TSTP Solution File: SET597+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 00:20:35 EDT 2022
% Result : Theorem 2.24s 1.18s
% Output : Proof 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n012.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 : Sun Jul 10 15:41:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.60 ____ _
% 0.21/0.60 ___ / __ \_____(_)___ ________ __________
% 0.21/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.21/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic
% 0.64/0.61 (ePrincess v.1.0)
% 0.64/0.61
% 0.64/0.61 (c) Philipp Rümmer, 2009-2015
% 0.64/0.61 (c) Peter Backeman, 2014-2015
% 0.64/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.61 Bug reports to peter@backeman.se
% 0.64/0.61
% 0.64/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.61
% 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.44/0.90 Prover 0: Preprocessing ...
% 1.72/1.03 Prover 0: Warning: ignoring some quantifiers
% 1.72/1.05 Prover 0: Constructing countermodel ...
% 2.24/1.18 Prover 0: proved (500ms)
% 2.24/1.18
% 2.24/1.18 No countermodel exists, formula is valid
% 2.24/1.18 % SZS status Theorem for theBenchmark
% 2.24/1.18
% 2.24/1.18 Generating proof ... Warning: ignoring some quantifiers
% 2.83/1.43 found it (size 25)
% 2.83/1.43
% 2.83/1.43 % SZS output start Proof for theBenchmark
% 2.83/1.44 Assumed formulas after preprocessing and simplification:
% 2.83/1.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (union(v1, v2) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v7) = v8) | ~ subset(v7, v6) | ~ subset(v5, v6) | subset(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v8) | member(v7, v6) | member(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v6) | member(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ member(v7, v5) | member(v7, v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v6, v5) = v7) | union(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | subset(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v5) | ~ subset(v5, v6) | member(v7, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ subset(v6, v5) | ~ subset(v5, v6)) & ? [v5] : ? [v6] : (v6 = v5 | ? [v7] : (( ~ member(v7, v6) | ~ member(v7, v5)) & (member(v7, v6) | member(v7, v5)))) & ? [v5] : ? [v6] : (subset(v5, v6) | ? [v7] : (member(v7, v5) & ~ member(v7, v6))) & ? [v5] : subset(v5, v5) & ((v3 = v0 & ( ~ subset(v2, v0) | ~ subset(v1, v0) | (subset(v2, v4) & subset(v1, v4) & ~ subset(v0, v4)))) | ( ~ (v3 = v0) & subset(v2, v0) & subset(v1, v0) & ! [v5] : ( ~ subset(v2, v5) | ~ subset(v1, v5) | subset(v0, v5)))))
% 3.08/1.47 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.08/1.47 | (1) union(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [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] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : subset(v0, v0) & ((all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)))) | ( ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0))))
% 3.08/1.48 |
% 3.08/1.48 | Applying alpha-rule on (1) yields:
% 3.08/1.48 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 3.08/1.48 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 3.08/1.48 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 3.08/1.48 | (5) ? [v0] : subset(v0, v0)
% 3.08/1.48 | (6) union(all_0_3_3, all_0_2_2) = all_0_1_1
% 3.08/1.48 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 3.08/1.48 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 3.08/1.48 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3))
% 3.08/1.48 | (10) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 3.08/1.48 | (11) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 3.08/1.48 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2))
% 3.08/1.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 3.08/1.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3))
% 3.08/1.48 | (15) (all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)))) | ( ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0)))
% 3.08/1.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 3.08/1.49 |
% 3.08/1.49 | Instantiating formula (4) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 3.08/1.49 | (17) union(all_0_2_2, all_0_3_3) = all_0_1_1
% 3.08/1.49 |
% 3.08/1.49 | Instantiating formula (12) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 3.08/1.49 | (18) subset(all_0_3_3, all_0_1_1)
% 3.08/1.49 |
% 3.08/1.49 | Instantiating formula (12) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 3.08/1.49 | (19) subset(all_0_2_2, all_0_1_1)
% 3.08/1.49 |
% 3.08/1.49 +-Applying beta-rule and splitting (15), into two cases.
% 3.08/1.49 |-Branch one:
% 3.08/1.49 | (20) all_0_1_1 = all_0_4_4 & ( ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)))
% 3.08/1.49 |
% 3.08/1.49 | Applying alpha-rule on (20) yields:
% 3.08/1.49 | (21) all_0_1_1 = all_0_4_4
% 3.08/1.49 | (22) ~ subset(all_0_2_2, all_0_4_4) | ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0))
% 3.08/1.49 |
% 3.08/1.49 | From (21) and (6) follows:
% 3.08/1.49 | (23) union(all_0_3_3, all_0_2_2) = all_0_4_4
% 3.08/1.49 |
% 3.08/1.49 | From (21) and (19) follows:
% 3.08/1.49 | (24) subset(all_0_2_2, all_0_4_4)
% 3.08/1.49 |
% 3.08/1.49 | From (21) and (18) follows:
% 3.08/1.49 | (25) subset(all_0_3_3, all_0_4_4)
% 3.08/1.49 |
% 3.08/1.49 +-Applying beta-rule and splitting (22), into two cases.
% 3.08/1.49 |-Branch one:
% 3.08/1.49 | (26) ~ subset(all_0_2_2, all_0_4_4)
% 3.08/1.49 |
% 3.08/1.49 | Using (24) and (26) yields:
% 3.08/1.49 | (27) $false
% 3.08/1.49 |
% 3.08/1.49 |-The branch is then unsatisfiable
% 3.08/1.49 |-Branch two:
% 3.08/1.49 | (24) subset(all_0_2_2, all_0_4_4)
% 3.08/1.49 | (29) ~ subset(all_0_3_3, all_0_4_4) | (subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0))
% 3.08/1.49 |
% 3.08/1.49 +-Applying beta-rule and splitting (29), into two cases.
% 3.08/1.49 |-Branch one:
% 3.08/1.49 | (30) ~ subset(all_0_3_3, all_0_4_4)
% 3.08/1.49 |
% 3.08/1.49 | Using (25) and (30) yields:
% 3.08/1.49 | (27) $false
% 3.08/1.49 |
% 3.08/1.49 |-The branch is then unsatisfiable
% 3.08/1.49 |-Branch two:
% 3.08/1.49 | (25) subset(all_0_3_3, all_0_4_4)
% 3.08/1.49 | (33) subset(all_0_2_2, all_0_0_0) & subset(all_0_3_3, all_0_0_0) & ~ subset(all_0_4_4, all_0_0_0)
% 3.08/1.49 |
% 3.08/1.49 | Applying alpha-rule on (33) yields:
% 3.08/1.49 | (34) subset(all_0_2_2, all_0_0_0)
% 3.08/1.49 | (35) subset(all_0_3_3, all_0_0_0)
% 3.08/1.49 | (36) ~ subset(all_0_4_4, all_0_0_0)
% 3.08/1.49 |
% 3.08/1.49 | Instantiating formula (16) with all_0_4_4, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_4_4, subset(all_0_2_2, all_0_0_0), subset(all_0_3_3, all_0_0_0), ~ subset(all_0_4_4, all_0_0_0), yields:
% 3.08/1.49 | (27) $false
% 3.08/1.49 |
% 3.08/1.49 |-The branch is then unsatisfiable
% 3.08/1.49 |-Branch two:
% 3.08/1.49 | (38) ~ (all_0_1_1 = all_0_4_4) & subset(all_0_2_2, all_0_4_4) & subset(all_0_3_3, all_0_4_4) & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0))
% 3.08/1.50 |
% 3.08/1.50 | Applying alpha-rule on (38) yields:
% 3.08/1.50 | (39) ~ (all_0_1_1 = all_0_4_4)
% 3.08/1.50 | (24) subset(all_0_2_2, all_0_4_4)
% 3.08/1.50 | (25) subset(all_0_3_3, all_0_4_4)
% 3.08/1.50 | (42) ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ subset(all_0_3_3, v0) | subset(all_0_4_4, v0))
% 3.08/1.50 |
% 3.08/1.50 | Instantiating formula (42) with all_0_1_1 and discharging atoms subset(all_0_2_2, all_0_1_1), subset(all_0_3_3, all_0_1_1), yields:
% 3.08/1.50 | (43) subset(all_0_4_4, all_0_1_1)
% 3.08/1.50 |
% 3.08/1.50 | Instantiating formula (16) with all_0_1_1, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, subset(all_0_2_2, all_0_4_4), subset(all_0_3_3, all_0_4_4), yields:
% 3.08/1.50 | (44) subset(all_0_1_1, all_0_4_4)
% 3.08/1.50 |
% 3.08/1.50 | Instantiating formula (2) with all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_1_1, all_0_4_4), subset(all_0_4_4, all_0_1_1), yields:
% 3.08/1.50 | (21) all_0_1_1 = all_0_4_4
% 3.08/1.50 |
% 3.08/1.50 | Equations (21) can reduce 39 to:
% 3.08/1.50 | (46) $false
% 3.08/1.50 |
% 3.08/1.50 |-The branch is then unsatisfiable
% 3.08/1.50 % SZS output end Proof for theBenchmark
% 3.08/1.50
% 3.08/1.50 877ms
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