TSTP Solution File: SET169+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET169+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 00:18:06 EDT 2022
% Result : Theorem 4.20s 1.66s
% Output : Proof 7.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET169+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 01:07:28 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.48/0.59 ____ _
% 0.48/0.59 ___ / __ \_____(_)___ ________ __________
% 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.59
% 0.48/0.59 A Theorem Prover for First-Order Logic
% 0.48/0.60 (ePrincess v.1.0)
% 0.48/0.60
% 0.48/0.60 (c) Philipp Rümmer, 2009-2015
% 0.48/0.60 (c) Peter Backeman, 2014-2015
% 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.60 Bug reports to peter@backeman.se
% 0.48/0.60
% 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.60
% 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.92 Prover 0: Preprocessing ...
% 1.94/1.12 Prover 0: Warning: ignoring some quantifiers
% 2.07/1.14 Prover 0: Constructing countermodel ...
% 2.54/1.31 Prover 0: gave up
% 2.54/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.54/1.33 Prover 1: Preprocessing ...
% 3.23/1.44 Prover 1: Constructing countermodel ...
% 4.20/1.66 Prover 1: proved (348ms)
% 4.20/1.66
% 4.20/1.66 No countermodel exists, formula is valid
% 4.20/1.66 % SZS status Theorem for theBenchmark
% 4.20/1.66
% 4.20/1.66 Generating proof ... found it (size 133)
% 6.63/2.19
% 6.63/2.19 % SZS output start Proof for theBenchmark
% 6.63/2.19 Assumed formulas after preprocessing and simplification:
% 6.63/2.19 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & union(v5, v6) = v7 & union(v1, v2) = v3 & intersection(v0, v3) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5 & equal_set(v4, v7) = v8 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (product(v10) = v11) | ~ (member(v9, v12) = v13) | ~ (member(v9, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & member(v12, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (difference(v11, v10) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : ? [v15] : (member(v9, v11) = v14 & member(v9, v10) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (union(v10, v11) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & member(v9, v11) = v15 & member(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (intersection(v10, v11) = v12) | ~ (member(v9, v12) = v13) | ? [v14] : ? [v15] : (member(v9, v11) = v15 & member(v9, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (sum(v10) = v11) | ~ (member(v9, v13) = 0) | ~ (member(v9, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & member(v13, v10) = 0 & member(v9, v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v10, v9) = v11) | ~ (member(v9, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v9, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (power_set(v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | v10 = v9 | ~ (unordered_pair(v10, v11) = v12) | ~ (member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (difference(v12, v11) = v10) | ~ (difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (union(v12, v11) = v10) | ~ (union(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (intersection(v12, v11) = v10) | ~ (intersection(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (equal_set(v12, v11) = v10) | ~ (equal_set(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (member(v12, v11) = v10) | ~ (member(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (difference(v11, v10) = v12) | ~ (member(v9, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v9, v11) = 0 & member(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10, v11) = v12) | ~ (member(v9, v12) = 0) | ? [v13] : ? [v14] : (member(v9, v11) = v14 & member(v9, v10) = v13 & (v14 = 0 | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v10, v11) = v12) | ~ (member(v9, v12) = 0) | (member(v9, v11) = 0 & member(v9, v10) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v9) = v10) | ~ (member(v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equal_set(v9, v10) = v11) | ? [v12] : ? [v13] : (subset(v10, v9) = v13 & subset(v9, v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v10) = v13 & member(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (product(v11) = v10) | ~ (product(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (sum(v11) = v10) | ~ (sum(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v10) = v11) | ~ (member(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (power_set(v11) = v10) | ~ (power_set(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sum(v10) = v11) | ~ (member(v9, v11) = 0) | ? [v12] : (member(v12, v10) = 0 & member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_set(v10) = v11) | ~ (member(v9, v11) = 0) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (member(v11, v9) = 0) | member(v11, v10) = 0) & ! [v9] : ! [v10] : ( ~ (equal_set(v9, v10) = 0) | (subset(v10, v9) = 0 & subset(v9, v10) = 0)) & ! [v9] : ~ (member(v9, empty_set) = 0))
% 6.63/2.23 | 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, all_0_8_8 yields:
% 6.63/2.23 | (1) ~ (all_0_0_0 = 0) & union(all_0_3_3, all_0_2_2) = all_0_1_1 & union(all_0_7_7, all_0_6_6) = all_0_5_5 & intersection(all_0_8_8, all_0_5_5) = all_0_4_4 & intersection(all_0_8_8, all_0_6_6) = all_0_2_2 & intersection(all_0_8_8, all_0_7_7) = all_0_3_3 & equal_set(all_0_4_4, 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)
% 6.63/2.24 |
% 6.63/2.24 | Applying alpha-rule on (1) yields:
% 6.63/2.24 | (2) ! [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))))
% 6.63/2.24 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.63/2.24 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.63/2.24 | (5) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.63/2.24 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.63/2.24 | (7) intersection(all_0_8_8, all_0_7_7) = all_0_3_3
% 6.63/2.24 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.63/2.24 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.63/2.24 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.63/2.24 | (11) ! [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)))
% 6.63/2.24 | (12) ! [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))
% 6.63/2.24 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.63/2.24 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.63/2.24 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.63/2.24 | (16) union(all_0_3_3, all_0_2_2) = all_0_1_1
% 6.63/2.24 | (17) ~ (all_0_0_0 = 0)
% 6.63/2.24 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.63/2.24 | (19) ! [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))
% 6.63/2.25 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.63/2.25 | (21) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.63/2.25 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 6.63/2.25 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.63/2.25 | (24) intersection(all_0_8_8, all_0_6_6) = all_0_2_2
% 6.63/2.25 | (25) ! [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)))
% 6.63/2.25 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.63/2.25 | (27) union(all_0_7_7, all_0_6_6) = all_0_5_5
% 6.63/2.25 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.63/2.25 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.63/2.25 | (30) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0
% 6.63/2.25 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.63/2.25 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.63/2.25 | (33) ! [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))
% 6.63/2.25 | (34) intersection(all_0_8_8, all_0_5_5) = all_0_4_4
% 6.63/2.25 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 6.63/2.25 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.63/2.25 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.63/2.25 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 7.03/2.25 | (39) ! [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))
% 7.03/2.25 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 7.03/2.25 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 7.03/2.25 |
% 7.03/2.25 | Instantiating formula (3) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_1_1) = all_0_0_0, yields:
% 7.03/2.25 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.25 |
% 7.03/2.25 +-Applying beta-rule and splitting (42), into two cases.
% 7.03/2.25 |-Branch one:
% 7.03/2.25 | (43) all_0_0_0 = 0
% 7.03/2.25 |
% 7.03/2.26 | Equations (43) can reduce 17 to:
% 7.03/2.26 | (44) $false
% 7.03/2.26 |
% 7.03/2.26 |-The branch is then unsatisfiable
% 7.03/2.26 |-Branch two:
% 7.03/2.26 | (17) ~ (all_0_0_0 = 0)
% 7.03/2.26 | (46) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.26 |
% 7.03/2.26 | Instantiating (46) with all_14_0_9, all_14_1_10 yields:
% 7.03/2.26 | (47) subset(all_0_1_1, all_0_4_4) = all_14_0_9 & subset(all_0_4_4, all_0_1_1) = all_14_1_10 & ( ~ (all_14_0_9 = 0) | ~ (all_14_1_10 = 0))
% 7.03/2.26 |
% 7.03/2.26 | Applying alpha-rule on (47) yields:
% 7.03/2.26 | (48) subset(all_0_1_1, all_0_4_4) = all_14_0_9
% 7.03/2.26 | (49) subset(all_0_4_4, all_0_1_1) = all_14_1_10
% 7.03/2.26 | (50) ~ (all_14_0_9 = 0) | ~ (all_14_1_10 = 0)
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (20) with all_14_0_9, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_0_9, yields:
% 7.03/2.26 | (51) all_14_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (20) with all_14_1_10, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_1_10, yields:
% 7.03/2.26 | (52) all_14_1_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 7.03/2.26 |
% 7.03/2.26 +-Applying beta-rule and splitting (50), into two cases.
% 7.03/2.26 |-Branch one:
% 7.03/2.26 | (53) ~ (all_14_0_9 = 0)
% 7.03/2.26 |
% 7.03/2.26 +-Applying beta-rule and splitting (51), into two cases.
% 7.03/2.26 |-Branch one:
% 7.03/2.26 | (54) all_14_0_9 = 0
% 7.03/2.26 |
% 7.03/2.26 | Equations (54) can reduce 53 to:
% 7.03/2.26 | (44) $false
% 7.03/2.26 |
% 7.03/2.26 |-The branch is then unsatisfiable
% 7.03/2.26 |-Branch two:
% 7.03/2.26 | (53) ~ (all_14_0_9 = 0)
% 7.03/2.26 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 7.03/2.26 |
% 7.03/2.26 | Instantiating (57) with all_53_0_11, all_53_1_12 yields:
% 7.03/2.26 | (58) ~ (all_53_0_11 = 0) & member(all_53_1_12, all_0_1_1) = 0 & member(all_53_1_12, all_0_4_4) = all_53_0_11
% 7.03/2.26 |
% 7.03/2.26 | Applying alpha-rule on (58) yields:
% 7.03/2.26 | (59) ~ (all_53_0_11 = 0)
% 7.03/2.26 | (60) member(all_53_1_12, all_0_1_1) = 0
% 7.03/2.26 | (61) member(all_53_1_12, all_0_4_4) = all_53_0_11
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (25) with all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_12 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_12, all_0_1_1) = 0, yields:
% 7.03/2.26 | (62) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_2_2) = v1 & member(all_53_1_12, all_0_3_3) = v0 & (v1 = 0 | v0 = 0))
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (36) with all_0_2_2, all_0_6_6, all_0_8_8, all_53_1_12 and discharging atoms intersection(all_0_8_8, all_0_6_6) = all_0_2_2, yields:
% 7.03/2.26 | (63) ~ (member(all_53_1_12, all_0_2_2) = 0) | (member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_8_8) = 0)
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (36) with all_0_3_3, all_0_7_7, all_0_8_8, all_53_1_12 and discharging atoms intersection(all_0_8_8, all_0_7_7) = all_0_3_3, yields:
% 7.03/2.26 | (64) ~ (member(all_53_1_12, all_0_3_3) = 0) | (member(all_53_1_12, all_0_7_7) = 0 & member(all_53_1_12, all_0_8_8) = 0)
% 7.03/2.26 |
% 7.03/2.26 | Instantiating formula (2) with all_53_0_11, all_0_4_4, all_0_5_5, all_0_8_8, all_53_1_12 and discharging atoms intersection(all_0_8_8, all_0_5_5) = all_0_4_4, member(all_53_1_12, all_0_4_4) = all_53_0_11, yields:
% 7.03/2.26 | (65) all_53_0_11 = 0 | ? [v0] : ? [v1] : (member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.26 |
% 7.03/2.26 | Instantiating (62) with all_68_0_13, all_68_1_14 yields:
% 7.03/2.26 | (66) member(all_53_1_12, all_0_2_2) = all_68_0_13 & member(all_53_1_12, all_0_3_3) = all_68_1_14 & (all_68_0_13 = 0 | all_68_1_14 = 0)
% 7.03/2.26 |
% 7.03/2.26 | Applying alpha-rule on (66) yields:
% 7.03/2.26 | (67) member(all_53_1_12, all_0_2_2) = all_68_0_13
% 7.03/2.26 | (68) member(all_53_1_12, all_0_3_3) = all_68_1_14
% 7.03/2.26 | (69) all_68_0_13 = 0 | all_68_1_14 = 0
% 7.03/2.26 |
% 7.03/2.26 +-Applying beta-rule and splitting (65), into two cases.
% 7.03/2.26 |-Branch one:
% 7.03/2.26 | (70) all_53_0_11 = 0
% 7.03/2.26 |
% 7.03/2.26 | Equations (70) can reduce 59 to:
% 7.03/2.26 | (44) $false
% 7.03/2.26 |
% 7.03/2.26 |-The branch is then unsatisfiable
% 7.03/2.26 |-Branch two:
% 7.03/2.26 | (59) ~ (all_53_0_11 = 0)
% 7.03/2.26 | (73) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.26 |
% 7.03/2.26 | Instantiating (73) with all_74_0_15, all_74_1_16 yields:
% 7.03/2.26 | (74) member(all_53_1_12, all_0_5_5) = all_74_0_15 & member(all_53_1_12, all_0_8_8) = all_74_1_16 & ( ~ (all_74_0_15 = 0) | ~ (all_74_1_16 = 0))
% 7.03/2.26 |
% 7.03/2.26 | Applying alpha-rule on (74) yields:
% 7.03/2.26 | (75) member(all_53_1_12, all_0_5_5) = all_74_0_15
% 7.03/2.27 | (76) member(all_53_1_12, all_0_8_8) = all_74_1_16
% 7.03/2.27 | (77) ~ (all_74_0_15 = 0) | ~ (all_74_1_16 = 0)
% 7.03/2.27 |
% 7.03/2.27 | Instantiating formula (15) with all_53_1_12, all_0_3_3, all_68_1_14, 0 and discharging atoms member(all_53_1_12, all_0_3_3) = all_68_1_14, yields:
% 7.03/2.27 | (78) all_68_1_14 = 0 | ~ (member(all_53_1_12, all_0_3_3) = 0)
% 7.03/2.27 |
% 7.03/2.27 | Instantiating formula (15) with all_53_1_12, all_0_8_8, all_74_1_16, all_68_0_13 and discharging atoms member(all_53_1_12, all_0_8_8) = all_74_1_16, yields:
% 7.03/2.27 | (79) all_74_1_16 = all_68_0_13 | ~ (member(all_53_1_12, all_0_8_8) = all_68_0_13)
% 7.03/2.27 |
% 7.03/2.27 | Instantiating formula (15) with all_53_1_12, all_0_8_8, all_74_1_16, all_68_1_14 and discharging atoms member(all_53_1_12, all_0_8_8) = all_74_1_16, yields:
% 7.03/2.27 | (80) all_74_1_16 = all_68_1_14 | ~ (member(all_53_1_12, all_0_8_8) = all_68_1_14)
% 7.03/2.27 |
% 7.03/2.27 | Instantiating formula (12) with all_74_0_15, all_0_5_5, all_0_6_6, all_0_7_7, all_53_1_12 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_53_1_12, all_0_5_5) = all_74_0_15, yields:
% 7.03/2.27 | (81) all_74_0_15 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_7_7) = v0)
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (64), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (82) ~ (member(all_53_1_12, all_0_3_3) = 0)
% 7.03/2.27 |
% 7.03/2.27 | Using (68) and (82) yields:
% 7.03/2.27 | (83) ~ (all_68_1_14 = 0)
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (69), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (84) all_68_0_13 = 0
% 7.03/2.27 |
% 7.03/2.27 | From (84) and (67) follows:
% 7.03/2.27 | (85) member(all_53_1_12, all_0_2_2) = 0
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (63), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (86) ~ (member(all_53_1_12, all_0_2_2) = 0)
% 7.03/2.27 |
% 7.03/2.27 | Using (85) and (86) yields:
% 7.03/2.27 | (87) $false
% 7.03/2.27 |
% 7.03/2.27 |-The branch is then unsatisfiable
% 7.03/2.27 |-Branch two:
% 7.03/2.27 | (85) member(all_53_1_12, all_0_2_2) = 0
% 7.03/2.27 | (89) member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_8_8) = 0
% 7.03/2.27 |
% 7.03/2.27 | Applying alpha-rule on (89) yields:
% 7.03/2.27 | (90) member(all_53_1_12, all_0_6_6) = 0
% 7.03/2.27 | (91) member(all_53_1_12, all_0_8_8) = 0
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (79), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (92) ~ (member(all_53_1_12, all_0_8_8) = all_68_0_13)
% 7.03/2.27 |
% 7.03/2.27 | From (84) and (92) follows:
% 7.03/2.27 | (93) ~ (member(all_53_1_12, all_0_8_8) = 0)
% 7.03/2.27 |
% 7.03/2.27 | Using (91) and (93) yields:
% 7.03/2.27 | (87) $false
% 7.03/2.27 |
% 7.03/2.27 |-The branch is then unsatisfiable
% 7.03/2.27 |-Branch two:
% 7.03/2.27 | (95) member(all_53_1_12, all_0_8_8) = all_68_0_13
% 7.03/2.27 | (96) all_74_1_16 = all_68_0_13
% 7.03/2.27 |
% 7.03/2.27 | Combining equations (84,96) yields a new equation:
% 7.03/2.27 | (97) all_74_1_16 = 0
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (77), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (98) ~ (all_74_0_15 = 0)
% 7.03/2.27 |
% 7.03/2.27 +-Applying beta-rule and splitting (81), into two cases.
% 7.03/2.27 |-Branch one:
% 7.03/2.27 | (99) all_74_0_15 = 0
% 7.03/2.27 |
% 7.03/2.27 | Equations (99) can reduce 98 to:
% 7.03/2.27 | (44) $false
% 7.03/2.27 |
% 7.03/2.27 |-The branch is then unsatisfiable
% 7.03/2.27 |-Branch two:
% 7.03/2.27 | (98) ~ (all_74_0_15 = 0)
% 7.03/2.27 | (102) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_7_7) = v0)
% 7.03/2.27 |
% 7.03/2.27 | Instantiating (102) with all_150_0_19, all_150_1_20 yields:
% 7.03/2.27 | (103) ~ (all_150_0_19 = 0) & ~ (all_150_1_20 = 0) & member(all_53_1_12, all_0_6_6) = all_150_0_19 & member(all_53_1_12, all_0_7_7) = all_150_1_20
% 7.03/2.27 |
% 7.03/2.27 | Applying alpha-rule on (103) yields:
% 7.03/2.27 | (104) ~ (all_150_0_19 = 0)
% 7.03/2.27 | (105) ~ (all_150_1_20 = 0)
% 7.03/2.27 | (106) member(all_53_1_12, all_0_6_6) = all_150_0_19
% 7.03/2.27 | (107) member(all_53_1_12, all_0_7_7) = all_150_1_20
% 7.03/2.27 |
% 7.03/2.27 | Instantiating formula (15) with all_53_1_12, all_0_6_6, all_150_0_19, 0 and discharging atoms member(all_53_1_12, all_0_6_6) = all_150_0_19, member(all_53_1_12, all_0_6_6) = 0, yields:
% 7.03/2.28 | (108) all_150_0_19 = 0
% 7.03/2.28 |
% 7.03/2.28 | Equations (108) can reduce 104 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (99) all_74_0_15 = 0
% 7.03/2.28 | (111) ~ (all_74_1_16 = 0)
% 7.03/2.28 |
% 7.03/2.28 | Equations (97) can reduce 111 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (113) ~ (all_68_0_13 = 0)
% 7.03/2.28 | (114) all_68_1_14 = 0
% 7.03/2.28 |
% 7.03/2.28 | Equations (114) can reduce 83 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (116) member(all_53_1_12, all_0_3_3) = 0
% 7.03/2.28 | (117) member(all_53_1_12, all_0_7_7) = 0 & member(all_53_1_12, all_0_8_8) = 0
% 7.03/2.28 |
% 7.03/2.28 | Applying alpha-rule on (117) yields:
% 7.03/2.28 | (118) member(all_53_1_12, all_0_7_7) = 0
% 7.03/2.28 | (91) member(all_53_1_12, all_0_8_8) = 0
% 7.03/2.28 |
% 7.03/2.28 +-Applying beta-rule and splitting (78), into two cases.
% 7.03/2.28 |-Branch one:
% 7.03/2.28 | (82) ~ (member(all_53_1_12, all_0_3_3) = 0)
% 7.03/2.28 |
% 7.03/2.28 | Using (116) and (82) yields:
% 7.03/2.28 | (87) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (116) member(all_53_1_12, all_0_3_3) = 0
% 7.03/2.28 | (114) all_68_1_14 = 0
% 7.03/2.28 |
% 7.03/2.28 +-Applying beta-rule and splitting (81), into two cases.
% 7.03/2.28 |-Branch one:
% 7.03/2.28 | (99) all_74_0_15 = 0
% 7.03/2.28 |
% 7.03/2.28 +-Applying beta-rule and splitting (80), into two cases.
% 7.03/2.28 |-Branch one:
% 7.03/2.28 | (125) ~ (member(all_53_1_12, all_0_8_8) = all_68_1_14)
% 7.03/2.28 |
% 7.03/2.28 | From (114) and (125) follows:
% 7.03/2.28 | (93) ~ (member(all_53_1_12, all_0_8_8) = 0)
% 7.03/2.28 |
% 7.03/2.28 | Using (91) and (93) yields:
% 7.03/2.28 | (87) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (128) member(all_53_1_12, all_0_8_8) = all_68_1_14
% 7.03/2.28 | (129) all_74_1_16 = all_68_1_14
% 7.03/2.28 |
% 7.03/2.28 | Combining equations (114,129) yields a new equation:
% 7.03/2.28 | (97) all_74_1_16 = 0
% 7.03/2.28 |
% 7.03/2.28 +-Applying beta-rule and splitting (77), into two cases.
% 7.03/2.28 |-Branch one:
% 7.03/2.28 | (98) ~ (all_74_0_15 = 0)
% 7.03/2.28 |
% 7.03/2.28 | Equations (99) can reduce 98 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (99) all_74_0_15 = 0
% 7.03/2.28 | (111) ~ (all_74_1_16 = 0)
% 7.03/2.28 |
% 7.03/2.28 | Equations (97) can reduce 111 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (98) ~ (all_74_0_15 = 0)
% 7.03/2.28 | (102) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_7_7) = v0)
% 7.03/2.28 |
% 7.03/2.28 | Instantiating (102) with all_113_0_23, all_113_1_24 yields:
% 7.03/2.28 | (138) ~ (all_113_0_23 = 0) & ~ (all_113_1_24 = 0) & member(all_53_1_12, all_0_6_6) = all_113_0_23 & member(all_53_1_12, all_0_7_7) = all_113_1_24
% 7.03/2.28 |
% 7.03/2.28 | Applying alpha-rule on (138) yields:
% 7.03/2.28 | (139) ~ (all_113_0_23 = 0)
% 7.03/2.28 | (140) ~ (all_113_1_24 = 0)
% 7.03/2.28 | (141) member(all_53_1_12, all_0_6_6) = all_113_0_23
% 7.03/2.28 | (142) member(all_53_1_12, all_0_7_7) = all_113_1_24
% 7.03/2.28 |
% 7.03/2.28 | Instantiating formula (15) with all_53_1_12, all_0_7_7, all_113_1_24, 0 and discharging atoms member(all_53_1_12, all_0_7_7) = all_113_1_24, member(all_53_1_12, all_0_7_7) = 0, yields:
% 7.03/2.28 | (143) all_113_1_24 = 0
% 7.03/2.28 |
% 7.03/2.28 | Equations (143) can reduce 140 to:
% 7.03/2.28 | (44) $false
% 7.03/2.28 |
% 7.03/2.28 |-The branch is then unsatisfiable
% 7.03/2.28 |-Branch two:
% 7.03/2.28 | (54) all_14_0_9 = 0
% 7.03/2.28 | (146) ~ (all_14_1_10 = 0)
% 7.03/2.29 |
% 7.03/2.29 +-Applying beta-rule and splitting (52), into two cases.
% 7.03/2.29 |-Branch one:
% 7.03/2.29 | (147) all_14_1_10 = 0
% 7.03/2.29 |
% 7.03/2.29 | Equations (147) can reduce 146 to:
% 7.03/2.29 | (44) $false
% 7.03/2.29 |
% 7.03/2.29 |-The branch is then unsatisfiable
% 7.03/2.29 |-Branch two:
% 7.03/2.29 | (146) ~ (all_14_1_10 = 0)
% 7.03/2.29 | (150) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 7.03/2.29 |
% 7.03/2.29 | Instantiating (150) with all_53_0_25, all_53_1_26 yields:
% 7.03/2.29 | (151) ~ (all_53_0_25 = 0) & member(all_53_1_26, all_0_1_1) = all_53_0_25 & member(all_53_1_26, all_0_4_4) = 0
% 7.03/2.29 |
% 7.03/2.29 | Applying alpha-rule on (151) yields:
% 7.03/2.29 | (152) ~ (all_53_0_25 = 0)
% 7.03/2.29 | (153) member(all_53_1_26, all_0_1_1) = all_53_0_25
% 7.03/2.29 | (154) member(all_53_1_26, all_0_4_4) = 0
% 7.03/2.29 |
% 7.03/2.29 | Instantiating formula (12) with all_53_0_25, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_26 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_26, all_0_1_1) = all_53_0_25, yields:
% 7.03/2.29 | (155) all_53_0_25 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_26, all_0_2_2) = v1 & member(all_53_1_26, all_0_3_3) = v0)
% 7.03/2.29 |
% 7.03/2.29 | Instantiating formula (25) with all_0_5_5, all_0_6_6, all_0_7_7, all_53_1_26 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 7.03/2.29 | (156) ~ (member(all_53_1_26, all_0_5_5) = 0) | ? [v0] : ? [v1] : (member(all_53_1_26, all_0_6_6) = v1 & member(all_53_1_26, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 7.03/2.29 |
% 7.03/2.29 | Instantiating formula (36) with all_0_4_4, all_0_5_5, all_0_8_8, all_53_1_26 and discharging atoms intersection(all_0_8_8, all_0_5_5) = all_0_4_4, member(all_53_1_26, all_0_4_4) = 0, yields:
% 7.03/2.29 | (157) member(all_53_1_26, all_0_5_5) = 0 & member(all_53_1_26, all_0_8_8) = 0
% 7.03/2.29 |
% 7.03/2.29 | Applying alpha-rule on (157) yields:
% 7.03/2.29 | (158) member(all_53_1_26, all_0_5_5) = 0
% 7.03/2.29 | (159) member(all_53_1_26, all_0_8_8) = 0
% 7.03/2.29 |
% 7.03/2.29 +-Applying beta-rule and splitting (156), into two cases.
% 7.03/2.29 |-Branch one:
% 7.03/2.29 | (160) ~ (member(all_53_1_26, all_0_5_5) = 0)
% 7.03/2.29 |
% 7.03/2.29 | Using (158) and (160) yields:
% 7.03/2.29 | (87) $false
% 7.03/2.29 |
% 7.03/2.29 |-The branch is then unsatisfiable
% 7.03/2.29 |-Branch two:
% 7.03/2.29 | (158) member(all_53_1_26, all_0_5_5) = 0
% 7.03/2.29 | (163) ? [v0] : ? [v1] : (member(all_53_1_26, all_0_6_6) = v1 & member(all_53_1_26, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 7.03/2.29 |
% 7.03/2.29 | Instantiating (163) with all_73_0_27, all_73_1_28 yields:
% 7.03/2.29 | (164) member(all_53_1_26, all_0_6_6) = all_73_0_27 & member(all_53_1_26, all_0_7_7) = all_73_1_28 & (all_73_0_27 = 0 | all_73_1_28 = 0)
% 7.03/2.29 |
% 7.03/2.29 | Applying alpha-rule on (164) yields:
% 7.03/2.29 | (165) member(all_53_1_26, all_0_6_6) = all_73_0_27
% 7.03/2.29 | (166) member(all_53_1_26, all_0_7_7) = all_73_1_28
% 7.03/2.29 | (167) all_73_0_27 = 0 | all_73_1_28 = 0
% 7.03/2.29 |
% 7.03/2.29 +-Applying beta-rule and splitting (155), into two cases.
% 7.03/2.29 |-Branch one:
% 7.03/2.29 | (168) all_53_0_25 = 0
% 7.03/2.29 |
% 7.03/2.29 | Equations (168) can reduce 152 to:
% 7.03/2.29 | (44) $false
% 7.03/2.29 |
% 7.03/2.29 |-The branch is then unsatisfiable
% 7.03/2.29 |-Branch two:
% 7.03/2.29 | (152) ~ (all_53_0_25 = 0)
% 7.03/2.29 | (171) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_26, all_0_2_2) = v1 & member(all_53_1_26, all_0_3_3) = v0)
% 7.03/2.29 |
% 7.03/2.29 | Instantiating (171) with all_78_0_29, all_78_1_30 yields:
% 7.03/2.29 | (172) ~ (all_78_0_29 = 0) & ~ (all_78_1_30 = 0) & member(all_53_1_26, all_0_2_2) = all_78_0_29 & member(all_53_1_26, all_0_3_3) = all_78_1_30
% 7.03/2.29 |
% 7.03/2.29 | Applying alpha-rule on (172) yields:
% 7.03/2.29 | (173) ~ (all_78_0_29 = 0)
% 7.03/2.29 | (174) ~ (all_78_1_30 = 0)
% 7.03/2.29 | (175) member(all_53_1_26, all_0_2_2) = all_78_0_29
% 7.03/2.29 | (176) member(all_53_1_26, all_0_3_3) = all_78_1_30
% 7.03/2.29 |
% 7.03/2.29 | Instantiating formula (15) with all_53_1_26, all_0_8_8, 0, all_78_0_29 and discharging atoms member(all_53_1_26, all_0_8_8) = 0, yields:
% 7.03/2.29 | (177) all_78_0_29 = 0 | ~ (member(all_53_1_26, all_0_8_8) = all_78_0_29)
% 7.03/2.30 |
% 7.03/2.30 | Instantiating formula (2) with all_78_0_29, all_0_2_2, all_0_6_6, all_0_8_8, all_53_1_26 and discharging atoms intersection(all_0_8_8, all_0_6_6) = all_0_2_2, member(all_53_1_26, all_0_2_2) = all_78_0_29, yields:
% 7.03/2.30 | (178) all_78_0_29 = 0 | ? [v0] : ? [v1] : (member(all_53_1_26, all_0_6_6) = v1 & member(all_53_1_26, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.30 |
% 7.03/2.30 | Instantiating formula (2) with all_78_1_30, all_0_3_3, all_0_7_7, all_0_8_8, all_53_1_26 and discharging atoms intersection(all_0_8_8, all_0_7_7) = all_0_3_3, member(all_53_1_26, all_0_3_3) = all_78_1_30, yields:
% 7.03/2.30 | (179) all_78_1_30 = 0 | ? [v0] : ? [v1] : (member(all_53_1_26, all_0_7_7) = v1 & member(all_53_1_26, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.30 |
% 7.03/2.30 +-Applying beta-rule and splitting (179), into two cases.
% 7.03/2.30 |-Branch one:
% 7.03/2.30 | (180) all_78_1_30 = 0
% 7.03/2.30 |
% 7.03/2.30 | Equations (180) can reduce 174 to:
% 7.03/2.30 | (44) $false
% 7.03/2.30 |
% 7.03/2.30 |-The branch is then unsatisfiable
% 7.03/2.30 |-Branch two:
% 7.03/2.30 | (174) ~ (all_78_1_30 = 0)
% 7.03/2.30 | (183) ? [v0] : ? [v1] : (member(all_53_1_26, all_0_7_7) = v1 & member(all_53_1_26, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.03/2.30 |
% 7.03/2.30 | Instantiating (183) with all_107_0_31, all_107_1_32 yields:
% 7.03/2.30 | (184) member(all_53_1_26, all_0_7_7) = all_107_0_31 & member(all_53_1_26, all_0_8_8) = all_107_1_32 & ( ~ (all_107_0_31 = 0) | ~ (all_107_1_32 = 0))
% 7.03/2.30 |
% 7.03/2.30 | Applying alpha-rule on (184) yields:
% 7.03/2.30 | (185) member(all_53_1_26, all_0_7_7) = all_107_0_31
% 7.03/2.30 | (186) member(all_53_1_26, all_0_8_8) = all_107_1_32
% 7.03/2.30 | (187) ~ (all_107_0_31 = 0) | ~ (all_107_1_32 = 0)
% 7.03/2.30 |
% 7.03/2.30 +-Applying beta-rule and splitting (177), into two cases.
% 7.03/2.30 |-Branch one:
% 7.03/2.30 | (188) ~ (member(all_53_1_26, all_0_8_8) = all_78_0_29)
% 7.03/2.30 |
% 7.03/2.30 | Instantiating formula (15) with all_53_1_26, all_0_7_7, all_107_0_31, all_73_1_28 and discharging atoms member(all_53_1_26, all_0_7_7) = all_107_0_31, member(all_53_1_26, all_0_7_7) = all_73_1_28, yields:
% 7.03/2.30 | (189) all_107_0_31 = all_73_1_28
% 7.03/2.30 |
% 7.03/2.30 | Instantiating formula (15) with all_53_1_26, all_0_8_8, all_107_1_32, 0 and discharging atoms member(all_53_1_26, all_0_8_8) = all_107_1_32, member(all_53_1_26, all_0_8_8) = 0, yields:
% 7.03/2.30 | (190) all_107_1_32 = 0
% 7.03/2.30 |
% 7.03/2.30 | Using (186) and (188) yields:
% 7.03/2.30 | (191) ~ (all_107_1_32 = all_78_0_29)
% 7.25/2.30 |
% 7.25/2.30 | Equations (190) can reduce 191 to:
% 7.25/2.30 | (192) ~ (all_78_0_29 = 0)
% 7.25/2.30 |
% 7.25/2.30 | Simplifying 192 yields:
% 7.25/2.30 | (173) ~ (all_78_0_29 = 0)
% 7.25/2.30 |
% 7.25/2.30 | From (190) and (186) follows:
% 7.25/2.30 | (159) member(all_53_1_26, all_0_8_8) = 0
% 7.25/2.30 |
% 7.25/2.30 +-Applying beta-rule and splitting (187), into two cases.
% 7.25/2.30 |-Branch one:
% 7.25/2.30 | (195) ~ (all_107_0_31 = 0)
% 7.25/2.30 |
% 7.25/2.30 | Equations (189) can reduce 195 to:
% 7.25/2.30 | (196) ~ (all_73_1_28 = 0)
% 7.25/2.30 |
% 7.25/2.30 +-Applying beta-rule and splitting (178), into two cases.
% 7.25/2.30 |-Branch one:
% 7.25/2.30 | (197) all_78_0_29 = 0
% 7.25/2.30 |
% 7.25/2.30 | Equations (197) can reduce 173 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 |-Branch two:
% 7.25/2.30 | (173) ~ (all_78_0_29 = 0)
% 7.25/2.30 | (200) ? [v0] : ? [v1] : (member(all_53_1_26, all_0_6_6) = v1 & member(all_53_1_26, all_0_8_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.25/2.30 |
% 7.25/2.30 | Instantiating (200) with all_133_0_33, all_133_1_34 yields:
% 7.25/2.30 | (201) member(all_53_1_26, all_0_6_6) = all_133_0_33 & member(all_53_1_26, all_0_8_8) = all_133_1_34 & ( ~ (all_133_0_33 = 0) | ~ (all_133_1_34 = 0))
% 7.25/2.30 |
% 7.25/2.30 | Applying alpha-rule on (201) yields:
% 7.25/2.30 | (202) member(all_53_1_26, all_0_6_6) = all_133_0_33
% 7.25/2.30 | (203) member(all_53_1_26, all_0_8_8) = all_133_1_34
% 7.25/2.30 | (204) ~ (all_133_0_33 = 0) | ~ (all_133_1_34 = 0)
% 7.25/2.30 |
% 7.25/2.30 +-Applying beta-rule and splitting (167), into two cases.
% 7.25/2.30 |-Branch one:
% 7.25/2.30 | (205) all_73_0_27 = 0
% 7.25/2.30 |
% 7.25/2.30 | From (205) and (165) follows:
% 7.25/2.30 | (206) member(all_53_1_26, all_0_6_6) = 0
% 7.25/2.30 |
% 7.25/2.30 | Instantiating formula (15) with all_53_1_26, all_0_6_6, all_133_0_33, 0 and discharging atoms member(all_53_1_26, all_0_6_6) = all_133_0_33, member(all_53_1_26, all_0_6_6) = 0, yields:
% 7.25/2.30 | (207) all_133_0_33 = 0
% 7.25/2.30 |
% 7.25/2.30 | Instantiating formula (15) with all_53_1_26, all_0_8_8, all_133_1_34, 0 and discharging atoms member(all_53_1_26, all_0_8_8) = all_133_1_34, member(all_53_1_26, all_0_8_8) = 0, yields:
% 7.25/2.30 | (208) all_133_1_34 = 0
% 7.25/2.30 |
% 7.25/2.30 +-Applying beta-rule and splitting (204), into two cases.
% 7.25/2.30 |-Branch one:
% 7.25/2.30 | (209) ~ (all_133_0_33 = 0)
% 7.25/2.30 |
% 7.25/2.30 | Equations (207) can reduce 209 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 |-Branch two:
% 7.25/2.30 | (207) all_133_0_33 = 0
% 7.25/2.30 | (212) ~ (all_133_1_34 = 0)
% 7.25/2.30 |
% 7.25/2.30 | Equations (208) can reduce 212 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 |-Branch two:
% 7.25/2.30 | (214) ~ (all_73_0_27 = 0)
% 7.25/2.30 | (215) all_73_1_28 = 0
% 7.25/2.30 |
% 7.25/2.30 | Equations (215) can reduce 196 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 |-Branch two:
% 7.25/2.30 | (217) all_107_0_31 = 0
% 7.25/2.30 | (218) ~ (all_107_1_32 = 0)
% 7.25/2.30 |
% 7.25/2.30 | Equations (190) can reduce 218 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 |-Branch two:
% 7.25/2.30 | (220) member(all_53_1_26, all_0_8_8) = all_78_0_29
% 7.25/2.30 | (197) all_78_0_29 = 0
% 7.25/2.30 |
% 7.25/2.30 | Equations (197) can reduce 173 to:
% 7.25/2.30 | (44) $false
% 7.25/2.30 |
% 7.25/2.30 |-The branch is then unsatisfiable
% 7.25/2.30 % SZS output end Proof for theBenchmark
% 7.25/2.30
% 7.25/2.30 1698ms
%------------------------------------------------------------------------------