TSTP Solution File: SET624+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 00:20:56 EDT 2022
% Result : Theorem 2.92s 1.43s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.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 : Sun Jul 10 21:23:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.60 ____ _
% 0.55/0.60 ___ / __ \_____(_)___ ________ __________
% 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.60
% 0.55/0.60 A Theorem Prover for First-Order Logic
% 0.55/0.61 (ePrincess v.1.0)
% 0.55/0.61
% 0.55/0.61 (c) Philipp Rümmer, 2009-2015
% 0.55/0.61 (c) Peter Backeman, 2014-2015
% 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.61 Bug reports to peter@backeman.se
% 0.55/0.61
% 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.61
% 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.79/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.33/0.92 Prover 0: Preprocessing ...
% 1.68/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.68/1.07 Prover 0: Constructing countermodel ...
% 2.92/1.42 Prover 0: proved (769ms)
% 2.92/1.43
% 2.92/1.43 No countermodel exists, formula is valid
% 2.92/1.43 % SZS status Theorem for theBenchmark
% 2.92/1.43
% 2.92/1.43 Generating proof ... Warning: ignoring some quantifiers
% 3.68/1.64 found it (size 27)
% 3.68/1.64
% 3.68/1.64 % SZS output start Proof for theBenchmark
% 3.68/1.64 Assumed formulas after preprocessing and simplification:
% 3.68/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (union(v1, v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v5) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v5) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v5, v4) = v6) | union(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | union(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ member(v6, v5) | ~ member(v6, v4) | intersect(v4, v5)) & ! [v4] : ! [v5] : ( ~ intersect(v4, v5) | intersect(v5, v4)) & ! [v4] : ! [v5] : ( ~ intersect(v4, v5) | ? [v6] : (member(v6, v5) & member(v6, v4))) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ member(v6, v5) | ~ member(v6, v4)) & (member(v6, v5) | member(v6, v4)))) & ((intersect(v0, v3) & ~ intersect(v0, v2) & ~ intersect(v0, v1)) | ( ~ intersect(v0, v3) & (intersect(v0, v2) | intersect(v0, v1)))))
% 3.68/1.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.68/1.68 | (1) union(all_0_2_2, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0) | intersect(v0, v1)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0)) & ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ((intersect(all_0_3_3, all_0_0_0) & ~ intersect(all_0_3_3, all_0_1_1) & ~ intersect(all_0_3_3, all_0_2_2)) | ( ~ intersect(all_0_3_3, all_0_0_0) & (intersect(all_0_3_3, all_0_1_1) | intersect(all_0_3_3, all_0_2_2))))
% 3.68/1.68 |
% 3.68/1.68 | Applying alpha-rule on (1) yields:
% 3.68/1.68 | (2) (intersect(all_0_3_3, all_0_0_0) & ~ intersect(all_0_3_3, all_0_1_1) & ~ intersect(all_0_3_3, all_0_2_2)) | ( ~ intersect(all_0_3_3, all_0_0_0) & (intersect(all_0_3_3, all_0_1_1) | intersect(all_0_3_3, all_0_2_2)))
% 3.68/1.69 | (3) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0)))
% 3.85/1.69 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3))
% 3.85/1.69 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v1) | ~ member(v2, v0) | intersect(v0, v1))
% 3.85/1.69 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 3.85/1.69 | (7) ! [v0] : ! [v1] : ( ~ intersect(v0, v1) | intersect(v1, v0))
% 3.85/1.69 | (8) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 3.85/1.69 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 3.85/1.69 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3))
% 3.85/1.69 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 3.85/1.69 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 3.85/1.69 | (13) union(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.85/1.69 |
% 3.85/1.69 +-Applying beta-rule and splitting (2), into two cases.
% 3.85/1.69 |-Branch one:
% 3.85/1.69 | (14) intersect(all_0_3_3, all_0_0_0) & ~ intersect(all_0_3_3, all_0_1_1) & ~ intersect(all_0_3_3, all_0_2_2)
% 3.85/1.69 |
% 3.85/1.69 | Applying alpha-rule on (14) yields:
% 3.85/1.69 | (15) intersect(all_0_3_3, all_0_0_0)
% 3.85/1.69 | (16) ~ intersect(all_0_3_3, all_0_1_1)
% 3.85/1.69 | (17) ~ intersect(all_0_3_3, all_0_2_2)
% 3.85/1.69 |
% 3.85/1.69 | Instantiating formula (3) with all_0_0_0, all_0_3_3 and discharging atoms intersect(all_0_3_3, all_0_0_0), yields:
% 3.85/1.69 | (18) ? [v0] : (member(v0, all_0_0_0) & member(v0, all_0_3_3))
% 3.85/1.69 |
% 3.85/1.69 | Instantiating (18) with all_30_0_6 yields:
% 3.85/1.69 | (19) member(all_30_0_6, all_0_0_0) & member(all_30_0_6, all_0_3_3)
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (19) yields:
% 3.85/1.70 | (20) member(all_30_0_6, all_0_0_0)
% 3.85/1.70 | (21) member(all_30_0_6, all_0_3_3)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (6) with all_0_0_0, all_30_0_6, all_0_1_1, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_30_0_6, all_0_0_0), yields:
% 3.85/1.70 | (22) member(all_30_0_6, all_0_1_1) | member(all_30_0_6, all_0_2_2)
% 3.85/1.70 |
% 3.85/1.70 +-Applying beta-rule and splitting (22), into two cases.
% 3.85/1.70 |-Branch one:
% 3.85/1.70 | (23) member(all_30_0_6, all_0_1_1)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (5) with all_30_0_6, all_0_1_1, all_0_3_3 and discharging atoms member(all_30_0_6, all_0_1_1), member(all_30_0_6, all_0_3_3), ~ intersect(all_0_3_3, all_0_1_1), yields:
% 3.85/1.70 | (24) $false
% 3.85/1.70 |
% 3.85/1.70 |-The branch is then unsatisfiable
% 3.85/1.70 |-Branch two:
% 3.85/1.70 | (25) ~ member(all_30_0_6, all_0_1_1)
% 3.85/1.70 | (26) member(all_30_0_6, all_0_2_2)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (5) with all_30_0_6, all_0_2_2, all_0_3_3 and discharging atoms member(all_30_0_6, all_0_2_2), member(all_30_0_6, all_0_3_3), ~ intersect(all_0_3_3, all_0_2_2), yields:
% 3.85/1.70 | (24) $false
% 3.85/1.70 |
% 3.85/1.70 |-The branch is then unsatisfiable
% 3.85/1.70 |-Branch two:
% 3.85/1.70 | (28) ~ intersect(all_0_3_3, all_0_0_0) & (intersect(all_0_3_3, all_0_1_1) | intersect(all_0_3_3, all_0_2_2))
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (28) yields:
% 3.85/1.70 | (29) ~ intersect(all_0_3_3, all_0_0_0)
% 3.85/1.70 | (30) intersect(all_0_3_3, all_0_1_1) | intersect(all_0_3_3, all_0_2_2)
% 3.85/1.70 |
% 3.85/1.70 +-Applying beta-rule and splitting (30), into two cases.
% 3.85/1.70 |-Branch one:
% 3.85/1.70 | (31) intersect(all_0_3_3, all_0_1_1)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (3) with all_0_1_1, all_0_3_3 and discharging atoms intersect(all_0_3_3, all_0_1_1), yields:
% 3.85/1.70 | (32) ? [v0] : (member(v0, all_0_1_1) & member(v0, all_0_3_3))
% 3.85/1.70 |
% 3.85/1.70 | Instantiating (32) with all_37_0_10 yields:
% 3.85/1.70 | (33) member(all_37_0_10, all_0_1_1) & member(all_37_0_10, all_0_3_3)
% 3.85/1.70 |
% 3.85/1.70 | Applying alpha-rule on (33) yields:
% 3.85/1.70 | (34) member(all_37_0_10, all_0_1_1)
% 3.85/1.70 | (35) member(all_37_0_10, all_0_3_3)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (10) with all_0_0_0, all_37_0_10, all_0_1_1, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_37_0_10, all_0_1_1), yields:
% 3.85/1.70 | (36) member(all_37_0_10, all_0_0_0)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (5) with all_37_0_10, all_0_0_0, all_0_3_3 and discharging atoms member(all_37_0_10, all_0_0_0), member(all_37_0_10, all_0_3_3), ~ intersect(all_0_3_3, all_0_0_0), yields:
% 3.85/1.70 | (24) $false
% 3.85/1.70 |
% 3.85/1.70 |-The branch is then unsatisfiable
% 3.85/1.70 |-Branch two:
% 3.85/1.70 | (16) ~ intersect(all_0_3_3, all_0_1_1)
% 3.85/1.70 | (39) intersect(all_0_3_3, all_0_2_2)
% 3.85/1.70 |
% 3.85/1.70 | Instantiating formula (3) with all_0_2_2, all_0_3_3 and discharging atoms intersect(all_0_3_3, all_0_2_2), yields:
% 3.85/1.70 | (40) ? [v0] : (member(v0, all_0_2_2) & member(v0, all_0_3_3))
% 3.85/1.71 |
% 3.85/1.71 | Instantiating (40) with all_37_0_12 yields:
% 3.85/1.71 | (41) member(all_37_0_12, all_0_2_2) & member(all_37_0_12, all_0_3_3)
% 3.85/1.71 |
% 3.85/1.71 | Applying alpha-rule on (41) yields:
% 3.85/1.71 | (42) member(all_37_0_12, all_0_2_2)
% 3.85/1.71 | (43) member(all_37_0_12, all_0_3_3)
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (4) with all_0_0_0, all_37_0_12, all_0_1_1, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_37_0_12, all_0_2_2), yields:
% 3.85/1.71 | (44) member(all_37_0_12, all_0_0_0)
% 3.85/1.71 |
% 3.85/1.71 | Instantiating formula (5) with all_37_0_12, all_0_0_0, all_0_3_3 and discharging atoms member(all_37_0_12, all_0_0_0), member(all_37_0_12, all_0_3_3), ~ intersect(all_0_3_3, all_0_0_0), yields:
% 3.85/1.71 | (24) $false
% 3.85/1.71 |
% 3.85/1.71 |-The branch is then unsatisfiable
% 3.85/1.71 % SZS output end Proof for theBenchmark
% 3.85/1.71
% 3.85/1.71 1092ms
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