49/1.66 | (15) intersection(all_0_6_6, all_0_4_4) = all_0_2_2
% 3.49/1.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 3.49/1.66 | (17) subset(all_0_6_6, all_0_5_5) = 0
% 3.49/1.66 |
% 3.49/1.66 | Instantiating formula (5) 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:
% 3.49/1.66 | (18) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.49/1.66 |
% 3.49/1.66 | Instantiating formula (2) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 3.84/1.66 | (19) intersection(all_0_3_3, all_0_5_5) = all_0_1_1
% 3.84/1.66 |
% 3.84/1.66 | Instantiating formula (2) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms intersection(all_0_6_6, all_0_4_4) = all_0_2_2, yields:
% 3.84/1.66 | (20) intersection(all_0_4_4, all_0_6_6) = all_0_2_2
% 3.84/1.66 |
% 3.84/1.66 +-Applying beta-rule and splitting (18), into two cases.
% 3.84/1.66 |-Branch one:
% 3.84/1.66 | (21) all_0_0_0 = 0
% 3.84/1.66 |
% 3.84/1.66 | Equations (21) can reduce 3 to:
% 3.84/1.66 | (22) $false
% 3.84/1.66 |
% 3.84/1.66 |-The branch is then unsatisfiable
% 3.84/1.66 |-Branch two:
% 3.84/1.66 | (3) ~ (all_0_0_0 = 0)
% 3.84/1.66 | (24) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.84/1.66 |
% 3.84/1.66 | Instantiating (24) with all_18_0_9, all_18_1_10 yields:
% 3.84/1.66 | (25) ~ (all_18_0_9 = 0) & member(all_18_1_10, all_0_1_1) = all_18_0_9 & member(all_18_1_10, all_0_2_2) = 0
% 3.84/1.66 |
% 3.84/1.66 | Applying alpha-rule on (25) yields:
% 3.84/1.66 | (26) ~ (all_18_0_9 = 0)
% 3.84/1.66 | (27) member(all_18_1_10, all_0_1_1) = all_18_0_9
% 3.84/1.66 | (28) member(all_18_1_10, all_0_2_2) = 0
% 3.84/1.66 |
% 3.84/1.66 | Instantiating formula (7) with all_18_0_9, all_0_1_1, all_18_1_10, all_0_5_5, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_5_5) = all_0_1_1, member(all_18_1_10, all_0_1_1) = all_18_0_9, yields:
% 3.84/1.66 | (29) all_18_0_9 = 0 | ? [v0] : ? [v1] : (member(all_18_1_10, all_0_3_3) = v0 & member(all_18_1_10, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.84/1.66 |
% 3.84/1.66 | Instantiating formula (11) with all_0_2_2, all_18_1_10, all_0_6_6, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_6_6) = all_0_2_2, member(all_18_1_10, all_0_2_2) = 0, yields:
% 3.84/1.66 | (30) member(all_18_1_10, all_0_4_4) = 0 & member(all_18_1_10, all_0_6_6) = 0
% 3.84/1.66 |
% 3.84/1.66 | Applying alpha-rule on (30) yields:
% 3.84/1.66 | (31) member(all_18_1_10, all_0_4_4) = 0
% 3.84/1.66 | (32) member(all_18_1_10, all_0_6_6) = 0
% 3.84/1.66 |
% 3.84/1.66 | Instantiating formula (14) with all_18_1_10, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 3.84/1.66 | (33) ~ (member(all_18_1_10, all_0_4_4) = 0) | member(all_18_1_10, all_0_3_3) = 0
% 3.84/1.66 |
% 3.84/1.66 | Instantiating formula (14) with all_18_1_10, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, yields:
% 3.84/1.66 | (34) ~ (member(all_18_1_10, all_0_6_6) = 0) | member(all_18_1_10, all_0_5_5) = 0
% 3.84/1.66 |
% 3.84/1.66 +-Applying beta-rule and splitting (33), into two cases.
% 3.84/1.66 |-Branch one:
% 3.84/1.66 | (35) ~ (member(all_18_1_10, all_0_4_4) = 0)
% 3.84/1.66 |
% 3.84/1.66 | Using (31) and (35) yields:
% 3.84/1.66 | (36) $false
% 3.84/1.66 |
% 3.84/1.66 |-The branch is then unsatisfiable
% 3.84/1.66 |-Branch two:
% 3.84/1.66 | (31) member(all_18_1_10, all_0_4_4) = 0
% 3.84/1.66 | (38) member(all_18_1_10, all_0_3_3) = 0
% 3.84/1.66 |
% 3.84/1.67 +-Applying beta-rule and splitting (34), into two cases.
% 3.84/1.67 |-Branch one:
% 3.84/1.67 | (39) ~ (member(all_18_1_10, all_0_6_6) = 0)
% 3.84/1.67 |
% 3.84/1.67 | Using (32) and (39) yields:
% 3.84/1.67 | (36) $false
% 3.84/1.67 |
% 3.84/1.67 |-The branch is then unsatisfiable
% 3.84/1.67 |-Branch two:
% 3.84/1.67 | (32) member(all_18_1_10, all_0_6_6) = 0
% 3.84/1.67 | (42) member(all_18_1_10, all_0_5_5) = 0
% 3.84/1.67 |
% 3.84/1.67 +-Applying beta-rule and splitting (29), into two cases.
% 3.84/1.67 |-Branch one:
% 3.84/1.67 | (43) all_18_0_9 = 0
% 3.84/1.67 |
% 3.84/1.67 | Equations (43) can reduce 26 to:
% 3.84/1.67 | (22) $false
% 3.84/1.67 |
% 3.84/1.67 |-The branch is then unsatisfiable
% 3.84/1.67 |-Branch two:
% 3.84/1.67 | (26) ~ (all_18_0_9 = 0)
% 3.84/1.67 | (46) ? [v0] : ? [v1] : (member(all_18_1_10, all_0_3_3) = v0 & member(all_18_1_10, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.84/1.67 |
% 3.84/1.67 | Instantiating (46) with all_42_0_11, all_42_1_12 yields:
% 3.84/1.67 | (47) member(all_18_1_10, all_0_3_3) = all_42_1_12 & member(all_18_1_10, all_0_5_5) = all_42_0_11 & ( ~ (all_42_0_11 = 0) | ~ (all_42_1_12 = 0))
% 3.84/1.67 |
% 3.84/1.67 | Applying alpha-rule on (47) yields:
% 3.84/1.67 | (48) member(all_18_1_10, all_0_3_3) = all_42_1_12
% 3.84/1.67 | (49) member(all_18_1_10, all_0_5_5) = all_42_0_11
% 3.84/1.67 | (50) ~ (all_42_0_11 = 0) | ~ (all_42_1_12 = 0)
% 3.84/1.67 |
% 3.84/1.67 | Instantiating formula (12) with all_18_1_10, all_0_3_3, all_42_1_12, 0 and discharging atoms member(all_18_1_10, all_0_3_3) = all_42_1_12, member(all_18_1_10, all_0_3_3) = 0, yields:
% 3.84/1.67 | (51) all_42_1_12 = 0
% 3.84/1.67 |
% 3.84/1.67 | Instantiating formula (12) with all_18_1_10, all_0_5_5, all_42_0_11, 0 and discharging atoms member(all_18_1_10, all_0_5_5) = all_42_0_11, member(all_18_1_10, all_0_5_5) = 0, yields:
% 3.84/1.67 | (52) all_42_0_11 = 0
% 3.84/1.67 |
% 3.84/1.67 +-Applying beta-rule and splitting (50), into two cases.
% 3.84/1.67 |-Branch one:
% 3.84/1.67 | (53) ~ (all_42_0_11 = 0)
% 3.84/1.67 |
% 3.84/1.67 | Equations (52) can reduce 53 to:
% 3.84/1.67 | (22) $false
% 3.84/1.67 |
% 3.84/1.67 |-The branch is then unsatisfiable
% 3.84/1.67 |-Branch two:
% 3.84/1.67 | (52) all_42_0_11 = 0
% 3.84/1.67 | (56) ~ (all_42_1_12 = 0)
% 3.84/1.67 |
% 3.84/1.67 | Equations (51) can reduce 56 to:
% 3.84/1.67 | (22) $false
% 3.84/1.67 |
% 3.84/1.67 |-The branch is then unsatisfiable
% 3.84/1.67 % SZS output end Proof for theBenchmark
% 3.84/1.67
% 3.84/1.67 1064ms
%------------------------------------------------------------------------------