TSTP Solution File: SET366+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 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 00:19:15 EDT 2022
% Result : Theorem 3.80s 1.56s
% Output : Proof 5.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n018.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 : Mon Jul 11 02:16:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.91 Prover 0: Preprocessing ...
% 2.09/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.09/1.14 Prover 0: Constructing countermodel ...
% 3.19/1.40 Prover 0: gave up
% 3.19/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.19/1.42 Prover 1: Preprocessing ...
% 3.76/1.52 Prover 1: Constructing countermodel ...
% 3.80/1.56 Prover 1: proved (162ms)
% 3.80/1.56
% 3.80/1.56 No countermodel exists, formula is valid
% 3.80/1.56 % SZS status Theorem for theBenchmark
% 3.80/1.56
% 3.80/1.56 Generating proof ... found it (size 16)
% 4.58/1.76
% 4.58/1.76 % SZS output start Proof for theBenchmark
% 4.58/1.76 Assumed formulas after preprocessing and simplification:
% 4.58/1.76 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & power_set(v0) = v1 & member(empty_set, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v6) = v7) | ~ (member(v3, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v8 & member(v3, v4) = v9 & ( ~ (v8 = 0) | v9 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & member(v3, v5) = v9 & member(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v9 & member(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (sum(v4) = v5) | ~ (member(v3, v7) = 0) | ~ (member(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = 0 & member(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v4, v3) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (power_set(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & subset(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v3 | v4 = v3 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unordered_pair(v6, v5) = v4) | ~ (unordered_pair(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (difference(v6, v5) = v4) | ~ (difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (union(v6, v5) = v4) | ~ (union(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_set(v6, v5) = v4) | ~ (equal_set(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (subset(v6, v5) = v4) | ~ (subset(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (member(v6, v5) = v4) | ~ (member(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v3, v5) = 0 & member(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ? [v8] : (member(v3, v5) = v8 & member(v3, v4) = v7 & (v8 = 0 | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = 0) | (member(v3, v5) = 0 & member(v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (singleton(v3) = v4) | ~ (member(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_set(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v4, v3) = v7 & subset(v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (product(v5) = v4) | ~ (product(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sum(v5) = v4) | ~ (sum(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v5) = v4) | ~ (singleton(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v4) = v5) | ~ (member(v3, v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (power_set(v5) = v4) | ~ (power_set(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v4) = v5) | ~ (member(v3, v5) = 0) | ? [v6] : (member(v6, v4) = 0 & member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ (member(v3, v5) = 0) | subset(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = 0) | ~ (member(v5, v3) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : ( ~ (equal_set(v3, v4) = 0) | (subset(v4, v3) = 0 & subset(v3, v4) = 0)) & ! [v3] : ~ (member(v3, empty_set) = 0))
% 4.95/1.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 4.95/1.81 | (1) ~ (all_0_0_0 = 0) & power_set(all_0_2_2) = all_0_1_1 & member(empty_set, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 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] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 5.00/1.82 |
% 5.00/1.82 | Applying alpha-rule on (1) yields:
% 5.00/1.82 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 5.00/1.82 | (3) ! [v0] : ~ (member(v0, empty_set) = 0)
% 5.03/1.82 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.03/1.82 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 5.03/1.82 | (6) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 5.03/1.82 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 5.03/1.82 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 5.03/1.82 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 5.03/1.82 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 5.03/1.82 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 5.03/1.82 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 5.03/1.82 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 5.03/1.82 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 5.03/1.82 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 5.03/1.82 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 5.03/1.82 | (17) member(empty_set, all_0_1_1) = all_0_0_0
% 5.03/1.82 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 5.03/1.82 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 5.03/1.82 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 5.03/1.82 | (21) ~ (all_0_0_0 = 0)
% 5.03/1.82 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 5.03/1.82 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 5.03/1.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 5.03/1.83 | (25) power_set(all_0_2_2) = all_0_1_1
% 5.03/1.83 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 5.03/1.83 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 5.03/1.83 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 5.03/1.83 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 5.03/1.83 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 5.03/1.83 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 5.03/1.83 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 5.03/1.83 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 5.03/1.83 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 5.03/1.83 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 5.03/1.83 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 5.03/1.83 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.03/1.83 |
% 5.03/1.83 | Instantiating formula (9) with all_0_0_0, all_0_1_1, all_0_2_2, empty_set and discharging atoms power_set(all_0_2_2) = all_0_1_1, member(empty_set, all_0_1_1) = all_0_0_0, yields:
% 5.03/1.83 | (38) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_2_2) = v0)
% 5.03/1.83 |
% 5.03/1.83 +-Applying beta-rule and splitting (38), into two cases.
% 5.03/1.83 |-Branch one:
% 5.03/1.83 | (39) all_0_0_0 = 0
% 5.03/1.83 |
% 5.03/1.83 | Equations (39) can reduce 21 to:
% 5.03/1.83 | (40) $false
% 5.03/1.83 |
% 5.03/1.83 |-The branch is then unsatisfiable
% 5.03/1.83 |-Branch two:
% 5.03/1.83 | (21) ~ (all_0_0_0 = 0)
% 5.03/1.83 | (42) ? [v0] : ( ~ (v0 = 0) & subset(empty_set, all_0_2_2) = v0)
% 5.03/1.83 |
% 5.03/1.83 | Instantiating (42) with all_10_0_3 yields:
% 5.03/1.83 | (43) ~ (all_10_0_3 = 0) & subset(empty_set, all_0_2_2) = all_10_0_3
% 5.03/1.83 |
% 5.03/1.83 | Applying alpha-rule on (43) yields:
% 5.03/1.83 | (44) ~ (all_10_0_3 = 0)
% 5.03/1.83 | (45) subset(empty_set, all_0_2_2) = all_10_0_3
% 5.03/1.83 |
% 5.03/1.83 | Instantiating formula (7) with all_10_0_3, all_0_2_2, empty_set and discharging atoms subset(empty_set, all_0_2_2) = all_10_0_3, yields:
% 5.03/1.84 | (46) all_10_0_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, empty_set) = 0)
% 5.03/1.84 |
% 5.03/1.84 +-Applying beta-rule and splitting (46), into two cases.
% 5.03/1.84 |-Branch one:
% 5.03/1.84 | (47) all_10_0_3 = 0
% 5.03/1.84 |
% 5.03/1.84 | Equations (47) can reduce 44 to:
% 5.03/1.84 | (40) $false
% 5.03/1.84 |
% 5.03/1.84 |-The branch is then unsatisfiable
% 5.03/1.84 |-Branch two:
% 5.03/1.84 | (44) ~ (all_10_0_3 = 0)
% 5.03/1.84 | (50) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, empty_set) = 0)
% 5.03/1.84 |
% 5.03/1.84 | Instantiating (50) with all_19_0_4, all_19_1_5 yields:
% 5.03/1.84 | (51) ~ (all_19_0_4 = 0) & member(all_19_1_5, all_0_2_2) = all_19_0_4 & member(all_19_1_5, empty_set) = 0
% 5.03/1.84 |
% 5.03/1.84 | Applying alpha-rule on (51) yields:
% 5.03/1.84 | (52) ~ (all_19_0_4 = 0)
% 5.03/1.84 | (53) member(all_19_1_5, all_0_2_2) = all_19_0_4
% 5.03/1.84 | (54) member(all_19_1_5, empty_set) = 0
% 5.03/1.84 |
% 5.03/1.84 | Instantiating formula (3) with all_19_1_5 and discharging atoms member(all_19_1_5, empty_set) = 0, yields:
% 5.03/1.84 | (55) $false
% 5.03/1.84 |
% 5.03/1.84 |-The branch is then unsatisfiable
% 5.03/1.84 % SZS output end Proof for theBenchmark
% 5.03/1.84
% 5.03/1.84 1250ms
%------------------------------------------------------------------------------