TSTP Solution File: SET987+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 00:23:38 EDT 2022
% Result : Theorem 2.05s 1.20s
% Output : Proof 2.84s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n017.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 11:19:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.58/0.60 ____ _
% 0.58/0.60 ___ / __ \_____(_)___ ________ __________
% 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.92 Prover 0: Preprocessing ...
% 1.75/1.08 Prover 0: Constructing countermodel ...
% 2.05/1.20 Prover 0: proved (545ms)
% 2.05/1.20
% 2.05/1.20 No countermodel exists, formula is valid
% 2.05/1.20 % SZS status Theorem for theBenchmark
% 2.05/1.20
% 2.05/1.20 Generating proof ... found it (size 6)
% 2.67/1.39
% 2.67/1.39 % SZS output start Proof for theBenchmark
% 2.67/1.39 Assumed formulas after preprocessing and simplification:
% 2.67/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v1) & singleton(v0) = v2 & set_difference(v3, v2) = v4 & set_union2(v1, v2) = v3 & empty(v6) & ~ empty(v5) & ~ in(v0, v1) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (singleton(v8) = v9) | ~ (set_difference(v7, v9) = v10) | in(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | ~ (set_difference(v7, v9) = v7) | ~ in(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)))
% 2.84/1.43 | 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, all_0_6_6 yields:
% 2.84/1.43 | (1) ~ (all_0_2_2 = all_0_5_5) & singleton(all_0_6_6) = all_0_4_4 & set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & set_union2(all_0_5_5, all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ in(all_0_6_6, all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v0) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [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] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.84/1.43 |
% 2.84/1.43 | Applying alpha-rule on (1) yields:
% 2.84/1.43 | (2) ~ (all_0_2_2 = all_0_5_5)
% 2.84/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.84/1.43 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 2.84/1.43 | (5) empty(all_0_0_0)
% 2.84/1.43 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 2.84/1.43 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.84/1.44 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | in(v1, v0))
% 2.84/1.44 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 2.84/1.44 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 2.84/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 2.84/1.44 | (12) ~ empty(all_0_1_1)
% 2.84/1.44 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.84/1.44 | (14) singleton(all_0_6_6) = all_0_4_4
% 2.84/1.44 | (15) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2
% 2.84/1.44 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 2.84/1.44 | (17) set_union2(all_0_5_5, all_0_4_4) = all_0_3_3
% 2.84/1.44 | (18) ~ in(all_0_6_6, all_0_5_5)
% 2.84/1.44 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v0) | ~ in(v1, v0))
% 2.84/1.44 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 2.84/1.44 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 2.84/1.44 |
% 2.84/1.44 | Instantiating formula (11) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, set_union2(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 2.84/1.44 | (22) set_difference(all_0_5_5, all_0_4_4) = all_0_2_2
% 2.84/1.44 |
% 2.84/1.44 | Instantiating formula (8) with all_0_2_2, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms singleton(all_0_6_6) = all_0_4_4, set_difference(all_0_5_5, all_0_4_4) = all_0_2_2, ~ in(all_0_6_6, all_0_5_5), yields:
% 2.84/1.44 | (23) all_0_2_2 = all_0_5_5
% 2.84/1.44 |
% 2.84/1.44 | Equations (23) can reduce 2 to:
% 2.84/1.44 | (24) $false
% 2.84/1.44 |
% 2.84/1.44 |-The branch is then unsatisfiable
% 2.84/1.44 % SZS output end Proof for theBenchmark
% 2.84/1.44
% 2.84/1.44 833ms
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