TSTP Solution File: SET586+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 00:20:28 EDT 2022
% Result : Theorem 2.98s 1.48s
% Output : Proof 3.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n026.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 07:37:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.62 ____ _
% 0.52/0.62 ___ / __ \_____(_)___ ________ __________
% 0.52/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.62
% 0.52/0.62 A Theorem Prover for First-Order Logic
% 0.52/0.62 (ePrincess v.1.0)
% 0.52/0.62
% 0.52/0.62 (c) Philipp Rümmer, 2009-2015
% 0.52/0.62 (c) Peter Backeman, 2014-2015
% 0.52/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.62 Bug reports to peter@backeman.se
% 0.52/0.62
% 0.52/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.62
% 0.52/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.37/0.93 Prover 0: Preprocessing ...
% 1.61/1.06 Prover 0: Warning: ignoring some quantifiers
% 1.69/1.09 Prover 0: Constructing countermodel ...
% 2.22/1.31 Prover 0: gave up
% 2.22/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.41/1.33 Prover 1: Preprocessing ...
% 2.62/1.39 Prover 1: Warning: ignoring some quantifiers
% 2.62/1.40 Prover 1: Constructing countermodel ...
% 2.98/1.48 Prover 1: proved (163ms)
% 2.98/1.48
% 2.98/1.48 No countermodel exists, formula is valid
% 2.98/1.48 % SZS status Theorem for theBenchmark
% 2.98/1.48
% 2.98/1.48 Generating proof ... Warning: ignoring some quantifiers
% 3.65/1.71 found it (size 29)
% 3.65/1.71
% 3.65/1.71 % SZS output start Proof for theBenchmark
% 3.65/1.71 Assumed formulas after preprocessing and simplification:
% 3.65/1.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & intersection(v1, v2) = v4 & intersection(v0, v2) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (intersection(v6, v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : (member(v8, v7) = v12 & member(v8, v6) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v7) = v9) | ~ (member(v8, v9) = 0) | (member(v8, v7) = 0 & 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] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | intersection(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v6) = v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : ? [v9] : ? [v10] : (member(v8, v7) = v10 & member(v8, v6) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = 0 | v9 = 0))))
% 3.65/1.74 | 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:
% 3.65/1.74 | (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 & intersection(all_0_4_4, all_0_3_3) = all_0_1_1 & intersection(all_0_5_5, all_0_3_3) = 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)))
% 3.65/1.74 |
% 3.65/1.74 | Applying alpha-rule on (1) yields:
% 3.65/1.74 | (2) intersection(all_0_5_5, all_0_3_3) = all_0_2_2
% 3.65/1.74 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 3.65/1.74 | (4) ! [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))))
% 3.65/1.75 | (5) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.65/1.75 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.65/1.75 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.65/1.75 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.65/1.75 | (9) subset(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.65/1.75 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 3.65/1.75 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 3.65/1.75 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 3.65/1.75 | (13) subset(all_0_5_5, all_0_4_4) = 0
% 3.65/1.75 | (14) intersection(all_0_4_4, all_0_3_3) = all_0_1_1
% 3.65/1.75 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.65/1.75 | (16) ~ (all_0_0_0 = 0)
% 3.65/1.75 |
% 3.65/1.75 | Instantiating formula (8) 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:
% 3.65/1.75 | (17) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.65/1.75 |
% 3.65/1.75 | Instantiating formula (10) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 3.65/1.75 | (18) intersection(all_0_3_3, all_0_4_4) = all_0_1_1
% 3.65/1.75 |
% 3.65/1.75 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms intersection(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 3.65/1.75 | (19) intersection(all_0_3_3, all_0_5_5) = all_0_2_2
% 3.65/1.75 |
% 3.65/1.75 +-Applying beta-rule and splitting (17), into two cases.
% 3.65/1.75 |-Branch one:
% 3.65/1.75 | (20) all_0_0_0 = 0
% 3.65/1.75 |
% 3.65/1.75 | Equations (20) can reduce 16 to:
% 3.65/1.75 | (21) $false
% 3.65/1.75 |
% 3.65/1.75 |-The branch is then unsatisfiable
% 3.65/1.75 |-Branch two:
% 3.65/1.75 | (16) ~ (all_0_0_0 = 0)
% 3.65/1.75 | (23) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.65/1.75 |
% 3.65/1.75 | Instantiating (23) with all_18_0_8, all_18_1_9 yields:
% 3.65/1.75 | (24) ~ (all_18_0_8 = 0) & member(all_18_1_9, all_0_1_1) = all_18_0_8 & member(all_18_1_9, all_0_2_2) = 0
% 3.65/1.75 |
% 3.65/1.75 | Applying alpha-rule on (24) yields:
% 3.65/1.75 | (25) ~ (all_18_0_8 = 0)
% 3.65/1.75 | (26) member(all_18_1_9, all_0_1_1) = all_18_0_8
% 3.65/1.75 | (27) member(all_18_1_9, all_0_2_2) = 0
% 3.65/1.75 |
% 3.65/1.75 | Instantiating formula (4) with all_18_0_8, all_0_1_1, all_18_1_9, all_0_4_4, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_18_1_9, all_0_1_1) = all_18_0_8, yields:
% 3.65/1.75 | (28) all_18_0_8 = 0 | ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.65/1.76 |
% 3.65/1.76 | Instantiating formula (3) with all_0_2_2, all_18_1_9, all_0_5_5, all_0_3_3 and discharging atoms intersection(all_0_3_3, all_0_5_5) = all_0_2_2, member(all_18_1_9, all_0_2_2) = 0, yields:
% 3.65/1.76 | (29) member(all_18_1_9, all_0_3_3) = 0 & member(all_18_1_9, all_0_5_5) = 0
% 3.65/1.76 |
% 3.65/1.76 | Applying alpha-rule on (29) yields:
% 3.65/1.76 | (30) member(all_18_1_9, all_0_3_3) = 0
% 3.65/1.76 | (31) member(all_18_1_9, all_0_5_5) = 0
% 3.65/1.76 |
% 3.65/1.76 | Instantiating formula (11) with all_18_1_9, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields:
% 3.65/1.76 | (32) ~ (member(all_18_1_9, all_0_5_5) = 0) | member(all_18_1_9, all_0_4_4) = 0
% 3.65/1.76 |
% 3.65/1.76 +-Applying beta-rule and splitting (32), into two cases.
% 3.65/1.76 |-Branch one:
% 3.65/1.76 | (33) ~ (member(all_18_1_9, all_0_5_5) = 0)
% 3.65/1.76 |
% 3.65/1.76 | Using (31) and (33) yields:
% 3.65/1.76 | (34) $false
% 3.65/1.76 |
% 3.65/1.76 |-The branch is then unsatisfiable
% 3.65/1.76 |-Branch two:
% 3.65/1.76 | (31) member(all_18_1_9, all_0_5_5) = 0
% 3.65/1.76 | (36) member(all_18_1_9, all_0_4_4) = 0
% 3.65/1.76 |
% 3.65/1.76 +-Applying beta-rule and splitting (28), into two cases.
% 3.65/1.76 |-Branch one:
% 3.65/1.76 | (37) all_18_0_8 = 0
% 3.65/1.76 |
% 3.65/1.76 | Equations (37) can reduce 25 to:
% 3.65/1.76 | (21) $false
% 3.65/1.76 |
% 3.65/1.76 |-The branch is then unsatisfiable
% 3.65/1.76 |-Branch two:
% 3.65/1.76 | (25) ~ (all_18_0_8 = 0)
% 3.65/1.76 | (40) ? [v0] : ? [v1] : (member(all_18_1_9, all_0_3_3) = v0 & member(all_18_1_9, all_0_4_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 3.65/1.76 |
% 3.65/1.76 | Instantiating (40) with all_38_0_10, all_38_1_11 yields:
% 3.65/1.76 | (41) member(all_18_1_9, all_0_3_3) = all_38_1_11 & member(all_18_1_9, all_0_4_4) = all_38_0_10 & ( ~ (all_38_0_10 = 0) | ~ (all_38_1_11 = 0))
% 3.65/1.76 |
% 3.65/1.76 | Applying alpha-rule on (41) yields:
% 3.65/1.76 | (42) member(all_18_1_9, all_0_3_3) = all_38_1_11
% 3.65/1.76 | (43) member(all_18_1_9, all_0_4_4) = all_38_0_10
% 3.65/1.76 | (44) ~ (all_38_0_10 = 0) | ~ (all_38_1_11 = 0)
% 3.65/1.76 |
% 3.65/1.76 | Instantiating formula (7) with all_18_1_9, all_0_3_3, all_38_1_11, 0 and discharging atoms member(all_18_1_9, all_0_3_3) = all_38_1_11, member(all_18_1_9, all_0_3_3) = 0, yields:
% 3.65/1.76 | (45) all_38_1_11 = 0
% 3.65/1.76 |
% 3.65/1.76 | Instantiating formula (7) with all_18_1_9, all_0_4_4, all_38_0_10, 0 and discharging atoms member(all_18_1_9, all_0_4_4) = all_38_0_10, member(all_18_1_9, all_0_4_4) = 0, yields:
% 3.65/1.76 | (46) all_38_0_10 = 0
% 3.89/1.76 |
% 3.89/1.76 +-Applying beta-rule and splitting (44), into two cases.
% 3.89/1.76 |-Branch one:
% 3.89/1.76 | (47) ~ (all_38_0_10 = 0)
% 3.89/1.76 |
% 3.89/1.76 | Equations (46) can reduce 47 to:
% 3.89/1.76 | (21) $false
% 3.89/1.76 |
% 3.89/1.76 |-The branch is then unsatisfiable
% 3.89/1.76 |-Branch two:
% 3.89/1.76 | (46) all_38_0_10 = 0
% 3.89/1.76 | (50) ~ (all_38_1_11 = 0)
% 3.89/1.76 |
% 3.89/1.76 | Equations (45) can reduce 50 to:
% 3.89/1.76 | (21) $false
% 3.89/1.76 |
% 3.89/1.76 |-The branch is then unsatisfiable
% 3.89/1.76 % SZS output end Proof for theBenchmark
% 3.89/1.76
% 3.89/1.76 1122ms
%------------------------------------------------------------------------------