TSTP Solution File: SET358+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 00:19:12 EDT 2022
% Result : Theorem 4.59s 1.77s
% Output : Proof 7.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n006.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 00:46:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.64/0.63 ____ _
% 0.64/0.63 ___ / __ \_____(_)___ ________ __________
% 0.64/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.64/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.64/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.64/0.63
% 0.64/0.63 A Theorem Prover for First-Order Logic
% 0.64/0.63 (ePrincess v.1.0)
% 0.64/0.63
% 0.64/0.63 (c) Philipp Rümmer, 2009-2015
% 0.64/0.63 (c) Peter Backeman, 2014-2015
% 0.64/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.64/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.64/0.63 Bug reports to peter@backeman.se
% 0.64/0.63
% 0.64/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.64/0.63
% 0.64/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.80/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.98 Prover 0: Preprocessing ...
% 2.11/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.11/1.19 Prover 0: Constructing countermodel ...
% 2.79/1.34 Prover 0: gave up
% 2.79/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.79/1.37 Prover 1: Preprocessing ...
% 3.27/1.47 Prover 1: Constructing countermodel ...
% 4.59/1.77 Prover 1: proved (427ms)
% 4.59/1.77
% 4.59/1.77 No countermodel exists, formula is valid
% 4.59/1.77 % SZS status Theorem for theBenchmark
% 4.59/1.77
% 4.59/1.77 Generating proof ... found it (size 133)
% 6.95/2.30
% 6.95/2.30 % SZS output start Proof for theBenchmark
% 6.95/2.30 Assumed formulas after preprocessing and simplification:
% 6.95/2.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & sum(v5) = v6 & sum(v1) = v3 & sum(v0) = v2 & union(v2, v3) = v4 & union(v0, v1) = v5 & equal_set(v4, v6) = v7 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0))
% 6.95/2.34 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 6.95/2.34 | (1) ~ (all_0_0_0 = 0) & sum(all_0_2_2) = all_0_1_1 & sum(all_0_6_6) = all_0_4_4 & sum(all_0_7_7) = all_0_5_5 & union(all_0_5_5, all_0_4_4) = all_0_3_3 & union(all_0_7_7, all_0_6_6) = all_0_2_2 & equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.15/2.35 |
% 7.15/2.35 | Applying alpha-rule on (1) yields:
% 7.15/2.35 | (2) union(all_0_5_5, all_0_4_4) = all_0_3_3
% 7.15/2.35 | (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)))
% 7.15/2.35 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.15/2.35 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 7.15/2.35 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 7.15/2.35 | (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))
% 7.15/2.35 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 7.15/2.35 | (9) sum(all_0_7_7) = all_0_5_5
% 7.15/2.35 | (10) ! [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))
% 7.15/2.35 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 7.15/2.35 | (12) ! [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))))
% 7.15/2.35 | (13) union(all_0_7_7, all_0_6_6) = all_0_2_2
% 7.15/2.35 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 7.15/2.35 | (15) ! [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))
% 7.15/2.35 | (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))))
% 7.15/2.35 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 7.15/2.35 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 7.15/2.35 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 7.15/2.36 | (20) ~ (all_0_0_0 = 0)
% 7.15/2.36 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 7.15/2.36 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 7.15/2.36 | (23) sum(all_0_6_6) = all_0_4_4
% 7.15/2.36 | (24) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 7.15/2.36 | (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))
% 7.15/2.36 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.15/2.36 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 7.15/2.36 | (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)))
% 7.15/2.36 | (29) sum(all_0_2_2) = all_0_1_1
% 7.15/2.36 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 7.15/2.36 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 7.15/2.36 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 7.15/2.36 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 7.15/2.36 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 7.15/2.36 | (35) ! [v0] : ~ (member(v0, empty_set) = 0)
% 7.15/2.36 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 7.15/2.36 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 7.15/2.36 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.15/2.36 | (39) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0
% 7.15/2.36 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 7.15/2.36 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 7.15/2.36 |
% 7.15/2.36 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 7.15/2.36 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.15/2.36 |
% 7.15/2.36 +-Applying beta-rule and splitting (42), into two cases.
% 7.15/2.36 |-Branch one:
% 7.15/2.36 | (43) all_0_0_0 = 0
% 7.15/2.36 |
% 7.15/2.36 | Equations (43) can reduce 20 to:
% 7.15/2.36 | (44) $false
% 7.15/2.36 |
% 7.15/2.36 |-The branch is then unsatisfiable
% 7.15/2.36 |-Branch two:
% 7.15/2.36 | (20) ~ (all_0_0_0 = 0)
% 7.15/2.36 | (46) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.15/2.37 |
% 7.15/2.37 | Instantiating (46) with all_14_0_8, all_14_1_9 yields:
% 7.15/2.37 | (47) subset(all_0_1_1, all_0_3_3) = all_14_0_8 & subset(all_0_3_3, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0))
% 7.15/2.37 |
% 7.15/2.37 | Applying alpha-rule on (47) yields:
% 7.15/2.37 | (48) subset(all_0_1_1, all_0_3_3) = all_14_0_8
% 7.15/2.37 | (49) subset(all_0_3_3, all_0_1_1) = all_14_1_9
% 7.15/2.37 | (50) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (19) with all_14_0_8, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_14_0_8, yields:
% 7.15/2.37 | (51) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (19) with all_14_1_9, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_14_1_9, yields:
% 7.15/2.37 | (52) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 7.15/2.37 |
% 7.15/2.37 +-Applying beta-rule and splitting (50), into two cases.
% 7.15/2.37 |-Branch one:
% 7.15/2.37 | (53) ~ (all_14_0_8 = 0)
% 7.15/2.37 |
% 7.15/2.37 +-Applying beta-rule and splitting (51), into two cases.
% 7.15/2.37 |-Branch one:
% 7.15/2.37 | (54) all_14_0_8 = 0
% 7.15/2.37 |
% 7.15/2.37 | Equations (54) can reduce 53 to:
% 7.15/2.37 | (44) $false
% 7.15/2.37 |
% 7.15/2.37 |-The branch is then unsatisfiable
% 7.15/2.37 |-Branch two:
% 7.15/2.37 | (53) ~ (all_14_0_8 = 0)
% 7.15/2.37 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating (57) with all_53_0_10, all_53_1_11 yields:
% 7.15/2.37 | (58) ~ (all_53_0_10 = 0) & member(all_53_1_11, all_0_1_1) = 0 & member(all_53_1_11, all_0_3_3) = all_53_0_10
% 7.15/2.37 |
% 7.15/2.37 | Applying alpha-rule on (58) yields:
% 7.15/2.37 | (59) ~ (all_53_0_10 = 0)
% 7.15/2.37 | (60) member(all_53_1_11, all_0_1_1) = 0
% 7.15/2.37 | (61) member(all_53_1_11, all_0_3_3) = all_53_0_10
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (32) with all_0_1_1, all_0_2_2, all_53_1_11 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_11, all_0_1_1) = 0, yields:
% 7.15/2.37 | (62) ? [v0] : (member(v0, all_0_2_2) = 0 & member(all_53_1_11, v0) = 0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (10) with all_53_0_10, all_0_3_3, all_0_4_4, all_0_5_5, all_53_1_11 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_53_1_11, all_0_3_3) = all_53_0_10, yields:
% 7.15/2.37 | (63) all_53_0_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_11, all_0_4_4) = v1 & member(all_53_1_11, all_0_5_5) = v0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating (62) with all_68_0_12 yields:
% 7.15/2.37 | (64) member(all_68_0_12, all_0_2_2) = 0 & member(all_53_1_11, all_68_0_12) = 0
% 7.15/2.37 |
% 7.15/2.37 | Applying alpha-rule on (64) yields:
% 7.15/2.37 | (65) member(all_68_0_12, all_0_2_2) = 0
% 7.15/2.37 | (66) member(all_53_1_11, all_68_0_12) = 0
% 7.15/2.37 |
% 7.15/2.37 +-Applying beta-rule and splitting (63), into two cases.
% 7.15/2.37 |-Branch one:
% 7.15/2.37 | (67) all_53_0_10 = 0
% 7.15/2.37 |
% 7.15/2.37 | Equations (67) can reduce 59 to:
% 7.15/2.37 | (44) $false
% 7.15/2.37 |
% 7.15/2.37 |-The branch is then unsatisfiable
% 7.15/2.37 |-Branch two:
% 7.15/2.37 | (59) ~ (all_53_0_10 = 0)
% 7.15/2.37 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_11, all_0_4_4) = v1 & member(all_53_1_11, all_0_5_5) = v0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating (70) with all_74_0_13, all_74_1_14 yields:
% 7.15/2.37 | (71) ~ (all_74_0_13 = 0) & ~ (all_74_1_14 = 0) & member(all_53_1_11, all_0_4_4) = all_74_0_13 & member(all_53_1_11, all_0_5_5) = all_74_1_14
% 7.15/2.37 |
% 7.15/2.37 | Applying alpha-rule on (71) yields:
% 7.15/2.37 | (72) ~ (all_74_0_13 = 0)
% 7.15/2.37 | (73) ~ (all_74_1_14 = 0)
% 7.15/2.37 | (74) member(all_53_1_11, all_0_4_4) = all_74_0_13
% 7.15/2.37 | (75) member(all_53_1_11, all_0_5_5) = all_74_1_14
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (3) with all_0_2_2, all_0_6_6, all_0_7_7, all_68_0_12 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_68_0_12, all_0_2_2) = 0, yields:
% 7.15/2.37 | (76) ? [v0] : ? [v1] : (member(all_68_0_12, all_0_6_6) = v1 & member(all_68_0_12, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (25) with all_0_1_1, all_74_0_13, all_0_4_4, all_0_6_6, all_53_1_11 and discharging atoms sum(all_0_6_6) = all_0_4_4, member(all_53_1_11, all_0_1_1) = 0, member(all_53_1_11, all_0_4_4) = all_74_0_13, yields:
% 7.15/2.37 | (77) all_74_0_13 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_6_6) = v0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (25) with all_68_0_12, all_74_0_13, all_0_4_4, all_0_6_6, all_53_1_11 and discharging atoms sum(all_0_6_6) = all_0_4_4, member(all_53_1_11, all_68_0_12) = 0, member(all_53_1_11, all_0_4_4) = all_74_0_13, yields:
% 7.15/2.37 | (78) all_74_0_13 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_6_6) = v0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating formula (25) with all_68_0_12, all_74_1_14, all_0_5_5, all_0_7_7, all_53_1_11 and discharging atoms sum(all_0_7_7) = all_0_5_5, member(all_53_1_11, all_68_0_12) = 0, member(all_53_1_11, all_0_5_5) = all_74_1_14, yields:
% 7.15/2.37 | (79) all_74_1_14 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_7_7) = v0)
% 7.15/2.37 |
% 7.15/2.37 | Instantiating (76) with all_89_0_15, all_89_1_16 yields:
% 7.15/2.37 | (80) member(all_68_0_12, all_0_6_6) = all_89_0_15 & member(all_68_0_12, all_0_7_7) = all_89_1_16 & (all_89_0_15 = 0 | all_89_1_16 = 0)
% 7.15/2.38 |
% 7.15/2.38 | Applying alpha-rule on (80) yields:
% 7.15/2.38 | (81) member(all_68_0_12, all_0_6_6) = all_89_0_15
% 7.15/2.38 | (82) member(all_68_0_12, all_0_7_7) = all_89_1_16
% 7.15/2.38 | (83) all_89_0_15 = 0 | all_89_1_16 = 0
% 7.15/2.38 |
% 7.15/2.38 +-Applying beta-rule and splitting (79), into two cases.
% 7.15/2.38 |-Branch one:
% 7.15/2.38 | (84) all_74_1_14 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (84) can reduce 73 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (73) ~ (all_74_1_14 = 0)
% 7.15/2.38 | (87) ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_7_7) = v0)
% 7.15/2.38 |
% 7.15/2.38 | Instantiating (87) with all_95_0_17 yields:
% 7.15/2.38 | (88) ~ (all_95_0_17 = 0) & member(all_68_0_12, all_0_7_7) = all_95_0_17
% 7.15/2.38 |
% 7.15/2.38 | Applying alpha-rule on (88) yields:
% 7.15/2.38 | (89) ~ (all_95_0_17 = 0)
% 7.15/2.38 | (90) member(all_68_0_12, all_0_7_7) = all_95_0_17
% 7.15/2.38 |
% 7.15/2.38 +-Applying beta-rule and splitting (77), into two cases.
% 7.15/2.38 |-Branch one:
% 7.15/2.38 | (91) all_74_0_13 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (91) can reduce 72 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (72) ~ (all_74_0_13 = 0)
% 7.15/2.38 | (94) ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_6_6) = v0)
% 7.15/2.38 |
% 7.15/2.38 +-Applying beta-rule and splitting (78), into two cases.
% 7.15/2.38 |-Branch one:
% 7.15/2.38 | (91) all_74_0_13 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (91) can reduce 72 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (72) ~ (all_74_0_13 = 0)
% 7.15/2.38 | (98) ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_6_6) = v0)
% 7.15/2.38 |
% 7.15/2.38 | Instantiating (98) with all_110_0_19 yields:
% 7.15/2.38 | (99) ~ (all_110_0_19 = 0) & member(all_68_0_12, all_0_6_6) = all_110_0_19
% 7.15/2.38 |
% 7.15/2.38 | Applying alpha-rule on (99) yields:
% 7.15/2.38 | (100) ~ (all_110_0_19 = 0)
% 7.15/2.38 | (101) member(all_68_0_12, all_0_6_6) = all_110_0_19
% 7.15/2.38 |
% 7.15/2.38 | Instantiating formula (37) with all_68_0_12, all_0_6_6, all_89_0_15, all_110_0_19 and discharging atoms member(all_68_0_12, all_0_6_6) = all_110_0_19, member(all_68_0_12, all_0_6_6) = all_89_0_15, yields:
% 7.15/2.38 | (102) all_110_0_19 = all_89_0_15
% 7.15/2.38 |
% 7.15/2.38 | Instantiating formula (37) with all_68_0_12, all_0_7_7, all_89_1_16, all_95_0_17 and discharging atoms member(all_68_0_12, all_0_7_7) = all_95_0_17, member(all_68_0_12, all_0_7_7) = all_89_1_16, yields:
% 7.15/2.38 | (103) all_95_0_17 = all_89_1_16
% 7.15/2.38 |
% 7.15/2.38 | Equations (102) can reduce 100 to:
% 7.15/2.38 | (104) ~ (all_89_0_15 = 0)
% 7.15/2.38 |
% 7.15/2.38 | Equations (103) can reduce 89 to:
% 7.15/2.38 | (105) ~ (all_89_1_16 = 0)
% 7.15/2.38 |
% 7.15/2.38 +-Applying beta-rule and splitting (83), into two cases.
% 7.15/2.38 |-Branch one:
% 7.15/2.38 | (106) all_89_0_15 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (106) can reduce 104 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (104) ~ (all_89_0_15 = 0)
% 7.15/2.38 | (109) all_89_1_16 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (109) can reduce 105 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (54) all_14_0_8 = 0
% 7.15/2.38 | (112) ~ (all_14_1_9 = 0)
% 7.15/2.38 |
% 7.15/2.38 +-Applying beta-rule and splitting (52), into two cases.
% 7.15/2.38 |-Branch one:
% 7.15/2.38 | (113) all_14_1_9 = 0
% 7.15/2.38 |
% 7.15/2.38 | Equations (113) can reduce 112 to:
% 7.15/2.38 | (44) $false
% 7.15/2.38 |
% 7.15/2.38 |-The branch is then unsatisfiable
% 7.15/2.38 |-Branch two:
% 7.15/2.38 | (112) ~ (all_14_1_9 = 0)
% 7.15/2.38 | (116) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 7.15/2.38 |
% 7.15/2.38 | Instantiating (116) with all_53_0_21, all_53_1_22 yields:
% 7.15/2.38 | (117) ~ (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_3_3) = 0
% 7.15/2.38 |
% 7.15/2.38 | Applying alpha-rule on (117) yields:
% 7.15/2.38 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.38 | (119) member(all_53_1_22, all_0_1_1) = all_53_0_21
% 7.15/2.38 | (120) member(all_53_1_22, all_0_3_3) = 0
% 7.15/2.38 |
% 7.15/2.38 | Instantiating formula (25) with all_0_3_3, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, member(all_53_1_22, all_0_3_3) = 0, yields:
% 7.15/2.39 | (121) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (32) with all_0_4_4, all_0_6_6, all_53_1_22 and discharging atoms sum(all_0_6_6) = all_0_4_4, yields:
% 7.15/2.39 | (122) ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : (member(v0, all_0_6_6) = 0 & member(all_53_1_22, v0) = 0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (32) with all_0_5_5, all_0_7_7, all_53_1_22 and discharging atoms sum(all_0_7_7) = all_0_5_5, yields:
% 7.15/2.39 | (123) ~ (member(all_53_1_22, all_0_5_5) = 0) | ? [v0] : (member(v0, all_0_7_7) = 0 & member(all_53_1_22, v0) = 0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (3) with all_0_3_3, all_0_4_4, all_0_5_5, all_53_1_22 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_53_1_22, all_0_3_3) = 0, yields:
% 7.15/2.39 | (124) ? [v0] : ? [v1] : (member(all_53_1_22, all_0_4_4) = v1 & member(all_53_1_22, all_0_5_5) = v0 & (v1 = 0 | v0 = 0))
% 7.15/2.39 |
% 7.15/2.39 | Instantiating (124) with all_68_0_23, all_68_1_24 yields:
% 7.15/2.39 | (125) member(all_53_1_22, all_0_4_4) = all_68_0_23 & member(all_53_1_22, all_0_5_5) = all_68_1_24 & (all_68_0_23 = 0 | all_68_1_24 = 0)
% 7.15/2.39 |
% 7.15/2.39 | Applying alpha-rule on (125) yields:
% 7.15/2.39 | (126) member(all_53_1_22, all_0_4_4) = all_68_0_23
% 7.15/2.39 | (127) member(all_53_1_22, all_0_5_5) = all_68_1_24
% 7.15/2.39 | (128) all_68_0_23 = 0 | all_68_1_24 = 0
% 7.15/2.39 |
% 7.15/2.39 +-Applying beta-rule and splitting (121), into two cases.
% 7.15/2.39 |-Branch one:
% 7.15/2.39 | (129) all_53_0_21 = 0
% 7.15/2.39 |
% 7.15/2.39 | Equations (129) can reduce 118 to:
% 7.15/2.39 | (44) $false
% 7.15/2.39 |
% 7.15/2.39 |-The branch is then unsatisfiable
% 7.15/2.39 |-Branch two:
% 7.15/2.39 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.39 | (132) ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (37) with all_53_1_22, all_0_5_5, all_68_1_24, 0 and discharging atoms member(all_53_1_22, all_0_5_5) = all_68_1_24, yields:
% 7.15/2.39 | (133) all_68_1_24 = 0 | ~ (member(all_53_1_22, all_0_5_5) = 0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (25) with all_0_4_4, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields:
% 7.15/2.39 | (134) all_53_0_21 = 0 | ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (25) with all_0_4_4, all_68_1_24, all_0_5_5, all_0_7_7, all_53_1_22 and discharging atoms sum(all_0_7_7) = all_0_5_5, member(all_53_1_22, all_0_5_5) = all_68_1_24, yields:
% 7.15/2.39 | (135) all_68_1_24 = 0 | ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_7_7) = v0)
% 7.15/2.39 |
% 7.15/2.39 | Instantiating formula (25) with all_0_5_5, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields:
% 7.15/2.39 | (136) all_53_0_21 = 0 | ~ (member(all_53_1_22, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0)
% 7.15/2.39 |
% 7.15/2.39 +-Applying beta-rule and splitting (123), into two cases.
% 7.15/2.39 |-Branch one:
% 7.15/2.39 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0)
% 7.15/2.39 |
% 7.15/2.39 | Using (127) and (137) yields:
% 7.15/2.39 | (138) ~ (all_68_1_24 = 0)
% 7.15/2.39 |
% 7.15/2.39 +-Applying beta-rule and splitting (128), into two cases.
% 7.15/2.39 |-Branch one:
% 7.15/2.39 | (139) all_68_0_23 = 0
% 7.15/2.39 |
% 7.15/2.39 | From (139) and (126) follows:
% 7.15/2.39 | (140) member(all_53_1_22, all_0_4_4) = 0
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (122), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0)
% 7.15/2.40 |
% 7.15/2.40 | Using (140) and (141) yields:
% 7.15/2.40 | (142) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0
% 7.15/2.40 | (144) ? [v0] : (member(v0, all_0_6_6) = 0 & member(all_53_1_22, v0) = 0)
% 7.15/2.40 |
% 7.15/2.40 | Instantiating (144) with all_112_0_28 yields:
% 7.15/2.40 | (145) member(all_112_0_28, all_0_6_6) = 0 & member(all_53_1_22, all_112_0_28) = 0
% 7.15/2.40 |
% 7.15/2.40 | Applying alpha-rule on (145) yields:
% 7.15/2.40 | (146) member(all_112_0_28, all_0_6_6) = 0
% 7.15/2.40 | (147) member(all_53_1_22, all_112_0_28) = 0
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (135), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0)
% 7.15/2.40 |
% 7.15/2.40 | Using (140) and (141) yields:
% 7.15/2.40 | (142) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0
% 7.15/2.40 | (151) all_68_1_24 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_7_7) = v0)
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (134), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0)
% 7.15/2.40 |
% 7.15/2.40 | Using (140) and (141) yields:
% 7.15/2.40 | (142) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0
% 7.15/2.40 | (155) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0)
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (155), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (129) all_53_0_21 = 0
% 7.15/2.40 |
% 7.15/2.40 | Equations (129) can reduce 118 to:
% 7.15/2.40 | (44) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.40 | (159) ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0)
% 7.15/2.40 |
% 7.15/2.40 | Instantiating formula (25) with all_112_0_28, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_112_0_28) = 0, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields:
% 7.15/2.40 | (160) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_112_0_28, all_0_2_2) = v0)
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (160), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (129) all_53_0_21 = 0
% 7.15/2.40 |
% 7.15/2.40 | Equations (129) can reduce 118 to:
% 7.15/2.40 | (44) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.40 | (164) ? [v0] : ( ~ (v0 = 0) & member(all_112_0_28, all_0_2_2) = v0)
% 7.15/2.40 |
% 7.15/2.40 | Instantiating (164) with all_160_0_34 yields:
% 7.15/2.40 | (165) ~ (all_160_0_34 = 0) & member(all_112_0_28, all_0_2_2) = all_160_0_34
% 7.15/2.40 |
% 7.15/2.40 | Applying alpha-rule on (165) yields:
% 7.15/2.40 | (166) ~ (all_160_0_34 = 0)
% 7.15/2.40 | (167) member(all_112_0_28, all_0_2_2) = all_160_0_34
% 7.15/2.40 |
% 7.15/2.40 | Instantiating formula (10) with all_160_0_34, all_0_2_2, all_0_6_6, all_0_7_7, all_112_0_28 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_112_0_28, all_0_2_2) = all_160_0_34, yields:
% 7.15/2.40 | (168) all_160_0_34 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_112_0_28, all_0_6_6) = v1 & member(all_112_0_28, all_0_7_7) = v0)
% 7.15/2.40 |
% 7.15/2.40 +-Applying beta-rule and splitting (168), into two cases.
% 7.15/2.40 |-Branch one:
% 7.15/2.40 | (169) all_160_0_34 = 0
% 7.15/2.40 |
% 7.15/2.40 | Equations (169) can reduce 166 to:
% 7.15/2.40 | (44) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.40 |-Branch two:
% 7.15/2.40 | (166) ~ (all_160_0_34 = 0)
% 7.15/2.40 | (172) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_112_0_28, all_0_6_6) = v1 & member(all_112_0_28, all_0_7_7) = v0)
% 7.15/2.40 |
% 7.15/2.40 | Instantiating (172) with all_177_0_35, all_177_1_36 yields:
% 7.15/2.40 | (173) ~ (all_177_0_35 = 0) & ~ (all_177_1_36 = 0) & member(all_112_0_28, all_0_6_6) = all_177_0_35 & member(all_112_0_28, all_0_7_7) = all_177_1_36
% 7.15/2.40 |
% 7.15/2.40 | Applying alpha-rule on (173) yields:
% 7.15/2.40 | (174) ~ (all_177_0_35 = 0)
% 7.15/2.40 | (175) ~ (all_177_1_36 = 0)
% 7.15/2.40 | (176) member(all_112_0_28, all_0_6_6) = all_177_0_35
% 7.15/2.40 | (177) member(all_112_0_28, all_0_7_7) = all_177_1_36
% 7.15/2.40 |
% 7.15/2.40 | Instantiating formula (37) with all_112_0_28, all_0_6_6, all_177_0_35, 0 and discharging atoms member(all_112_0_28, all_0_6_6) = all_177_0_35, member(all_112_0_28, all_0_6_6) = 0, yields:
% 7.15/2.40 | (178) all_177_0_35 = 0
% 7.15/2.40 |
% 7.15/2.40 | Equations (178) can reduce 174 to:
% 7.15/2.40 | (44) $false
% 7.15/2.40 |
% 7.15/2.40 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (180) ~ (all_68_0_23 = 0)
% 7.15/2.41 | (181) all_68_1_24 = 0
% 7.15/2.41 |
% 7.15/2.41 | Equations (181) can reduce 138 to:
% 7.15/2.41 | (44) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0
% 7.15/2.41 | (184) ? [v0] : (member(v0, all_0_7_7) = 0 & member(all_53_1_22, v0) = 0)
% 7.15/2.41 |
% 7.15/2.41 | Instantiating (184) with all_100_0_37 yields:
% 7.15/2.41 | (185) member(all_100_0_37, all_0_7_7) = 0 & member(all_53_1_22, all_100_0_37) = 0
% 7.15/2.41 |
% 7.15/2.41 | Applying alpha-rule on (185) yields:
% 7.15/2.41 | (186) member(all_100_0_37, all_0_7_7) = 0
% 7.15/2.41 | (187) member(all_53_1_22, all_100_0_37) = 0
% 7.15/2.41 |
% 7.15/2.41 +-Applying beta-rule and splitting (133), into two cases.
% 7.15/2.41 |-Branch one:
% 7.15/2.41 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0)
% 7.15/2.41 |
% 7.15/2.41 | Using (183) and (137) yields:
% 7.15/2.41 | (142) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0
% 7.15/2.41 | (181) all_68_1_24 = 0
% 7.15/2.41 |
% 7.15/2.41 | From (181) and (127) follows:
% 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0
% 7.15/2.41 |
% 7.15/2.41 +-Applying beta-rule and splitting (136), into two cases.
% 7.15/2.41 |-Branch one:
% 7.15/2.41 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0)
% 7.15/2.41 |
% 7.15/2.41 | Using (183) and (137) yields:
% 7.15/2.41 | (142) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0
% 7.15/2.41 | (196) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0)
% 7.15/2.41 |
% 7.15/2.41 +-Applying beta-rule and splitting (196), into two cases.
% 7.15/2.41 |-Branch one:
% 7.15/2.41 | (129) all_53_0_21 = 0
% 7.15/2.41 |
% 7.15/2.41 | Equations (129) can reduce 118 to:
% 7.15/2.41 | (44) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.41 | (200) ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0)
% 7.15/2.41 |
% 7.15/2.41 | Instantiating formula (25) with all_100_0_37, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_100_0_37) = 0, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields:
% 7.15/2.41 | (201) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_100_0_37, all_0_2_2) = v0)
% 7.15/2.41 |
% 7.15/2.41 +-Applying beta-rule and splitting (201), into two cases.
% 7.15/2.41 |-Branch one:
% 7.15/2.41 | (129) all_53_0_21 = 0
% 7.15/2.41 |
% 7.15/2.41 | Equations (129) can reduce 118 to:
% 7.15/2.41 | (44) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (118) ~ (all_53_0_21 = 0)
% 7.15/2.41 | (205) ? [v0] : ( ~ (v0 = 0) & member(all_100_0_37, all_0_2_2) = v0)
% 7.15/2.41 |
% 7.15/2.41 | Instantiating (205) with all_140_0_41 yields:
% 7.15/2.41 | (206) ~ (all_140_0_41 = 0) & member(all_100_0_37, all_0_2_2) = all_140_0_41
% 7.15/2.41 |
% 7.15/2.41 | Applying alpha-rule on (206) yields:
% 7.15/2.41 | (207) ~ (all_140_0_41 = 0)
% 7.15/2.41 | (208) member(all_100_0_37, all_0_2_2) = all_140_0_41
% 7.15/2.41 |
% 7.15/2.41 | Instantiating formula (10) with all_140_0_41, all_0_2_2, all_0_6_6, all_0_7_7, all_100_0_37 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_100_0_37, all_0_2_2) = all_140_0_41, yields:
% 7.15/2.41 | (209) all_140_0_41 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_100_0_37, all_0_6_6) = v1 & member(all_100_0_37, all_0_7_7) = v0)
% 7.15/2.41 |
% 7.15/2.41 +-Applying beta-rule and splitting (209), into two cases.
% 7.15/2.41 |-Branch one:
% 7.15/2.41 | (210) all_140_0_41 = 0
% 7.15/2.41 |
% 7.15/2.41 | Equations (210) can reduce 207 to:
% 7.15/2.41 | (44) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 |-Branch two:
% 7.15/2.41 | (207) ~ (all_140_0_41 = 0)
% 7.15/2.41 | (213) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_100_0_37, all_0_6_6) = v1 & member(all_100_0_37, all_0_7_7) = v0)
% 7.15/2.41 |
% 7.15/2.41 | Instantiating (213) with all_157_0_42, all_157_1_43 yields:
% 7.15/2.41 | (214) ~ (all_157_0_42 = 0) & ~ (all_157_1_43 = 0) & member(all_100_0_37, all_0_6_6) = all_157_0_42 & member(all_100_0_37, all_0_7_7) = all_157_1_43
% 7.15/2.41 |
% 7.15/2.41 | Applying alpha-rule on (214) yields:
% 7.15/2.41 | (215) ~ (all_157_0_42 = 0)
% 7.15/2.41 | (216) ~ (all_157_1_43 = 0)
% 7.15/2.41 | (217) member(all_100_0_37, all_0_6_6) = all_157_0_42
% 7.15/2.41 | (218) member(all_100_0_37, all_0_7_7) = all_157_1_43
% 7.15/2.41 |
% 7.15/2.41 | Instantiating formula (37) with all_100_0_37, all_0_7_7, all_157_1_43, 0 and discharging atoms member(all_100_0_37, all_0_7_7) = all_157_1_43, member(all_100_0_37, all_0_7_7) = 0, yields:
% 7.15/2.41 | (219) all_157_1_43 = 0
% 7.15/2.41 |
% 7.15/2.41 | Equations (219) can reduce 216 to:
% 7.15/2.41 | (44) $false
% 7.15/2.41 |
% 7.15/2.41 |-The branch is then unsatisfiable
% 7.15/2.41 % SZS output end Proof for theBenchmark
% 7.15/2.41
% 7.15/2.41 1768ms
%------------------------------------------------------------------------------