TSTP Solution File: SET372+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET372+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 00:19:17 EDT 2022
% Result : Theorem 8.72s 2.71s
% Output : Proof 10.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET372+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 19:13:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.57/0.59 ____ _
% 0.57/0.59 ___ / __ \_____(_)___ ________ __________
% 0.57/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.59
% 0.57/0.59 A Theorem Prover for First-Order Logic
% 0.57/0.59 (ePrincess v.1.0)
% 0.57/0.59
% 0.57/0.59 (c) Philipp Rümmer, 2009-2015
% 0.57/0.59 (c) Peter Backeman, 2014-2015
% 0.57/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59 Bug reports to peter@backeman.se
% 0.57/0.59
% 0.57/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59
% 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.92 Prover 0: Preprocessing ...
% 1.97/1.12 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.14 Prover 0: Constructing countermodel ...
% 7.60/2.44 Prover 0: gave up
% 7.60/2.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.60/2.46 Prover 1: Preprocessing ...
% 8.06/2.54 Prover 1: Constructing countermodel ...
% 8.72/2.70 Prover 1: proved (262ms)
% 8.72/2.71
% 8.72/2.71 No countermodel exists, formula is valid
% 8.72/2.71 % SZS status Theorem for theBenchmark
% 8.72/2.71
% 8.72/2.71 Generating proof ... found it (size 123)
% 10.50/3.06
% 10.50/3.06 % SZS output start Proof for theBenchmark
% 10.50/3.06 Assumed formulas after preprocessing and simplification:
% 10.50/3.06 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & intersection(v4, v5) = v6 & intersection(v0, v1) = v2 & power_set(v2) = v3 & power_set(v1) = v5 & power_set(v0) = v4 & equal_set(v3, 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))
% 10.50/3.10 | 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:
% 10.50/3.10 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_5_5 & power_set(all_0_5_5) = all_0_4_4 & power_set(all_0_6_6) = all_0_2_2 & power_set(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)
% 10.50/3.10 |
% 10.50/3.10 | Applying alpha-rule on (1) yields:
% 10.50/3.10 | (2) power_set(all_0_6_6) = all_0_2_2
% 10.50/3.10 | (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)))
% 10.50/3.10 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.50/3.10 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 10.50/3.10 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 10.50/3.11 | (7) ! [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))
% 10.50/3.11 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 10.50/3.11 | (9) ! [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))
% 10.50/3.11 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 10.50/3.11 | (11) ! [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))))
% 10.50/3.11 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 10.50/3.11 | (13) power_set(all_0_7_7) = all_0_3_3
% 10.50/3.11 | (14) ! [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))
% 10.50/3.11 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 10.50/3.11 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 10.50/3.11 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 10.50/3.11 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 10.50/3.11 | (19) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0
% 10.50/3.11 | (20) intersection(all_0_3_3, all_0_2_2) = all_0_1_1
% 10.50/3.11 | (21) ~ (all_0_0_0 = 0)
% 10.50/3.11 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 10.50/3.11 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.50/3.11 | (24) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.50/3.11 | (25) ! [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))
% 10.50/3.11 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.50/3.11 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 10.50/3.11 | (28) ! [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)))
% 10.50/3.11 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 10.50/3.11 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 10.50/3.11 | (31) intersection(all_0_7_7, all_0_6_6) = all_0_5_5
% 10.50/3.11 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 10.50/3.11 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 10.50/3.11 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 10.50/3.11 | (35) ! [v0] : ~ (member(v0, empty_set) = 0)
% 10.50/3.11 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.50/3.11 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 10.50/3.11 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.50/3.11 | (39) power_set(all_0_5_5) = all_0_4_4
% 10.50/3.11 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 10.50/3.11 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 10.50/3.11 |
% 10.50/3.12 | Instantiating formula (15) 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:
% 10.50/3.12 | (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)))
% 10.50/3.12 |
% 10.50/3.12 +-Applying beta-rule and splitting (42), into two cases.
% 10.50/3.12 |-Branch one:
% 10.50/3.12 | (43) all_0_0_0 = 0
% 10.50/3.12 |
% 10.50/3.12 | Equations (43) can reduce 21 to:
% 10.50/3.12 | (44) $false
% 10.50/3.12 |
% 10.50/3.12 |-The branch is then unsatisfiable
% 10.50/3.12 |-Branch two:
% 10.50/3.12 | (21) ~ (all_0_0_0 = 0)
% 10.50/3.12 | (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)))
% 10.50/3.12 |
% 10.50/3.12 | Instantiating (46) with all_14_0_8, all_14_1_9 yields:
% 10.50/3.12 | (47) subset(all_0_1_1, all_0_4_4) = all_14_0_8 & subset(all_0_4_4, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0))
% 10.50/3.12 |
% 10.50/3.12 | Applying alpha-rule on (47) yields:
% 10.50/3.12 | (48) subset(all_0_1_1, all_0_4_4) = all_14_0_8
% 10.50/3.12 | (49) subset(all_0_4_4, all_0_1_1) = all_14_1_9
% 10.50/3.12 | (50) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (18) with all_14_0_8, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_0_8, yields:
% 10.50/3.12 | (51) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (18) with all_14_1_9, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_1_9, yields:
% 10.50/3.12 | (52) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 10.50/3.12 |
% 10.50/3.12 +-Applying beta-rule and splitting (50), into two cases.
% 10.50/3.12 |-Branch one:
% 10.50/3.12 | (53) ~ (all_14_0_8 = 0)
% 10.50/3.12 |
% 10.50/3.12 +-Applying beta-rule and splitting (51), into two cases.
% 10.50/3.12 |-Branch one:
% 10.50/3.12 | (54) all_14_0_8 = 0
% 10.50/3.12 |
% 10.50/3.12 | Equations (54) can reduce 53 to:
% 10.50/3.12 | (44) $false
% 10.50/3.12 |
% 10.50/3.12 |-The branch is then unsatisfiable
% 10.50/3.12 |-Branch two:
% 10.50/3.12 | (53) ~ (all_14_0_8 = 0)
% 10.50/3.12 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 10.50/3.12 |
% 10.50/3.12 | Instantiating (57) with all_53_0_10, all_53_1_11 yields:
% 10.50/3.12 | (58) ~ (all_53_0_10 = 0) & member(all_53_1_11, all_0_1_1) = 0 & member(all_53_1_11, all_0_4_4) = all_53_0_10
% 10.50/3.12 |
% 10.50/3.12 | Applying alpha-rule on (58) yields:
% 10.50/3.12 | (59) ~ (all_53_0_10 = 0)
% 10.50/3.12 | (60) member(all_53_1_11, all_0_1_1) = 0
% 10.50/3.12 | (61) member(all_53_1_11, all_0_4_4) = all_53_0_10
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_11 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_11, all_0_1_1) = 0, yields:
% 10.50/3.12 | (62) member(all_53_1_11, all_0_2_2) = 0 & member(all_53_1_11, all_0_3_3) = 0
% 10.50/3.12 |
% 10.50/3.12 | Applying alpha-rule on (62) yields:
% 10.50/3.12 | (63) member(all_53_1_11, all_0_2_2) = 0
% 10.50/3.12 | (64) member(all_53_1_11, all_0_3_3) = 0
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (23) with all_0_2_2, all_0_6_6, all_53_1_11 and discharging atoms power_set(all_0_6_6) = all_0_2_2, yields:
% 10.50/3.12 | (65) ~ (member(all_53_1_11, all_0_2_2) = 0) | subset(all_53_1_11, all_0_6_6) = 0
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (23) with all_0_3_3, all_0_7_7, all_53_1_11 and discharging atoms power_set(all_0_7_7) = all_0_3_3, yields:
% 10.50/3.12 | (66) ~ (member(all_53_1_11, all_0_3_3) = 0) | subset(all_53_1_11, all_0_7_7) = 0
% 10.50/3.12 |
% 10.50/3.12 | Instantiating formula (38) with all_53_0_10, all_0_4_4, all_0_5_5, all_53_1_11 and discharging atoms power_set(all_0_5_5) = all_0_4_4, member(all_53_1_11, all_0_4_4) = all_53_0_10, yields:
% 10.50/3.12 | (67) all_53_0_10 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_11, all_0_5_5) = v0)
% 10.50/3.12 |
% 10.50/3.12 +-Applying beta-rule and splitting (66), into two cases.
% 10.50/3.12 |-Branch one:
% 10.50/3.12 | (68) ~ (member(all_53_1_11, all_0_3_3) = 0)
% 10.50/3.12 |
% 10.50/3.12 | Using (64) and (68) yields:
% 10.50/3.12 | (69) $false
% 10.50/3.12 |
% 10.50/3.12 |-The branch is then unsatisfiable
% 10.50/3.12 |-Branch two:
% 10.50/3.12 | (64) member(all_53_1_11, all_0_3_3) = 0
% 10.50/3.12 | (71) subset(all_53_1_11, all_0_7_7) = 0
% 10.50/3.12 |
% 10.50/3.12 +-Applying beta-rule and splitting (67), into two cases.
% 10.50/3.12 |-Branch one:
% 10.50/3.12 | (72) all_53_0_10 = 0
% 10.50/3.12 |
% 10.50/3.12 | Equations (72) can reduce 59 to:
% 10.50/3.12 | (44) $false
% 10.50/3.12 |
% 10.50/3.12 |-The branch is then unsatisfiable
% 10.50/3.12 |-Branch two:
% 10.50/3.12 | (59) ~ (all_53_0_10 = 0)
% 10.50/3.12 | (75) ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_11, all_0_5_5) = v0)
% 10.50/3.12 |
% 10.50/3.12 | Instantiating (75) with all_76_0_12 yields:
% 10.50/3.12 | (76) ~ (all_76_0_12 = 0) & subset(all_53_1_11, all_0_5_5) = all_76_0_12
% 10.50/3.12 |
% 10.50/3.12 | Applying alpha-rule on (76) yields:
% 10.50/3.12 | (77) ~ (all_76_0_12 = 0)
% 10.50/3.12 | (78) subset(all_53_1_11, all_0_5_5) = all_76_0_12
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (65), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (79) ~ (member(all_53_1_11, all_0_2_2) = 0)
% 10.50/3.13 |
% 10.50/3.13 | Using (63) and (79) yields:
% 10.50/3.13 | (69) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (63) member(all_53_1_11, all_0_2_2) = 0
% 10.50/3.13 | (82) subset(all_53_1_11, all_0_6_6) = 0
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (18) with all_76_0_12, all_0_5_5, all_53_1_11 and discharging atoms subset(all_53_1_11, all_0_5_5) = all_76_0_12, yields:
% 10.50/3.13 | (83) all_76_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_11) = 0 & member(v0, all_0_5_5) = v1)
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (83), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (84) all_76_0_12 = 0
% 10.50/3.13 |
% 10.50/3.13 | Equations (84) can reduce 77 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (77) ~ (all_76_0_12 = 0)
% 10.50/3.13 | (87) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_11) = 0 & member(v0, all_0_5_5) = v1)
% 10.50/3.13 |
% 10.50/3.13 | Instantiating (87) with all_101_0_13, all_101_1_14 yields:
% 10.50/3.13 | (88) ~ (all_101_0_13 = 0) & member(all_101_1_14, all_53_1_11) = 0 & member(all_101_1_14, all_0_5_5) = all_101_0_13
% 10.50/3.13 |
% 10.50/3.13 | Applying alpha-rule on (88) yields:
% 10.50/3.13 | (89) ~ (all_101_0_13 = 0)
% 10.50/3.13 | (90) member(all_101_1_14, all_53_1_11) = 0
% 10.50/3.13 | (91) member(all_101_1_14, all_0_5_5) = all_101_0_13
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (40) with all_101_1_14, all_0_6_6, all_53_1_11 and discharging atoms subset(all_53_1_11, all_0_6_6) = 0, member(all_101_1_14, all_53_1_11) = 0, yields:
% 10.50/3.13 | (92) member(all_101_1_14, all_0_6_6) = 0
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (40) with all_101_1_14, all_0_7_7, all_53_1_11 and discharging atoms subset(all_53_1_11, all_0_7_7) = 0, member(all_101_1_14, all_53_1_11) = 0, yields:
% 10.50/3.13 | (93) member(all_101_1_14, all_0_7_7) = 0
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (11) with all_101_0_13, all_0_5_5, all_0_6_6, all_0_7_7, all_101_1_14 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_101_1_14, all_0_5_5) = all_101_0_13, yields:
% 10.50/3.13 | (94) all_101_0_13 = 0 | ? [v0] : ? [v1] : (member(all_101_1_14, all_0_6_6) = v1 & member(all_101_1_14, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (94), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (95) all_101_0_13 = 0
% 10.50/3.13 |
% 10.50/3.13 | Equations (95) can reduce 89 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (89) ~ (all_101_0_13 = 0)
% 10.50/3.13 | (98) ? [v0] : ? [v1] : (member(all_101_1_14, all_0_6_6) = v1 & member(all_101_1_14, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.50/3.13 |
% 10.50/3.13 | Instantiating (98) with all_121_0_15, all_121_1_16 yields:
% 10.50/3.13 | (99) member(all_101_1_14, all_0_6_6) = all_121_0_15 & member(all_101_1_14, all_0_7_7) = all_121_1_16 & ( ~ (all_121_0_15 = 0) | ~ (all_121_1_16 = 0))
% 10.50/3.13 |
% 10.50/3.13 | Applying alpha-rule on (99) yields:
% 10.50/3.13 | (100) member(all_101_1_14, all_0_6_6) = all_121_0_15
% 10.50/3.13 | (101) member(all_101_1_14, all_0_7_7) = all_121_1_16
% 10.50/3.13 | (102) ~ (all_121_0_15 = 0) | ~ (all_121_1_16 = 0)
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (37) with all_101_1_14, all_0_6_6, all_121_0_15, 0 and discharging atoms member(all_101_1_14, all_0_6_6) = all_121_0_15, member(all_101_1_14, all_0_6_6) = 0, yields:
% 10.50/3.13 | (103) all_121_0_15 = 0
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (37) with all_101_1_14, all_0_7_7, all_121_1_16, 0 and discharging atoms member(all_101_1_14, all_0_7_7) = all_121_1_16, member(all_101_1_14, all_0_7_7) = 0, yields:
% 10.50/3.13 | (104) all_121_1_16 = 0
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (102), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (105) ~ (all_121_0_15 = 0)
% 10.50/3.13 |
% 10.50/3.13 | Equations (103) can reduce 105 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (103) all_121_0_15 = 0
% 10.50/3.13 | (108) ~ (all_121_1_16 = 0)
% 10.50/3.13 |
% 10.50/3.13 | Equations (104) can reduce 108 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (54) all_14_0_8 = 0
% 10.50/3.13 | (111) ~ (all_14_1_9 = 0)
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (52), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (112) all_14_1_9 = 0
% 10.50/3.13 |
% 10.50/3.13 | Equations (112) can reduce 111 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (111) ~ (all_14_1_9 = 0)
% 10.50/3.13 | (115) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 10.50/3.13 |
% 10.50/3.13 | Instantiating (115) with all_53_0_17, all_53_1_18 yields:
% 10.50/3.13 | (116) ~ (all_53_0_17 = 0) & member(all_53_1_18, all_0_1_1) = all_53_0_17 & member(all_53_1_18, all_0_4_4) = 0
% 10.50/3.13 |
% 10.50/3.13 | Applying alpha-rule on (116) yields:
% 10.50/3.13 | (117) ~ (all_53_0_17 = 0)
% 10.50/3.13 | (118) member(all_53_1_18, all_0_1_1) = all_53_0_17
% 10.50/3.13 | (119) member(all_53_1_18, all_0_4_4) = 0
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (11) with all_53_0_17, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_18 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_18, all_0_1_1) = all_53_0_17, yields:
% 10.50/3.13 | (120) all_53_0_17 = 0 | ? [v0] : ? [v1] : (member(all_53_1_18, all_0_2_2) = v1 & member(all_53_1_18, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (23) with all_0_4_4, all_0_5_5, all_53_1_18 and discharging atoms power_set(all_0_5_5) = all_0_4_4, member(all_53_1_18, all_0_4_4) = 0, yields:
% 10.50/3.13 | (121) subset(all_53_1_18, all_0_5_5) = 0
% 10.50/3.13 |
% 10.50/3.13 +-Applying beta-rule and splitting (120), into two cases.
% 10.50/3.13 |-Branch one:
% 10.50/3.13 | (122) all_53_0_17 = 0
% 10.50/3.13 |
% 10.50/3.13 | Equations (122) can reduce 117 to:
% 10.50/3.13 | (44) $false
% 10.50/3.13 |
% 10.50/3.13 |-The branch is then unsatisfiable
% 10.50/3.13 |-Branch two:
% 10.50/3.13 | (117) ~ (all_53_0_17 = 0)
% 10.50/3.13 | (125) ? [v0] : ? [v1] : (member(all_53_1_18, all_0_2_2) = v1 & member(all_53_1_18, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.50/3.13 |
% 10.50/3.13 | Instantiating (125) with all_73_0_19, all_73_1_20 yields:
% 10.50/3.13 | (126) member(all_53_1_18, all_0_2_2) = all_73_0_19 & member(all_53_1_18, all_0_3_3) = all_73_1_20 & ( ~ (all_73_0_19 = 0) | ~ (all_73_1_20 = 0))
% 10.50/3.13 |
% 10.50/3.13 | Applying alpha-rule on (126) yields:
% 10.50/3.13 | (127) member(all_53_1_18, all_0_2_2) = all_73_0_19
% 10.50/3.13 | (128) member(all_53_1_18, all_0_3_3) = all_73_1_20
% 10.50/3.13 | (129) ~ (all_73_0_19 = 0) | ~ (all_73_1_20 = 0)
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (38) with all_73_0_19, all_0_2_2, all_0_6_6, all_53_1_18 and discharging atoms power_set(all_0_6_6) = all_0_2_2, member(all_53_1_18, all_0_2_2) = all_73_0_19, yields:
% 10.50/3.13 | (130) all_73_0_19 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_18, all_0_6_6) = v0)
% 10.50/3.13 |
% 10.50/3.13 | Instantiating formula (23) with all_0_2_2, all_0_6_6, all_53_1_18 and discharging atoms power_set(all_0_6_6) = all_0_2_2, yields:
% 10.50/3.13 | (131) ~ (member(all_53_1_18, all_0_2_2) = 0) | subset(all_53_1_18, all_0_6_6) = 0
% 10.50/3.14 |
% 10.50/3.14 | Instantiating formula (38) with all_73_1_20, all_0_3_3, all_0_7_7, all_53_1_18 and discharging atoms power_set(all_0_7_7) = all_0_3_3, member(all_53_1_18, all_0_3_3) = all_73_1_20, yields:
% 10.50/3.14 | (132) all_73_1_20 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_18, all_0_7_7) = v0)
% 10.50/3.14 |
% 10.50/3.14 +-Applying beta-rule and splitting (131), into two cases.
% 10.50/3.14 |-Branch one:
% 10.50/3.14 | (133) ~ (member(all_53_1_18, all_0_2_2) = 0)
% 10.50/3.14 |
% 10.50/3.14 | Using (127) and (133) yields:
% 10.50/3.14 | (134) ~ (all_73_0_19 = 0)
% 10.50/3.14 |
% 10.50/3.14 +-Applying beta-rule and splitting (130), into two cases.
% 10.50/3.14 |-Branch one:
% 10.50/3.14 | (135) all_73_0_19 = 0
% 10.50/3.14 |
% 10.50/3.14 | Equations (135) can reduce 134 to:
% 10.50/3.14 | (44) $false
% 10.50/3.14 |
% 10.50/3.14 |-The branch is then unsatisfiable
% 10.50/3.14 |-Branch two:
% 10.50/3.14 | (134) ~ (all_73_0_19 = 0)
% 10.50/3.14 | (138) ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_18, all_0_6_6) = v0)
% 10.50/3.14 |
% 10.50/3.14 | Instantiating (138) with all_170_0_21 yields:
% 10.50/3.14 | (139) ~ (all_170_0_21 = 0) & subset(all_53_1_18, all_0_6_6) = all_170_0_21
% 10.50/3.14 |
% 10.50/3.14 | Applying alpha-rule on (139) yields:
% 10.50/3.14 | (140) ~ (all_170_0_21 = 0)
% 10.50/3.14 | (141) subset(all_53_1_18, all_0_6_6) = all_170_0_21
% 10.50/3.14 |
% 10.50/3.14 | Instantiating formula (18) with all_170_0_21, all_0_6_6, all_53_1_18 and discharging atoms subset(all_53_1_18, all_0_6_6) = all_170_0_21, yields:
% 10.50/3.14 | (142) all_170_0_21 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_18) = 0 & member(v0, all_0_6_6) = v1)
% 10.50/3.14 |
% 10.50/3.14 +-Applying beta-rule and splitting (142), into two cases.
% 10.50/3.14 |-Branch one:
% 10.50/3.14 | (143) all_170_0_21 = 0
% 10.50/3.14 |
% 10.50/3.14 | Equations (143) can reduce 140 to:
% 10.50/3.14 | (44) $false
% 10.50/3.14 |
% 10.50/3.14 |-The branch is then unsatisfiable
% 10.50/3.14 |-Branch two:
% 10.50/3.14 | (140) ~ (all_170_0_21 = 0)
% 10.50/3.14 | (146) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_18) = 0 & member(v0, all_0_6_6) = v1)
% 10.50/3.14 |
% 10.50/3.14 | Instantiating (146) with all_183_0_22, all_183_1_23 yields:
% 10.50/3.14 | (147) ~ (all_183_0_22 = 0) & member(all_183_1_23, all_53_1_18) = 0 & member(all_183_1_23, all_0_6_6) = all_183_0_22
% 10.50/3.14 |
% 10.50/3.14 | Applying alpha-rule on (147) yields:
% 10.50/3.14 | (148) ~ (all_183_0_22 = 0)
% 10.50/3.14 | (149) member(all_183_1_23, all_53_1_18) = 0
% 10.50/3.14 | (150) member(all_183_1_23, all_0_6_6) = all_183_0_22
% 10.50/3.14 |
% 10.50/3.14 | Instantiating formula (37) with all_183_1_23, all_0_6_6, all_183_0_22, 0 and discharging atoms member(all_183_1_23, all_0_6_6) = all_183_0_22, yields:
% 10.50/3.14 | (151) all_183_0_22 = 0 | ~ (member(all_183_1_23, all_0_6_6) = 0)
% 10.50/3.14 |
% 10.50/3.14 | Instantiating formula (34) with all_0_5_5, all_0_6_6, all_0_7_7, all_183_1_23 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 10.50/3.14 | (152) ~ (member(all_183_1_23, all_0_5_5) = 0) | (member(all_183_1_23, all_0_6_6) = 0 & member(all_183_1_23, all_0_7_7) = 0)
% 10.50/3.14 |
% 10.50/3.14 | Instantiating formula (40) with all_183_1_23, all_0_5_5, all_53_1_18 and discharging atoms subset(all_53_1_18, all_0_5_5) = 0, member(all_183_1_23, all_53_1_18) = 0, yields:
% 10.50/3.14 | (153) member(all_183_1_23, all_0_5_5) = 0
% 10.50/3.14 |
% 10.50/3.14 +-Applying beta-rule and splitting (152), into two cases.
% 10.50/3.14 |-Branch one:
% 10.50/3.14 | (154) ~ (member(all_183_1_23, all_0_5_5) = 0)
% 10.50/3.14 |
% 10.50/3.14 | Using (153) and (154) yields:
% 10.50/3.14 | (69) $false
% 10.50/3.14 |
% 10.50/3.14 |-The branch is then unsatisfiable
% 10.50/3.14 |-Branch two:
% 10.50/3.14 | (153) member(all_183_1_23, all_0_5_5) = 0
% 10.90/3.14 | (157) member(all_183_1_23, all_0_6_6) = 0 & member(all_183_1_23, all_0_7_7) = 0
% 10.90/3.14 |
% 10.90/3.14 | Applying alpha-rule on (157) yields:
% 10.90/3.14 | (158) member(all_183_1_23, all_0_6_6) = 0
% 10.90/3.14 | (159) member(all_183_1_23, all_0_7_7) = 0
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (151), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (160) ~ (member(all_183_1_23, all_0_6_6) = 0)
% 10.90/3.14 |
% 10.90/3.14 | Using (158) and (160) yields:
% 10.90/3.14 | (69) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (158) member(all_183_1_23, all_0_6_6) = 0
% 10.90/3.14 | (163) all_183_0_22 = 0
% 10.90/3.14 |
% 10.90/3.14 | Equations (163) can reduce 148 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (165) member(all_53_1_18, all_0_2_2) = 0
% 10.90/3.14 | (166) subset(all_53_1_18, all_0_6_6) = 0
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (130), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (135) all_73_0_19 = 0
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (129), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (134) ~ (all_73_0_19 = 0)
% 10.90/3.14 |
% 10.90/3.14 | Equations (135) can reduce 134 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (135) all_73_0_19 = 0
% 10.90/3.14 | (171) ~ (all_73_1_20 = 0)
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (132), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (172) all_73_1_20 = 0
% 10.90/3.14 |
% 10.90/3.14 | Equations (172) can reduce 171 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (171) ~ (all_73_1_20 = 0)
% 10.90/3.14 | (175) ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_18, all_0_7_7) = v0)
% 10.90/3.14 |
% 10.90/3.14 | Instantiating (175) with all_174_0_27 yields:
% 10.90/3.14 | (176) ~ (all_174_0_27 = 0) & subset(all_53_1_18, all_0_7_7) = all_174_0_27
% 10.90/3.14 |
% 10.90/3.14 | Applying alpha-rule on (176) yields:
% 10.90/3.14 | (177) ~ (all_174_0_27 = 0)
% 10.90/3.14 | (178) subset(all_53_1_18, all_0_7_7) = all_174_0_27
% 10.90/3.14 |
% 10.90/3.14 | Instantiating formula (18) with all_174_0_27, all_0_7_7, all_53_1_18 and discharging atoms subset(all_53_1_18, all_0_7_7) = all_174_0_27, yields:
% 10.90/3.14 | (179) all_174_0_27 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_18) = 0 & member(v0, all_0_7_7) = v1)
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (179), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (180) all_174_0_27 = 0
% 10.90/3.14 |
% 10.90/3.14 | Equations (180) can reduce 177 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (177) ~ (all_174_0_27 = 0)
% 10.90/3.14 | (183) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_53_1_18) = 0 & member(v0, all_0_7_7) = v1)
% 10.90/3.14 |
% 10.90/3.14 | Instantiating (183) with all_191_0_28, all_191_1_29 yields:
% 10.90/3.14 | (184) ~ (all_191_0_28 = 0) & member(all_191_1_29, all_53_1_18) = 0 & member(all_191_1_29, all_0_7_7) = all_191_0_28
% 10.90/3.14 |
% 10.90/3.14 | Applying alpha-rule on (184) yields:
% 10.90/3.14 | (185) ~ (all_191_0_28 = 0)
% 10.90/3.14 | (186) member(all_191_1_29, all_53_1_18) = 0
% 10.90/3.14 | (187) member(all_191_1_29, all_0_7_7) = all_191_0_28
% 10.90/3.14 |
% 10.90/3.14 | Instantiating formula (37) with all_191_1_29, all_0_7_7, all_191_0_28, 0 and discharging atoms member(all_191_1_29, all_0_7_7) = all_191_0_28, yields:
% 10.90/3.14 | (188) all_191_0_28 = 0 | ~ (member(all_191_1_29, all_0_7_7) = 0)
% 10.90/3.14 |
% 10.90/3.14 | Instantiating formula (34) with all_0_5_5, all_0_6_6, all_0_7_7, all_191_1_29 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 10.90/3.14 | (189) ~ (member(all_191_1_29, all_0_5_5) = 0) | (member(all_191_1_29, all_0_6_6) = 0 & member(all_191_1_29, all_0_7_7) = 0)
% 10.90/3.14 |
% 10.90/3.14 | Instantiating formula (40) with all_191_1_29, all_0_5_5, all_53_1_18 and discharging atoms subset(all_53_1_18, all_0_5_5) = 0, member(all_191_1_29, all_53_1_18) = 0, yields:
% 10.90/3.14 | (190) member(all_191_1_29, all_0_5_5) = 0
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (189), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (191) ~ (member(all_191_1_29, all_0_5_5) = 0)
% 10.90/3.14 |
% 10.90/3.14 | Using (190) and (191) yields:
% 10.90/3.14 | (69) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (190) member(all_191_1_29, all_0_5_5) = 0
% 10.90/3.14 | (194) member(all_191_1_29, all_0_6_6) = 0 & member(all_191_1_29, all_0_7_7) = 0
% 10.90/3.14 |
% 10.90/3.14 | Applying alpha-rule on (194) yields:
% 10.90/3.14 | (195) member(all_191_1_29, all_0_6_6) = 0
% 10.90/3.14 | (196) member(all_191_1_29, all_0_7_7) = 0
% 10.90/3.14 |
% 10.90/3.14 +-Applying beta-rule and splitting (188), into two cases.
% 10.90/3.14 |-Branch one:
% 10.90/3.14 | (197) ~ (member(all_191_1_29, all_0_7_7) = 0)
% 10.90/3.14 |
% 10.90/3.14 | Using (196) and (197) yields:
% 10.90/3.14 | (69) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (196) member(all_191_1_29, all_0_7_7) = 0
% 10.90/3.14 | (200) all_191_0_28 = 0
% 10.90/3.14 |
% 10.90/3.14 | Equations (200) can reduce 185 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 |-Branch two:
% 10.90/3.14 | (134) ~ (all_73_0_19 = 0)
% 10.90/3.14 | (138) ? [v0] : ( ~ (v0 = 0) & subset(all_53_1_18, all_0_6_6) = v0)
% 10.90/3.14 |
% 10.90/3.14 | Instantiating formula (37) with all_53_1_18, all_0_2_2, 0, all_73_0_19 and discharging atoms member(all_53_1_18, all_0_2_2) = all_73_0_19, member(all_53_1_18, all_0_2_2) = 0, yields:
% 10.90/3.14 | (135) all_73_0_19 = 0
% 10.90/3.14 |
% 10.90/3.14 | Equations (135) can reduce 134 to:
% 10.90/3.14 | (44) $false
% 10.90/3.14 |
% 10.90/3.14 |-The branch is then unsatisfiable
% 10.90/3.14 % SZS output end Proof for theBenchmark
% 10.90/3.14
% 10.90/3.14 2543ms
%------------------------------------------------------------------------------