TSTP Solution File: SET143+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET143+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:17:53 EDT 2022
% Result : Theorem 3.95s 1.66s
% Output : Proof 6.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET143+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 21:13:17 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.61/0.67 ____ _
% 0.61/0.67 ___ / __ \_____(_)___ ________ __________
% 0.61/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.67
% 0.61/0.67 A Theorem Prover for First-Order Logic
% 0.61/0.67 (ePrincess v.1.0)
% 0.61/0.67
% 0.61/0.67 (c) Philipp Rümmer, 2009-2015
% 0.61/0.67 (c) Peter Backeman, 2014-2015
% 0.61/0.67 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.67 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.67 Bug reports to peter@backeman.se
% 0.61/0.67
% 0.61/0.67 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.67
% 0.61/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.72 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/1.00 Prover 0: Preprocessing ...
% 2.08/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.08/1.22 Prover 0: Constructing countermodel ...
% 2.75/1.38 Prover 0: gave up
% 2.75/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.75/1.41 Prover 1: Preprocessing ...
% 3.18/1.51 Prover 1: Constructing countermodel ...
% 3.95/1.66 Prover 1: proved (277ms)
% 3.95/1.66
% 3.95/1.66 No countermodel exists, formula is valid
% 3.95/1.66 % SZS status Theorem for theBenchmark
% 3.95/1.66
% 3.95/1.66 Generating proof ... found it (size 81)
% 5.87/2.08
% 5.87/2.08 % SZS output start Proof for theBenchmark
% 5.87/2.08 Assumed formulas after preprocessing and simplification:
% 5.87/2.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection(v3, v2) = v4 & intersection(v1, v2) = v5 & intersection(v0, v5) = v6 & intersection(v0, v1) = v3 & equal_set(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))
% 6.09/2.12 | 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:
% 6.09/2.12 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_4_4, all_0_5_5) = all_0_3_3 & intersection(all_0_6_6, all_0_5_5) = all_0_2_2 & intersection(all_0_7_7, all_0_2_2) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_4_4 & equal_set(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)
% 6.09/2.13 |
% 6.09/2.13 | Applying alpha-rule on (1) yields:
% 6.09/2.13 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.09/2.13 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.09/2.13 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 6.09/2.13 | (5) ! [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)))
% 6.09/2.13 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.09/2.13 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.09/2.13 | (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))
% 6.09/2.13 | (9) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.09/2.13 | (10) ! [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))
% 6.09/2.13 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.09/2.13 | (12) ~ (all_0_0_0 = 0)
% 6.09/2.13 | (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))))
% 6.09/2.14 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 6.09/2.14 | (15) intersection(all_0_6_6, all_0_5_5) = all_0_2_2
% 6.09/2.14 | (16) ! [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))
% 6.09/2.14 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.09/2.14 | (18) intersection(all_0_7_7, all_0_2_2) = all_0_1_1
% 6.09/2.14 | (19) ! [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))
% 6.09/2.14 | (20) intersection(all_0_7_7, all_0_6_6) = all_0_4_4
% 6.09/2.14 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.09/2.14 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.09/2.14 | (23) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.09/2.14 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 6.09/2.14 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.09/2.14 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.09/2.14 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.09/2.14 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.09/2.14 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.09/2.14 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.09/2.14 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.09/2.14 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.09/2.14 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.09/2.14 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.09/2.14 | (35) intersection(all_0_4_4, all_0_5_5) = all_0_3_3
% 6.09/2.14 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 6.09/2.14 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.09/2.14 | (38) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0
% 6.09/2.14 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.09/2.15 | (40) ! [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)))
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (22) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 6.09/2.15 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/2.15 |
% 6.09/2.15 +-Applying beta-rule and splitting (41), into two cases.
% 6.09/2.15 |-Branch one:
% 6.09/2.15 | (42) all_0_0_0 = 0
% 6.09/2.15 |
% 6.09/2.15 | Equations (42) can reduce 12 to:
% 6.09/2.15 | (43) $false
% 6.09/2.15 |
% 6.09/2.15 |-The branch is then unsatisfiable
% 6.09/2.15 |-Branch two:
% 6.09/2.15 | (12) ~ (all_0_0_0 = 0)
% 6.09/2.15 | (45) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/2.15 |
% 6.09/2.15 | Instantiating (45) with all_14_0_8, all_14_1_9 yields:
% 6.09/2.15 | (46) subset(all_0_1_1, all_0_3_3) = all_14_0_8 & subset(all_0_3_3, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0))
% 6.09/2.15 |
% 6.09/2.15 | Applying alpha-rule on (46) yields:
% 6.09/2.15 | (47) subset(all_0_1_1, all_0_3_3) = all_14_0_8
% 6.09/2.15 | (48) subset(all_0_3_3, all_0_1_1) = all_14_1_9
% 6.09/2.15 | (49) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (39) with all_14_0_8, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_14_0_8, yields:
% 6.09/2.15 | (50) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (39) with all_14_1_9, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_14_1_9, yields:
% 6.09/2.15 | (51) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 6.09/2.15 |
% 6.09/2.15 +-Applying beta-rule and splitting (49), into two cases.
% 6.09/2.15 |-Branch one:
% 6.09/2.15 | (52) ~ (all_14_0_8 = 0)
% 6.09/2.15 |
% 6.09/2.15 +-Applying beta-rule and splitting (50), into two cases.
% 6.09/2.15 |-Branch one:
% 6.09/2.15 | (53) all_14_0_8 = 0
% 6.09/2.15 |
% 6.09/2.15 | Equations (53) can reduce 52 to:
% 6.09/2.15 | (43) $false
% 6.09/2.15 |
% 6.09/2.15 |-The branch is then unsatisfiable
% 6.09/2.15 |-Branch two:
% 6.09/2.15 | (52) ~ (all_14_0_8 = 0)
% 6.09/2.15 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 6.09/2.15 |
% 6.09/2.15 | Instantiating (56) with all_42_0_10, all_42_1_11 yields:
% 6.09/2.15 | (57) ~ (all_42_0_10 = 0) & member(all_42_1_11, all_0_1_1) = 0 & member(all_42_1_11, all_0_3_3) = all_42_0_10
% 6.09/2.15 |
% 6.09/2.15 | Applying alpha-rule on (57) yields:
% 6.09/2.15 | (58) ~ (all_42_0_10 = 0)
% 6.09/2.15 | (59) member(all_42_1_11, all_0_1_1) = 0
% 6.09/2.15 | (60) member(all_42_1_11, all_0_3_3) = all_42_0_10
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (37) with all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_11 and discharging atoms intersection(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 6.09/2.15 | (61) ~ (member(all_42_1_11, all_0_2_2) = 0) | (member(all_42_1_11, all_0_5_5) = 0 & member(all_42_1_11, all_0_6_6) = 0)
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (37) with all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_11 and discharging atoms intersection(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_11, all_0_1_1) = 0, yields:
% 6.09/2.15 | (62) member(all_42_1_11, all_0_2_2) = 0 & member(all_42_1_11, all_0_7_7) = 0
% 6.09/2.15 |
% 6.09/2.15 | Applying alpha-rule on (62) yields:
% 6.09/2.15 | (63) member(all_42_1_11, all_0_2_2) = 0
% 6.09/2.15 | (64) member(all_42_1_11, all_0_7_7) = 0
% 6.09/2.15 |
% 6.09/2.15 | Instantiating formula (13) with all_42_0_10, all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_11 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_11, all_0_3_3) = all_42_0_10, yields:
% 6.09/2.15 | (65) all_42_0_10 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/2.16 |
% 6.09/2.16 +-Applying beta-rule and splitting (61), into two cases.
% 6.09/2.16 |-Branch one:
% 6.09/2.16 | (66) ~ (member(all_42_1_11, all_0_2_2) = 0)
% 6.09/2.16 |
% 6.09/2.16 | Using (63) and (66) yields:
% 6.09/2.16 | (67) $false
% 6.09/2.16 |
% 6.09/2.16 |-The branch is then unsatisfiable
% 6.09/2.16 |-Branch two:
% 6.09/2.16 | (63) member(all_42_1_11, all_0_2_2) = 0
% 6.09/2.16 | (69) member(all_42_1_11, all_0_5_5) = 0 & member(all_42_1_11, all_0_6_6) = 0
% 6.09/2.16 |
% 6.09/2.16 | Applying alpha-rule on (69) yields:
% 6.09/2.16 | (70) member(all_42_1_11, all_0_5_5) = 0
% 6.09/2.16 | (71) member(all_42_1_11, all_0_6_6) = 0
% 6.09/2.16 |
% 6.09/2.16 +-Applying beta-rule and splitting (65), into two cases.
% 6.09/2.16 |-Branch one:
% 6.09/2.16 | (72) all_42_0_10 = 0
% 6.09/2.16 |
% 6.09/2.16 | Equations (72) can reduce 58 to:
% 6.09/2.16 | (43) $false
% 6.09/2.16 |
% 6.09/2.16 |-The branch is then unsatisfiable
% 6.09/2.16 |-Branch two:
% 6.09/2.16 | (58) ~ (all_42_0_10 = 0)
% 6.09/2.16 | (75) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/2.16 |
% 6.09/2.16 | Instantiating (75) with all_65_0_12, all_65_1_13 yields:
% 6.09/2.16 | (76) member(all_42_1_11, all_0_4_4) = all_65_1_13 & member(all_42_1_11, all_0_5_5) = all_65_0_12 & ( ~ (all_65_0_12 = 0) | ~ (all_65_1_13 = 0))
% 6.09/2.16 |
% 6.09/2.16 | Applying alpha-rule on (76) yields:
% 6.09/2.16 | (77) member(all_42_1_11, all_0_4_4) = all_65_1_13
% 6.09/2.16 | (78) member(all_42_1_11, all_0_5_5) = all_65_0_12
% 6.09/2.16 | (79) ~ (all_65_0_12 = 0) | ~ (all_65_1_13 = 0)
% 6.09/2.16 |
% 6.09/2.16 | Instantiating formula (3) with all_42_1_11, all_0_5_5, all_65_0_12, 0 and discharging atoms member(all_42_1_11, all_0_5_5) = all_65_0_12, member(all_42_1_11, all_0_5_5) = 0, yields:
% 6.09/2.16 | (80) all_65_0_12 = 0
% 6.09/2.16 |
% 6.09/2.16 +-Applying beta-rule and splitting (79), into two cases.
% 6.09/2.16 |-Branch one:
% 6.09/2.16 | (81) ~ (all_65_0_12 = 0)
% 6.09/2.16 |
% 6.09/2.16 | Equations (80) can reduce 81 to:
% 6.09/2.16 | (43) $false
% 6.09/2.16 |
% 6.09/2.16 |-The branch is then unsatisfiable
% 6.09/2.16 |-Branch two:
% 6.09/2.16 | (80) all_65_0_12 = 0
% 6.09/2.16 | (84) ~ (all_65_1_13 = 0)
% 6.09/2.16 |
% 6.09/2.16 | Instantiating formula (13) with all_65_1_13, all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_11 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_4_4, member(all_42_1_11, all_0_4_4) = all_65_1_13, yields:
% 6.09/2.16 | (85) all_65_1_13 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.09/2.16 |
% 6.30/2.16 +-Applying beta-rule and splitting (85), into two cases.
% 6.30/2.16 |-Branch one:
% 6.30/2.16 | (86) all_65_1_13 = 0
% 6.30/2.16 |
% 6.30/2.16 | Equations (86) can reduce 84 to:
% 6.30/2.16 | (43) $false
% 6.30/2.16 |
% 6.30/2.16 |-The branch is then unsatisfiable
% 6.30/2.16 |-Branch two:
% 6.30/2.16 | (84) ~ (all_65_1_13 = 0)
% 6.30/2.16 | (89) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.30/2.16 |
% 6.30/2.16 | Instantiating (89) with all_106_0_14, all_106_1_15 yields:
% 6.30/2.16 | (90) member(all_42_1_11, all_0_6_6) = all_106_0_14 & member(all_42_1_11, all_0_7_7) = all_106_1_15 & ( ~ (all_106_0_14 = 0) | ~ (all_106_1_15 = 0))
% 6.30/2.16 |
% 6.30/2.16 | Applying alpha-rule on (90) yields:
% 6.30/2.16 | (91) member(all_42_1_11, all_0_6_6) = all_106_0_14
% 6.30/2.16 | (92) member(all_42_1_11, all_0_7_7) = all_106_1_15
% 6.30/2.16 | (93) ~ (all_106_0_14 = 0) | ~ (all_106_1_15 = 0)
% 6.30/2.16 |
% 6.30/2.16 | Instantiating formula (3) with all_42_1_11, all_0_6_6, all_106_0_14, 0 and discharging atoms member(all_42_1_11, all_0_6_6) = all_106_0_14, member(all_42_1_11, all_0_6_6) = 0, yields:
% 6.30/2.16 | (94) all_106_0_14 = 0
% 6.30/2.16 |
% 6.30/2.16 | Instantiating formula (3) with all_42_1_11, all_0_7_7, all_106_1_15, 0 and discharging atoms member(all_42_1_11, all_0_7_7) = all_106_1_15, member(all_42_1_11, all_0_7_7) = 0, yields:
% 6.30/2.16 | (95) all_106_1_15 = 0
% 6.30/2.16 |
% 6.30/2.16 +-Applying beta-rule and splitting (93), into two cases.
% 6.30/2.16 |-Branch one:
% 6.30/2.16 | (96) ~ (all_106_0_14 = 0)
% 6.30/2.16 |
% 6.30/2.16 | Equations (94) can reduce 96 to:
% 6.30/2.16 | (43) $false
% 6.30/2.16 |
% 6.30/2.16 |-The branch is then unsatisfiable
% 6.30/2.16 |-Branch two:
% 6.30/2.16 | (94) all_106_0_14 = 0
% 6.30/2.16 | (99) ~ (all_106_1_15 = 0)
% 6.30/2.16 |
% 6.30/2.16 | Equations (95) can reduce 99 to:
% 6.30/2.16 | (43) $false
% 6.30/2.16 |
% 6.30/2.16 |-The branch is then unsatisfiable
% 6.30/2.17 |-Branch two:
% 6.30/2.17 | (53) all_14_0_8 = 0
% 6.30/2.17 | (102) ~ (all_14_1_9 = 0)
% 6.30/2.17 |
% 6.30/2.17 +-Applying beta-rule and splitting (51), into two cases.
% 6.30/2.17 |-Branch one:
% 6.30/2.17 | (103) all_14_1_9 = 0
% 6.30/2.17 |
% 6.30/2.17 | Equations (103) can reduce 102 to:
% 6.30/2.17 | (43) $false
% 6.30/2.17 |
% 6.30/2.17 |-The branch is then unsatisfiable
% 6.30/2.17 |-Branch two:
% 6.30/2.17 | (102) ~ (all_14_1_9 = 0)
% 6.30/2.17 | (106) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 6.30/2.17 |
% 6.30/2.17 | Instantiating (106) with all_42_0_16, all_42_1_17 yields:
% 6.30/2.17 | (107) ~ (all_42_0_16 = 0) & member(all_42_1_17, all_0_1_1) = all_42_0_16 & member(all_42_1_17, all_0_3_3) = 0
% 6.30/2.17 |
% 6.30/2.17 | Applying alpha-rule on (107) yields:
% 6.30/2.17 | (108) ~ (all_42_0_16 = 0)
% 6.30/2.17 | (109) member(all_42_1_17, all_0_1_1) = all_42_0_16
% 6.30/2.17 | (110) member(all_42_1_17, all_0_3_3) = 0
% 6.30/2.17 |
% 6.30/2.17 | Instantiating formula (13) with all_42_0_16, all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_17 and discharging atoms intersection(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_17, all_0_1_1) = all_42_0_16, yields:
% 6.30/2.17 | (111) all_42_0_16 = 0 | ? [v0] : ? [v1] : (member(all_42_1_17, all_0_2_2) = v1 & member(all_42_1_17, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.30/2.17 |
% 6.30/2.17 | Instantiating formula (37) with all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_17 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_17, all_0_3_3) = 0, yields:
% 6.30/2.17 | (112) member(all_42_1_17, all_0_4_4) = 0 & member(all_42_1_17, all_0_5_5) = 0
% 6.30/2.17 |
% 6.30/2.17 | Applying alpha-rule on (112) yields:
% 6.30/2.17 | (113) member(all_42_1_17, all_0_4_4) = 0
% 6.30/2.17 | (114) member(all_42_1_17, all_0_5_5) = 0
% 6.30/2.17 |
% 6.30/2.17 | Instantiating formula (37) with all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_17 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 6.30/2.17 | (115) ~ (member(all_42_1_17, all_0_4_4) = 0) | (member(all_42_1_17, all_0_6_6) = 0 & member(all_42_1_17, all_0_7_7) = 0)
% 6.30/2.17 |
% 6.30/2.17 +-Applying beta-rule and splitting (115), into two cases.
% 6.30/2.17 |-Branch one:
% 6.30/2.17 | (116) ~ (member(all_42_1_17, all_0_4_4) = 0)
% 6.30/2.17 |
% 6.30/2.17 | Using (113) and (116) yields:
% 6.30/2.17 | (67) $false
% 6.30/2.17 |
% 6.30/2.17 |-The branch is then unsatisfiable
% 6.30/2.17 |-Branch two:
% 6.30/2.17 | (113) member(all_42_1_17, all_0_4_4) = 0
% 6.30/2.17 | (119) member(all_42_1_17, all_0_6_6) = 0 & member(all_42_1_17, all_0_7_7) = 0
% 6.30/2.17 |
% 6.30/2.17 | Applying alpha-rule on (119) yields:
% 6.30/2.17 | (120) member(all_42_1_17, all_0_6_6) = 0
% 6.30/2.17 | (121) member(all_42_1_17, all_0_7_7) = 0
% 6.30/2.17 |
% 6.30/2.17 +-Applying beta-rule and splitting (111), into two cases.
% 6.30/2.17 |-Branch one:
% 6.30/2.17 | (122) all_42_0_16 = 0
% 6.30/2.17 |
% 6.30/2.17 | Equations (122) can reduce 108 to:
% 6.30/2.17 | (43) $false
% 6.30/2.17 |
% 6.30/2.17 |-The branch is then unsatisfiable
% 6.30/2.17 |-Branch two:
% 6.30/2.17 | (108) ~ (all_42_0_16 = 0)
% 6.30/2.17 | (125) ? [v0] : ? [v1] : (member(all_42_1_17, all_0_2_2) = v1 & member(all_42_1_17, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.30/2.17 |
% 6.30/2.17 | Instantiating (125) with all_69_0_18, all_69_1_19 yields:
% 6.30/2.17 | (126) member(all_42_1_17, all_0_2_2) = all_69_0_18 & member(all_42_1_17, all_0_7_7) = all_69_1_19 & ( ~ (all_69_0_18 = 0) | ~ (all_69_1_19 = 0))
% 6.30/2.17 |
% 6.30/2.17 | Applying alpha-rule on (126) yields:
% 6.30/2.17 | (127) member(all_42_1_17, all_0_2_2) = all_69_0_18
% 6.30/2.17 | (128) member(all_42_1_17, all_0_7_7) = all_69_1_19
% 6.30/2.17 | (129) ~ (all_69_0_18 = 0) | ~ (all_69_1_19 = 0)
% 6.30/2.17 |
% 6.30/2.17 | Instantiating formula (3) with all_42_1_17, all_0_7_7, all_69_1_19, 0 and discharging atoms member(all_42_1_17, all_0_7_7) = all_69_1_19, member(all_42_1_17, all_0_7_7) = 0, yields:
% 6.30/2.17 | (130) all_69_1_19 = 0
% 6.30/2.17 |
% 6.30/2.17 +-Applying beta-rule and splitting (129), into two cases.
% 6.30/2.17 |-Branch one:
% 6.30/2.17 | (131) ~ (all_69_0_18 = 0)
% 6.30/2.17 |
% 6.30/2.17 | Instantiating formula (13) with all_69_0_18, all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_17 and discharging atoms intersection(all_0_6_6, all_0_5_5) = all_0_2_2, member(all_42_1_17, all_0_2_2) = all_69_0_18, yields:
% 6.30/2.17 | (132) all_69_0_18 = 0 | ? [v0] : ? [v1] : (member(all_42_1_17, all_0_5_5) = v1 & member(all_42_1_17, all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.30/2.17 |
% 6.30/2.17 +-Applying beta-rule and splitting (132), into two cases.
% 6.30/2.17 |-Branch one:
% 6.30/2.17 | (133) all_69_0_18 = 0
% 6.30/2.18 |
% 6.30/2.18 | Equations (133) can reduce 131 to:
% 6.30/2.18 | (43) $false
% 6.30/2.18 |
% 6.30/2.18 |-The branch is then unsatisfiable
% 6.30/2.18 |-Branch two:
% 6.30/2.18 | (131) ~ (all_69_0_18 = 0)
% 6.30/2.18 | (136) ? [v0] : ? [v1] : (member(all_42_1_17, all_0_5_5) = v1 & member(all_42_1_17, all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.30/2.18 |
% 6.30/2.18 | Instantiating (136) with all_110_0_22, all_110_1_23 yields:
% 6.30/2.18 | (137) member(all_42_1_17, all_0_5_5) = all_110_0_22 & member(all_42_1_17, all_0_6_6) = all_110_1_23 & ( ~ (all_110_0_22 = 0) | ~ (all_110_1_23 = 0))
% 6.30/2.18 |
% 6.30/2.18 | Applying alpha-rule on (137) yields:
% 6.30/2.18 | (138) member(all_42_1_17, all_0_5_5) = all_110_0_22
% 6.30/2.18 | (139) member(all_42_1_17, all_0_6_6) = all_110_1_23
% 6.30/2.18 | (140) ~ (all_110_0_22 = 0) | ~ (all_110_1_23 = 0)
% 6.30/2.18 |
% 6.30/2.18 | Instantiating formula (3) with all_42_1_17, all_0_5_5, all_110_0_22, 0 and discharging atoms member(all_42_1_17, all_0_5_5) = all_110_0_22, member(all_42_1_17, all_0_5_5) = 0, yields:
% 6.30/2.18 | (141) all_110_0_22 = 0
% 6.30/2.18 |
% 6.30/2.18 | Instantiating formula (3) with all_42_1_17, all_0_6_6, all_110_1_23, 0 and discharging atoms member(all_42_1_17, all_0_6_6) = all_110_1_23, member(all_42_1_17, all_0_6_6) = 0, yields:
% 6.30/2.18 | (142) all_110_1_23 = 0
% 6.30/2.18 |
% 6.30/2.18 +-Applying beta-rule and splitting (140), into two cases.
% 6.30/2.18 |-Branch one:
% 6.30/2.18 | (143) ~ (all_110_0_22 = 0)
% 6.30/2.18 |
% 6.30/2.18 | Equations (141) can reduce 143 to:
% 6.30/2.18 | (43) $false
% 6.30/2.18 |
% 6.30/2.18 |-The branch is then unsatisfiable
% 6.30/2.18 |-Branch two:
% 6.30/2.18 | (141) all_110_0_22 = 0
% 6.30/2.18 | (146) ~ (all_110_1_23 = 0)
% 6.30/2.18 |
% 6.30/2.18 | Equations (142) can reduce 146 to:
% 6.30/2.18 | (43) $false
% 6.30/2.18 |
% 6.30/2.18 |-The branch is then unsatisfiable
% 6.30/2.18 |-Branch two:
% 6.30/2.18 | (133) all_69_0_18 = 0
% 6.30/2.18 | (149) ~ (all_69_1_19 = 0)
% 6.30/2.18 |
% 6.30/2.18 | Equations (130) can reduce 149 to:
% 6.30/2.18 | (43) $false
% 6.30/2.18 |
% 6.30/2.18 |-The branch is then unsatisfiable
% 6.30/2.18 % SZS output end Proof for theBenchmark
% 6.30/2.18
% 6.30/2.18 1505ms
%------------------------------------------------------------------------------