TSTP Solution File: SET155+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET155+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 00:17:59 EDT 2022
% Result : Theorem 4.49s 1.69s
% Output : Proof 7.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET155+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 04:40:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ____ _
% 0.20/0.59 ___ / __ \_____(_)___ ________ __________
% 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.92 Prover 0: Preprocessing ...
% 2.03/1.11 Prover 0: Warning: ignoring some quantifiers
% 2.03/1.14 Prover 0: Constructing countermodel ...
% 3.20/1.39 Prover 0: gave up
% 3.20/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.20/1.41 Prover 1: Preprocessing ...
% 3.77/1.51 Prover 1: Constructing countermodel ...
% 4.49/1.69 Prover 1: proved (305ms)
% 4.49/1.69
% 4.49/1.69 No countermodel exists, formula is valid
% 4.49/1.69 % SZS status Theorem for theBenchmark
% 4.49/1.69
% 4.49/1.69 Generating proof ... found it (size 106)
% 6.52/2.18
% 6.52/2.18 % SZS output start Proof for theBenchmark
% 6.52/2.18 Assumed formulas after preprocessing and simplification:
% 6.52/2.18 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & difference(v2, v3) = v4 & difference(v2, v1) = v6 & difference(v2, v0) = v5 & union(v0, v1) = v3 & intersection(v5, v6) = v7 & equal_set(v4, v7) = v8 & subset(v1, v2) = 0 & subset(v0, v2) = 0 & ! [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))
% 6.83/2.22 | 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:
% 6.83/2.22 | (1) ~ (all_0_0_0 = 0) & difference(all_0_6_6, all_0_5_5) = all_0_4_4 & difference(all_0_6_6, all_0_7_7) = all_0_2_2 & difference(all_0_6_6, all_0_8_8) = all_0_3_3 & union(all_0_8_8, all_0_7_7) = all_0_5_5 & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 & subset(all_0_7_7, all_0_6_6) = 0 & subset(all_0_8_8, all_0_6_6) = 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)
% 6.83/2.23 |
% 6.83/2.23 | Applying alpha-rule on (1) yields:
% 6.83/2.23 | (2) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.83/2.23 | (3) ! [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)))
% 6.83/2.23 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.83/2.23 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.83/2.23 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.83/2.24 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 6.83/2.24 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.83/2.24 | (9) difference(all_0_6_6, all_0_5_5) = all_0_4_4
% 6.83/2.24 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.83/2.24 | (11) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0
% 6.83/2.24 | (12) ! [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))
% 6.83/2.24 | (13) subset(all_0_7_7, all_0_6_6) = 0
% 6.83/2.24 | (14) ! [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))
% 6.83/2.24 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.83/2.24 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.83/2.24 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.83/2.24 | (18) ~ (all_0_0_0 = 0)
% 6.83/2.24 | (19) subset(all_0_8_8, all_0_6_6) = 0
% 6.83/2.24 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.83/2.24 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.83/2.24 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.83/2.24 | (23) difference(all_0_6_6, all_0_7_7) = all_0_2_2
% 6.83/2.24 | (24) ! [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))
% 6.83/2.24 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.83/2.24 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.83/2.24 | (27) union(all_0_8_8, all_0_7_7) = all_0_5_5
% 6.83/2.24 | (28) intersection(all_0_3_3, all_0_2_2) = all_0_1_1
% 6.83/2.24 | (29) difference(all_0_6_6, all_0_8_8) = all_0_3_3
% 6.83/2.24 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.83/2.24 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.83/2.24 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.83/2.24 | (33) ! [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))))
% 6.83/2.24 | (34) ! [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)))
% 6.83/2.24 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 6.83/2.25 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.83/2.25 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.83/2.25 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 6.83/2.25 | (39) ! [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))
% 6.83/2.25 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.83/2.25 | (41) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.83/2.25 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.83/2.25 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 6.83/2.25 |
% 6.83/2.25 | Instantiating formula (16) 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:
% 6.83/2.25 | (44) 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)))
% 6.83/2.25 |
% 6.83/2.25 +-Applying beta-rule and splitting (44), into two cases.
% 6.83/2.25 |-Branch one:
% 6.83/2.25 | (45) all_0_0_0 = 0
% 6.83/2.25 |
% 6.83/2.25 | Equations (45) can reduce 18 to:
% 6.83/2.25 | (46) $false
% 6.83/2.25 |
% 6.83/2.25 |-The branch is then unsatisfiable
% 6.83/2.25 |-Branch two:
% 6.83/2.25 | (18) ~ (all_0_0_0 = 0)
% 6.83/2.25 | (48) ? [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)))
% 6.83/2.25 |
% 6.83/2.25 | Instantiating (48) with all_14_0_9, all_14_1_10 yields:
% 6.83/2.25 | (49) 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))
% 6.83/2.25 |
% 6.83/2.25 | Applying alpha-rule on (49) yields:
% 6.83/2.25 | (50) subset(all_0_1_1, all_0_4_4) = all_14_0_9
% 6.83/2.25 | (51) subset(all_0_4_4, all_0_1_1) = all_14_1_10
% 6.83/2.25 | (52) ~ (all_14_0_9 = 0) | ~ (all_14_1_10 = 0)
% 6.83/2.25 |
% 6.83/2.25 | Instantiating formula (25) 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:
% 6.83/2.25 | (53) all_14_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 6.83/2.25 |
% 6.83/2.25 | Instantiating formula (25) 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:
% 6.83/2.25 | (54) all_14_1_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 6.83/2.25 |
% 6.83/2.25 +-Applying beta-rule and splitting (52), into two cases.
% 6.83/2.25 |-Branch one:
% 6.83/2.25 | (55) ~ (all_14_0_9 = 0)
% 6.83/2.25 |
% 6.83/2.25 +-Applying beta-rule and splitting (53), into two cases.
% 6.83/2.25 |-Branch one:
% 6.83/2.25 | (56) all_14_0_9 = 0
% 6.83/2.25 |
% 6.83/2.25 | Equations (56) can reduce 55 to:
% 6.83/2.25 | (46) $false
% 6.83/2.25 |
% 6.83/2.25 |-The branch is then unsatisfiable
% 6.83/2.25 |-Branch two:
% 6.83/2.25 | (55) ~ (all_14_0_9 = 0)
% 6.83/2.25 | (59) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 6.83/2.25 |
% 6.83/2.25 | Instantiating (59) with all_53_0_11, all_53_1_12 yields:
% 6.83/2.25 | (60) ~ (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
% 6.83/2.26 |
% 6.83/2.26 | Applying alpha-rule on (60) yields:
% 6.83/2.26 | (61) ~ (all_53_0_11 = 0)
% 6.83/2.26 | (62) member(all_53_1_12, all_0_1_1) = 0
% 6.83/2.26 | (63) member(all_53_1_12, all_0_4_4) = all_53_0_11
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (43) with all_0_2_2, all_0_6_6, all_0_7_7, all_53_1_12 and discharging atoms difference(all_0_6_6, all_0_7_7) = all_0_2_2, yields:
% 6.83/2.26 | (64) ~ (member(all_53_1_12, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_7_7) = v0)
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (43) with all_0_3_3, all_0_6_6, all_0_8_8, all_53_1_12 and discharging atoms difference(all_0_6_6, all_0_8_8) = all_0_3_3, yields:
% 6.83/2.26 | (65) ~ (member(all_53_1_12, all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_8_8) = v0)
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (3) with all_0_5_5, all_0_7_7, all_0_8_8, all_53_1_12 and discharging atoms union(all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 6.83/2.26 | (66) ~ (member(all_53_1_12, all_0_5_5) = 0) | ? [v0] : ? [v1] : (member(all_53_1_12, all_0_7_7) = v1 & member(all_53_1_12, all_0_8_8) = v0 & (v1 = 0 | v0 = 0))
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (37) with all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_12 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_12, all_0_1_1) = 0, yields:
% 6.83/2.26 | (67) member(all_53_1_12, all_0_2_2) = 0 & member(all_53_1_12, all_0_3_3) = 0
% 6.83/2.26 |
% 6.83/2.26 | Applying alpha-rule on (67) yields:
% 6.83/2.26 | (68) member(all_53_1_12, all_0_2_2) = 0
% 6.83/2.26 | (69) member(all_53_1_12, all_0_3_3) = 0
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (34) with all_53_0_11, all_0_4_4, all_0_6_6, all_0_5_5, all_53_1_12 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_4_4, member(all_53_1_12, all_0_4_4) = all_53_0_11, yields:
% 6.83/2.26 | (70) all_53_0_11 = 0 | ? [v0] : ? [v1] : (member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.83/2.26 |
% 6.83/2.26 +-Applying beta-rule and splitting (64), into two cases.
% 6.83/2.26 |-Branch one:
% 6.83/2.26 | (71) ~ (member(all_53_1_12, all_0_2_2) = 0)
% 6.83/2.26 |
% 6.83/2.26 | Using (68) and (71) yields:
% 6.83/2.26 | (72) $false
% 6.83/2.26 |
% 6.83/2.26 |-The branch is then unsatisfiable
% 6.83/2.26 |-Branch two:
% 6.83/2.26 | (68) member(all_53_1_12, all_0_2_2) = 0
% 6.83/2.26 | (74) ? [v0] : ( ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_7_7) = v0)
% 6.83/2.26 |
% 6.83/2.26 | Instantiating (74) with all_76_0_13 yields:
% 6.83/2.26 | (75) ~ (all_76_0_13 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_7_7) = all_76_0_13
% 6.83/2.26 |
% 6.83/2.26 | Applying alpha-rule on (75) yields:
% 6.83/2.26 | (76) ~ (all_76_0_13 = 0)
% 6.83/2.26 | (77) member(all_53_1_12, all_0_6_6) = 0
% 6.83/2.26 | (78) member(all_53_1_12, all_0_7_7) = all_76_0_13
% 6.83/2.26 |
% 6.83/2.26 +-Applying beta-rule and splitting (65), into two cases.
% 6.83/2.26 |-Branch one:
% 6.83/2.26 | (79) ~ (member(all_53_1_12, all_0_3_3) = 0)
% 6.83/2.26 |
% 6.83/2.26 | Using (69) and (79) yields:
% 6.83/2.26 | (72) $false
% 6.83/2.26 |
% 6.83/2.26 |-The branch is then unsatisfiable
% 6.83/2.26 |-Branch two:
% 6.83/2.26 | (69) member(all_53_1_12, all_0_3_3) = 0
% 6.83/2.26 | (82) ? [v0] : ( ~ (v0 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_8_8) = v0)
% 6.83/2.26 |
% 6.83/2.26 | Instantiating (82) with all_81_0_14 yields:
% 6.83/2.26 | (83) ~ (all_81_0_14 = 0) & member(all_53_1_12, all_0_6_6) = 0 & member(all_53_1_12, all_0_8_8) = all_81_0_14
% 6.83/2.26 |
% 6.83/2.26 | Applying alpha-rule on (83) yields:
% 6.83/2.26 | (84) ~ (all_81_0_14 = 0)
% 6.83/2.26 | (77) member(all_53_1_12, all_0_6_6) = 0
% 6.83/2.26 | (86) member(all_53_1_12, all_0_8_8) = all_81_0_14
% 6.83/2.26 |
% 6.83/2.26 +-Applying beta-rule and splitting (70), into two cases.
% 6.83/2.26 |-Branch one:
% 6.83/2.26 | (87) all_53_0_11 = 0
% 6.83/2.26 |
% 6.83/2.26 | Equations (87) can reduce 61 to:
% 6.83/2.26 | (46) $false
% 6.83/2.26 |
% 6.83/2.26 |-The branch is then unsatisfiable
% 6.83/2.26 |-Branch two:
% 6.83/2.26 | (61) ~ (all_53_0_11 = 0)
% 6.83/2.26 | (90) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.83/2.26 |
% 6.83/2.26 | Instantiating (90) with all_86_0_15, all_86_1_16 yields:
% 6.83/2.26 | (91) member(all_53_1_12, all_0_5_5) = all_86_0_15 & member(all_53_1_12, all_0_6_6) = all_86_1_16 & ( ~ (all_86_1_16 = 0) | all_86_0_15 = 0)
% 6.83/2.26 |
% 6.83/2.26 | Applying alpha-rule on (91) yields:
% 6.83/2.26 | (92) member(all_53_1_12, all_0_5_5) = all_86_0_15
% 6.83/2.26 | (93) member(all_53_1_12, all_0_6_6) = all_86_1_16
% 6.83/2.26 | (94) ~ (all_86_1_16 = 0) | all_86_0_15 = 0
% 6.83/2.26 |
% 6.83/2.26 +-Applying beta-rule and splitting (66), into two cases.
% 6.83/2.26 |-Branch one:
% 6.83/2.26 | (95) ~ (member(all_53_1_12, all_0_5_5) = 0)
% 6.83/2.26 |
% 6.83/2.26 | Instantiating formula (40) with all_53_1_12, all_0_6_6, all_86_1_16, 0 and discharging atoms member(all_53_1_12, all_0_6_6) = all_86_1_16, member(all_53_1_12, all_0_6_6) = 0, yields:
% 6.83/2.27 | (96) all_86_1_16 = 0
% 6.83/2.27 |
% 6.83/2.27 | Using (92) and (95) yields:
% 6.83/2.27 | (97) ~ (all_86_0_15 = 0)
% 6.83/2.27 |
% 6.83/2.27 +-Applying beta-rule and splitting (94), into two cases.
% 6.83/2.27 |-Branch one:
% 6.83/2.27 | (98) ~ (all_86_1_16 = 0)
% 6.83/2.27 |
% 6.83/2.27 | Equations (96) can reduce 98 to:
% 6.83/2.27 | (46) $false
% 6.83/2.27 |
% 6.83/2.27 |-The branch is then unsatisfiable
% 6.83/2.27 |-Branch two:
% 6.83/2.27 | (96) all_86_1_16 = 0
% 6.83/2.27 | (101) all_86_0_15 = 0
% 6.83/2.27 |
% 6.83/2.27 | Equations (101) can reduce 97 to:
% 6.83/2.27 | (46) $false
% 6.83/2.27 |
% 6.83/2.27 |-The branch is then unsatisfiable
% 6.83/2.27 |-Branch two:
% 6.83/2.27 | (103) member(all_53_1_12, all_0_5_5) = 0
% 6.83/2.27 | (104) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_7_7) = v1 & member(all_53_1_12, all_0_8_8) = v0 & (v1 = 0 | v0 = 0))
% 6.83/2.27 |
% 6.83/2.27 | Instantiating (104) with all_92_0_17, all_92_1_18 yields:
% 6.83/2.27 | (105) member(all_53_1_12, all_0_7_7) = all_92_0_17 & member(all_53_1_12, all_0_8_8) = all_92_1_18 & (all_92_0_17 = 0 | all_92_1_18 = 0)
% 6.83/2.27 |
% 6.83/2.27 | Applying alpha-rule on (105) yields:
% 6.83/2.27 | (106) member(all_53_1_12, all_0_7_7) = all_92_0_17
% 6.83/2.27 | (107) member(all_53_1_12, all_0_8_8) = all_92_1_18
% 6.83/2.27 | (108) all_92_0_17 = 0 | all_92_1_18 = 0
% 6.83/2.27 |
% 6.83/2.27 | Instantiating formula (40) with all_53_1_12, all_0_7_7, all_76_0_13, all_92_0_17 and discharging atoms member(all_53_1_12, all_0_7_7) = all_92_0_17, member(all_53_1_12, all_0_7_7) = all_76_0_13, yields:
% 6.83/2.27 | (109) all_92_0_17 = all_76_0_13
% 6.83/2.27 |
% 6.83/2.27 | Instantiating formula (40) with all_53_1_12, all_0_8_8, all_81_0_14, all_92_1_18 and discharging atoms member(all_53_1_12, all_0_8_8) = all_92_1_18, member(all_53_1_12, all_0_8_8) = all_81_0_14, yields:
% 6.83/2.27 | (110) all_92_1_18 = all_81_0_14
% 6.83/2.27 |
% 6.83/2.27 +-Applying beta-rule and splitting (108), into two cases.
% 6.83/2.27 |-Branch one:
% 6.83/2.27 | (111) all_92_0_17 = 0
% 6.83/2.27 |
% 6.83/2.27 | Combining equations (111,109) yields a new equation:
% 6.83/2.27 | (112) all_76_0_13 = 0
% 6.83/2.27 |
% 6.83/2.27 | Equations (112) can reduce 76 to:
% 6.83/2.27 | (46) $false
% 6.83/2.27 |
% 6.83/2.27 |-The branch is then unsatisfiable
% 6.83/2.27 |-Branch two:
% 6.83/2.27 | (114) ~ (all_92_0_17 = 0)
% 6.83/2.27 | (115) all_92_1_18 = 0
% 6.83/2.27 |
% 6.83/2.27 | Combining equations (110,115) yields a new equation:
% 6.83/2.27 | (116) all_81_0_14 = 0
% 6.83/2.27 |
% 6.83/2.27 | Simplifying 116 yields:
% 6.83/2.27 | (117) all_81_0_14 = 0
% 6.83/2.27 |
% 6.83/2.27 | Equations (117) can reduce 84 to:
% 6.83/2.27 | (46) $false
% 6.83/2.27 |
% 6.83/2.27 |-The branch is then unsatisfiable
% 6.83/2.27 |-Branch two:
% 6.83/2.27 | (56) all_14_0_9 = 0
% 6.83/2.27 | (120) ~ (all_14_1_10 = 0)
% 6.83/2.27 |
% 6.83/2.27 +-Applying beta-rule and splitting (54), into two cases.
% 6.83/2.27 |-Branch one:
% 6.83/2.27 | (121) all_14_1_10 = 0
% 6.83/2.27 |
% 6.83/2.27 | Equations (121) can reduce 120 to:
% 6.83/2.27 | (46) $false
% 6.83/2.27 |
% 6.83/2.27 |-The branch is then unsatisfiable
% 6.83/2.27 |-Branch two:
% 6.83/2.27 | (120) ~ (all_14_1_10 = 0)
% 6.83/2.27 | (124) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 6.83/2.27 |
% 6.83/2.27 | Instantiating (124) with all_53_0_19, all_53_1_20 yields:
% 6.83/2.27 | (125) ~ (all_53_0_19 = 0) & member(all_53_1_20, all_0_1_1) = all_53_0_19 & member(all_53_1_20, all_0_4_4) = 0
% 6.83/2.27 |
% 6.83/2.27 | Applying alpha-rule on (125) yields:
% 6.83/2.27 | (126) ~ (all_53_0_19 = 0)
% 6.83/2.27 | (127) member(all_53_1_20, all_0_1_1) = all_53_0_19
% 6.83/2.27 | (128) member(all_53_1_20, all_0_4_4) = 0
% 6.83/2.27 |
% 6.83/2.27 | Instantiating formula (33) with all_53_0_19, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_20 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_20, all_0_1_1) = all_53_0_19, yields:
% 6.83/2.27 | (129) all_53_0_19 = 0 | ? [v0] : ? [v1] : (member(all_53_1_20, all_0_2_2) = v1 & member(all_53_1_20, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.83/2.27 |
% 6.83/2.27 | Instantiating formula (43) with all_0_4_4, all_0_6_6, all_0_5_5, all_53_1_20 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_4_4, member(all_53_1_20, all_0_4_4) = 0, yields:
% 6.83/2.27 | (130) ? [v0] : ( ~ (v0 = 0) & member(all_53_1_20, all_0_5_5) = v0 & member(all_53_1_20, all_0_6_6) = 0)
% 6.83/2.28 |
% 6.83/2.28 | Instantiating (130) with all_68_0_21 yields:
% 6.83/2.28 | (131) ~ (all_68_0_21 = 0) & member(all_53_1_20, all_0_5_5) = all_68_0_21 & member(all_53_1_20, all_0_6_6) = 0
% 6.83/2.28 |
% 6.83/2.28 | Applying alpha-rule on (131) yields:
% 6.83/2.28 | (132) ~ (all_68_0_21 = 0)
% 6.83/2.28 | (133) member(all_53_1_20, all_0_5_5) = all_68_0_21
% 6.83/2.28 | (134) member(all_53_1_20, all_0_6_6) = 0
% 6.83/2.28 |
% 6.83/2.28 +-Applying beta-rule and splitting (129), into two cases.
% 6.83/2.28 |-Branch one:
% 6.83/2.28 | (135) all_53_0_19 = 0
% 6.83/2.28 |
% 6.83/2.28 | Equations (135) can reduce 126 to:
% 6.83/2.28 | (46) $false
% 6.83/2.28 |
% 6.83/2.28 |-The branch is then unsatisfiable
% 6.83/2.28 |-Branch two:
% 6.83/2.28 | (126) ~ (all_53_0_19 = 0)
% 6.83/2.28 | (138) ? [v0] : ? [v1] : (member(all_53_1_20, all_0_2_2) = v1 & member(all_53_1_20, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.83/2.28 |
% 6.83/2.28 | Instantiating (138) with all_74_0_22, all_74_1_23 yields:
% 6.83/2.28 | (139) member(all_53_1_20, all_0_2_2) = all_74_0_22 & member(all_53_1_20, all_0_3_3) = all_74_1_23 & ( ~ (all_74_0_22 = 0) | ~ (all_74_1_23 = 0))
% 6.83/2.28 |
% 6.83/2.28 | Applying alpha-rule on (139) yields:
% 6.83/2.28 | (140) member(all_53_1_20, all_0_2_2) = all_74_0_22
% 6.83/2.28 | (141) member(all_53_1_20, all_0_3_3) = all_74_1_23
% 6.83/2.28 | (142) ~ (all_74_0_22 = 0) | ~ (all_74_1_23 = 0)
% 6.83/2.28 |
% 6.83/2.28 | Instantiating formula (34) with all_74_0_22, all_0_2_2, all_0_6_6, all_0_7_7, all_53_1_20 and discharging atoms difference(all_0_6_6, all_0_7_7) = all_0_2_2, member(all_53_1_20, all_0_2_2) = all_74_0_22, yields:
% 6.83/2.28 | (143) all_74_0_22 = 0 | ? [v0] : ? [v1] : (member(all_53_1_20, all_0_6_6) = v0 & member(all_53_1_20, all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.83/2.28 |
% 6.83/2.28 | Instantiating formula (34) with all_74_1_23, all_0_3_3, all_0_6_6, all_0_8_8, all_53_1_20 and discharging atoms difference(all_0_6_6, all_0_8_8) = all_0_3_3, member(all_53_1_20, all_0_3_3) = all_74_1_23, yields:
% 6.83/2.28 | (144) all_74_1_23 = 0 | ? [v0] : ? [v1] : (member(all_53_1_20, all_0_6_6) = v0 & member(all_53_1_20, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 6.83/2.28 |
% 6.83/2.28 | Instantiating formula (39) with all_68_0_21, all_0_5_5, all_0_7_7, all_0_8_8, all_53_1_20 and discharging atoms union(all_0_8_8, all_0_7_7) = all_0_5_5, member(all_53_1_20, all_0_5_5) = all_68_0_21, yields:
% 6.83/2.28 | (145) all_68_0_21 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_20, all_0_7_7) = v1 & member(all_53_1_20, all_0_8_8) = v0)
% 6.83/2.28 |
% 6.83/2.28 +-Applying beta-rule and splitting (145), into two cases.
% 6.83/2.28 |-Branch one:
% 6.83/2.28 | (146) all_68_0_21 = 0
% 6.83/2.28 |
% 6.83/2.28 | Equations (146) can reduce 132 to:
% 6.83/2.28 | (46) $false
% 6.83/2.28 |
% 6.83/2.28 |-The branch is then unsatisfiable
% 6.83/2.28 |-Branch two:
% 6.83/2.28 | (132) ~ (all_68_0_21 = 0)
% 6.83/2.28 | (149) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_20, all_0_7_7) = v1 & member(all_53_1_20, all_0_8_8) = v0)
% 7.19/2.28 |
% 7.19/2.28 | Instantiating (149) with all_94_0_24, all_94_1_25 yields:
% 7.19/2.28 | (150) ~ (all_94_0_24 = 0) & ~ (all_94_1_25 = 0) & member(all_53_1_20, all_0_7_7) = all_94_0_24 & member(all_53_1_20, all_0_8_8) = all_94_1_25
% 7.19/2.28 |
% 7.19/2.28 | Applying alpha-rule on (150) yields:
% 7.19/2.28 | (151) ~ (all_94_0_24 = 0)
% 7.19/2.28 | (152) ~ (all_94_1_25 = 0)
% 7.19/2.28 | (153) member(all_53_1_20, all_0_7_7) = all_94_0_24
% 7.19/2.28 | (154) member(all_53_1_20, all_0_8_8) = all_94_1_25
% 7.19/2.28 |
% 7.19/2.28 +-Applying beta-rule and splitting (144), into two cases.
% 7.19/2.28 |-Branch one:
% 7.19/2.28 | (155) all_74_1_23 = 0
% 7.19/2.28 |
% 7.19/2.28 +-Applying beta-rule and splitting (142), into two cases.
% 7.19/2.28 |-Branch one:
% 7.19/2.28 | (156) ~ (all_74_0_22 = 0)
% 7.19/2.28 |
% 7.19/2.28 +-Applying beta-rule and splitting (143), into two cases.
% 7.19/2.28 |-Branch one:
% 7.19/2.28 | (157) all_74_0_22 = 0
% 7.19/2.28 |
% 7.19/2.28 | Equations (157) can reduce 156 to:
% 7.19/2.28 | (46) $false
% 7.19/2.28 |
% 7.19/2.28 |-The branch is then unsatisfiable
% 7.19/2.28 |-Branch two:
% 7.19/2.28 | (156) ~ (all_74_0_22 = 0)
% 7.19/2.28 | (160) ? [v0] : ? [v1] : (member(all_53_1_20, all_0_6_6) = v0 & member(all_53_1_20, all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 7.19/2.29 |
% 7.19/2.29 | Instantiating (160) with all_128_0_26, all_128_1_27 yields:
% 7.19/2.29 | (161) member(all_53_1_20, all_0_6_6) = all_128_1_27 & member(all_53_1_20, all_0_7_7) = all_128_0_26 & ( ~ (all_128_1_27 = 0) | all_128_0_26 = 0)
% 7.19/2.29 |
% 7.19/2.29 | Applying alpha-rule on (161) yields:
% 7.19/2.29 | (162) member(all_53_1_20, all_0_6_6) = all_128_1_27
% 7.19/2.29 | (163) member(all_53_1_20, all_0_7_7) = all_128_0_26
% 7.19/2.29 | (164) ~ (all_128_1_27 = 0) | all_128_0_26 = 0
% 7.19/2.29 |
% 7.19/2.29 | Instantiating formula (40) with all_53_1_20, all_0_6_6, all_128_1_27, 0 and discharging atoms member(all_53_1_20, all_0_6_6) = all_128_1_27, member(all_53_1_20, all_0_6_6) = 0, yields:
% 7.19/2.29 | (165) all_128_1_27 = 0
% 7.19/2.29 |
% 7.19/2.29 | Instantiating formula (40) with all_53_1_20, all_0_7_7, all_94_0_24, all_128_0_26 and discharging atoms member(all_53_1_20, all_0_7_7) = all_128_0_26, member(all_53_1_20, all_0_7_7) = all_94_0_24, yields:
% 7.19/2.29 | (166) all_128_0_26 = all_94_0_24
% 7.19/2.29 |
% 7.19/2.29 +-Applying beta-rule and splitting (164), into two cases.
% 7.19/2.29 |-Branch one:
% 7.19/2.29 | (167) ~ (all_128_1_27 = 0)
% 7.19/2.29 |
% 7.19/2.29 | Equations (165) can reduce 167 to:
% 7.19/2.29 | (46) $false
% 7.19/2.29 |
% 7.19/2.29 |-The branch is then unsatisfiable
% 7.19/2.29 |-Branch two:
% 7.19/2.29 | (165) all_128_1_27 = 0
% 7.19/2.29 | (170) all_128_0_26 = 0
% 7.19/2.29 |
% 7.19/2.29 | Combining equations (170,166) yields a new equation:
% 7.19/2.29 | (171) all_94_0_24 = 0
% 7.19/2.29 |
% 7.19/2.29 | Equations (171) can reduce 151 to:
% 7.19/2.29 | (46) $false
% 7.19/2.29 |
% 7.19/2.29 |-The branch is then unsatisfiable
% 7.19/2.29 |-Branch two:
% 7.19/2.29 | (157) all_74_0_22 = 0
% 7.19/2.29 | (174) ~ (all_74_1_23 = 0)
% 7.19/2.29 |
% 7.19/2.29 | Equations (155) can reduce 174 to:
% 7.19/2.29 | (46) $false
% 7.19/2.29 |
% 7.19/2.29 |-The branch is then unsatisfiable
% 7.19/2.29 |-Branch two:
% 7.19/2.29 | (174) ~ (all_74_1_23 = 0)
% 7.19/2.29 | (177) ? [v0] : ? [v1] : (member(all_53_1_20, all_0_6_6) = v0 & member(all_53_1_20, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 7.19/2.29 |
% 7.19/2.29 | Instantiating (177) with all_108_0_28, all_108_1_29 yields:
% 7.19/2.29 | (178) member(all_53_1_20, all_0_6_6) = all_108_1_29 & member(all_53_1_20, all_0_8_8) = all_108_0_28 & ( ~ (all_108_1_29 = 0) | all_108_0_28 = 0)
% 7.19/2.29 |
% 7.19/2.29 | Applying alpha-rule on (178) yields:
% 7.19/2.29 | (179) member(all_53_1_20, all_0_6_6) = all_108_1_29
% 7.19/2.29 | (180) member(all_53_1_20, all_0_8_8) = all_108_0_28
% 7.19/2.29 | (181) ~ (all_108_1_29 = 0) | all_108_0_28 = 0
% 7.19/2.29 |
% 7.19/2.29 | Instantiating formula (40) with all_53_1_20, all_0_6_6, all_108_1_29, 0 and discharging atoms member(all_53_1_20, all_0_6_6) = all_108_1_29, member(all_53_1_20, all_0_6_6) = 0, yields:
% 7.19/2.29 | (182) all_108_1_29 = 0
% 7.19/2.29 |
% 7.19/2.29 | Instantiating formula (40) with all_53_1_20, all_0_8_8, all_94_1_25, all_108_0_28 and discharging atoms member(all_53_1_20, all_0_8_8) = all_108_0_28, member(all_53_1_20, all_0_8_8) = all_94_1_25, yields:
% 7.19/2.29 | (183) all_108_0_28 = all_94_1_25
% 7.19/2.29 |
% 7.19/2.29 +-Applying beta-rule and splitting (181), into two cases.
% 7.19/2.29 |-Branch one:
% 7.19/2.29 | (184) ~ (all_108_1_29 = 0)
% 7.19/2.29 |
% 7.19/2.29 | Equations (182) can reduce 184 to:
% 7.19/2.29 | (46) $false
% 7.19/2.29 |
% 7.19/2.29 |-The branch is then unsatisfiable
% 7.19/2.29 |-Branch two:
% 7.19/2.29 | (182) all_108_1_29 = 0
% 7.19/2.29 | (187) all_108_0_28 = 0
% 7.19/2.29 |
% 7.19/2.29 | Combining equations (187,183) yields a new equation:
% 7.19/2.29 | (188) all_94_1_25 = 0
% 7.19/2.29 |
% 7.19/2.29 | Equations (188) can reduce 152 to:
% 7.19/2.29 | (46) $false
% 7.19/2.29 |
% 7.19/2.29 |-The branch is then unsatisfiable
% 7.19/2.29 % SZS output end Proof for theBenchmark
% 7.19/2.29
% 7.19/2.29 1681ms
%------------------------------------------------------------------------------