TSTP Solution File: SET881+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 00:22:54 EDT 2022
% Result : Theorem 1.90s 1.21s
% Output : Proof 2.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 11:55:57 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.67/0.62 ____ _
% 0.67/0.62 ___ / __ \_____(_)___ ________ __________
% 0.67/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.62
% 0.67/0.62 A Theorem Prover for First-Order Logic
% 0.67/0.63 (ePrincess v.1.0)
% 0.67/0.63
% 0.67/0.63 (c) Philipp Rümmer, 2009-2015
% 0.67/0.63 (c) Peter Backeman, 2014-2015
% 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.63 Bug reports to peter@backeman.se
% 0.67/0.63
% 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.63
% 0.67/0.63 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
% 1.36/0.94 Prover 0: Preprocessing ...
% 1.72/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.72/1.11 Prover 0: Constructing countermodel ...
% 1.90/1.21 Prover 0: proved (524ms)
% 1.90/1.21
% 1.90/1.21 No countermodel exists, formula is valid
% 1.90/1.21 % SZS status Theorem for theBenchmark
% 1.90/1.21
% 1.90/1.21 Generating proof ... Warning: ignoring some quantifiers
% 2.63/1.35 found it (size 6)
% 2.63/1.35
% 2.63/1.35 % SZS output start Proof for theBenchmark
% 2.63/1.35 Assumed formulas after preprocessing and simplification:
% 2.63/1.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = empty_set) & singleton(v0) = v2 & set_difference(v2, v3) = v4 & unordered_pair(v0, v1) = v3 & empty(v6) & empty(empty_set) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (singleton(v7) = v9) | ~ (set_difference(v9, v8) = v10) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v7) = v9) | ~ (set_difference(v9, v8) = empty_set) | in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)))
% 2.67/1.39 | 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:
% 2.67/1.39 | (1) ~ (all_0_2_2 = empty_set) & singleton(all_0_6_6) = all_0_4_4 & set_difference(all_0_4_4, all_0_3_3) = all_0_2_2 & unordered_pair(all_0_6_6, 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 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = empty_set) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.67/1.40 |
% 2.67/1.40 | Applying alpha-rule on (1) yields:
% 2.67/1.40 | (2) ~ (all_0_2_2 = empty_set)
% 2.67/1.40 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 2.67/1.40 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 2.67/1.40 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 2.67/1.40 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 2.67/1.40 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 2.67/1.40 | (8) empty(all_0_0_0)
% 2.67/1.40 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 2.67/1.40 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 2.67/1.40 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = empty_set) | in(v0, v1))
% 2.67/1.40 | (12) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 2.67/1.40 | (13) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3
% 2.67/1.40 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 2.67/1.40 | (15) set_difference(all_0_4_4, all_0_3_3) = all_0_2_2
% 2.67/1.40 | (16) ~ empty(all_0_1_1)
% 2.67/1.40 | (17) empty(empty_set)
% 2.67/1.40 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ in(v0, v1))
% 2.67/1.40 | (19) singleton(all_0_6_6) = all_0_4_4
% 2.67/1.40 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 2.67/1.40 |
% 2.67/1.40 | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 2.67/1.40 | (21) in(all_0_6_6, all_0_3_3)
% 2.67/1.40 |
% 2.67/1.40 | Instantiating formula (18) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, set_difference(all_0_4_4, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_3_3), yields:
% 2.67/1.40 | (22) all_0_2_2 = empty_set
% 2.67/1.40 |
% 2.67/1.40 | Equations (22) can reduce 2 to:
% 2.67/1.40 | (23) $false
% 2.67/1.40 |
% 2.67/1.41 |-The branch is then unsatisfiable
% 2.67/1.41 % SZS output end Proof for theBenchmark
% 2.67/1.41
% 2.67/1.41 765ms
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