TSTP Solution File: SET698+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 00:21:29 EDT 2022
% Result : Theorem 4.03s 1.64s
% Output : Proof 6.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET698+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n004.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 07:46:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.91 Prover 0: Preprocessing ...
% 1.95/1.11 Prover 0: Warning: ignoring some quantifiers
% 1.95/1.13 Prover 0: Constructing countermodel ...
% 2.71/1.35 Prover 0: gave up
% 2.71/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.95/1.37 Prover 1: Preprocessing ...
% 3.38/1.48 Prover 1: Constructing countermodel ...
% 4.03/1.64 Prover 1: proved (286ms)
% 4.03/1.64
% 4.03/1.64 No countermodel exists, formula is valid
% 4.03/1.64 % SZS status Theorem for theBenchmark
% 4.03/1.64
% 4.03/1.64 Generating proof ... found it (size 112)
% 6.03/2.09
% 6.03/2.09 % SZS output start Proof for theBenchmark
% 6.03/2.09 Assumed formulas after preprocessing and simplification:
% 6.03/2.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (difference(v2, v0) = v4 & union(v4, v1) = v5 & equal_set(v5, v2) = v6 & subset(v1, v2) = 0 & subset(v0, v2) = 0 & subset(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ~ (member(v7, empty_set) = 0) & ((v6 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v6 = 0))))
% 6.27/2.13 | 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:
% 6.27/2.13 | (1) difference(all_0_4_4, all_0_6_6) = all_0_2_2 & union(all_0_2_2, all_0_5_5) = all_0_1_1 & equal_set(all_0_1_1, all_0_4_4) = all_0_0_0 & subset(all_0_5_5, all_0_4_4) = 0 & subset(all_0_6_6, all_0_4_4) = 0 & subset(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [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) & ((all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0)))
% 6.27/2.14 |
% 6.27/2.14 | Applying alpha-rule on (1) yields:
% 6.27/2.14 | (2) union(all_0_2_2, all_0_5_5) = all_0_1_1
% 6.27/2.15 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.27/2.15 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.27/2.15 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.27/2.15 | (6) ! [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)))
% 6.27/2.15 | (7) equal_set(all_0_1_1, all_0_4_4) = all_0_0_0
% 6.27/2.15 | (8) ! [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))
% 6.27/2.15 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.27/2.15 | (10) subset(all_0_6_6, all_0_4_4) = 0
% 6.27/2.15 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 6.27/2.15 | (12) difference(all_0_4_4, all_0_6_6) = all_0_2_2
% 6.27/2.15 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.27/2.15 | (14) (all_0_0_0 = 0 & ~ (all_0_3_3 = 0)) | (all_0_3_3 = 0 & ~ (all_0_0_0 = 0))
% 6.27/2.15 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.27/2.15 | (16) ! [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))
% 6.27/2.15 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.27/2.15 | (18) ! [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))
% 6.27/2.15 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.27/2.15 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.27/2.15 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.27/2.15 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.27/2.15 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.27/2.15 | (24) subset(all_0_6_6, all_0_5_5) = all_0_3_3
% 6.27/2.15 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.27/2.15 | (26) subset(all_0_5_5, all_0_4_4) = 0
% 6.27/2.15 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.27/2.16 | (28) ! [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))))
% 6.27/2.16 | (29) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.27/2.16 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 6.27/2.16 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.27/2.16 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.27/2.16 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.27/2.16 | (34) ! [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))
% 6.27/2.16 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 6.27/2.16 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.27/2.16 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 6.27/2.16 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.27/2.16 | (39) ! [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)))
% 6.27/2.16 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.27/2.16 | (41) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.27/2.16 |
% 6.27/2.16 | Instantiating formula (20) with all_0_6_6, all_0_5_5, all_0_3_3, 0 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 6.27/2.16 | (42) all_0_3_3 = 0 | ~ (subset(all_0_6_6, all_0_5_5) = 0)
% 6.27/2.16 |
% 6.27/2.16 | Instantiating formula (41) with all_0_4_4, all_0_1_1 yields:
% 6.27/2.16 | (43) ~ (equal_set(all_0_1_1, all_0_4_4) = 0) | (subset(all_0_1_1, all_0_4_4) = 0 & subset(all_0_4_4, all_0_1_1) = 0)
% 6.27/2.16 |
% 6.27/2.16 | Instantiating formula (21) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms equal_set(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 6.27/2.16 | (44) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v0 & subset(all_0_4_4, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.27/2.16 |
% 6.27/2.16 | Instantiating formula (32) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields:
% 6.27/2.16 | (45) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0)
% 6.27/2.16 |
% 6.27/2.16 +-Applying beta-rule and splitting (14), into two cases.
% 6.27/2.16 |-Branch one:
% 6.27/2.16 | (46) all_0_0_0 = 0 & ~ (all_0_3_3 = 0)
% 6.27/2.16 |
% 6.27/2.16 | Applying alpha-rule on (46) yields:
% 6.27/2.16 | (47) all_0_0_0 = 0
% 6.27/2.16 | (48) ~ (all_0_3_3 = 0)
% 6.27/2.16 |
% 6.27/2.16 | From (47) and (7) follows:
% 6.27/2.17 | (49) equal_set(all_0_1_1, all_0_4_4) = 0
% 6.27/2.17 |
% 6.27/2.17 +-Applying beta-rule and splitting (43), into two cases.
% 6.27/2.17 |-Branch one:
% 6.27/2.17 | (50) ~ (equal_set(all_0_1_1, all_0_4_4) = 0)
% 6.27/2.17 |
% 6.27/2.17 | Using (49) and (50) yields:
% 6.27/2.17 | (51) $false
% 6.27/2.17 |
% 6.27/2.17 |-The branch is then unsatisfiable
% 6.27/2.17 |-Branch two:
% 6.27/2.17 | (49) equal_set(all_0_1_1, all_0_4_4) = 0
% 6.27/2.17 | (53) subset(all_0_1_1, all_0_4_4) = 0 & subset(all_0_4_4, all_0_1_1) = 0
% 6.27/2.17 |
% 6.27/2.17 | Applying alpha-rule on (53) yields:
% 6.27/2.17 | (54) subset(all_0_1_1, all_0_4_4) = 0
% 6.27/2.17 | (55) subset(all_0_4_4, all_0_1_1) = 0
% 6.27/2.17 |
% 6.27/2.17 +-Applying beta-rule and splitting (45), into two cases.
% 6.27/2.17 |-Branch one:
% 6.27/2.17 | (56) all_0_3_3 = 0
% 6.27/2.17 |
% 6.27/2.17 | Equations (56) can reduce 48 to:
% 6.27/2.17 | (57) $false
% 6.27/2.17 |
% 6.27/2.17 |-The branch is then unsatisfiable
% 6.27/2.17 |-Branch two:
% 6.27/2.17 | (48) ~ (all_0_3_3 = 0)
% 6.27/2.17 | (59) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0)
% 6.27/2.17 |
% 6.27/2.17 | Instantiating (59) with all_17_0_7, all_17_1_8 yields:
% 6.27/2.17 | (60) ~ (all_17_0_7 = 0) & member(all_17_1_8, all_0_5_5) = all_17_0_7 & member(all_17_1_8, all_0_6_6) = 0
% 6.27/2.17 |
% 6.27/2.17 | Applying alpha-rule on (60) yields:
% 6.27/2.17 | (61) ~ (all_17_0_7 = 0)
% 6.27/2.17 | (62) member(all_17_1_8, all_0_5_5) = all_17_0_7
% 6.27/2.17 | (63) member(all_17_1_8, all_0_6_6) = 0
% 6.27/2.17 |
% 6.27/2.17 | Instantiating formula (30) with all_17_1_8, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, member(all_17_1_8, all_0_6_6) = 0, yields:
% 6.27/2.17 | (64) member(all_17_1_8, all_0_4_4) = 0
% 6.27/2.17 |
% 6.27/2.17 | Instantiating formula (30) with all_17_1_8, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = 0, member(all_17_1_8, all_0_4_4) = 0, yields:
% 6.27/2.17 | (65) member(all_17_1_8, all_0_1_1) = 0
% 6.27/2.17 |
% 6.27/2.17 | Instantiating formula (37) with all_0_2_2, all_0_4_4, all_0_6_6, all_17_1_8 and discharging atoms difference(all_0_4_4, all_0_6_6) = all_0_2_2, yields:
% 6.27/2.17 | (66) ~ (member(all_17_1_8, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_17_1_8, all_0_4_4) = 0 & member(all_17_1_8, all_0_6_6) = v0)
% 6.27/2.17 |
% 6.27/2.17 | Instantiating formula (6) with all_0_1_1, all_0_5_5, all_0_2_2, all_17_1_8 and discharging atoms union(all_0_2_2, all_0_5_5) = all_0_1_1, member(all_17_1_8, all_0_1_1) = 0, yields:
% 6.27/2.17 | (67) ? [v0] : ? [v1] : (member(all_17_1_8, all_0_2_2) = v0 & member(all_17_1_8, all_0_5_5) = v1 & (v1 = 0 | v0 = 0))
% 6.27/2.17 |
% 6.27/2.17 | Instantiating (67) with all_60_0_9, all_60_1_10 yields:
% 6.27/2.17 | (68) member(all_17_1_8, all_0_2_2) = all_60_1_10 & member(all_17_1_8, all_0_5_5) = all_60_0_9 & (all_60_0_9 = 0 | all_60_1_10 = 0)
% 6.27/2.17 |
% 6.27/2.17 | Applying alpha-rule on (68) yields:
% 6.27/2.17 | (69) member(all_17_1_8, all_0_2_2) = all_60_1_10
% 6.27/2.17 | (70) member(all_17_1_8, all_0_5_5) = all_60_0_9
% 6.27/2.17 | (71) all_60_0_9 = 0 | all_60_1_10 = 0
% 6.27/2.17 |
% 6.27/2.17 +-Applying beta-rule and splitting (66), into two cases.
% 6.27/2.17 |-Branch one:
% 6.27/2.17 | (72) ~ (member(all_17_1_8, all_0_2_2) = 0)
% 6.27/2.17 |
% 6.27/2.17 | Instantiating formula (33) with all_17_1_8, all_0_5_5, all_60_0_9, all_17_0_7 and discharging atoms member(all_17_1_8, all_0_5_5) = all_60_0_9, member(all_17_1_8, all_0_5_5) = all_17_0_7, yields:
% 6.27/2.17 | (73) all_60_0_9 = all_17_0_7
% 6.27/2.17 |
% 6.27/2.17 | Using (69) and (72) yields:
% 6.27/2.17 | (74) ~ (all_60_1_10 = 0)
% 6.27/2.17 |
% 6.27/2.17 +-Applying beta-rule and splitting (71), into two cases.
% 6.27/2.17 |-Branch one:
% 6.27/2.17 | (75) all_60_0_9 = 0
% 6.27/2.17 |
% 6.27/2.17 | Combining equations (75,73) yields a new equation:
% 6.27/2.17 | (76) all_17_0_7 = 0
% 6.27/2.17 |
% 6.27/2.17 | Equations (76) can reduce 61 to:
% 6.27/2.17 | (57) $false
% 6.27/2.17 |
% 6.27/2.17 |-The branch is then unsatisfiable
% 6.27/2.17 |-Branch two:
% 6.27/2.17 | (78) ~ (all_60_0_9 = 0)
% 6.27/2.17 | (79) all_60_1_10 = 0
% 6.27/2.17 |
% 6.27/2.18 | Equations (79) can reduce 74 to:
% 6.27/2.18 | (57) $false
% 6.27/2.18 |
% 6.27/2.18 |-The branch is then unsatisfiable
% 6.27/2.18 |-Branch two:
% 6.27/2.18 | (81) member(all_17_1_8, all_0_2_2) = 0
% 6.27/2.18 | (82) ? [v0] : ( ~ (v0 = 0) & member(all_17_1_8, all_0_4_4) = 0 & member(all_17_1_8, all_0_6_6) = v0)
% 6.27/2.18 |
% 6.27/2.18 | Instantiating (82) with all_66_0_11 yields:
% 6.27/2.18 | (83) ~ (all_66_0_11 = 0) & member(all_17_1_8, all_0_4_4) = 0 & member(all_17_1_8, all_0_6_6) = all_66_0_11
% 6.27/2.18 |
% 6.27/2.18 | Applying alpha-rule on (83) yields:
% 6.27/2.18 | (84) ~ (all_66_0_11 = 0)
% 6.27/2.18 | (64) member(all_17_1_8, all_0_4_4) = 0
% 6.27/2.18 | (86) member(all_17_1_8, all_0_6_6) = all_66_0_11
% 6.27/2.18 |
% 6.27/2.18 | Instantiating formula (33) with all_17_1_8, all_0_6_6, all_66_0_11, 0 and discharging atoms member(all_17_1_8, all_0_6_6) = all_66_0_11, member(all_17_1_8, all_0_6_6) = 0, yields:
% 6.27/2.18 | (87) all_66_0_11 = 0
% 6.27/2.18 |
% 6.27/2.18 | Equations (87) can reduce 84 to:
% 6.27/2.18 | (57) $false
% 6.27/2.18 |
% 6.27/2.18 |-The branch is then unsatisfiable
% 6.27/2.18 |-Branch two:
% 6.27/2.18 | (89) all_0_3_3 = 0 & ~ (all_0_0_0 = 0)
% 6.27/2.18 |
% 6.27/2.18 | Applying alpha-rule on (89) yields:
% 6.27/2.18 | (56) all_0_3_3 = 0
% 6.27/2.18 | (91) ~ (all_0_0_0 = 0)
% 6.27/2.18 |
% 6.27/2.18 | From (56) and (24) follows:
% 6.27/2.18 | (92) subset(all_0_6_6, all_0_5_5) = 0
% 6.27/2.18 |
% 6.27/2.18 +-Applying beta-rule and splitting (44), into two cases.
% 6.27/2.18 |-Branch one:
% 6.27/2.18 | (47) all_0_0_0 = 0
% 6.27/2.18 |
% 6.27/2.18 | Equations (47) can reduce 91 to:
% 6.27/2.18 | (57) $false
% 6.27/2.18 |
% 6.27/2.18 |-The branch is then unsatisfiable
% 6.27/2.18 |-Branch two:
% 6.27/2.18 | (91) ~ (all_0_0_0 = 0)
% 6.27/2.18 | (96) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v0 & subset(all_0_4_4, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.27/2.18 |
% 6.27/2.18 | Instantiating (96) with all_14_0_12, all_14_1_13 yields:
% 6.27/2.18 | (97) subset(all_0_1_1, all_0_4_4) = all_14_1_13 & subset(all_0_4_4, all_0_1_1) = all_14_0_12 & ( ~ (all_14_0_12 = 0) | ~ (all_14_1_13 = 0))
% 6.27/2.18 |
% 6.27/2.18 | Applying alpha-rule on (97) yields:
% 6.27/2.18 | (98) subset(all_0_1_1, all_0_4_4) = all_14_1_13
% 6.27/2.18 | (99) subset(all_0_4_4, all_0_1_1) = all_14_0_12
% 6.27/2.18 | (100) ~ (all_14_0_12 = 0) | ~ (all_14_1_13 = 0)
% 6.27/2.18 |
% 6.27/2.18 | Instantiating formula (32) with all_14_1_13, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_1_13, yields:
% 6.27/2.18 | (101) all_14_1_13 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 6.27/2.18 |
% 6.27/2.18 | Instantiating formula (32) with all_14_0_12, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_0_12, yields:
% 6.27/2.18 | (102) all_14_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 6.27/2.18 |
% 6.27/2.18 +-Applying beta-rule and splitting (42), into two cases.
% 6.27/2.18 |-Branch one:
% 6.27/2.18 | (103) ~ (subset(all_0_6_6, all_0_5_5) = 0)
% 6.27/2.18 |
% 6.27/2.18 | Using (92) and (103) yields:
% 6.27/2.18 | (51) $false
% 6.27/2.18 |
% 6.27/2.18 |-The branch is then unsatisfiable
% 6.27/2.18 |-Branch two:
% 6.27/2.18 | (92) subset(all_0_6_6, all_0_5_5) = 0
% 6.27/2.18 | (56) all_0_3_3 = 0
% 6.27/2.18 |
% 6.27/2.18 +-Applying beta-rule and splitting (100), into two cases.
% 6.27/2.18 |-Branch one:
% 6.27/2.18 | (107) ~ (all_14_0_12 = 0)
% 6.27/2.18 |
% 6.27/2.18 +-Applying beta-rule and splitting (102), into two cases.
% 6.27/2.18 |-Branch one:
% 6.27/2.18 | (108) all_14_0_12 = 0
% 6.27/2.18 |
% 6.27/2.18 | Equations (108) can reduce 107 to:
% 6.27/2.18 | (57) $false
% 6.27/2.18 |
% 6.27/2.18 |-The branch is then unsatisfiable
% 6.27/2.18 |-Branch two:
% 6.27/2.18 | (107) ~ (all_14_0_12 = 0)
% 6.27/2.18 | (111) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 6.27/2.18 |
% 6.27/2.18 | Instantiating (111) with all_34_0_14, all_34_1_15 yields:
% 6.27/2.18 | (112) ~ (all_34_0_14 = 0) & member(all_34_1_15, all_0_1_1) = all_34_0_14 & member(all_34_1_15, all_0_4_4) = 0
% 6.27/2.18 |
% 6.27/2.18 | Applying alpha-rule on (112) yields:
% 6.27/2.18 | (113) ~ (all_34_0_14 = 0)
% 6.27/2.18 | (114) member(all_34_1_15, all_0_1_1) = all_34_0_14
% 6.27/2.18 | (115) member(all_34_1_15, all_0_4_4) = 0
% 6.27/2.18 |
% 6.27/2.18 | Instantiating formula (18) with all_34_0_14, all_0_1_1, all_0_5_5, all_0_2_2, all_34_1_15 and discharging atoms union(all_0_2_2, all_0_5_5) = all_0_1_1, member(all_34_1_15, all_0_1_1) = all_34_0_14, yields:
% 6.27/2.18 | (116) all_34_0_14 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_34_1_15, all_0_2_2) = v0 & member(all_34_1_15, all_0_5_5) = v1)
% 6.27/2.18 |
% 6.27/2.19 | Instantiating formula (30) with all_34_1_15, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, yields:
% 6.27/2.19 | (117) ~ (member(all_34_1_15, all_0_6_6) = 0) | member(all_34_1_15, all_0_5_5) = 0
% 6.27/2.19 |
% 6.27/2.19 +-Applying beta-rule and splitting (116), into two cases.
% 6.27/2.19 |-Branch one:
% 6.27/2.19 | (118) all_34_0_14 = 0
% 6.27/2.19 |
% 6.27/2.19 | Equations (118) can reduce 113 to:
% 6.27/2.19 | (57) $false
% 6.27/2.19 |
% 6.27/2.19 |-The branch is then unsatisfiable
% 6.27/2.19 |-Branch two:
% 6.27/2.19 | (113) ~ (all_34_0_14 = 0)
% 6.27/2.19 | (121) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_34_1_15, all_0_2_2) = v0 & member(all_34_1_15, all_0_5_5) = v1)
% 6.27/2.19 |
% 6.27/2.19 | Instantiating (121) with all_55_0_16, all_55_1_17 yields:
% 6.27/2.19 | (122) ~ (all_55_0_16 = 0) & ~ (all_55_1_17 = 0) & member(all_34_1_15, all_0_2_2) = all_55_1_17 & member(all_34_1_15, all_0_5_5) = all_55_0_16
% 6.27/2.19 |
% 6.27/2.19 | Applying alpha-rule on (122) yields:
% 6.27/2.19 | (123) ~ (all_55_0_16 = 0)
% 6.27/2.19 | (124) ~ (all_55_1_17 = 0)
% 6.27/2.19 | (125) member(all_34_1_15, all_0_2_2) = all_55_1_17
% 6.27/2.19 | (126) member(all_34_1_15, all_0_5_5) = all_55_0_16
% 6.27/2.19 |
% 6.27/2.19 +-Applying beta-rule and splitting (117), into two cases.
% 6.27/2.19 |-Branch one:
% 6.27/2.19 | (127) ~ (member(all_34_1_15, all_0_6_6) = 0)
% 6.27/2.19 |
% 6.27/2.19 | Instantiating formula (39) with all_55_1_17, all_0_2_2, all_0_4_4, all_0_6_6, all_34_1_15 and discharging atoms difference(all_0_4_4, all_0_6_6) = all_0_2_2, member(all_34_1_15, all_0_2_2) = all_55_1_17, yields:
% 6.27/2.19 | (128) all_55_1_17 = 0 | ? [v0] : ? [v1] : (member(all_34_1_15, all_0_4_4) = v0 & member(all_34_1_15, all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.27/2.19 |
% 6.27/2.19 +-Applying beta-rule and splitting (128), into two cases.
% 6.27/2.19 |-Branch one:
% 6.27/2.19 | (129) all_55_1_17 = 0
% 6.27/2.19 |
% 6.27/2.19 | Equations (129) can reduce 124 to:
% 6.27/2.19 | (57) $false
% 6.27/2.19 |
% 6.27/2.19 |-The branch is then unsatisfiable
% 6.27/2.19 |-Branch two:
% 6.27/2.19 | (124) ~ (all_55_1_17 = 0)
% 6.27/2.19 | (132) ? [v0] : ? [v1] : (member(all_34_1_15, all_0_4_4) = v0 & member(all_34_1_15, all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.27/2.19 |
% 6.27/2.19 | Instantiating (132) with all_98_0_22, all_98_1_23 yields:
% 6.27/2.19 | (133) member(all_34_1_15, all_0_4_4) = all_98_1_23 & member(all_34_1_15, all_0_6_6) = all_98_0_22 & ( ~ (all_98_1_23 = 0) | all_98_0_22 = 0)
% 6.27/2.19 |
% 6.27/2.19 | Applying alpha-rule on (133) yields:
% 6.27/2.19 | (134) member(all_34_1_15, all_0_4_4) = all_98_1_23
% 6.27/2.19 | (135) member(all_34_1_15, all_0_6_6) = all_98_0_22
% 6.27/2.19 | (136) ~ (all_98_1_23 = 0) | all_98_0_22 = 0
% 6.27/2.19 |
% 6.27/2.19 | Instantiating formula (33) with all_34_1_15, all_0_4_4, all_98_1_23, 0 and discharging atoms member(all_34_1_15, all_0_4_4) = all_98_1_23, member(all_34_1_15, all_0_4_4) = 0, yields:
% 6.27/2.19 | (137) all_98_1_23 = 0
% 6.27/2.19 |
% 6.27/2.19 | Using (135) and (127) yields:
% 6.27/2.19 | (138) ~ (all_98_0_22 = 0)
% 6.27/2.19 |
% 6.27/2.19 +-Applying beta-rule and splitting (136), into two cases.
% 6.27/2.19 |-Branch one:
% 6.27/2.19 | (139) ~ (all_98_1_23 = 0)
% 6.27/2.19 |
% 6.27/2.19 | Equations (137) can reduce 139 to:
% 6.27/2.19 | (57) $false
% 6.27/2.19 |
% 6.27/2.19 |-The branch is then unsatisfiable
% 6.27/2.19 |-Branch two:
% 6.27/2.19 | (137) all_98_1_23 = 0
% 6.27/2.19 | (142) all_98_0_22 = 0
% 6.27/2.19 |
% 6.27/2.19 | Equations (142) can reduce 138 to:
% 6.27/2.19 | (57) $false
% 6.27/2.19 |
% 6.27/2.19 |-The branch is then unsatisfiable
% 6.27/2.19 |-Branch two:
% 6.27/2.19 | (144) member(all_34_1_15, all_0_6_6) = 0
% 6.27/2.19 | (145) member(all_34_1_15, all_0_5_5) = 0
% 6.27/2.20 |
% 6.27/2.20 | Instantiating formula (33) with all_34_1_15, all_0_5_5, all_55_0_16, 0 and discharging atoms member(all_34_1_15, all_0_5_5) = all_55_0_16, member(all_34_1_15, all_0_5_5) = 0, yields:
% 6.27/2.20 | (146) all_55_0_16 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (146) can reduce 123 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (108) all_14_0_12 = 0
% 6.27/2.20 | (149) ~ (all_14_1_13 = 0)
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (101), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (150) all_14_1_13 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (150) can reduce 149 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (149) ~ (all_14_1_13 = 0)
% 6.27/2.20 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 6.27/2.20 |
% 6.27/2.20 | Instantiating (153) with all_34_0_24, all_34_1_25 yields:
% 6.27/2.20 | (154) ~ (all_34_0_24 = 0) & member(all_34_1_25, all_0_1_1) = 0 & member(all_34_1_25, all_0_4_4) = all_34_0_24
% 6.27/2.20 |
% 6.27/2.20 | Applying alpha-rule on (154) yields:
% 6.27/2.20 | (155) ~ (all_34_0_24 = 0)
% 6.27/2.20 | (156) member(all_34_1_25, all_0_1_1) = 0
% 6.27/2.20 | (157) member(all_34_1_25, all_0_4_4) = all_34_0_24
% 6.27/2.20 |
% 6.27/2.20 | Instantiating formula (33) with all_34_1_25, all_0_4_4, all_34_0_24, 0 and discharging atoms member(all_34_1_25, all_0_4_4) = all_34_0_24, yields:
% 6.27/2.20 | (158) all_34_0_24 = 0 | ~ (member(all_34_1_25, all_0_4_4) = 0)
% 6.27/2.20 |
% 6.27/2.20 | Instantiating formula (37) with all_0_2_2, all_0_4_4, all_0_6_6, all_34_1_25 and discharging atoms difference(all_0_4_4, all_0_6_6) = all_0_2_2, yields:
% 6.27/2.20 | (159) ~ (member(all_34_1_25, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_34_1_25, all_0_4_4) = 0 & member(all_34_1_25, all_0_6_6) = v0)
% 6.27/2.20 |
% 6.27/2.20 | Instantiating formula (6) with all_0_1_1, all_0_5_5, all_0_2_2, all_34_1_25 and discharging atoms union(all_0_2_2, all_0_5_5) = all_0_1_1, member(all_34_1_25, all_0_1_1) = 0, yields:
% 6.27/2.20 | (160) ? [v0] : ? [v1] : (member(all_34_1_25, all_0_2_2) = v0 & member(all_34_1_25, all_0_5_5) = v1 & (v1 = 0 | v0 = 0))
% 6.27/2.20 |
% 6.27/2.20 | Instantiating formula (30) with all_34_1_25, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = 0, yields:
% 6.27/2.20 | (161) ~ (member(all_34_1_25, all_0_5_5) = 0) | member(all_34_1_25, all_0_4_4) = 0
% 6.27/2.20 |
% 6.27/2.20 | Instantiating (160) with all_49_0_26, all_49_1_27 yields:
% 6.27/2.20 | (162) member(all_34_1_25, all_0_2_2) = all_49_1_27 & member(all_34_1_25, all_0_5_5) = all_49_0_26 & (all_49_0_26 = 0 | all_49_1_27 = 0)
% 6.27/2.20 |
% 6.27/2.20 | Applying alpha-rule on (162) yields:
% 6.27/2.20 | (163) member(all_34_1_25, all_0_2_2) = all_49_1_27
% 6.27/2.20 | (164) member(all_34_1_25, all_0_5_5) = all_49_0_26
% 6.27/2.20 | (165) all_49_0_26 = 0 | all_49_1_27 = 0
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (161), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (166) ~ (member(all_34_1_25, all_0_5_5) = 0)
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (159), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (167) ~ (member(all_34_1_25, all_0_2_2) = 0)
% 6.27/2.20 |
% 6.27/2.20 | Using (163) and (167) yields:
% 6.27/2.20 | (168) ~ (all_49_1_27 = 0)
% 6.27/2.20 |
% 6.27/2.20 | Using (164) and (166) yields:
% 6.27/2.20 | (169) ~ (all_49_0_26 = 0)
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (165), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (170) all_49_0_26 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (170) can reduce 169 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (169) ~ (all_49_0_26 = 0)
% 6.27/2.20 | (173) all_49_1_27 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (173) can reduce 168 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (175) member(all_34_1_25, all_0_2_2) = 0
% 6.27/2.20 | (176) ? [v0] : ( ~ (v0 = 0) & member(all_34_1_25, all_0_4_4) = 0 & member(all_34_1_25, all_0_6_6) = v0)
% 6.27/2.20 |
% 6.27/2.20 | Instantiating (176) with all_63_0_28 yields:
% 6.27/2.20 | (177) ~ (all_63_0_28 = 0) & member(all_34_1_25, all_0_4_4) = 0 & member(all_34_1_25, all_0_6_6) = all_63_0_28
% 6.27/2.20 |
% 6.27/2.20 | Applying alpha-rule on (177) yields:
% 6.27/2.20 | (178) ~ (all_63_0_28 = 0)
% 6.27/2.20 | (179) member(all_34_1_25, all_0_4_4) = 0
% 6.27/2.20 | (180) member(all_34_1_25, all_0_6_6) = all_63_0_28
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (158), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (181) ~ (member(all_34_1_25, all_0_4_4) = 0)
% 6.27/2.20 |
% 6.27/2.20 | Using (179) and (181) yields:
% 6.27/2.20 | (51) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (179) member(all_34_1_25, all_0_4_4) = 0
% 6.27/2.20 | (184) all_34_0_24 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (184) can reduce 155 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (186) member(all_34_1_25, all_0_5_5) = 0
% 6.27/2.20 | (179) member(all_34_1_25, all_0_4_4) = 0
% 6.27/2.20 |
% 6.27/2.20 +-Applying beta-rule and splitting (158), into two cases.
% 6.27/2.20 |-Branch one:
% 6.27/2.20 | (181) ~ (member(all_34_1_25, all_0_4_4) = 0)
% 6.27/2.20 |
% 6.27/2.20 | Using (179) and (181) yields:
% 6.27/2.20 | (51) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 |-Branch two:
% 6.27/2.20 | (179) member(all_34_1_25, all_0_4_4) = 0
% 6.27/2.20 | (184) all_34_0_24 = 0
% 6.27/2.20 |
% 6.27/2.20 | Equations (184) can reduce 155 to:
% 6.27/2.20 | (57) $false
% 6.27/2.20 |
% 6.27/2.20 |-The branch is then unsatisfiable
% 6.27/2.20 % SZS output end Proof for theBenchmark
% 6.27/2.20
% 6.27/2.20 1613ms
%------------------------------------------------------------------------------