TSTP Solution File: SET171+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET171+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 00:18:08 EDT 2022
% Result : Theorem 4.26s 1.65s
% Output : Proof 7.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET171+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n028.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 : Sun Jul 10 06:31:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.54/0.60 ____ _
% 0.54/0.60 ___ / __ \_____(_)___ ________ __________
% 0.54/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic
% 0.54/0.60 (ePrincess v.1.0)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2015
% 0.54/0.60 (c) Peter Backeman, 2014-2015
% 0.54/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.60 Bug reports to peter@backeman.se
% 0.54/0.60
% 0.54/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.60
% 0.54/0.60 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
% 1.53/0.92 Prover 0: Preprocessing ...
% 2.01/1.10 Prover 0: Warning: ignoring some quantifiers
% 2.01/1.13 Prover 0: Constructing countermodel ...
% 2.60/1.29 Prover 0: gave up
% 2.60/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.82/1.32 Prover 1: Preprocessing ...
% 3.10/1.42 Prover 1: Constructing countermodel ...
% 4.26/1.65 Prover 1: proved (350ms)
% 4.26/1.65
% 4.26/1.65 No countermodel exists, formula is valid
% 4.26/1.65 % SZS status Theorem for theBenchmark
% 4.26/1.65
% 4.26/1.65 Generating proof ... found it (size 122)
% 6.75/2.24
% 6.75/2.24 % SZS output start Proof for theBenchmark
% 6.75/2.24 Assumed formulas after preprocessing and simplification:
% 6.75/2.24 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & union(v0, v3) = v4 & union(v0, v2) = v6 & union(v0, v1) = v5 & intersection(v5, v6) = v7 & intersection(v1, v2) = v3 & 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))
% 6.75/2.28 | 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:
% 6.75/2.28 | (1) ~ (all_0_0_0 = 0) & union(all_0_8_8, all_0_5_5) = all_0_4_4 & union(all_0_8_8, all_0_6_6) = all_0_2_2 & union(all_0_8_8, all_0_7_7) = all_0_3_3 & 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 & 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)
% 7.10/2.29 |
% 7.10/2.30 | Applying alpha-rule on (1) yields:
% 7.10/2.30 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.10/2.30 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.10/2.30 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 7.10/2.30 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 7.10/2.30 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 7.10/2.30 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 7.10/2.30 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 7.10/2.30 | (9) ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.10/2.30 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 7.10/2.30 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 7.10/2.30 | (12) union(all_0_8_8, all_0_6_6) = all_0_2_2
% 7.10/2.30 | (13) union(all_0_8_8, all_0_7_7) = all_0_3_3
% 7.10/2.30 | (14) ! [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))))
% 7.10/2.30 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 7.10/2.30 | (16) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0
% 7.10/2.30 | (17) ! [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))
% 7.10/2.30 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 7.10/2.30 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 7.10/2.30 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 7.10/2.30 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 7.10/2.30 | (22) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.10/2.30 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 7.10/2.30 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 7.10/2.30 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 7.10/2.30 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 7.10/2.30 | (27) ~ (all_0_0_0 = 0)
% 7.10/2.30 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 7.10/2.31 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 7.10/2.31 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.10/2.31 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 7.10/2.31 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.10/2.31 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 7.10/2.31 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.10/2.31 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 7.10/2.31 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 7.10/2.31 | (37) union(all_0_8_8, all_0_5_5) = all_0_4_4
% 7.10/2.31 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 7.10/2.31 | (39) intersection(all_0_7_7, all_0_6_6) = all_0_5_5
% 7.10/2.31 | (40) intersection(all_0_3_3, all_0_2_2) = all_0_1_1
% 7.10/2.31 | (41) ! [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)))
% 7.10/2.31 |
% 7.10/2.31 | Instantiating formula (21) 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:
% 7.10/2.31 | (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)))
% 7.10/2.31 |
% 7.10/2.31 +-Applying beta-rule and splitting (42), into two cases.
% 7.10/2.31 |-Branch one:
% 7.10/2.31 | (43) all_0_0_0 = 0
% 7.10/2.31 |
% 7.10/2.31 | Equations (43) can reduce 27 to:
% 7.10/2.31 | (44) $false
% 7.10/2.31 |
% 7.10/2.31 |-The branch is then unsatisfiable
% 7.10/2.31 |-Branch two:
% 7.10/2.31 | (27) ~ (all_0_0_0 = 0)
% 7.10/2.31 | (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)))
% 7.10/2.31 |
% 7.10/2.31 | Instantiating (46) with all_14_0_9, all_14_1_10 yields:
% 7.10/2.31 | (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))
% 7.10/2.31 |
% 7.10/2.31 | Applying alpha-rule on (47) yields:
% 7.10/2.31 | (48) subset(all_0_1_1, all_0_4_4) = all_14_0_9
% 7.10/2.31 | (49) subset(all_0_4_4, all_0_1_1) = all_14_1_10
% 7.10/2.31 | (50) ~ (all_14_0_9 = 0) | ~ (all_14_1_10 = 0)
% 7.10/2.31 |
% 7.10/2.31 | Instantiating formula (38) 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:
% 7.10/2.31 | (51) all_14_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 7.10/2.31 |
% 7.10/2.31 | Instantiating formula (38) 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:
% 7.10/2.31 | (52) all_14_1_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 7.10/2.31 |
% 7.10/2.32 +-Applying beta-rule and splitting (50), into two cases.
% 7.10/2.32 |-Branch one:
% 7.10/2.32 | (53) ~ (all_14_0_9 = 0)
% 7.10/2.32 |
% 7.10/2.32 +-Applying beta-rule and splitting (51), into two cases.
% 7.10/2.32 |-Branch one:
% 7.10/2.32 | (54) all_14_0_9 = 0
% 7.10/2.32 |
% 7.10/2.32 | Equations (54) can reduce 53 to:
% 7.10/2.32 | (44) $false
% 7.10/2.32 |
% 7.10/2.32 |-The branch is then unsatisfiable
% 7.10/2.32 |-Branch two:
% 7.10/2.32 | (53) ~ (all_14_0_9 = 0)
% 7.10/2.32 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1)
% 7.10/2.32 |
% 7.10/2.32 | Instantiating (57) with all_53_0_11, all_53_1_12 yields:
% 7.10/2.32 | (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
% 7.10/2.32 |
% 7.10/2.32 | Applying alpha-rule on (58) yields:
% 7.10/2.32 | (59) ~ (all_53_0_11 = 0)
% 7.10/2.32 | (60) member(all_53_1_12, all_0_1_1) = 0
% 7.10/2.32 | (61) member(all_53_1_12, all_0_4_4) = all_53_0_11
% 7.10/2.32 |
% 7.10/2.32 | Instantiating formula (5) with all_0_2_2, all_0_6_6, all_0_8_8, all_53_1_12 and discharging atoms union(all_0_8_8, all_0_6_6) = all_0_2_2, yields:
% 7.10/2.32 | (62) ~ (member(all_53_1_12, all_0_2_2) = 0) | ? [v0] : ? [v1] : (member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_8_8) = v0 & (v1 = 0 | v0 = 0))
% 7.10/2.32 |
% 7.10/2.32 | Instantiating formula (5) with all_0_3_3, 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_3_3, yields:
% 7.10/2.32 | (63) ~ (member(all_53_1_12, all_0_3_3) = 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))
% 7.10/2.32 |
% 7.10/2.32 | Instantiating formula (36) 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:
% 7.10/2.32 | (64) member(all_53_1_12, all_0_2_2) = 0 & member(all_53_1_12, all_0_3_3) = 0
% 7.10/2.32 |
% 7.10/2.32 | Applying alpha-rule on (64) yields:
% 7.10/2.32 | (65) member(all_53_1_12, all_0_2_2) = 0
% 7.10/2.32 | (66) member(all_53_1_12, all_0_3_3) = 0
% 7.10/2.32 |
% 7.10/2.32 | Instantiating formula (17) with all_53_0_11, all_0_4_4, all_0_5_5, all_0_8_8, all_53_1_12 and discharging atoms union(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:
% 7.10/2.32 | (67) all_53_0_11 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_8_8) = v0)
% 7.10/2.32 |
% 7.10/2.32 +-Applying beta-rule and splitting (63), into two cases.
% 7.10/2.32 |-Branch one:
% 7.10/2.32 | (68) ~ (member(all_53_1_12, all_0_3_3) = 0)
% 7.10/2.32 |
% 7.10/2.32 | Using (66) and (68) yields:
% 7.10/2.32 | (69) $false
% 7.10/2.32 |
% 7.10/2.32 |-The branch is then unsatisfiable
% 7.10/2.32 |-Branch two:
% 7.10/2.32 | (66) member(all_53_1_12, all_0_3_3) = 0
% 7.10/2.32 | (71) ? [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))
% 7.10/2.32 |
% 7.10/2.32 | Instantiating (71) with all_76_0_13, all_76_1_14 yields:
% 7.10/2.32 | (72) member(all_53_1_12, all_0_7_7) = all_76_0_13 & member(all_53_1_12, all_0_8_8) = all_76_1_14 & (all_76_0_13 = 0 | all_76_1_14 = 0)
% 7.10/2.32 |
% 7.10/2.32 | Applying alpha-rule on (72) yields:
% 7.10/2.32 | (73) member(all_53_1_12, all_0_7_7) = all_76_0_13
% 7.10/2.32 | (74) member(all_53_1_12, all_0_8_8) = all_76_1_14
% 7.10/2.32 | (75) all_76_0_13 = 0 | all_76_1_14 = 0
% 7.10/2.32 |
% 7.10/2.32 +-Applying beta-rule and splitting (62), into two cases.
% 7.10/2.32 |-Branch one:
% 7.10/2.32 | (76) ~ (member(all_53_1_12, all_0_2_2) = 0)
% 7.10/2.32 |
% 7.10/2.32 | Using (65) and (76) yields:
% 7.10/2.32 | (69) $false
% 7.10/2.32 |
% 7.10/2.32 |-The branch is then unsatisfiable
% 7.10/2.32 |-Branch two:
% 7.10/2.32 | (65) member(all_53_1_12, all_0_2_2) = 0
% 7.10/2.32 | (79) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_8_8) = v0 & (v1 = 0 | v0 = 0))
% 7.10/2.32 |
% 7.10/2.32 | Instantiating (79) with all_82_0_15, all_82_1_16 yields:
% 7.10/2.32 | (80) member(all_53_1_12, all_0_6_6) = all_82_0_15 & member(all_53_1_12, all_0_8_8) = all_82_1_16 & (all_82_0_15 = 0 | all_82_1_16 = 0)
% 7.10/2.32 |
% 7.10/2.32 | Applying alpha-rule on (80) yields:
% 7.10/2.32 | (81) member(all_53_1_12, all_0_6_6) = all_82_0_15
% 7.10/2.32 | (82) member(all_53_1_12, all_0_8_8) = all_82_1_16
% 7.10/2.32 | (83) all_82_0_15 = 0 | all_82_1_16 = 0
% 7.10/2.32 |
% 7.10/2.32 +-Applying beta-rule and splitting (67), into two cases.
% 7.10/2.32 |-Branch one:
% 7.10/2.32 | (84) all_53_0_11 = 0
% 7.10/2.32 |
% 7.10/2.32 | Equations (84) can reduce 59 to:
% 7.10/2.32 | (44) $false
% 7.10/2.32 |
% 7.10/2.32 |-The branch is then unsatisfiable
% 7.10/2.32 |-Branch two:
% 7.10/2.32 | (59) ~ (all_53_0_11 = 0)
% 7.10/2.32 | (87) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_12, all_0_5_5) = v1 & member(all_53_1_12, all_0_8_8) = v0)
% 7.10/2.32 |
% 7.10/2.32 | Instantiating (87) with all_87_0_17, all_87_1_18 yields:
% 7.10/2.32 | (88) ~ (all_87_0_17 = 0) & ~ (all_87_1_18 = 0) & member(all_53_1_12, all_0_5_5) = all_87_0_17 & member(all_53_1_12, all_0_8_8) = all_87_1_18
% 7.10/2.32 |
% 7.10/2.32 | Applying alpha-rule on (88) yields:
% 7.10/2.32 | (89) ~ (all_87_0_17 = 0)
% 7.10/2.33 | (90) ~ (all_87_1_18 = 0)
% 7.10/2.33 | (91) member(all_53_1_12, all_0_5_5) = all_87_0_17
% 7.10/2.33 | (92) member(all_53_1_12, all_0_8_8) = all_87_1_18
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (3) with all_53_1_12, all_0_8_8, all_82_1_16, all_87_1_18 and discharging atoms member(all_53_1_12, all_0_8_8) = all_87_1_18, member(all_53_1_12, all_0_8_8) = all_82_1_16, yields:
% 7.10/2.33 | (93) all_87_1_18 = all_82_1_16
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (3) with all_53_1_12, all_0_8_8, all_76_1_14, all_87_1_18 and discharging atoms member(all_53_1_12, all_0_8_8) = all_87_1_18, member(all_53_1_12, all_0_8_8) = all_76_1_14, yields:
% 7.10/2.33 | (94) all_87_1_18 = all_76_1_14
% 7.10/2.33 |
% 7.10/2.33 | Combining equations (94,93) yields a new equation:
% 7.10/2.33 | (95) all_82_1_16 = all_76_1_14
% 7.10/2.33 |
% 7.10/2.33 | Combining equations (95,93) yields a new equation:
% 7.10/2.33 | (94) all_87_1_18 = all_76_1_14
% 7.10/2.33 |
% 7.10/2.33 | Equations (94) can reduce 90 to:
% 7.10/2.33 | (97) ~ (all_76_1_14 = 0)
% 7.10/2.33 |
% 7.10/2.33 +-Applying beta-rule and splitting (83), into two cases.
% 7.10/2.33 |-Branch one:
% 7.10/2.33 | (98) all_82_0_15 = 0
% 7.10/2.33 |
% 7.10/2.33 | From (98) and (81) follows:
% 7.10/2.33 | (99) member(all_53_1_12, all_0_6_6) = 0
% 7.10/2.33 |
% 7.10/2.33 +-Applying beta-rule and splitting (75), into two cases.
% 7.10/2.33 |-Branch one:
% 7.10/2.33 | (100) all_76_0_13 = 0
% 7.10/2.33 |
% 7.10/2.33 | From (100) and (73) follows:
% 7.10/2.33 | (101) member(all_53_1_12, all_0_7_7) = 0
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (14) with all_87_0_17, all_0_5_5, all_0_6_6, all_0_7_7, all_53_1_12 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, member(all_53_1_12, all_0_5_5) = all_87_0_17, yields:
% 7.10/2.33 | (102) all_87_0_17 = 0 | ? [v0] : ? [v1] : (member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.10/2.33 |
% 7.10/2.33 +-Applying beta-rule and splitting (102), into two cases.
% 7.10/2.33 |-Branch one:
% 7.10/2.33 | (103) all_87_0_17 = 0
% 7.10/2.33 |
% 7.10/2.33 | Equations (103) can reduce 89 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (89) ~ (all_87_0_17 = 0)
% 7.10/2.33 | (106) ? [v0] : ? [v1] : (member(all_53_1_12, all_0_6_6) = v1 & member(all_53_1_12, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.10/2.33 |
% 7.10/2.33 | Instantiating (106) with all_136_0_19, all_136_1_20 yields:
% 7.10/2.33 | (107) member(all_53_1_12, all_0_6_6) = all_136_0_19 & member(all_53_1_12, all_0_7_7) = all_136_1_20 & ( ~ (all_136_0_19 = 0) | ~ (all_136_1_20 = 0))
% 7.10/2.33 |
% 7.10/2.33 | Applying alpha-rule on (107) yields:
% 7.10/2.33 | (108) member(all_53_1_12, all_0_6_6) = all_136_0_19
% 7.10/2.33 | (109) member(all_53_1_12, all_0_7_7) = all_136_1_20
% 7.10/2.33 | (110) ~ (all_136_0_19 = 0) | ~ (all_136_1_20 = 0)
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (3) with all_53_1_12, all_0_6_6, all_136_0_19, 0 and discharging atoms member(all_53_1_12, all_0_6_6) = all_136_0_19, member(all_53_1_12, all_0_6_6) = 0, yields:
% 7.10/2.33 | (111) all_136_0_19 = 0
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (3) with all_53_1_12, all_0_7_7, all_136_1_20, 0 and discharging atoms member(all_53_1_12, all_0_7_7) = all_136_1_20, member(all_53_1_12, all_0_7_7) = 0, yields:
% 7.10/2.33 | (112) all_136_1_20 = 0
% 7.10/2.33 |
% 7.10/2.33 +-Applying beta-rule and splitting (110), into two cases.
% 7.10/2.33 |-Branch one:
% 7.10/2.33 | (113) ~ (all_136_0_19 = 0)
% 7.10/2.33 |
% 7.10/2.33 | Equations (111) can reduce 113 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (111) all_136_0_19 = 0
% 7.10/2.33 | (116) ~ (all_136_1_20 = 0)
% 7.10/2.33 |
% 7.10/2.33 | Equations (112) can reduce 116 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (118) ~ (all_76_0_13 = 0)
% 7.10/2.33 | (119) all_76_1_14 = 0
% 7.10/2.33 |
% 7.10/2.33 | Equations (119) can reduce 97 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (121) ~ (all_82_0_15 = 0)
% 7.10/2.33 | (122) all_82_1_16 = 0
% 7.10/2.33 |
% 7.10/2.33 | Combining equations (95,122) yields a new equation:
% 7.10/2.33 | (123) all_76_1_14 = 0
% 7.10/2.33 |
% 7.10/2.33 | Simplifying 123 yields:
% 7.10/2.33 | (119) all_76_1_14 = 0
% 7.10/2.33 |
% 7.10/2.33 | Equations (119) can reduce 97 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (54) all_14_0_9 = 0
% 7.10/2.33 | (127) ~ (all_14_1_10 = 0)
% 7.10/2.33 |
% 7.10/2.33 +-Applying beta-rule and splitting (52), into two cases.
% 7.10/2.33 |-Branch one:
% 7.10/2.33 | (128) all_14_1_10 = 0
% 7.10/2.33 |
% 7.10/2.33 | Equations (128) can reduce 127 to:
% 7.10/2.33 | (44) $false
% 7.10/2.33 |
% 7.10/2.33 |-The branch is then unsatisfiable
% 7.10/2.33 |-Branch two:
% 7.10/2.33 | (127) ~ (all_14_1_10 = 0)
% 7.10/2.33 | (131) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0)
% 7.10/2.33 |
% 7.10/2.33 | Instantiating (131) with all_53_0_21, all_53_1_22 yields:
% 7.10/2.33 | (132) ~ (all_53_0_21 = 0) & member(all_53_1_22, all_0_1_1) = all_53_0_21 & member(all_53_1_22, all_0_4_4) = 0
% 7.10/2.33 |
% 7.10/2.33 | Applying alpha-rule on (132) yields:
% 7.10/2.33 | (133) ~ (all_53_0_21 = 0)
% 7.10/2.33 | (134) member(all_53_1_22, all_0_1_1) = all_53_0_21
% 7.10/2.33 | (135) member(all_53_1_22, all_0_4_4) = 0
% 7.10/2.33 |
% 7.10/2.33 | Instantiating formula (14) with all_53_0_21, all_0_1_1, all_0_2_2, all_0_3_3, all_53_1_22 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields:
% 7.10/2.34 | (136) all_53_0_21 = 0 | ? [v0] : ? [v1] : (member(all_53_1_22, all_0_2_2) = v1 & member(all_53_1_22, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (5) with all_0_4_4, all_0_5_5, all_0_8_8, all_53_1_22 and discharging atoms union(all_0_8_8, all_0_5_5) = all_0_4_4, member(all_53_1_22, all_0_4_4) = 0, yields:
% 7.10/2.34 | (137) ? [v0] : ? [v1] : (member(all_53_1_22, all_0_5_5) = v1 & member(all_53_1_22, all_0_8_8) = v0 & (v1 = 0 | v0 = 0))
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (36) with all_0_5_5, all_0_6_6, all_0_7_7, all_53_1_22 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_5_5, yields:
% 7.10/2.34 | (138) ~ (member(all_53_1_22, all_0_5_5) = 0) | (member(all_53_1_22, all_0_6_6) = 0 & member(all_53_1_22, all_0_7_7) = 0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating (137) with all_68_0_23, all_68_1_24 yields:
% 7.10/2.34 | (139) member(all_53_1_22, all_0_5_5) = all_68_0_23 & member(all_53_1_22, all_0_8_8) = all_68_1_24 & (all_68_0_23 = 0 | all_68_1_24 = 0)
% 7.10/2.34 |
% 7.10/2.34 | Applying alpha-rule on (139) yields:
% 7.10/2.34 | (140) member(all_53_1_22, all_0_5_5) = all_68_0_23
% 7.10/2.34 | (141) member(all_53_1_22, all_0_8_8) = all_68_1_24
% 7.10/2.34 | (142) all_68_0_23 = 0 | all_68_1_24 = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (136), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (143) all_53_0_21 = 0
% 7.10/2.34 |
% 7.10/2.34 | Equations (143) can reduce 133 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (133) ~ (all_53_0_21 = 0)
% 7.10/2.34 | (146) ? [v0] : ? [v1] : (member(all_53_1_22, all_0_2_2) = v1 & member(all_53_1_22, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.10/2.34 |
% 7.10/2.34 | Instantiating (146) with all_74_0_25, all_74_1_26 yields:
% 7.10/2.34 | (147) member(all_53_1_22, all_0_2_2) = all_74_0_25 & member(all_53_1_22, all_0_3_3) = all_74_1_26 & ( ~ (all_74_0_25 = 0) | ~ (all_74_1_26 = 0))
% 7.10/2.34 |
% 7.10/2.34 | Applying alpha-rule on (147) yields:
% 7.10/2.34 | (148) member(all_53_1_22, all_0_2_2) = all_74_0_25
% 7.10/2.34 | (149) member(all_53_1_22, all_0_3_3) = all_74_1_26
% 7.10/2.34 | (150) ~ (all_74_0_25 = 0) | ~ (all_74_1_26 = 0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (17) with all_74_0_25, all_0_2_2, all_0_6_6, all_0_8_8, all_53_1_22 and discharging atoms union(all_0_8_8, all_0_6_6) = all_0_2_2, member(all_53_1_22, all_0_2_2) = all_74_0_25, yields:
% 7.10/2.34 | (151) all_74_0_25 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_6_6) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (17) with all_74_1_26, all_0_3_3, all_0_7_7, all_0_8_8, all_53_1_22 and discharging atoms union(all_0_8_8, all_0_7_7) = all_0_3_3, member(all_53_1_22, all_0_3_3) = all_74_1_26, yields:
% 7.10/2.34 | (152) all_74_1_26 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_7_7) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (138), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (153) ~ (member(all_53_1_22, all_0_5_5) = 0)
% 7.10/2.34 |
% 7.10/2.34 | Using (140) and (153) yields:
% 7.10/2.34 | (154) ~ (all_68_0_23 = 0)
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (142), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (155) all_68_0_23 = 0
% 7.10/2.34 |
% 7.10/2.34 | Equations (155) can reduce 154 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (154) ~ (all_68_0_23 = 0)
% 7.10/2.34 | (158) all_68_1_24 = 0
% 7.10/2.34 |
% 7.10/2.34 | From (158) and (141) follows:
% 7.10/2.34 | (159) member(all_53_1_22, all_0_8_8) = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (152), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (160) all_74_1_26 = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (151), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (161) all_74_0_25 = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (150), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (162) ~ (all_74_0_25 = 0)
% 7.10/2.34 |
% 7.10/2.34 | Equations (161) can reduce 162 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (161) all_74_0_25 = 0
% 7.10/2.34 | (165) ~ (all_74_1_26 = 0)
% 7.10/2.34 |
% 7.10/2.34 | Equations (160) can reduce 165 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (162) ~ (all_74_0_25 = 0)
% 7.10/2.34 | (168) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_6_6) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating (168) with all_123_0_29, all_123_1_30 yields:
% 7.10/2.34 | (169) ~ (all_123_0_29 = 0) & ~ (all_123_1_30 = 0) & member(all_53_1_22, all_0_6_6) = all_123_0_29 & member(all_53_1_22, all_0_8_8) = all_123_1_30
% 7.10/2.34 |
% 7.10/2.34 | Applying alpha-rule on (169) yields:
% 7.10/2.34 | (170) ~ (all_123_0_29 = 0)
% 7.10/2.34 | (171) ~ (all_123_1_30 = 0)
% 7.10/2.34 | (172) member(all_53_1_22, all_0_6_6) = all_123_0_29
% 7.10/2.34 | (173) member(all_53_1_22, all_0_8_8) = all_123_1_30
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (3) with all_53_1_22, all_0_8_8, all_123_1_30, 0 and discharging atoms member(all_53_1_22, all_0_8_8) = all_123_1_30, member(all_53_1_22, all_0_8_8) = 0, yields:
% 7.10/2.34 | (174) all_123_1_30 = 0
% 7.10/2.34 |
% 7.10/2.34 | Equations (174) can reduce 171 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (165) ~ (all_74_1_26 = 0)
% 7.10/2.34 | (177) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_7_7) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating (177) with all_119_0_31, all_119_1_32 yields:
% 7.10/2.34 | (178) ~ (all_119_0_31 = 0) & ~ (all_119_1_32 = 0) & member(all_53_1_22, all_0_7_7) = all_119_0_31 & member(all_53_1_22, all_0_8_8) = all_119_1_32
% 7.10/2.34 |
% 7.10/2.34 | Applying alpha-rule on (178) yields:
% 7.10/2.34 | (179) ~ (all_119_0_31 = 0)
% 7.10/2.34 | (180) ~ (all_119_1_32 = 0)
% 7.10/2.34 | (181) member(all_53_1_22, all_0_7_7) = all_119_0_31
% 7.10/2.34 | (182) member(all_53_1_22, all_0_8_8) = all_119_1_32
% 7.10/2.34 |
% 7.10/2.34 | Instantiating formula (3) with all_53_1_22, all_0_8_8, all_119_1_32, 0 and discharging atoms member(all_53_1_22, all_0_8_8) = all_119_1_32, member(all_53_1_22, all_0_8_8) = 0, yields:
% 7.10/2.34 | (183) all_119_1_32 = 0
% 7.10/2.34 |
% 7.10/2.34 | Equations (183) can reduce 180 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (185) member(all_53_1_22, all_0_5_5) = 0
% 7.10/2.34 | (186) member(all_53_1_22, all_0_6_6) = 0 & member(all_53_1_22, all_0_7_7) = 0
% 7.10/2.34 |
% 7.10/2.34 | Applying alpha-rule on (186) yields:
% 7.10/2.34 | (187) member(all_53_1_22, all_0_6_6) = 0
% 7.10/2.34 | (188) member(all_53_1_22, all_0_7_7) = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (151), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (161) all_74_0_25 = 0
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (150), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (162) ~ (all_74_0_25 = 0)
% 7.10/2.34 |
% 7.10/2.34 | Equations (161) can reduce 162 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (161) all_74_0_25 = 0
% 7.10/2.34 | (165) ~ (all_74_1_26 = 0)
% 7.10/2.34 |
% 7.10/2.34 +-Applying beta-rule and splitting (152), into two cases.
% 7.10/2.34 |-Branch one:
% 7.10/2.34 | (160) all_74_1_26 = 0
% 7.10/2.34 |
% 7.10/2.34 | Equations (160) can reduce 165 to:
% 7.10/2.34 | (44) $false
% 7.10/2.34 |
% 7.10/2.34 |-The branch is then unsatisfiable
% 7.10/2.34 |-Branch two:
% 7.10/2.34 | (165) ~ (all_74_1_26 = 0)
% 7.10/2.34 | (177) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_7_7) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.34 |
% 7.10/2.34 | Instantiating (177) with all_114_0_33, all_114_1_34 yields:
% 7.10/2.34 | (198) ~ (all_114_0_33 = 0) & ~ (all_114_1_34 = 0) & member(all_53_1_22, all_0_7_7) = all_114_0_33 & member(all_53_1_22, all_0_8_8) = all_114_1_34
% 7.10/2.35 |
% 7.10/2.35 | Applying alpha-rule on (198) yields:
% 7.10/2.35 | (199) ~ (all_114_0_33 = 0)
% 7.10/2.35 | (200) ~ (all_114_1_34 = 0)
% 7.10/2.35 | (201) member(all_53_1_22, all_0_7_7) = all_114_0_33
% 7.10/2.35 | (202) member(all_53_1_22, all_0_8_8) = all_114_1_34
% 7.10/2.35 |
% 7.10/2.35 | Instantiating formula (3) with all_53_1_22, all_0_7_7, all_114_0_33, 0 and discharging atoms member(all_53_1_22, all_0_7_7) = all_114_0_33, member(all_53_1_22, all_0_7_7) = 0, yields:
% 7.10/2.35 | (203) all_114_0_33 = 0
% 7.10/2.35 |
% 7.10/2.35 | Equations (203) can reduce 199 to:
% 7.10/2.35 | (44) $false
% 7.10/2.35 |
% 7.10/2.35 |-The branch is then unsatisfiable
% 7.10/2.35 |-Branch two:
% 7.10/2.35 | (162) ~ (all_74_0_25 = 0)
% 7.10/2.35 | (168) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_22, all_0_6_6) = v1 & member(all_53_1_22, all_0_8_8) = v0)
% 7.10/2.35 |
% 7.10/2.35 | Instantiating (168) with all_106_0_35, all_106_1_36 yields:
% 7.10/2.35 | (207) ~ (all_106_0_35 = 0) & ~ (all_106_1_36 = 0) & member(all_53_1_22, all_0_6_6) = all_106_0_35 & member(all_53_1_22, all_0_8_8) = all_106_1_36
% 7.10/2.35 |
% 7.10/2.35 | Applying alpha-rule on (207) yields:
% 7.10/2.35 | (208) ~ (all_106_0_35 = 0)
% 7.10/2.35 | (209) ~ (all_106_1_36 = 0)
% 7.10/2.35 | (210) member(all_53_1_22, all_0_6_6) = all_106_0_35
% 7.10/2.35 | (211) member(all_53_1_22, all_0_8_8) = all_106_1_36
% 7.10/2.35 |
% 7.10/2.35 | Instantiating formula (3) with all_53_1_22, all_0_6_6, all_106_0_35, 0 and discharging atoms member(all_53_1_22, all_0_6_6) = all_106_0_35, member(all_53_1_22, all_0_6_6) = 0, yields:
% 7.10/2.35 | (212) all_106_0_35 = 0
% 7.10/2.35 |
% 7.10/2.35 | Equations (212) can reduce 208 to:
% 7.10/2.35 | (44) $false
% 7.10/2.35 |
% 7.10/2.35 |-The branch is then unsatisfiable
% 7.10/2.35 % SZS output end Proof for theBenchmark
% 7.10/2.35
% 7.10/2.35 1734ms
%------------------------------------------------------------------------------