TSTP Solution File: SET694+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET694+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 00:21:27 EDT 2022
% Result : Theorem 6.79s 2.26s
% Output : Proof 9.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET694+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 10 09:11:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.63/0.61 ____ _
% 0.63/0.61 ___ / __ \_____(_)___ ________ __________
% 0.63/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.61
% 0.63/0.61 A Theorem Prover for First-Order Logic
% 0.63/0.61 (ePrincess v.1.0)
% 0.63/0.61
% 0.63/0.61 (c) Philipp Rümmer, 2009-2015
% 0.63/0.61 (c) Peter Backeman, 2014-2015
% 0.63/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.61 Bug reports to peter@backeman.se
% 0.63/0.61
% 0.63/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.61
% 0.63/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.96 Prover 0: Preprocessing ...
% 1.99/1.16 Prover 0: Warning: ignoring some quantifiers
% 1.99/1.18 Prover 0: Constructing countermodel ...
% 5.67/2.04 Prover 0: gave up
% 5.67/2.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.67/2.07 Prover 1: Preprocessing ...
% 6.33/2.15 Prover 1: Constructing countermodel ...
% 6.79/2.25 Prover 1: proved (210ms)
% 6.79/2.26
% 6.79/2.26 No countermodel exists, formula is valid
% 6.79/2.26 % SZS status Theorem for theBenchmark
% 6.79/2.26
% 6.79/2.26 Generating proof ... found it (size 54)
% 8.51/2.63
% 8.51/2.63 % SZS output start Proof for theBenchmark
% 8.51/2.63 Assumed formulas after preprocessing and simplification:
% 8.51/2.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & union(v2, v3) = v4 & union(v0, v1) = v5 & power_set(v5) = v6 & power_set(v1) = v3 & power_set(v0) = v2 & subset(v4, v6) = v7 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0))
% 8.51/2.66 | 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, all_0_7_7 yields:
% 8.51/2.66 | (1) ~ (all_0_0_0 = 0) & union(all_0_5_5, all_0_4_4) = all_0_3_3 & union(all_0_7_7, all_0_6_6) = all_0_2_2 & power_set(all_0_2_2) = all_0_1_1 & power_set(all_0_6_6) = all_0_4_4 & power_set(all_0_7_7) = all_0_5_5 & subset(all_0_3_3, 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)
% 8.51/2.68 |
% 8.51/2.68 | Applying alpha-rule on (1) yields:
% 8.51/2.68 | (2) power_set(all_0_6_6) = all_0_4_4
% 8.51/2.68 | (3) union(all_0_5_5, all_0_4_4) = all_0_3_3
% 8.51/2.68 | (4) ! [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)))
% 8.51/2.68 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.51/2.68 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 8.51/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 8.51/2.68 | (8) ! [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))
% 8.51/2.68 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 8.51/2.68 | (10) ! [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))
% 8.51/2.68 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 8.51/2.68 | (12) subset(all_0_3_3, all_0_1_1) = all_0_0_0
% 8.51/2.68 | (13) ! [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))))
% 8.51/2.68 | (14) union(all_0_7_7, all_0_6_6) = all_0_2_2
% 8.51/2.68 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 8.51/2.68 | (16) power_set(all_0_7_7) = all_0_5_5
% 8.51/2.68 | (17) ! [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))
% 8.51/2.68 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 8.51/2.68 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 8.51/2.68 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 8.51/2.68 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 8.51/2.68 | (22) ~ (all_0_0_0 = 0)
% 8.51/2.68 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 8.51/2.68 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.51/2.69 | (25) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 8.51/2.69 | (26) ! [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))
% 8.51/2.69 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.51/2.69 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 8.51/2.69 | (29) ! [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)))
% 8.51/2.69 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 8.51/2.69 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 8.51/2.69 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 8.51/2.69 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 8.51/2.69 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 8.51/2.69 | (35) ! [v0] : ~ (member(v0, empty_set) = 0)
% 8.51/2.69 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 8.51/2.69 | (37) power_set(all_0_2_2) = all_0_1_1
% 8.51/2.69 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 8.51/2.69 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.96/2.69 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 8.96/2.69 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 8.96/2.69 |
% 8.96/2.69 | Instantiating formula (21) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 8.97/2.69 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 8.97/2.69 |
% 8.97/2.69 +-Applying beta-rule and splitting (42), into two cases.
% 8.97/2.69 |-Branch one:
% 8.97/2.69 | (43) all_0_0_0 = 0
% 8.97/2.69 |
% 8.97/2.69 | Equations (43) can reduce 22 to:
% 8.97/2.69 | (44) $false
% 8.97/2.69 |
% 8.97/2.69 |-The branch is then unsatisfiable
% 8.97/2.69 |-Branch two:
% 8.97/2.69 | (22) ~ (all_0_0_0 = 0)
% 8.97/2.70 | (46) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 8.97/2.70 |
% 8.97/2.70 | Instantiating (46) with all_14_0_8, all_14_1_9 yields:
% 8.97/2.70 | (47) ~ (all_14_0_8 = 0) & member(all_14_1_9, all_0_1_1) = all_14_0_8 & member(all_14_1_9, all_0_3_3) = 0
% 8.97/2.70 |
% 8.97/2.70 | Applying alpha-rule on (47) yields:
% 8.97/2.70 | (48) ~ (all_14_0_8 = 0)
% 8.97/2.70 | (49) member(all_14_1_9, all_0_1_1) = all_14_0_8
% 8.97/2.70 | (50) member(all_14_1_9, all_0_3_3) = 0
% 8.97/2.70 |
% 8.97/2.70 | Instantiating formula (39) with all_14_0_8, all_0_1_1, all_0_2_2, all_14_1_9 and discharging atoms power_set(all_0_2_2) = all_0_1_1, member(all_14_1_9, all_0_1_1) = all_14_0_8, yields:
% 8.97/2.70 | (51) all_14_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_14_1_9, all_0_2_2) = v0)
% 8.97/2.70 |
% 8.97/2.70 | Instantiating formula (4) with all_0_3_3, all_0_4_4, all_0_5_5, all_14_1_9 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_14_1_9, all_0_3_3) = 0, yields:
% 8.97/2.70 | (52) ? [v0] : ? [v1] : (member(all_14_1_9, all_0_4_4) = v1 & member(all_14_1_9, all_0_5_5) = v0 & (v1 = 0 | v0 = 0))
% 8.97/2.70 |
% 8.97/2.70 | Instantiating formula (24) with all_0_4_4, all_0_6_6, all_14_1_9 and discharging atoms power_set(all_0_6_6) = all_0_4_4, yields:
% 8.97/2.70 | (53) ~ (member(all_14_1_9, all_0_4_4) = 0) | subset(all_14_1_9, all_0_6_6) = 0
% 8.97/2.70 |
% 8.97/2.70 | Instantiating formula (24) with all_0_5_5, all_0_7_7, all_14_1_9 and discharging atoms power_set(all_0_7_7) = all_0_5_5, yields:
% 8.97/2.70 | (54) ~ (member(all_14_1_9, all_0_5_5) = 0) | subset(all_14_1_9, all_0_7_7) = 0
% 8.97/2.70 |
% 8.97/2.70 | Instantiating (52) with all_29_0_10, all_29_1_11 yields:
% 8.97/2.70 | (55) member(all_14_1_9, all_0_4_4) = all_29_0_10 & member(all_14_1_9, all_0_5_5) = all_29_1_11 & (all_29_0_10 = 0 | all_29_1_11 = 0)
% 9.00/2.70 |
% 9.00/2.70 | Applying alpha-rule on (55) yields:
% 9.00/2.70 | (56) member(all_14_1_9, all_0_4_4) = all_29_0_10
% 9.00/2.70 | (57) member(all_14_1_9, all_0_5_5) = all_29_1_11
% 9.00/2.70 | (58) all_29_0_10 = 0 | all_29_1_11 = 0
% 9.00/2.70 |
% 9.00/2.70 +-Applying beta-rule and splitting (51), into two cases.
% 9.00/2.70 |-Branch one:
% 9.00/2.70 | (59) all_14_0_8 = 0
% 9.00/2.70 |
% 9.00/2.70 | Equations (59) can reduce 48 to:
% 9.00/2.70 | (44) $false
% 9.00/2.70 |
% 9.00/2.70 |-The branch is then unsatisfiable
% 9.00/2.70 |-Branch two:
% 9.00/2.70 | (48) ~ (all_14_0_8 = 0)
% 9.00/2.70 | (62) ? [v0] : ( ~ (v0 = 0) & subset(all_14_1_9, all_0_2_2) = v0)
% 9.00/2.70 |
% 9.00/2.70 | Instantiating (62) with all_35_0_12 yields:
% 9.00/2.70 | (63) ~ (all_35_0_12 = 0) & subset(all_14_1_9, all_0_2_2) = all_35_0_12
% 9.00/2.70 |
% 9.00/2.70 | Applying alpha-rule on (63) yields:
% 9.00/2.70 | (64) ~ (all_35_0_12 = 0)
% 9.00/2.70 | (65) subset(all_14_1_9, all_0_2_2) = all_35_0_12
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (21) with all_35_0_12, all_0_2_2, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_2_2) = all_35_0_12, yields:
% 9.00/2.70 | (66) all_35_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_14_1_9) = 0 & member(v0, all_0_2_2) = v1)
% 9.00/2.70 |
% 9.00/2.70 +-Applying beta-rule and splitting (66), into two cases.
% 9.00/2.70 |-Branch one:
% 9.00/2.70 | (67) all_35_0_12 = 0
% 9.00/2.70 |
% 9.00/2.70 | Equations (67) can reduce 64 to:
% 9.00/2.70 | (44) $false
% 9.00/2.70 |
% 9.00/2.70 |-The branch is then unsatisfiable
% 9.00/2.70 |-Branch two:
% 9.00/2.70 | (64) ~ (all_35_0_12 = 0)
% 9.00/2.70 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_14_1_9) = 0 & member(v0, all_0_2_2) = v1)
% 9.00/2.71 |
% 9.00/2.71 | Instantiating (70) with all_56_0_13, all_56_1_14 yields:
% 9.00/2.71 | (71) ~ (all_56_0_13 = 0) & member(all_56_1_14, all_14_1_9) = 0 & member(all_56_1_14, all_0_2_2) = all_56_0_13
% 9.00/2.71 |
% 9.00/2.71 | Applying alpha-rule on (71) yields:
% 9.00/2.71 | (72) ~ (all_56_0_13 = 0)
% 9.00/2.71 | (73) member(all_56_1_14, all_14_1_9) = 0
% 9.00/2.71 | (74) member(all_56_1_14, all_0_2_2) = all_56_0_13
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (10) with all_56_0_13, all_0_2_2, all_0_6_6, all_0_7_7, all_56_1_14 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_56_1_14, all_0_2_2) = all_56_0_13, yields:
% 9.00/2.71 | (75) all_56_0_13 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_56_1_14, all_0_6_6) = v1 & member(all_56_1_14, all_0_7_7) = v0)
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (75), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (76) all_56_0_13 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (76) can reduce 72 to:
% 9.00/2.71 | (44) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (72) ~ (all_56_0_13 = 0)
% 9.00/2.71 | (79) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_56_1_14, all_0_6_6) = v1 & member(all_56_1_14, all_0_7_7) = v0)
% 9.00/2.71 |
% 9.00/2.71 | Instantiating (79) with all_77_0_15, all_77_1_16 yields:
% 9.00/2.71 | (80) ~ (all_77_0_15 = 0) & ~ (all_77_1_16 = 0) & member(all_56_1_14, all_0_6_6) = all_77_0_15 & member(all_56_1_14, all_0_7_7) = all_77_1_16
% 9.00/2.71 |
% 9.00/2.71 | Applying alpha-rule on (80) yields:
% 9.00/2.71 | (81) ~ (all_77_0_15 = 0)
% 9.00/2.71 | (82) ~ (all_77_1_16 = 0)
% 9.00/2.71 | (83) member(all_56_1_14, all_0_6_6) = all_77_0_15
% 9.00/2.71 | (84) member(all_56_1_14, all_0_7_7) = all_77_1_16
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (38) with all_56_1_14, all_0_6_6, all_77_0_15, 0 and discharging atoms member(all_56_1_14, all_0_6_6) = all_77_0_15, yields:
% 9.00/2.71 | (85) all_77_0_15 = 0 | ~ (member(all_56_1_14, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (38) with all_56_1_14, all_0_7_7, all_77_1_16, 0 and discharging atoms member(all_56_1_14, all_0_7_7) = all_77_1_16, yields:
% 9.00/2.71 | (86) all_77_1_16 = 0 | ~ (member(all_56_1_14, all_0_7_7) = 0)
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (54), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (87) ~ (member(all_14_1_9, all_0_5_5) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (57) and (87) yields:
% 9.00/2.71 | (88) ~ (all_29_1_11 = 0)
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (58), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (89) all_29_0_10 = 0
% 9.00/2.71 |
% 9.00/2.71 | From (89) and (56) follows:
% 9.00/2.71 | (90) member(all_14_1_9, all_0_4_4) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (53), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (91) ~ (member(all_14_1_9, all_0_4_4) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (90) and (91) yields:
% 9.00/2.71 | (92) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (90) member(all_14_1_9, all_0_4_4) = 0
% 9.00/2.71 | (94) subset(all_14_1_9, all_0_6_6) = 0
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (40) with all_56_1_14, all_0_6_6, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_6_6) = 0, member(all_56_1_14, all_14_1_9) = 0, yields:
% 9.00/2.71 | (95) member(all_56_1_14, all_0_6_6) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (85), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (96) ~ (member(all_56_1_14, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (95) and (96) yields:
% 9.00/2.71 | (92) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (95) member(all_56_1_14, all_0_6_6) = 0
% 9.00/2.71 | (99) all_77_0_15 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (99) can reduce 81 to:
% 9.00/2.71 | (44) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (101) ~ (all_29_0_10 = 0)
% 9.00/2.71 | (102) all_29_1_11 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (102) can reduce 88 to:
% 9.00/2.71 | (44) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (104) member(all_14_1_9, all_0_5_5) = 0
% 9.00/2.71 | (105) subset(all_14_1_9, all_0_7_7) = 0
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (40) with all_56_1_14, all_0_7_7, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_7_7) = 0, member(all_56_1_14, all_14_1_9) = 0, yields:
% 9.00/2.71 | (106) member(all_56_1_14, all_0_7_7) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (86), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (107) ~ (member(all_56_1_14, all_0_7_7) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (106) and (107) yields:
% 9.00/2.71 | (92) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (106) member(all_56_1_14, all_0_7_7) = 0
% 9.00/2.71 | (110) all_77_1_16 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (110) can reduce 82 to:
% 9.00/2.71 | (44) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 % SZS output end Proof for theBenchmark
% 9.00/2.72
% 9.00/2.72 2097ms
%------------------------------------------------------------------------------