TSTP Solution File: SET014+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET014+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 00:16:01 EDT 2022
% Result : Theorem 2.72s 1.37s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 10 13:11:11 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.57 ____ _
% 0.17/0.57 ___ / __ \_____(_)___ ________ __________
% 0.17/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.17/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.17/0.57
% 0.17/0.57 A Theorem Prover for First-Order Logic
% 0.17/0.57 (ePrincess v.1.0)
% 0.17/0.57
% 0.17/0.57 (c) Philipp Rümmer, 2009-2015
% 0.17/0.57 (c) Peter Backeman, 2014-2015
% 0.17/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.57 Bug reports to peter@backeman.se
% 0.17/0.57
% 0.17/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.57
% 0.17/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.89 Prover 0: Preprocessing ...
% 1.65/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.65/1.04 Prover 0: Constructing countermodel ...
% 1.79/1.16 Prover 0: gave up
% 1.79/1.17 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.22/1.18 Prover 1: Preprocessing ...
% 2.47/1.25 Prover 1: Warning: ignoring some quantifiers
% 2.47/1.25 Prover 1: Constructing countermodel ...
% 2.72/1.37 Prover 1: proved (206ms)
% 2.72/1.37
% 2.72/1.37 No countermodel exists, formula is valid
% 2.72/1.37 % SZS status Theorem for theBenchmark
% 2.72/1.37
% 2.72/1.37 Generating proof ... Warning: ignoring some quantifiers
% 3.36/1.61 found it (size 41)
% 3.36/1.61
% 3.36/1.61 % SZS output start Proof for theBenchmark
% 3.36/1.61 Assumed formulas after preprocessing and simplification:
% 3.36/1.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 & union(v0, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v7, v6) = v11 & member(v7, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : ? [v10] : (member(v7, v6) = v10 & member(v7, v5) = v9 & (v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v5) = v6)) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : ? [v8] : ? [v9] : (member(v7, v6) = v9 & member(v7, v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)) & (v9 = 0 | v8 = 0))))
% 3.65/1.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.65/1.64 | (1) ~ (all_0_0_0 = 0) & subset(all_0_1_1, all_0_3_3) = all_0_0_0 & subset(all_0_2_2, all_0_3_3) = 0 & subset(all_0_4_4, all_0_3_3) = 0 & union(all_0_4_4, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 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] : ( ~ (union(v0, v1) = v2) | union(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)))
% 3.65/1.65 |
% 3.65/1.65 | Applying alpha-rule on (1) yields:
% 3.65/1.65 | (2) union(all_0_4_4, all_0_2_2) = all_0_1_1
% 3.65/1.65 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.65/1.65 | (4) ~ (all_0_0_0 = 0)
% 3.65/1.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 3.65/1.65 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.65/1.65 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5))
% 3.65/1.65 | (8) subset(all_0_1_1, all_0_3_3) = all_0_0_0
% 3.65/1.65 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.65/1.65 | (10) subset(all_0_4_4, all_0_3_3) = 0
% 3.65/1.65 | (11) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 3.65/1.65 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 3.65/1.65 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 3.65/1.66 | (14) subset(all_0_2_2, all_0_3_3) = 0
% 3.65/1.66 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 3.65/1.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (6) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 3.65/1.66 | (17) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 3.65/1.66 | (18) union(all_0_2_2, all_0_4_4) = all_0_1_1
% 3.65/1.66 |
% 3.65/1.66 +-Applying beta-rule and splitting (17), into two cases.
% 3.65/1.66 |-Branch one:
% 3.65/1.66 | (19) all_0_0_0 = 0
% 3.65/1.66 |
% 3.65/1.66 | Equations (19) can reduce 4 to:
% 3.65/1.66 | (20) $false
% 3.65/1.66 |
% 3.65/1.66 |-The branch is then unsatisfiable
% 3.65/1.66 |-Branch two:
% 3.65/1.66 | (4) ~ (all_0_0_0 = 0)
% 3.65/1.66 | (22) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 3.65/1.66 |
% 3.65/1.66 | Instantiating (22) with all_18_0_7, all_18_1_8 yields:
% 3.65/1.66 | (23) ~ (all_18_0_7 = 0) & member(all_18_1_8, all_0_1_1) = 0 & member(all_18_1_8, all_0_3_3) = all_18_0_7
% 3.65/1.66 |
% 3.65/1.66 | Applying alpha-rule on (23) yields:
% 3.65/1.66 | (24) ~ (all_18_0_7 = 0)
% 3.65/1.66 | (25) member(all_18_1_8, all_0_1_1) = 0
% 3.65/1.66 | (26) member(all_18_1_8, all_0_3_3) = all_18_0_7
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (16) with all_18_1_8, all_0_3_3, all_18_0_7, 0 and discharging atoms member(all_18_1_8, all_0_3_3) = all_18_0_7, yields:
% 3.65/1.66 | (27) all_18_0_7 = 0 | ~ (member(all_18_1_8, all_0_3_3) = 0)
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (5) with all_0_1_1, all_18_1_8, all_0_2_2, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_2_2) = all_0_1_1, member(all_18_1_8, all_0_1_1) = 0, yields:
% 3.65/1.66 | (28) ? [v0] : ? [v1] : (member(all_18_1_8, all_0_2_2) = v1 & member(all_18_1_8, all_0_4_4) = v0 & (v1 = 0 | v0 = 0))
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (5) with all_0_1_1, all_18_1_8, all_0_4_4, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_4_4) = all_0_1_1, member(all_18_1_8, all_0_1_1) = 0, yields:
% 3.65/1.66 | (29) ? [v0] : ? [v1] : (member(all_18_1_8, all_0_2_2) = v0 & member(all_18_1_8, all_0_4_4) = v1 & (v1 = 0 | v0 = 0))
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (12) with all_18_1_8, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = 0, yields:
% 3.65/1.66 | (30) ~ (member(all_18_1_8, all_0_2_2) = 0) | member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.66 |
% 3.65/1.66 | Instantiating formula (12) with all_18_1_8, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 3.65/1.66 | (31) ~ (member(all_18_1_8, all_0_4_4) = 0) | member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.66 |
% 3.65/1.66 | Instantiating (29) with all_29_0_9, all_29_1_10 yields:
% 3.65/1.66 | (32) member(all_18_1_8, all_0_2_2) = all_29_1_10 & member(all_18_1_8, all_0_4_4) = all_29_0_9 & (all_29_0_9 = 0 | all_29_1_10 = 0)
% 3.65/1.66 |
% 3.65/1.66 | Applying alpha-rule on (32) yields:
% 3.65/1.66 | (33) member(all_18_1_8, all_0_2_2) = all_29_1_10
% 3.65/1.66 | (34) member(all_18_1_8, all_0_4_4) = all_29_0_9
% 3.65/1.66 | (35) all_29_0_9 = 0 | all_29_1_10 = 0
% 3.65/1.66 |
% 3.65/1.66 | Instantiating (28) with all_31_0_11, all_31_1_12 yields:
% 3.65/1.66 | (36) member(all_18_1_8, all_0_2_2) = all_31_0_11 & member(all_18_1_8, all_0_4_4) = all_31_1_12 & (all_31_0_11 = 0 | all_31_1_12 = 0)
% 3.65/1.66 |
% 3.65/1.66 | Applying alpha-rule on (36) yields:
% 3.65/1.66 | (37) member(all_18_1_8, all_0_2_2) = all_31_0_11
% 3.65/1.66 | (38) member(all_18_1_8, all_0_4_4) = all_31_1_12
% 3.65/1.66 | (39) all_31_0_11 = 0 | all_31_1_12 = 0
% 3.65/1.66 |
% 3.65/1.66 +-Applying beta-rule and splitting (31), into two cases.
% 3.65/1.66 |-Branch one:
% 3.65/1.67 | (40) ~ (member(all_18_1_8, all_0_4_4) = 0)
% 3.65/1.67 |
% 3.65/1.67 +-Applying beta-rule and splitting (30), into two cases.
% 3.65/1.67 |-Branch one:
% 3.65/1.67 | (41) ~ (member(all_18_1_8, all_0_2_2) = 0)
% 3.65/1.67 |
% 3.65/1.67 | Instantiating formula (16) with all_18_1_8, all_0_2_2, all_29_1_10, all_31_0_11 and discharging atoms member(all_18_1_8, all_0_2_2) = all_31_0_11, member(all_18_1_8, all_0_2_2) = all_29_1_10, yields:
% 3.65/1.67 | (42) all_31_0_11 = all_29_1_10
% 3.65/1.67 |
% 3.65/1.67 | Instantiating formula (16) with all_18_1_8, all_0_4_4, all_29_0_9, all_31_1_12 and discharging atoms member(all_18_1_8, all_0_4_4) = all_31_1_12, member(all_18_1_8, all_0_4_4) = all_29_0_9, yields:
% 3.65/1.67 | (43) all_31_1_12 = all_29_0_9
% 3.65/1.67 |
% 3.65/1.67 | Using (37) and (41) yields:
% 3.65/1.67 | (44) ~ (all_31_0_11 = 0)
% 3.65/1.67 |
% 3.65/1.67 | Using (38) and (40) yields:
% 3.65/1.67 | (45) ~ (all_31_1_12 = 0)
% 3.65/1.67 |
% 3.65/1.67 | Equations (42) can reduce 44 to:
% 3.65/1.67 | (46) ~ (all_29_1_10 = 0)
% 3.65/1.67 |
% 3.65/1.67 | Equations (43) can reduce 45 to:
% 3.65/1.67 | (47) ~ (all_29_0_9 = 0)
% 3.65/1.67 |
% 3.65/1.67 +-Applying beta-rule and splitting (35), into two cases.
% 3.65/1.67 |-Branch one:
% 3.65/1.67 | (48) all_29_0_9 = 0
% 3.65/1.67 |
% 3.65/1.67 | Equations (48) can reduce 47 to:
% 3.65/1.67 | (20) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 |-Branch two:
% 3.65/1.67 | (47) ~ (all_29_0_9 = 0)
% 3.65/1.67 | (51) all_29_1_10 = 0
% 3.65/1.67 |
% 3.65/1.67 | Equations (51) can reduce 46 to:
% 3.65/1.67 | (20) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 |-Branch two:
% 3.65/1.67 | (53) member(all_18_1_8, all_0_2_2) = 0
% 3.65/1.67 | (54) member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.67 |
% 3.65/1.67 +-Applying beta-rule and splitting (27), into two cases.
% 3.65/1.67 |-Branch one:
% 3.65/1.67 | (55) ~ (member(all_18_1_8, all_0_3_3) = 0)
% 3.65/1.67 |
% 3.65/1.67 | Using (54) and (55) yields:
% 3.65/1.67 | (56) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 |-Branch two:
% 3.65/1.67 | (54) member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.67 | (58) all_18_0_7 = 0
% 3.65/1.67 |
% 3.65/1.67 | Equations (58) can reduce 24 to:
% 3.65/1.67 | (20) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 |-Branch two:
% 3.65/1.67 | (60) member(all_18_1_8, all_0_4_4) = 0
% 3.65/1.67 | (54) member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.67 |
% 3.65/1.67 +-Applying beta-rule and splitting (27), into two cases.
% 3.65/1.67 |-Branch one:
% 3.65/1.67 | (55) ~ (member(all_18_1_8, all_0_3_3) = 0)
% 3.65/1.67 |
% 3.65/1.67 | Using (54) and (55) yields:
% 3.65/1.67 | (56) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 |-Branch two:
% 3.65/1.67 | (54) member(all_18_1_8, all_0_3_3) = 0
% 3.65/1.67 | (58) all_18_0_7 = 0
% 3.65/1.67 |
% 3.65/1.67 | Equations (58) can reduce 24 to:
% 3.65/1.67 | (20) $false
% 3.65/1.67 |
% 3.65/1.67 |-The branch is then unsatisfiable
% 3.65/1.67 % SZS output end Proof for theBenchmark
% 3.65/1.67
% 3.65/1.67 1091ms
%------------------------------------------------------------------------------