TSTP Solution File: SET880+1 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 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 00:22:53 EDT 2022
% Result : Theorem 1.81s 1.15s
% Output : Proof 2.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 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 04:06:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.59/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.32/0.89 Prover 0: Preprocessing ...
% 1.67/1.02 Prover 0: Warning: ignoring some quantifiers
% 1.67/1.04 Prover 0: Constructing countermodel ...
% 1.81/1.14 Prover 0: proved (515ms)
% 1.81/1.15
% 1.81/1.15 No countermodel exists, formula is valid
% 1.81/1.15 % SZS status Theorem for theBenchmark
% 1.81/1.15
% 1.81/1.15 Generating proof ... Warning: ignoring some quantifiers
% 2.59/1.32 found it (size 6)
% 2.59/1.32
% 2.59/1.32 % SZS output start Proof for theBenchmark
% 2.59/1.32 Assumed formulas after preprocessing and simplification:
% 2.59/1.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v1 = v0) & set_difference(v2, v3) = empty_set & singleton(v1) = v3 & singleton(v0) = v2 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(v8, v7) = v9) | ~ (singleton(v6) = v8) | ~ in(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_difference(v9, v8) = v7) | ~ (set_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v6) = v7) | ~ in(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_difference(v8, v7) = empty_set) | ~ (singleton(v6) = v8) | in(v6, v7)) & ? [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (singleton(v7) = v8) | ? [v9] : (( ~ (v9 = v7) | ~ in(v7, v6)) & (v9 = v7 | in(v9, v6)))) & ! [v6] : ! [v7] : ( ~ (singleton(v6) = v7) | in(v6, v7)) & ! [v6] : ! [v7] : ( ~ in(v7, v6) | ~ in(v6, v7)))
% 2.59/1.35 | 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:
% 2.59/1.35 | (1) ~ (all_0_4_4 = all_0_5_5) & set_difference(all_0_3_3, all_0_2_2) = empty_set & singleton(all_0_4_4) = all_0_2_2 & singleton(all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = empty_set) | ~ (singleton(v0) = v2) | in(v0, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.59/1.35 |
% 2.59/1.35 | Applying alpha-rule on (1) yields:
% 2.59/1.35 | (2) set_difference(all_0_3_3, all_0_2_2) = empty_set
% 2.59/1.36 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.59/1.36 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.59/1.36 | (5) singleton(all_0_4_4) = all_0_2_2
% 2.59/1.36 | (6) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.59/1.36 | (7) ~ empty(all_0_1_1)
% 2.59/1.36 | (8) empty(empty_set)
% 2.59/1.36 | (9) ~ (all_0_4_4 = all_0_5_5)
% 2.59/1.36 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v2, v1) = empty_set) | ~ (singleton(v0) = v2) | in(v0, v1))
% 2.59/1.36 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.59/1.36 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.59/1.36 | (13) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.59/1.36 | (14) empty(all_0_0_0)
% 2.59/1.36 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ in(v0, v1))
% 2.59/1.36 | (16) singleton(all_0_5_5) = all_0_3_3
% 2.59/1.36 |
% 2.59/1.36 | Instantiating formula (10) with all_0_3_3, all_0_2_2, all_0_5_5 and discharging atoms set_difference(all_0_3_3, all_0_2_2) = empty_set, singleton(all_0_5_5) = all_0_3_3, yields:
% 2.59/1.36 | (17) in(all_0_5_5, all_0_2_2)
% 2.59/1.36 |
% 2.59/1.36 | Instantiating formula (12) with all_0_5_5, all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, in(all_0_5_5, all_0_2_2), yields:
% 2.59/1.36 | (18) all_0_4_4 = all_0_5_5
% 2.59/1.36 |
% 2.59/1.36 | Equations (18) can reduce 9 to:
% 2.59/1.36 | (19) $false
% 2.59/1.36 |
% 2.72/1.36 |-The branch is then unsatisfiable
% 2.72/1.36 % SZS output end Proof for theBenchmark
% 2.72/1.37
% 2.72/1.37 777ms
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