TSTP Solution File: SET588+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 00:20:29 EDT 2022
% Result : Theorem 2.63s 1.37s
% Output : Proof 3.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n010.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 : Sat Jul 9 20:53:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.62 ____ _
% 0.46/0.62 ___ / __ \_____(_)___ ________ __________
% 0.46/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.62
% 0.46/0.62 A Theorem Prover for First-Order Logic
% 0.46/0.62 (ePrincess v.1.0)
% 0.46/0.62
% 0.46/0.62 (c) Philipp Rümmer, 2009-2015
% 0.46/0.62 (c) Peter Backeman, 2014-2015
% 0.46/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.62 Bug reports to peter@backeman.se
% 0.46/0.62
% 0.46/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.62
% 0.46/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.38/0.95 Prover 0: Preprocessing ...
% 1.50/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.66/1.07 Prover 0: Constructing countermodel ...
% 1.98/1.21 Prover 0: gave up
% 1.98/1.21 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.98/1.23 Prover 1: Preprocessing ...
% 2.38/1.29 Prover 1: Constructing countermodel ...
% 2.63/1.37 Prover 1: proved (155ms)
% 2.63/1.37
% 2.63/1.37 No countermodel exists, formula is valid
% 2.63/1.37 % SZS status Theorem for theBenchmark
% 2.63/1.37
% 2.63/1.37 Generating proof ... found it (size 29)
% 3.33/1.60
% 3.33/1.60 % SZS output start Proof for theBenchmark
% 3.33/1.60 Assumed formulas after preprocessing and simplification:
% 3.33/1.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & difference(v1, v2) = v4 & difference(v0, v2) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (difference(v6, v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : (member(v8, v7) = v12 & member(v8, v6) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (subset(v9, v8) = v7) | ~ (subset(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (member(v9, v8) = v7) | ~ (member(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10 & 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] : (v7 = 0 | ~ (subset(v6, v6) = v7)))
% 3.33/1.63 | 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:
% 3.33/1.63 | (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 & difference(all_0_4_4, all_0_3_3) = all_0_1_1 & difference(all_0_5_5, all_0_3_3) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & 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] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.33/1.64 |
% 3.33/1.64 | Applying alpha-rule on (1) yields:
% 3.33/1.64 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 3.33/1.64 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 3.33/1.64 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 3.33/1.64 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 3.33/1.64 | (6) difference(all_0_4_4, all_0_3_3) = all_0_1_1
% 3.33/1.64 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 3.33/1.64 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 3.33/1.64 | (9) subset(all_0_5_5, all_0_4_4) = 0
% 3.33/1.64 | (10) ~ (all_0_0_0 = 0)
% 3.33/1.64 | (11) subset(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.33/1.64 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 3.33/1.64 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 3.33/1.64 | (14) difference(all_0_5_5, all_0_3_3) = all_0_2_2
% 3.33/1.64 |
% 3.33/1.64 | 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:
% 3.33/1.64 | (15) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.33/1.64 |
% 3.33/1.64 +-Applying beta-rule and splitting (15), into two cases.
% 3.33/1.64 |-Branch one:
% 3.33/1.64 | (16) all_0_0_0 = 0
% 3.33/1.64 |
% 3.33/1.64 | Equations (16) can reduce 10 to:
% 3.33/1.64 | (17) $false
% 3.33/1.64 |
% 3.33/1.65 |-The branch is then unsatisfiable
% 3.33/1.65 |-Branch two:
% 3.33/1.65 | (10) ~ (all_0_0_0 = 0)
% 3.33/1.65 | (19) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 3.33/1.65 |
% 3.33/1.65 | Instantiating (19) with all_18_0_6, all_18_1_7 yields:
% 3.33/1.65 | (20) ~ (all_18_0_6 = 0) & member(all_18_1_7, all_0_1_1) = all_18_0_6 & member(all_18_1_7, all_0_2_2) = 0
% 3.33/1.65 |
% 3.33/1.65 | Applying alpha-rule on (20) yields:
% 3.33/1.65 | (21) ~ (all_18_0_6 = 0)
% 3.33/1.65 | (22) member(all_18_1_7, all_0_1_1) = all_18_0_6
% 3.33/1.65 | (23) member(all_18_1_7, all_0_2_2) = 0
% 3.33/1.65 |
% 3.33/1.65 | Instantiating formula (4) with all_18_0_6, all_0_1_1, all_18_1_7, all_0_3_3, all_0_4_4 and discharging atoms difference(all_0_4_4, all_0_3_3) = all_0_1_1, member(all_18_1_7, all_0_1_1) = all_18_0_6, yields:
% 3.33/1.65 | (24) all_18_0_6 = 0 | ? [v0] : ? [v1] : (member(all_18_1_7, all_0_3_3) = v1 & member(all_18_1_7, all_0_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 3.33/1.65 |
% 3.33/1.65 | Instantiating formula (12) with all_0_2_2, all_18_1_7, all_0_3_3, all_0_5_5 and discharging atoms difference(all_0_5_5, all_0_3_3) = all_0_2_2, member(all_18_1_7, all_0_2_2) = 0, yields:
% 3.33/1.65 | (25) ? [v0] : ( ~ (v0 = 0) & member(all_18_1_7, all_0_3_3) = v0 & member(all_18_1_7, all_0_5_5) = 0)
% 3.33/1.65 |
% 3.33/1.65 | Instantiating formula (3) with all_18_1_7, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields:
% 3.33/1.65 | (26) ~ (member(all_18_1_7, all_0_5_5) = 0) | member(all_18_1_7, all_0_4_4) = 0
% 3.33/1.65 |
% 3.33/1.65 | Instantiating (25) with all_29_0_8 yields:
% 3.33/1.65 | (27) ~ (all_29_0_8 = 0) & member(all_18_1_7, all_0_3_3) = all_29_0_8 & member(all_18_1_7, all_0_5_5) = 0
% 3.33/1.65 |
% 3.33/1.65 | Applying alpha-rule on (27) yields:
% 3.33/1.65 | (28) ~ (all_29_0_8 = 0)
% 3.33/1.65 | (29) member(all_18_1_7, all_0_3_3) = all_29_0_8
% 3.33/1.65 | (30) member(all_18_1_7, all_0_5_5) = 0
% 3.33/1.65 |
% 3.33/1.65 +-Applying beta-rule and splitting (26), into two cases.
% 3.33/1.65 |-Branch one:
% 3.33/1.65 | (31) ~ (member(all_18_1_7, all_0_5_5) = 0)
% 3.33/1.65 |
% 3.33/1.65 | Using (30) and (31) yields:
% 3.33/1.65 | (32) $false
% 3.33/1.65 |
% 3.33/1.65 |-The branch is then unsatisfiable
% 3.33/1.65 |-Branch two:
% 3.33/1.65 | (30) member(all_18_1_7, all_0_5_5) = 0
% 3.33/1.65 | (34) member(all_18_1_7, all_0_4_4) = 0
% 3.33/1.65 |
% 3.33/1.65 +-Applying beta-rule and splitting (24), into two cases.
% 3.33/1.65 |-Branch one:
% 3.33/1.65 | (35) all_18_0_6 = 0
% 3.33/1.65 |
% 3.33/1.65 | Equations (35) can reduce 21 to:
% 3.33/1.65 | (17) $false
% 3.33/1.65 |
% 3.33/1.65 |-The branch is then unsatisfiable
% 3.33/1.65 |-Branch two:
% 3.33/1.65 | (21) ~ (all_18_0_6 = 0)
% 3.33/1.65 | (38) ? [v0] : ? [v1] : (member(all_18_1_7, all_0_3_3) = v1 & member(all_18_1_7, all_0_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 3.33/1.65 |
% 3.33/1.65 | Instantiating (38) with all_38_0_9, all_38_1_10 yields:
% 3.33/1.65 | (39) member(all_18_1_7, all_0_3_3) = all_38_0_9 & member(all_18_1_7, all_0_4_4) = all_38_1_10 & ( ~ (all_38_1_10 = 0) | all_38_0_9 = 0)
% 3.33/1.65 |
% 3.33/1.65 | Applying alpha-rule on (39) yields:
% 3.33/1.65 | (40) member(all_18_1_7, all_0_3_3) = all_38_0_9
% 3.33/1.65 | (41) member(all_18_1_7, all_0_4_4) = all_38_1_10
% 3.33/1.65 | (42) ~ (all_38_1_10 = 0) | all_38_0_9 = 0
% 3.33/1.65 |
% 3.33/1.65 | Instantiating formula (7) with all_18_1_7, all_0_3_3, all_29_0_8, all_38_0_9 and discharging atoms member(all_18_1_7, all_0_3_3) = all_38_0_9, member(all_18_1_7, all_0_3_3) = all_29_0_8, yields:
% 3.33/1.65 | (43) all_38_0_9 = all_29_0_8
% 3.33/1.65 |
% 3.33/1.65 | Instantiating formula (7) with all_18_1_7, all_0_4_4, all_38_1_10, 0 and discharging atoms member(all_18_1_7, all_0_4_4) = all_38_1_10, member(all_18_1_7, all_0_4_4) = 0, yields:
% 3.33/1.65 | (44) all_38_1_10 = 0
% 3.33/1.65 |
% 3.33/1.65 +-Applying beta-rule and splitting (42), into two cases.
% 3.33/1.65 |-Branch one:
% 3.33/1.65 | (45) ~ (all_38_1_10 = 0)
% 3.33/1.65 |
% 3.33/1.65 | Equations (44) can reduce 45 to:
% 3.33/1.65 | (17) $false
% 3.33/1.65 |
% 3.33/1.65 |-The branch is then unsatisfiable
% 3.33/1.65 |-Branch two:
% 3.33/1.65 | (44) all_38_1_10 = 0
% 3.33/1.65 | (48) all_38_0_9 = 0
% 3.33/1.65 |
% 3.33/1.65 | Combining equations (48,43) yields a new equation:
% 3.33/1.66 | (49) all_29_0_8 = 0
% 3.33/1.66 |
% 3.33/1.66 | Equations (49) can reduce 28 to:
% 3.33/1.66 | (17) $false
% 3.33/1.66 |
% 3.33/1.66 |-The branch is then unsatisfiable
% 3.33/1.66 % SZS output end Proof for theBenchmark
% 3.33/1.66
% 3.33/1.66 1022ms
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