TSTP Solution File: SET908+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 00:23:04 EDT 2022
% Result : Theorem 2.10s 1.20s
% Output : Proof 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n005.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 19:17:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.58 ____ _
% 0.50/0.58 ___ / __ \_____(_)___ ________ __________
% 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.58
% 0.50/0.58 A Theorem Prover for First-Order Logic
% 0.50/0.58 (ePrincess v.1.0)
% 0.50/0.58
% 0.50/0.58 (c) Philipp Rümmer, 2009-2015
% 0.50/0.58 (c) Peter Backeman, 2014-2015
% 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.58 Bug reports to peter@backeman.se
% 0.50/0.58
% 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.58
% 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.25/0.89 Prover 0: Preprocessing ...
% 1.75/1.07 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.08 Prover 0: Constructing countermodel ...
% 2.10/1.20 Prover 0: proved (571ms)
% 2.10/1.20
% 2.10/1.20 No countermodel exists, formula is valid
% 2.10/1.20 % SZS status Theorem for theBenchmark
% 2.10/1.20
% 2.10/1.20 Generating proof ... Warning: ignoring some quantifiers
% 2.79/1.40 found it (size 7)
% 2.79/1.40
% 2.79/1.40 % SZS output start Proof for theBenchmark
% 2.79/1.40 Assumed formulas after preprocessing and simplification:
% 2.79/1.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (singleton(v0) = v2 & set_union2(v2, v1) = empty_set & empty(v4) & empty(empty_set) & ~ empty(v3) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_union2(v8, v7) = v6) | ~ (set_union2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v6) | in(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v6) | in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v5) | in(v8, v7)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (set_union2(v6, v7) = v8) | ? [v9] : (( ~ in(v9, v5) | ( ~ in(v9, v7) & ~ in(v9, v6))) & (in(v9, v7) | in(v9, v6) | in(v9, v5)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v5) = v6) | ~ in(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | set_union2(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | set_union2(v6, v5) = v7) & ? [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v6) = v7) | ? [v8] : (( ~ (v8 = v6) | ~ in(v6, v5)) & (v8 = v6 | in(v8, v5)))) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_union2(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (singleton(v5) = v6) | in(v5, v6)) & ! [v5] : ! [v6] : ( ~ in(v6, v5) | ~ in(v5, v6)) & ! [v5] : ~ in(v5, empty_set) & ? [v5] : (v5 = empty_set | ? [v6] : in(v6, v5)))
% 2.97/1.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.97/1.44 | (1) singleton(all_0_4_4) = all_0_2_2 & set_union2(all_0_2_2, all_0_3_3) = empty_set & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, 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_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 2.97/1.45 |
% 2.97/1.45 | Applying alpha-rule on (1) yields:
% 2.97/1.45 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.97/1.45 | (3) ! [v0] : ~ in(v0, empty_set)
% 2.97/1.45 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 2.97/1.45 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 2.97/1.45 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.97/1.45 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.97/1.45 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.97/1.45 | (9) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 2.97/1.45 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 2.97/1.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 2.97/1.46 | (12) set_union2(all_0_2_2, all_0_3_3) = empty_set
% 2.97/1.46 | (13) singleton(all_0_4_4) = all_0_2_2
% 2.97/1.46 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.97/1.46 | (15) empty(all_0_0_0)
% 2.97/1.46 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 2.97/1.46 | (17) ~ empty(all_0_1_1)
% 2.97/1.46 | (18) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 2.97/1.46 | (19) empty(empty_set)
% 2.97/1.46 | (20) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 2.97/1.46 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 2.97/1.46 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 2.97/1.46 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.97/1.46 |
% 2.97/1.46 | Instantiating formula (16) with all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, yields:
% 2.97/1.46 | (24) in(all_0_4_4, all_0_2_2)
% 2.97/1.46 |
% 2.97/1.46 | Instantiating formula (8) with empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_2_2, all_0_3_3) = empty_set, yields:
% 2.97/1.46 | (25) set_union2(all_0_3_3, all_0_2_2) = empty_set
% 2.97/1.46 |
% 2.97/1.46 | Instantiating formula (5) with all_0_4_4, empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_2_2) = empty_set, in(all_0_4_4, all_0_2_2), yields:
% 3.07/1.46 | (26) in(all_0_4_4, empty_set)
% 3.07/1.46 |
% 3.07/1.46 | Instantiating formula (3) with all_0_4_4 and discharging atoms in(all_0_4_4, empty_set), yields:
% 3.07/1.46 | (27) $false
% 3.07/1.46 |
% 3.07/1.46 |-The branch is then unsatisfiable
% 3.07/1.46 % SZS output end Proof for theBenchmark
% 3.07/1.46
% 3.07/1.46 875ms
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