TSTP Solution File: SET772+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET772+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 00:21:58 EDT 2022
% Result : Theorem 5.70s 1.98s
% Output : Proof 12.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET772+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 12:42:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.61 ____ _
% 0.55/0.61 ___ / __ \_____(_)___ ________ __________
% 0.55/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.61
% 0.55/0.61 A Theorem Prover for First-Order Logic
% 0.55/0.61 (ePrincess v.1.0)
% 0.55/0.61
% 0.55/0.61 (c) Philipp Rümmer, 2009-2015
% 0.55/0.61 (c) Peter Backeman, 2014-2015
% 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.61 Bug reports to peter@backeman.se
% 0.55/0.61
% 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.61
% 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.98 Prover 0: Preprocessing ...
% 2.71/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.71/1.26 Prover 0: Constructing countermodel ...
% 3.31/1.40 Prover 0: gave up
% 3.31/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.31/1.44 Prover 1: Preprocessing ...
% 4.46/1.64 Prover 1: Constructing countermodel ...
% 5.70/1.97 Prover 1: proved (570ms)
% 5.70/1.98
% 5.70/1.98 No countermodel exists, formula is valid
% 5.70/1.98 % SZS status Theorem for theBenchmark
% 5.70/1.98
% 5.70/1.98 Generating proof ... found it (size 295)
% 11.58/3.27
% 11.58/3.27 % SZS output start Proof for theBenchmark
% 11.58/3.27 Assumed formulas after preprocessing and simplification:
% 11.58/3.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & equivalence(v2, v1) = v3 & partition(v0, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (pre_order(v4, v5) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v4, v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v4, v7, v8) = v13 & member(v8, v5) = v12 & member(v7, v5) = v11 & member(v6, v5) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equivalence_class(v6, v5, v4) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : (apply(v4, v6, v7) = v11 & member(v7, v5) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equivalence(v5, v4) = 0) | ~ (apply(v5, v6, v8) = v9) | ~ (apply(v5, v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v5, v7, v8) = v13 & member(v8, v4) = v12 & member(v7, v4) = v11 & member(v6, v4) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v7) = v8) | ~ (member(v4, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v9 & member(v4, v5) = v10 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & member(v4, v6) = v10 & member(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (partition(v4, v5) = 0) | ~ (member(v8, v6) = 0) | ~ (member(v7, v4) = 0) | ~ (member(v6, v4) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v8, v7) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (sum(v5) = v6) | ~ (member(v4, v8) = 0) | ~ (member(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (equivalence_class(v8, v7, v6) = v5) | ~ (equivalence_class(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (apply(v8, v7, v6) = v5) | ~ (apply(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (equivalence_class(v6, v5, v4) = v8) | ~ (member(v7, v8) = 0) | (apply(v4, v6, v7) = 0 & member(v7, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pre_order(v4, v5) = 0) | ~ (apply(v4, v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equivalence(v5, v4) = 0) | ~ (apply(v5, v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (partition(v4, v5) = 0) | ~ (subset(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = 0 & member(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v5, v4) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (power_set(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & subset(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v4 | v5 = v4 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (apply(v2, v4, v5) = v6) | ~ (member(v4, v7) = 0) | ? [v8] : ? [v9] : ((member(v7, v0) = v8 & member(v5, v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0))) | (member(v5, v1) = v9 & member(v4, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (pre_order(v7, v6) = v5) | ~ (pre_order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equivalence(v7, v6) = v5) | ~ (equivalence(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (partition(v7, v6) = v5) | ~ (partition(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (disjoint(v7, v6) = v5) | ~ (disjoint(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unordered_pair(v7, v6) = v5) | ~ (unordered_pair(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_set(v7, v6) = v5) | ~ (equal_set(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (equivalence(v5, v4) = 0) | ~ (apply(v5, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (apply(v5, v7, v6) = v10 & member(v7, v4) = v9 & member(v6, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v4, v6) = 0 & member(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ? [v9] : (member(v4, v6) = v9 & member(v4, v5) = v8 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = 0) | (member(v4, v6) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (pre_order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = 0) & apply(v4, v8, v9) = 0 & apply(v4, v7, v9) = v15 & apply(v4, v7, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0) | (v8 = 0 & ~ (v9 = 0) & apply(v4, v7, v7) = v9 & member(v7, v5) = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equivalence(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = 0) & apply(v5, v8, v9) = 0 & apply(v5, v7, v9) = v15 & apply(v5, v7, v8) = 0 & member(v9, v4) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v11 = 0 & v10 = 0 & v9 = 0 & ~ (v12 = 0) & apply(v5, v8, v7) = v12 & apply(v5, v7, v8) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v8 = 0 & ~ (v9 = 0) & apply(v5, v7, v7) = v9 & member(v7, v4) = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (partition(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v10 = 0 & v9 = 0 & ~ (v8 = v7) & member(v11, v8) = 0 & member(v11, v7) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0) | (v8 = 0 & ~ (v9 = 0) & subset(v7, v5) = v9 & member(v7, v4) = 0) | (v8 = 0 & member(v7, v5) = 0 & ! [v14] : ( ~ (member(v7, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & member(v14, v4) = v15))))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (disjoint(v4, v5) = v6) | ? [v7] : (member(v7, v5) = 0 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (singleton(v4) = v5) | ~ (member(v4, v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_set(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v5, v4) = v8 & subset(v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (product(v6) = v5) | ~ (product(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sum(v6) = v5) | ~ (sum(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v6) = v5) | ~ (singleton(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v5) = v6) | ~ (member(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (power_set(v6) = v5) | ~ (power_set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (partition(v4, v5) = 0) | ~ (member(v6, v5) = 0) | ? [v7] : (member(v7, v4) = 0 & member(v6, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (disjoint(v4, v5) = 0) | ~ (member(v6, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v6, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v5) = v6) | ~ (member(v4, v6) = 0) | ? [v7] : (member(v7, v5) = 0 & member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ (member(v4, v6) = 0) | subset(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ( ~ (apply(v2, v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v7 = 0 & member(v6, v0) = 0 & member(v5, v6) = 0 & member(v4, v6) = 0) | (member(v5, v1) = v7 & member(v4, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v4] : ! [v5] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) & ! [v4] : ~ (member(v4, empty_set) = 0))
% 11.58/3.32 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 11.58/3.32 | (1) ~ (all_0_0_0 = 0) & equivalence(all_0_1_1, all_0_2_2) = all_0_0_0 & partition(all_0_3_3, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 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 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) & ! [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] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [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] : (v2 = 0 | ~ (apply(all_0_1_1, v0, v1) = v2) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : ((member(v3, all_0_3_3) = v4 & member(v1, v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))) | (member(v1, all_0_2_2) = v5 & member(v0, all_0_2_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [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] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [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 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 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] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) & ! [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] : ( ~ (apply(all_0_1_1, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & member(v2, all_0_3_3) = 0 & member(v1, v2) = 0 & member(v0, v2) = 0) | (member(v1, all_0_2_2) = v3 & member(v0, all_0_2_2) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 11.58/3.34 |
% 11.58/3.34 | Applying alpha-rule on (1) yields:
% 11.58/3.34 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 11.58/3.34 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 11.58/3.34 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0)))
% 11.58/3.34 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 11.58/3.34 | (6) ! [v0] : ~ (member(v0, empty_set) = 0)
% 11.58/3.34 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 11.58/3.34 | (8) ! [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))))
% 11.58/3.34 | (9) ! [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)))
% 11.58/3.34 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 11.58/3.34 | (11) ! [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))
% 11.58/3.34 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0))
% 11.58/3.34 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 11.58/3.34 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 11.58/3.34 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 11.58/3.34 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0)))
% 11.58/3.35 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0))
% 11.58/3.35 | (18) ! [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))
% 11.58/3.35 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0))
% 11.58/3.35 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 11.58/3.35 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5))
% 11.58/3.35 | (22) ! [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)))
% 11.58/3.35 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11)))))
% 11.58/3.35 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 11.58/3.35 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 11.58/3.35 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 11.58/3.35 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 11.58/3.35 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 11.58/3.35 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 11.58/3.35 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))
% 11.58/3.35 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 11.58/3.35 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 11.58/3.35 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 11.58/3.35 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 11.58/3.35 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 11.58/3.35 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 11.58/3.36 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 11.58/3.36 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 11.58/3.36 | (39) ! [v0] : ! [v1] : ( ~ (apply(all_0_1_1, v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & member(v2, all_0_3_3) = 0 & member(v1, v2) = 0 & member(v0, v2) = 0) | (member(v1, all_0_2_2) = v3 & member(v0, all_0_2_2) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 11.58/3.36 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 11.58/3.36 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 11.58/3.36 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0))
% 11.58/3.36 | (43) equivalence(all_0_1_1, all_0_2_2) = all_0_0_0
% 11.58/3.36 | (44) partition(all_0_3_3, all_0_2_2) = 0
% 11.58/3.36 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 11.58/3.36 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (apply(all_0_1_1, v0, v1) = v2) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : ((member(v3, all_0_3_3) = v4 & member(v1, v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))) | (member(v1, all_0_2_2) = v5 & member(v0, all_0_2_2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 11.58/3.36 | (47) ! [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))
% 11.58/3.36 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 11.58/3.36 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 11.58/3.36 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 11.58/3.36 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 11.58/3.36 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 11.58/3.36 | (53) ~ (all_0_0_0 = 0)
% 11.58/3.36 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 11.58/3.36 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 11.58/3.36 | (56) ! [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))
% 11.58/3.36 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 11.58/3.36 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 11.58/3.36 | (59) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 11.58/3.36 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 11.58/3.36 |
% 11.58/3.36 | Instantiating formula (4) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equivalence(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 11.58/3.36 | (61) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_2_2) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_2_2) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_2_2) = 0))
% 11.58/3.36 |
% 11.58/3.36 +-Applying beta-rule and splitting (61), into two cases.
% 11.58/3.36 |-Branch one:
% 11.58/3.36 | (62) all_0_0_0 = 0
% 11.58/3.36 |
% 11.58/3.36 | Equations (62) can reduce 53 to:
% 11.58/3.36 | (63) $false
% 11.58/3.36 |
% 11.58/3.36 |-The branch is then unsatisfiable
% 11.58/3.36 |-Branch two:
% 11.58/3.36 | (53) ~ (all_0_0_0 = 0)
% 11.58/3.37 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_1_1, v1, v2) = 0 & apply(all_0_1_1, v0, v2) = v8 & apply(all_0_1_1, v0, v1) = 0 & member(v2, all_0_2_2) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_2_2) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_1_1, v1, v0) = v5 & apply(all_0_1_1, v0, v1) = 0 & member(v1, all_0_2_2) = 0 & member(v0, all_0_2_2) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_1_1, v0, v0) = v2 & member(v0, all_0_2_2) = 0))
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (65) with all_10_0_4, all_10_1_5, all_10_2_6, all_10_3_7, all_10_4_8, all_10_5_9, all_10_6_10, all_10_7_11, all_10_8_12 yields:
% 11.58/3.37 | (66) (all_10_1_5 = 0 & all_10_2_6 = 0 & all_10_3_7 = 0 & all_10_4_8 = 0 & all_10_5_9 = 0 & ~ (all_10_0_4 = 0) & apply(all_0_1_1, all_10_7_11, all_10_6_10) = 0 & apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_6_10, all_0_2_2) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0) | (all_10_4_8 = 0 & all_10_5_9 = 0 & all_10_6_10 = 0 & ~ (all_10_3_7 = 0) & apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0) | (all_10_7_11 = 0 & ~ (all_10_6_10 = 0) & apply(all_0_1_1, all_10_8_12, all_10_8_12) = all_10_6_10 & member(all_10_8_12, all_0_2_2) = 0)
% 11.58/3.37 |
% 11.58/3.37 +-Applying beta-rule and splitting (66), into two cases.
% 11.58/3.37 |-Branch one:
% 11.58/3.37 | (67) (all_10_1_5 = 0 & all_10_2_6 = 0 & all_10_3_7 = 0 & all_10_4_8 = 0 & all_10_5_9 = 0 & ~ (all_10_0_4 = 0) & apply(all_0_1_1, all_10_7_11, all_10_6_10) = 0 & apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_6_10, all_0_2_2) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0) | (all_10_4_8 = 0 & all_10_5_9 = 0 & all_10_6_10 = 0 & ~ (all_10_3_7 = 0) & apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0)
% 11.58/3.37 |
% 11.58/3.37 +-Applying beta-rule and splitting (67), into two cases.
% 11.58/3.37 |-Branch one:
% 11.58/3.37 | (68) all_10_1_5 = 0 & all_10_2_6 = 0 & all_10_3_7 = 0 & all_10_4_8 = 0 & all_10_5_9 = 0 & ~ (all_10_0_4 = 0) & apply(all_0_1_1, all_10_7_11, all_10_6_10) = 0 & apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_6_10, all_0_2_2) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (68) yields:
% 11.58/3.37 | (69) member(all_10_8_12, all_0_2_2) = 0
% 11.58/3.37 | (70) all_10_4_8 = 0
% 11.58/3.37 | (71) ~ (all_10_0_4 = 0)
% 11.58/3.37 | (72) all_10_2_6 = 0
% 11.58/3.37 | (73) all_10_3_7 = 0
% 11.58/3.37 | (74) all_10_5_9 = 0
% 11.58/3.37 | (75) member(all_10_7_11, all_0_2_2) = 0
% 11.58/3.37 | (76) apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4
% 11.58/3.37 | (77) apply(all_0_1_1, all_10_7_11, all_10_6_10) = 0
% 11.58/3.37 | (78) apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0
% 11.58/3.37 | (79) all_10_1_5 = 0
% 11.58/3.37 | (80) member(all_10_6_10, all_0_2_2) = 0
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (39) with all_10_6_10, all_10_7_11 and discharging atoms apply(all_0_1_1, all_10_7_11, all_10_6_10) = 0, yields:
% 11.58/3.37 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & member(v0, all_0_3_3) = 0 & member(all_10_6_10, v0) = 0 & member(all_10_7_11, v0) = 0) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_10_7_11, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (39) with all_10_7_11, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0, yields:
% 11.58/3.37 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & member(v0, all_0_3_3) = 0 & member(all_10_7_11, v0) = 0 & member(all_10_8_12, v0) = 0) | (member(all_10_7_11, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (12) with all_10_6_10, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_6_10, all_0_2_2) = 0, yields:
% 11.58/3.37 | (83) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_6_10, v0) = 0)
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (12) with all_10_7_11, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_7_11, all_0_2_2) = 0, yields:
% 11.58/3.37 | (84) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_7_11, v0) = 0)
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (46) with all_0_2_2, all_10_0_4, all_10_6_10, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4, member(all_10_8_12, all_0_2_2) = 0, yields:
% 11.58/3.37 | (85) all_10_0_4 = 0 | ? [v0] : ? [v1] : ((member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.37 |
% 11.58/3.37 | Instantiating formula (12) with all_10_8_12, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_8_12, all_0_2_2) = 0, yields:
% 11.58/3.37 | (86) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_8_12, v0) = 0)
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (86) with all_31_0_13 yields:
% 11.58/3.37 | (87) member(all_31_0_13, all_0_3_3) = 0 & member(all_10_8_12, all_31_0_13) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (87) yields:
% 11.58/3.37 | (88) member(all_31_0_13, all_0_3_3) = 0
% 11.58/3.37 | (89) member(all_10_8_12, all_31_0_13) = 0
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (84) with all_33_0_14 yields:
% 11.58/3.37 | (90) member(all_33_0_14, all_0_3_3) = 0 & member(all_10_7_11, all_33_0_14) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (90) yields:
% 11.58/3.37 | (91) member(all_33_0_14, all_0_3_3) = 0
% 11.58/3.37 | (92) member(all_10_7_11, all_33_0_14) = 0
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (83) with all_35_0_15 yields:
% 11.58/3.37 | (93) member(all_35_0_15, all_0_3_3) = 0 & member(all_10_6_10, all_35_0_15) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (93) yields:
% 11.58/3.37 | (94) member(all_35_0_15, all_0_3_3) = 0
% 11.58/3.37 | (95) member(all_10_6_10, all_35_0_15) = 0
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (82) with all_37_0_16, all_37_1_17, all_37_2_18, all_37_3_19 yields:
% 11.58/3.37 | (96) (all_37_0_16 = 0 & all_37_1_17 = 0 & all_37_2_18 = 0 & member(all_37_3_19, all_0_3_3) = 0 & member(all_10_7_11, all_37_3_19) = 0 & member(all_10_8_12, all_37_3_19) = 0) | (member(all_10_7_11, all_0_2_2) = all_37_2_18 & member(all_10_8_12, all_0_2_2) = all_37_3_19 & ( ~ (all_37_2_18 = 0) | ~ (all_37_3_19 = 0)))
% 11.58/3.37 |
% 11.58/3.37 | Instantiating (81) with all_38_0_20, all_38_1_21, all_38_2_22, all_38_3_23 yields:
% 11.58/3.37 | (97) (all_38_0_20 = 0 & all_38_1_21 = 0 & all_38_2_22 = 0 & member(all_38_3_23, all_0_3_3) = 0 & member(all_10_6_10, all_38_3_23) = 0 & member(all_10_7_11, all_38_3_23) = 0) | (member(all_10_6_10, all_0_2_2) = all_38_2_22 & member(all_10_7_11, all_0_2_2) = all_38_3_23 & ( ~ (all_38_2_22 = 0) | ~ (all_38_3_23 = 0)))
% 11.58/3.37 |
% 11.58/3.37 +-Applying beta-rule and splitting (96), into two cases.
% 11.58/3.37 |-Branch one:
% 11.58/3.37 | (98) all_37_0_16 = 0 & all_37_1_17 = 0 & all_37_2_18 = 0 & member(all_37_3_19, all_0_3_3) = 0 & member(all_10_7_11, all_37_3_19) = 0 & member(all_10_8_12, all_37_3_19) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (98) yields:
% 11.58/3.37 | (99) member(all_37_3_19, all_0_3_3) = 0
% 11.58/3.37 | (100) member(all_10_8_12, all_37_3_19) = 0
% 11.58/3.37 | (101) all_37_1_17 = 0
% 11.58/3.37 | (102) member(all_10_7_11, all_37_3_19) = 0
% 11.58/3.37 | (103) all_37_2_18 = 0
% 11.58/3.37 | (104) all_37_0_16 = 0
% 11.58/3.37 |
% 11.58/3.37 +-Applying beta-rule and splitting (97), into two cases.
% 11.58/3.37 |-Branch one:
% 11.58/3.37 | (105) all_38_0_20 = 0 & all_38_1_21 = 0 & all_38_2_22 = 0 & member(all_38_3_23, all_0_3_3) = 0 & member(all_10_6_10, all_38_3_23) = 0 & member(all_10_7_11, all_38_3_23) = 0
% 11.58/3.37 |
% 11.58/3.37 | Applying alpha-rule on (105) yields:
% 11.58/3.37 | (106) member(all_10_7_11, all_38_3_23) = 0
% 11.58/3.37 | (107) all_38_2_22 = 0
% 11.58/3.37 | (108) all_38_0_20 = 0
% 11.58/3.37 | (109) member(all_10_6_10, all_38_3_23) = 0
% 11.58/3.37 | (110) member(all_38_3_23, all_0_3_3) = 0
% 11.58/3.37 | (111) all_38_1_21 = 0
% 11.58/3.37 |
% 11.58/3.37 +-Applying beta-rule and splitting (85), into two cases.
% 11.58/3.37 |-Branch one:
% 11.58/3.37 | (112) all_10_0_4 = 0
% 11.58/3.37 |
% 11.58/3.37 | Equations (112) can reduce 71 to:
% 11.58/3.37 | (63) $false
% 11.58/3.37 |
% 11.58/3.37 |-The branch is then unsatisfiable
% 11.58/3.37 |-Branch two:
% 11.58/3.37 | (71) ~ (all_10_0_4 = 0)
% 11.58/3.37 | (115) ? [v0] : ? [v1] : ((member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.38 |
% 11.58/3.38 | Instantiating (115) with all_51_0_24, all_51_1_25 yields:
% 11.58/3.38 | (116) (member(all_10_6_10, all_0_2_2) = all_51_0_24 & member(all_10_8_12, all_0_2_2) = all_51_1_25 & ( ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0))) | (member(all_10_6_10, all_0_2_2) = all_51_0_24 & member(all_0_2_2, all_0_3_3) = all_51_1_25 & ( ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0)))
% 11.58/3.38 |
% 11.58/3.38 +-Applying beta-rule and splitting (116), into two cases.
% 11.58/3.38 |-Branch one:
% 11.58/3.38 | (117) member(all_10_6_10, all_0_2_2) = all_51_0_24 & member(all_10_8_12, all_0_2_2) = all_51_1_25 & ( ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0))
% 11.58/3.38 |
% 11.58/3.38 | Applying alpha-rule on (117) yields:
% 11.58/3.38 | (118) member(all_10_6_10, all_0_2_2) = all_51_0_24
% 11.58/3.38 | (119) member(all_10_8_12, all_0_2_2) = all_51_1_25
% 11.58/3.38 | (120) ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (14) with all_10_6_10, all_0_2_2, all_51_0_24, 0 and discharging atoms member(all_10_6_10, all_0_2_2) = all_51_0_24, member(all_10_6_10, all_0_2_2) = 0, yields:
% 11.58/3.38 | (121) all_51_0_24 = 0
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_51_1_25, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_51_1_25, member(all_10_8_12, all_0_2_2) = 0, yields:
% 11.58/3.38 | (122) all_51_1_25 = 0
% 11.58/3.38 |
% 11.58/3.38 +-Applying beta-rule and splitting (120), into two cases.
% 11.58/3.38 |-Branch one:
% 11.58/3.38 | (123) ~ (all_51_0_24 = 0)
% 11.58/3.38 |
% 11.58/3.38 | Equations (121) can reduce 123 to:
% 11.58/3.38 | (63) $false
% 11.58/3.38 |
% 11.58/3.38 |-The branch is then unsatisfiable
% 11.58/3.38 |-Branch two:
% 11.58/3.38 | (121) all_51_0_24 = 0
% 11.58/3.38 | (126) ~ (all_51_1_25 = 0)
% 11.58/3.38 |
% 11.58/3.38 | Equations (122) can reduce 126 to:
% 11.58/3.38 | (63) $false
% 11.58/3.38 |
% 11.58/3.38 |-The branch is then unsatisfiable
% 11.58/3.38 |-Branch two:
% 11.58/3.38 | (128) member(all_10_6_10, all_0_2_2) = all_51_0_24 & member(all_0_2_2, all_0_3_3) = all_51_1_25 & ( ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0))
% 11.58/3.38 |
% 11.58/3.38 | Applying alpha-rule on (128) yields:
% 11.58/3.38 | (118) member(all_10_6_10, all_0_2_2) = all_51_0_24
% 11.58/3.38 | (130) member(all_0_2_2, all_0_3_3) = all_51_1_25
% 11.58/3.38 | (120) ~ (all_51_0_24 = 0) | ~ (all_51_1_25 = 0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (14) with all_10_6_10, all_0_2_2, all_51_0_24, 0 and discharging atoms member(all_10_6_10, all_0_2_2) = all_51_0_24, member(all_10_6_10, all_0_2_2) = 0, yields:
% 11.58/3.38 | (121) all_51_0_24 = 0
% 11.58/3.38 |
% 11.58/3.38 | From (121) and (118) follows:
% 11.58/3.38 | (80) member(all_10_6_10, all_0_2_2) = 0
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (21) with all_10_6_10, all_35_0_15, all_38_3_23, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_38_3_23, all_0_3_3) = 0, member(all_35_0_15, all_0_3_3) = 0, member(all_10_6_10, all_38_3_23) = 0, yields:
% 11.58/3.38 | (134) all_38_3_23 = all_35_0_15 | ? [v0] : ( ~ (v0 = 0) & member(all_10_6_10, all_35_0_15) = v0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (21) with all_10_7_11, all_38_3_23, all_33_0_14, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_38_3_23, all_0_3_3) = 0, member(all_33_0_14, all_0_3_3) = 0, member(all_10_7_11, all_33_0_14) = 0, yields:
% 11.58/3.38 | (135) all_38_3_23 = all_33_0_14 | ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_38_3_23) = v0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (21) with all_10_7_11, all_38_3_23, all_31_0_13, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_38_3_23, all_0_3_3) = 0, member(all_31_0_13, all_0_3_3) = 0, yields:
% 11.58/3.38 | (136) all_38_3_23 = all_31_0_13 | ~ (member(all_10_7_11, all_31_0_13) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_38_3_23) = v0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (46) with all_37_3_19, all_10_0_4, all_10_6_10, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4, member(all_10_8_12, all_37_3_19) = 0, yields:
% 11.58/3.38 | (137) all_10_0_4 = 0 | ? [v0] : ? [v1] : ((member(all_37_3_19, all_0_3_3) = v0 & member(all_10_6_10, all_37_3_19) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (21) with all_10_8_12, all_31_0_13, all_37_3_19, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_37_3_19, all_0_3_3) = 0, member(all_31_0_13, all_0_3_3) = 0, member(all_10_8_12, all_37_3_19) = 0, yields:
% 11.58/3.38 | (138) all_37_3_19 = all_31_0_13 | ? [v0] : ( ~ (v0 = 0) & member(all_10_8_12, all_31_0_13) = v0)
% 11.58/3.38 |
% 11.58/3.38 | Instantiating formula (46) with all_31_0_13, all_10_0_4, all_10_6_10, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_6_10) = all_10_0_4, member(all_10_8_12, all_31_0_13) = 0, yields:
% 11.58/3.38 | (139) all_10_0_4 = 0 | ? [v0] : ? [v1] : ((member(all_31_0_13, all_0_3_3) = v0 & member(all_10_6_10, all_31_0_13) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.38 |
% 11.58/3.38 +-Applying beta-rule and splitting (138), into two cases.
% 11.58/3.38 |-Branch one:
% 11.58/3.38 | (140) all_37_3_19 = all_31_0_13
% 11.58/3.38 |
% 11.58/3.38 | From (140) and (102) follows:
% 11.58/3.38 | (141) member(all_10_7_11, all_31_0_13) = 0
% 11.58/3.38 |
% 11.58/3.38 +-Applying beta-rule and splitting (139), into two cases.
% 11.58/3.38 |-Branch one:
% 11.58/3.38 | (112) all_10_0_4 = 0
% 11.58/3.38 |
% 11.58/3.38 | Equations (112) can reduce 71 to:
% 11.58/3.38 | (63) $false
% 11.58/3.38 |
% 11.58/3.38 |-The branch is then unsatisfiable
% 11.58/3.38 |-Branch two:
% 11.58/3.38 | (71) ~ (all_10_0_4 = 0)
% 11.58/3.38 | (145) ? [v0] : ? [v1] : ((member(all_31_0_13, all_0_3_3) = v0 & member(all_10_6_10, all_31_0_13) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 11.58/3.38 |
% 11.58/3.38 +-Applying beta-rule and splitting (134), into two cases.
% 11.58/3.38 |-Branch one:
% 12.15/3.38 | (146) all_38_3_23 = all_35_0_15
% 12.15/3.38 |
% 12.15/3.38 | From (146) and (110) follows:
% 12.15/3.38 | (94) member(all_35_0_15, all_0_3_3) = 0
% 12.15/3.38 |
% 12.15/3.38 | From (146) and (109) follows:
% 12.15/3.38 | (95) member(all_10_6_10, all_35_0_15) = 0
% 12.15/3.38 |
% 12.15/3.38 | From (146) and (106) follows:
% 12.15/3.38 | (149) member(all_10_7_11, all_35_0_15) = 0
% 12.15/3.38 |
% 12.15/3.38 +-Applying beta-rule and splitting (136), into two cases.
% 12.15/3.38 |-Branch one:
% 12.15/3.38 | (150) ~ (member(all_10_7_11, all_31_0_13) = 0)
% 12.15/3.38 |
% 12.15/3.38 | Using (141) and (150) yields:
% 12.15/3.38 | (151) $false
% 12.15/3.38 |
% 12.15/3.38 |-The branch is then unsatisfiable
% 12.15/3.38 |-Branch two:
% 12.15/3.38 | (141) member(all_10_7_11, all_31_0_13) = 0
% 12.15/3.38 | (153) all_38_3_23 = all_31_0_13 | ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_38_3_23) = v0)
% 12.15/3.38 |
% 12.15/3.38 +-Applying beta-rule and splitting (137), into two cases.
% 12.15/3.38 |-Branch one:
% 12.15/3.38 | (112) all_10_0_4 = 0
% 12.15/3.38 |
% 12.15/3.38 | Equations (112) can reduce 71 to:
% 12.15/3.38 | (63) $false
% 12.15/3.38 |
% 12.15/3.38 |-The branch is then unsatisfiable
% 12.15/3.38 |-Branch two:
% 12.15/3.38 | (71) ~ (all_10_0_4 = 0)
% 12.15/3.38 | (157) ? [v0] : ? [v1] : ((member(all_37_3_19, all_0_3_3) = v0 & member(all_10_6_10, all_37_3_19) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_6_10, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.38 |
% 12.15/3.38 | Instantiating (157) with all_94_0_28, all_94_1_29 yields:
% 12.15/3.38 | (158) (member(all_37_3_19, all_0_3_3) = all_94_1_29 & member(all_10_6_10, all_37_3_19) = all_94_0_28 & ( ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0))) | (member(all_10_6_10, all_0_2_2) = all_94_0_28 & member(all_10_8_12, all_0_2_2) = all_94_1_29 & ( ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0)))
% 12.15/3.38 |
% 12.15/3.38 +-Applying beta-rule and splitting (135), into two cases.
% 12.15/3.38 |-Branch one:
% 12.15/3.38 | (159) all_38_3_23 = all_33_0_14
% 12.15/3.38 |
% 12.15/3.38 | Combining equations (146,159) yields a new equation:
% 12.15/3.38 | (160) all_35_0_15 = all_33_0_14
% 12.15/3.38 |
% 12.15/3.38 | Simplifying 160 yields:
% 12.15/3.38 | (161) all_35_0_15 = all_33_0_14
% 12.15/3.38 |
% 12.15/3.38 | From (161) and (94) follows:
% 12.15/3.38 | (91) member(all_33_0_14, all_0_3_3) = 0
% 12.15/3.38 |
% 12.15/3.38 | From (161) and (95) follows:
% 12.15/3.38 | (163) member(all_10_6_10, all_33_0_14) = 0
% 12.15/3.38 |
% 12.15/3.38 | From (161) and (149) follows:
% 12.15/3.38 | (92) member(all_10_7_11, all_33_0_14) = 0
% 12.15/3.38 |
% 12.15/3.39 +-Applying beta-rule and splitting (153), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (165) all_38_3_23 = all_31_0_13
% 12.15/3.39 |
% 12.15/3.39 | Combining equations (159,165) yields a new equation:
% 12.15/3.39 | (166) all_33_0_14 = all_31_0_13
% 12.15/3.39 |
% 12.15/3.39 | Simplifying 166 yields:
% 12.15/3.39 | (167) all_33_0_14 = all_31_0_13
% 12.15/3.39 |
% 12.15/3.39 | From (167) and (91) follows:
% 12.15/3.39 | (88) member(all_31_0_13, all_0_3_3) = 0
% 12.15/3.39 |
% 12.15/3.39 | From (167) and (163) follows:
% 12.15/3.39 | (169) member(all_10_6_10, all_31_0_13) = 0
% 12.15/3.39 |
% 12.15/3.39 +-Applying beta-rule and splitting (158), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (170) member(all_37_3_19, all_0_3_3) = all_94_1_29 & member(all_10_6_10, all_37_3_19) = all_94_0_28 & ( ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0))
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (170) yields:
% 12.15/3.39 | (171) member(all_37_3_19, all_0_3_3) = all_94_1_29
% 12.15/3.39 | (172) member(all_10_6_10, all_37_3_19) = all_94_0_28
% 12.15/3.39 | (173) ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0)
% 12.15/3.39 |
% 12.15/3.39 | From (140) and (171) follows:
% 12.15/3.39 | (174) member(all_31_0_13, all_0_3_3) = all_94_1_29
% 12.15/3.39 |
% 12.15/3.39 | From (140) and (172) follows:
% 12.15/3.39 | (175) member(all_10_6_10, all_31_0_13) = all_94_0_28
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_31_0_13, all_0_3_3, all_94_1_29, 0 and discharging atoms member(all_31_0_13, all_0_3_3) = all_94_1_29, member(all_31_0_13, all_0_3_3) = 0, yields:
% 12.15/3.39 | (176) all_94_1_29 = 0
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_6_10, all_31_0_13, 0, all_94_0_28 and discharging atoms member(all_10_6_10, all_31_0_13) = all_94_0_28, member(all_10_6_10, all_31_0_13) = 0, yields:
% 12.15/3.39 | (177) all_94_0_28 = 0
% 12.15/3.39 |
% 12.15/3.39 +-Applying beta-rule and splitting (173), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (178) ~ (all_94_0_28 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (177) can reduce 178 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (177) all_94_0_28 = 0
% 12.15/3.39 | (181) ~ (all_94_1_29 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (176) can reduce 181 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (183) member(all_10_6_10, all_0_2_2) = all_94_0_28 & member(all_10_8_12, all_0_2_2) = all_94_1_29 & ( ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0))
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (183) yields:
% 12.15/3.39 | (184) member(all_10_6_10, all_0_2_2) = all_94_0_28
% 12.15/3.39 | (185) member(all_10_8_12, all_0_2_2) = all_94_1_29
% 12.15/3.39 | (173) ~ (all_94_0_28 = 0) | ~ (all_94_1_29 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_6_10, all_0_2_2, all_94_0_28, 0 and discharging atoms member(all_10_6_10, all_0_2_2) = all_94_0_28, member(all_10_6_10, all_0_2_2) = 0, yields:
% 12.15/3.39 | (177) all_94_0_28 = 0
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_94_1_29, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_94_1_29, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.39 | (176) all_94_1_29 = 0
% 12.15/3.39 |
% 12.15/3.39 +-Applying beta-rule and splitting (173), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (178) ~ (all_94_0_28 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (177) can reduce 178 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (177) all_94_0_28 = 0
% 12.15/3.39 | (181) ~ (all_94_1_29 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (176) can reduce 181 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (194) ~ (all_38_3_23 = all_31_0_13)
% 12.15/3.39 | (195) ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_38_3_23) = v0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating (195) with all_103_0_38 yields:
% 12.15/3.39 | (196) ~ (all_103_0_38 = 0) & member(all_10_7_11, all_38_3_23) = all_103_0_38
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (196) yields:
% 12.15/3.39 | (197) ~ (all_103_0_38 = 0)
% 12.15/3.39 | (198) member(all_10_7_11, all_38_3_23) = all_103_0_38
% 12.15/3.39 |
% 12.15/3.39 | From (159) and (198) follows:
% 12.15/3.39 | (199) member(all_10_7_11, all_33_0_14) = all_103_0_38
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_7_11, all_33_0_14, all_103_0_38, 0 and discharging atoms member(all_10_7_11, all_33_0_14) = all_103_0_38, member(all_10_7_11, all_33_0_14) = 0, yields:
% 12.15/3.39 | (200) all_103_0_38 = 0
% 12.15/3.39 |
% 12.15/3.39 | Equations (200) can reduce 197 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (202) ~ (all_38_3_23 = all_33_0_14)
% 12.15/3.39 | (195) ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_38_3_23) = v0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating (195) with all_99_0_43 yields:
% 12.15/3.39 | (204) ~ (all_99_0_43 = 0) & member(all_10_7_11, all_38_3_23) = all_99_0_43
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (204) yields:
% 12.15/3.39 | (205) ~ (all_99_0_43 = 0)
% 12.15/3.39 | (206) member(all_10_7_11, all_38_3_23) = all_99_0_43
% 12.15/3.39 |
% 12.15/3.39 | From (146) and (206) follows:
% 12.15/3.39 | (207) member(all_10_7_11, all_35_0_15) = all_99_0_43
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_7_11, all_35_0_15, all_99_0_43, 0 and discharging atoms member(all_10_7_11, all_35_0_15) = all_99_0_43, member(all_10_7_11, all_35_0_15) = 0, yields:
% 12.15/3.39 | (208) all_99_0_43 = 0
% 12.15/3.39 |
% 12.15/3.39 | Equations (208) can reduce 205 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (210) ~ (all_38_3_23 = all_35_0_15)
% 12.15/3.39 | (211) ? [v0] : ( ~ (v0 = 0) & member(all_10_6_10, all_35_0_15) = v0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating (211) with all_87_0_47 yields:
% 12.15/3.39 | (212) ~ (all_87_0_47 = 0) & member(all_10_6_10, all_35_0_15) = all_87_0_47
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (212) yields:
% 12.15/3.39 | (213) ~ (all_87_0_47 = 0)
% 12.15/3.39 | (214) member(all_10_6_10, all_35_0_15) = all_87_0_47
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_6_10, all_35_0_15, all_87_0_47, 0 and discharging atoms member(all_10_6_10, all_35_0_15) = all_87_0_47, member(all_10_6_10, all_35_0_15) = 0, yields:
% 12.15/3.39 | (215) all_87_0_47 = 0
% 12.15/3.39 |
% 12.15/3.39 | Equations (215) can reduce 213 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (217) ~ (all_37_3_19 = all_31_0_13)
% 12.15/3.39 | (218) ? [v0] : ( ~ (v0 = 0) & member(all_10_8_12, all_31_0_13) = v0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating (218) with all_79_0_55 yields:
% 12.15/3.39 | (219) ~ (all_79_0_55 = 0) & member(all_10_8_12, all_31_0_13) = all_79_0_55
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (219) yields:
% 12.15/3.39 | (220) ~ (all_79_0_55 = 0)
% 12.15/3.39 | (221) member(all_10_8_12, all_31_0_13) = all_79_0_55
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_8_12, all_31_0_13, all_79_0_55, 0 and discharging atoms member(all_10_8_12, all_31_0_13) = all_79_0_55, member(all_10_8_12, all_31_0_13) = 0, yields:
% 12.15/3.39 | (222) all_79_0_55 = 0
% 12.15/3.39 |
% 12.15/3.39 | Equations (222) can reduce 220 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (224) member(all_10_6_10, all_0_2_2) = all_38_2_22 & member(all_10_7_11, all_0_2_2) = all_38_3_23 & ( ~ (all_38_2_22 = 0) | ~ (all_38_3_23 = 0))
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (224) yields:
% 12.15/3.39 | (225) member(all_10_6_10, all_0_2_2) = all_38_2_22
% 12.15/3.39 | (226) member(all_10_7_11, all_0_2_2) = all_38_3_23
% 12.15/3.39 | (227) ~ (all_38_2_22 = 0) | ~ (all_38_3_23 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_6_10, all_0_2_2, all_38_2_22, 0 and discharging atoms member(all_10_6_10, all_0_2_2) = all_38_2_22, member(all_10_6_10, all_0_2_2) = 0, yields:
% 12.15/3.39 | (107) all_38_2_22 = 0
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_38_3_23, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_38_3_23, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.39 | (229) all_38_3_23 = 0
% 12.15/3.39 |
% 12.15/3.39 +-Applying beta-rule and splitting (227), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (230) ~ (all_38_2_22 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (107) can reduce 230 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (107) all_38_2_22 = 0
% 12.15/3.39 | (233) ~ (all_38_3_23 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (229) can reduce 233 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (235) member(all_10_7_11, all_0_2_2) = all_37_2_18 & member(all_10_8_12, all_0_2_2) = all_37_3_19 & ( ~ (all_37_2_18 = 0) | ~ (all_37_3_19 = 0))
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (235) yields:
% 12.15/3.39 | (236) member(all_10_7_11, all_0_2_2) = all_37_2_18
% 12.15/3.39 | (237) member(all_10_8_12, all_0_2_2) = all_37_3_19
% 12.15/3.39 | (238) ~ (all_37_2_18 = 0) | ~ (all_37_3_19 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_37_2_18, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_37_2_18, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.39 | (103) all_37_2_18 = 0
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_37_3_19, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_37_3_19, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.39 | (240) all_37_3_19 = 0
% 12.15/3.39 |
% 12.15/3.39 +-Applying beta-rule and splitting (238), into two cases.
% 12.15/3.39 |-Branch one:
% 12.15/3.39 | (241) ~ (all_37_2_18 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (103) can reduce 241 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (103) all_37_2_18 = 0
% 12.15/3.39 | (244) ~ (all_37_3_19 = 0)
% 12.15/3.39 |
% 12.15/3.39 | Equations (240) can reduce 244 to:
% 12.15/3.39 | (63) $false
% 12.15/3.39 |
% 12.15/3.39 |-The branch is then unsatisfiable
% 12.15/3.39 |-Branch two:
% 12.15/3.39 | (246) all_10_4_8 = 0 & all_10_5_9 = 0 & all_10_6_10 = 0 & ~ (all_10_3_7 = 0) & apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7 & apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0 & member(all_10_7_11, all_0_2_2) = 0 & member(all_10_8_12, all_0_2_2) = 0
% 12.15/3.39 |
% 12.15/3.39 | Applying alpha-rule on (246) yields:
% 12.15/3.39 | (69) member(all_10_8_12, all_0_2_2) = 0
% 12.15/3.39 | (70) all_10_4_8 = 0
% 12.15/3.39 | (249) apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7
% 12.15/3.39 | (250) ~ (all_10_3_7 = 0)
% 12.15/3.39 | (251) all_10_6_10 = 0
% 12.15/3.39 | (74) all_10_5_9 = 0
% 12.15/3.39 | (75) member(all_10_7_11, all_0_2_2) = 0
% 12.15/3.39 | (78) apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (39) with all_10_7_11, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_7_11) = 0, yields:
% 12.15/3.39 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & member(v0, all_0_3_3) = 0 & member(all_10_7_11, v0) = 0 & member(all_10_8_12, v0) = 0) | (member(all_10_7_11, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (12) with all_10_7_11, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.39 | (84) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_7_11, v0) = 0)
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (46) with all_0_2_2, all_10_3_7, all_10_8_12, all_10_7_11 and discharging atoms apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.39 | (257) all_10_3_7 = 0 | ? [v0] : ? [v1] : ((member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.39 |
% 12.15/3.39 | Instantiating formula (12) with all_10_8_12, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.40 | (86) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_8_12, v0) = 0)
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (86) with all_31_0_68 yields:
% 12.15/3.40 | (259) member(all_31_0_68, all_0_3_3) = 0 & member(all_10_8_12, all_31_0_68) = 0
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (259) yields:
% 12.15/3.40 | (260) member(all_31_0_68, all_0_3_3) = 0
% 12.15/3.40 | (261) member(all_10_8_12, all_31_0_68) = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (84) with all_33_0_69 yields:
% 12.15/3.40 | (262) member(all_33_0_69, all_0_3_3) = 0 & member(all_10_7_11, all_33_0_69) = 0
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (262) yields:
% 12.15/3.40 | (263) member(all_33_0_69, all_0_3_3) = 0
% 12.15/3.40 | (264) member(all_10_7_11, all_33_0_69) = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (82) with all_35_0_70, all_35_1_71, all_35_2_72, all_35_3_73 yields:
% 12.15/3.40 | (265) (all_35_0_70 = 0 & all_35_1_71 = 0 & all_35_2_72 = 0 & member(all_35_3_73, all_0_3_3) = 0 & member(all_10_7_11, all_35_3_73) = 0 & member(all_10_8_12, all_35_3_73) = 0) | (member(all_10_7_11, all_0_2_2) = all_35_2_72 & member(all_10_8_12, all_0_2_2) = all_35_3_73 & ( ~ (all_35_2_72 = 0) | ~ (all_35_3_73 = 0)))
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (265), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (266) all_35_0_70 = 0 & all_35_1_71 = 0 & all_35_2_72 = 0 & member(all_35_3_73, all_0_3_3) = 0 & member(all_10_7_11, all_35_3_73) = 0 & member(all_10_8_12, all_35_3_73) = 0
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (266) yields:
% 12.15/3.40 | (267) all_35_2_72 = 0
% 12.15/3.40 | (268) all_35_0_70 = 0
% 12.15/3.40 | (269) member(all_10_7_11, all_35_3_73) = 0
% 12.15/3.40 | (270) member(all_10_8_12, all_35_3_73) = 0
% 12.15/3.40 | (271) member(all_35_3_73, all_0_3_3) = 0
% 12.15/3.40 | (272) all_35_1_71 = 0
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (257), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (73) all_10_3_7 = 0
% 12.15/3.40 |
% 12.15/3.40 | Equations (73) can reduce 250 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (250) ~ (all_10_3_7 = 0)
% 12.15/3.40 | (276) ? [v0] : ? [v1] : ((member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (276) with all_43_0_74, all_43_1_75 yields:
% 12.15/3.40 | (277) (member(all_10_7_11, all_0_2_2) = all_43_1_75 & member(all_10_8_12, all_0_2_2) = all_43_0_74 & ( ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0))) | (member(all_10_8_12, all_0_2_2) = all_43_0_74 & member(all_0_2_2, all_0_3_3) = all_43_1_75 & ( ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0)))
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (277), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (278) member(all_10_7_11, all_0_2_2) = all_43_1_75 & member(all_10_8_12, all_0_2_2) = all_43_0_74 & ( ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0))
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (278) yields:
% 12.15/3.40 | (279) member(all_10_7_11, all_0_2_2) = all_43_1_75
% 12.15/3.40 | (280) member(all_10_8_12, all_0_2_2) = all_43_0_74
% 12.15/3.40 | (281) ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_43_1_75, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_43_1_75, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.40 | (282) all_43_1_75 = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_43_0_74, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_43_0_74, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.40 | (283) all_43_0_74 = 0
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (281), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (284) ~ (all_43_0_74 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Equations (283) can reduce 284 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (283) all_43_0_74 = 0
% 12.15/3.40 | (287) ~ (all_43_1_75 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Equations (282) can reduce 287 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (289) member(all_10_8_12, all_0_2_2) = all_43_0_74 & member(all_0_2_2, all_0_3_3) = all_43_1_75 & ( ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0))
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (289) yields:
% 12.15/3.40 | (280) member(all_10_8_12, all_0_2_2) = all_43_0_74
% 12.15/3.40 | (291) member(all_0_2_2, all_0_3_3) = all_43_1_75
% 12.15/3.40 | (281) ~ (all_43_0_74 = 0) | ~ (all_43_1_75 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_43_0_74, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_43_0_74, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.40 | (283) all_43_0_74 = 0
% 12.15/3.40 |
% 12.15/3.40 | From (283) and (280) follows:
% 12.15/3.40 | (69) member(all_10_8_12, all_0_2_2) = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (46) with all_35_3_73, all_10_3_7, all_10_8_12, all_10_7_11 and discharging atoms apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7, member(all_10_7_11, all_35_3_73) = 0, yields:
% 12.15/3.40 | (295) all_10_3_7 = 0 | ? [v0] : ? [v1] : ((member(all_35_3_73, all_0_3_3) = v0 & member(all_10_8_12, all_35_3_73) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (21) with all_10_7_11, all_35_3_73, all_33_0_69, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_35_3_73, all_0_3_3) = 0, member(all_33_0_69, all_0_3_3) = 0, member(all_10_7_11, all_33_0_69) = 0, yields:
% 12.15/3.40 | (296) all_35_3_73 = all_33_0_69 | ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_35_3_73) = v0)
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (46) with all_33_0_69, all_10_3_7, all_10_8_12, all_10_7_11 and discharging atoms apply(all_0_1_1, all_10_7_11, all_10_8_12) = all_10_3_7, member(all_10_7_11, all_33_0_69) = 0, yields:
% 12.15/3.40 | (297) all_10_3_7 = 0 | ? [v0] : ? [v1] : ((member(all_33_0_69, all_0_3_3) = v0 & member(all_10_8_12, all_33_0_69) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (21) with all_10_8_12, all_35_3_73, all_31_0_68, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_35_3_73, all_0_3_3) = 0, member(all_31_0_68, all_0_3_3) = 0, member(all_10_8_12, all_31_0_68) = 0, yields:
% 12.15/3.40 | (298) all_35_3_73 = all_31_0_68 | ? [v0] : ( ~ (v0 = 0) & member(all_10_8_12, all_35_3_73) = v0)
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (298), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (299) all_35_3_73 = all_31_0_68
% 12.15/3.40 |
% 12.15/3.40 | From (299) and (269) follows:
% 12.15/3.40 | (300) member(all_10_7_11, all_31_0_68) = 0
% 12.15/3.40 |
% 12.15/3.40 | From (299) and (270) follows:
% 12.15/3.40 | (261) member(all_10_8_12, all_31_0_68) = 0
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (296), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (302) all_35_3_73 = all_33_0_69
% 12.15/3.40 |
% 12.15/3.40 | Combining equations (302,299) yields a new equation:
% 12.15/3.40 | (303) all_33_0_69 = all_31_0_68
% 12.15/3.40 |
% 12.15/3.40 | Simplifying 303 yields:
% 12.15/3.40 | (304) all_33_0_69 = all_31_0_68
% 12.15/3.40 |
% 12.15/3.40 | From (304) and (263) follows:
% 12.15/3.40 | (260) member(all_31_0_68, all_0_3_3) = 0
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (297), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (73) all_10_3_7 = 0
% 12.15/3.40 |
% 12.15/3.40 | Equations (73) can reduce 250 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (250) ~ (all_10_3_7 = 0)
% 12.15/3.40 | (309) ? [v0] : ? [v1] : ((member(all_33_0_69, all_0_3_3) = v0 & member(all_10_8_12, all_33_0_69) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (309) with all_83_0_76, all_83_1_77 yields:
% 12.15/3.40 | (310) (member(all_33_0_69, all_0_3_3) = all_83_1_77 & member(all_10_8_12, all_33_0_69) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0))) | (member(all_10_7_11, all_0_2_2) = all_83_1_77 & member(all_10_8_12, all_0_2_2) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0)))
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (295), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (73) all_10_3_7 = 0
% 12.15/3.40 |
% 12.15/3.40 | Equations (73) can reduce 250 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (250) ~ (all_10_3_7 = 0)
% 12.15/3.40 | (314) ? [v0] : ? [v1] : ((member(all_35_3_73, all_0_3_3) = v0 & member(all_10_8_12, all_35_3_73) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_7_11, all_0_2_2) = v0 & member(all_10_8_12, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.15/3.40 |
% 12.15/3.40 | Instantiating (314) with all_88_0_78, all_88_1_79 yields:
% 12.15/3.40 | (315) (member(all_35_3_73, all_0_3_3) = all_88_1_79 & member(all_10_8_12, all_35_3_73) = all_88_0_78 & ( ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0))) | (member(all_10_7_11, all_0_2_2) = all_88_1_79 & member(all_10_8_12, all_0_2_2) = all_88_0_78 & ( ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0)))
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (315), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (316) member(all_35_3_73, all_0_3_3) = all_88_1_79 & member(all_10_8_12, all_35_3_73) = all_88_0_78 & ( ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0))
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (316) yields:
% 12.15/3.40 | (317) member(all_35_3_73, all_0_3_3) = all_88_1_79
% 12.15/3.40 | (318) member(all_10_8_12, all_35_3_73) = all_88_0_78
% 12.15/3.40 | (319) ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0)
% 12.15/3.40 |
% 12.15/3.40 | From (299) and (317) follows:
% 12.15/3.40 | (320) member(all_31_0_68, all_0_3_3) = all_88_1_79
% 12.15/3.40 |
% 12.15/3.40 | From (299) and (318) follows:
% 12.15/3.40 | (321) member(all_10_8_12, all_31_0_68) = all_88_0_78
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (310), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (322) member(all_33_0_69, all_0_3_3) = all_83_1_77 & member(all_10_8_12, all_33_0_69) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0))
% 12.15/3.40 |
% 12.15/3.40 | Applying alpha-rule on (322) yields:
% 12.15/3.40 | (323) member(all_33_0_69, all_0_3_3) = all_83_1_77
% 12.15/3.40 | (324) member(all_10_8_12, all_33_0_69) = all_83_0_76
% 12.15/3.40 | (325) ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0)
% 12.15/3.40 |
% 12.15/3.40 | From (304) and (324) follows:
% 12.15/3.40 | (326) member(all_10_8_12, all_31_0_68) = all_83_0_76
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_31_0_68, all_0_3_3, all_88_1_79, 0 and discharging atoms member(all_31_0_68, all_0_3_3) = all_88_1_79, member(all_31_0_68, all_0_3_3) = 0, yields:
% 12.15/3.40 | (327) all_88_1_79 = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_10_8_12, all_31_0_68, all_88_0_78, 0 and discharging atoms member(all_10_8_12, all_31_0_68) = all_88_0_78, member(all_10_8_12, all_31_0_68) = 0, yields:
% 12.15/3.40 | (328) all_88_0_78 = 0
% 12.15/3.40 |
% 12.15/3.40 | Instantiating formula (14) with all_10_8_12, all_31_0_68, all_83_0_76, all_88_0_78 and discharging atoms member(all_10_8_12, all_31_0_68) = all_88_0_78, member(all_10_8_12, all_31_0_68) = all_83_0_76, yields:
% 12.15/3.40 | (329) all_88_0_78 = all_83_0_76
% 12.15/3.40 |
% 12.15/3.40 | Combining equations (328,329) yields a new equation:
% 12.15/3.40 | (330) all_83_0_76 = 0
% 12.15/3.40 |
% 12.15/3.40 | Combining equations (330,329) yields a new equation:
% 12.15/3.40 | (328) all_88_0_78 = 0
% 12.15/3.40 |
% 12.15/3.40 +-Applying beta-rule and splitting (319), into two cases.
% 12.15/3.40 |-Branch one:
% 12.15/3.40 | (332) ~ (all_88_0_78 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Equations (328) can reduce 332 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.40 | (328) all_88_0_78 = 0
% 12.15/3.40 | (335) ~ (all_88_1_79 = 0)
% 12.15/3.40 |
% 12.15/3.40 | Equations (327) can reduce 335 to:
% 12.15/3.40 | (63) $false
% 12.15/3.40 |
% 12.15/3.40 |-The branch is then unsatisfiable
% 12.15/3.40 |-Branch two:
% 12.15/3.41 | (337) member(all_10_7_11, all_0_2_2) = all_83_1_77 & member(all_10_8_12, all_0_2_2) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0))
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (337) yields:
% 12.15/3.41 | (338) member(all_10_7_11, all_0_2_2) = all_83_1_77
% 12.15/3.41 | (339) member(all_10_8_12, all_0_2_2) = all_83_0_76
% 12.15/3.41 | (325) ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_83_1_77, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_83_1_77, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.41 | (341) all_83_1_77 = 0
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_83_0_76, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_83_0_76, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.41 | (330) all_83_0_76 = 0
% 12.15/3.41 |
% 12.15/3.41 +-Applying beta-rule and splitting (325), into two cases.
% 12.15/3.41 |-Branch one:
% 12.15/3.41 | (343) ~ (all_83_0_76 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (330) can reduce 343 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (330) all_83_0_76 = 0
% 12.15/3.41 | (346) ~ (all_83_1_77 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (341) can reduce 346 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (348) member(all_10_7_11, all_0_2_2) = all_88_1_79 & member(all_10_8_12, all_0_2_2) = all_88_0_78 & ( ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0))
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (348) yields:
% 12.15/3.41 | (349) member(all_10_7_11, all_0_2_2) = all_88_1_79
% 12.15/3.41 | (350) member(all_10_8_12, all_0_2_2) = all_88_0_78
% 12.15/3.41 | (319) ~ (all_88_0_78 = 0) | ~ (all_88_1_79 = 0)
% 12.15/3.41 |
% 12.15/3.41 +-Applying beta-rule and splitting (310), into two cases.
% 12.15/3.41 |-Branch one:
% 12.15/3.41 | (322) member(all_33_0_69, all_0_3_3) = all_83_1_77 & member(all_10_8_12, all_33_0_69) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0))
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (322) yields:
% 12.15/3.41 | (323) member(all_33_0_69, all_0_3_3) = all_83_1_77
% 12.15/3.41 | (324) member(all_10_8_12, all_33_0_69) = all_83_0_76
% 12.15/3.41 | (325) ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0)
% 12.15/3.41 |
% 12.15/3.41 | From (304) and (323) follows:
% 12.15/3.41 | (356) member(all_31_0_68, all_0_3_3) = all_83_1_77
% 12.15/3.41 |
% 12.15/3.41 | From (304) and (324) follows:
% 12.15/3.41 | (326) member(all_10_8_12, all_31_0_68) = all_83_0_76
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_31_0_68, all_0_3_3, all_83_1_77, 0 and discharging atoms member(all_31_0_68, all_0_3_3) = all_83_1_77, member(all_31_0_68, all_0_3_3) = 0, yields:
% 12.15/3.41 | (341) all_83_1_77 = 0
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_8_12, all_31_0_68, all_83_0_76, 0 and discharging atoms member(all_10_8_12, all_31_0_68) = all_83_0_76, member(all_10_8_12, all_31_0_68) = 0, yields:
% 12.15/3.41 | (330) all_83_0_76 = 0
% 12.15/3.41 |
% 12.15/3.41 +-Applying beta-rule and splitting (325), into two cases.
% 12.15/3.41 |-Branch one:
% 12.15/3.41 | (343) ~ (all_83_0_76 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (330) can reduce 343 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (330) all_83_0_76 = 0
% 12.15/3.41 | (346) ~ (all_83_1_77 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (341) can reduce 346 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (337) member(all_10_7_11, all_0_2_2) = all_83_1_77 & member(all_10_8_12, all_0_2_2) = all_83_0_76 & ( ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0))
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (337) yields:
% 12.15/3.41 | (338) member(all_10_7_11, all_0_2_2) = all_83_1_77
% 12.15/3.41 | (339) member(all_10_8_12, all_0_2_2) = all_83_0_76
% 12.15/3.41 | (325) ~ (all_83_0_76 = 0) | ~ (all_83_1_77 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_88_1_79, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_88_1_79, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.41 | (327) all_88_1_79 = 0
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_83_1_77, all_88_1_79 and discharging atoms member(all_10_7_11, all_0_2_2) = all_88_1_79, member(all_10_7_11, all_0_2_2) = all_83_1_77, yields:
% 12.15/3.41 | (370) all_88_1_79 = all_83_1_77
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_88_0_78, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_88_0_78, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.41 | (328) all_88_0_78 = 0
% 12.15/3.41 |
% 12.15/3.41 | Combining equations (327,370) yields a new equation:
% 12.15/3.41 | (341) all_83_1_77 = 0
% 12.15/3.41 |
% 12.15/3.41 | Combining equations (341,370) yields a new equation:
% 12.15/3.41 | (327) all_88_1_79 = 0
% 12.15/3.41 |
% 12.15/3.41 +-Applying beta-rule and splitting (319), into two cases.
% 12.15/3.41 |-Branch one:
% 12.15/3.41 | (332) ~ (all_88_0_78 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (328) can reduce 332 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (328) all_88_0_78 = 0
% 12.15/3.41 | (335) ~ (all_88_1_79 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (327) can reduce 335 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (379) ~ (all_35_3_73 = all_33_0_69)
% 12.15/3.41 | (380) ? [v0] : ( ~ (v0 = 0) & member(all_10_7_11, all_35_3_73) = v0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating (380) with all_79_0_80 yields:
% 12.15/3.41 | (381) ~ (all_79_0_80 = 0) & member(all_10_7_11, all_35_3_73) = all_79_0_80
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (381) yields:
% 12.15/3.41 | (382) ~ (all_79_0_80 = 0)
% 12.15/3.41 | (383) member(all_10_7_11, all_35_3_73) = all_79_0_80
% 12.15/3.41 |
% 12.15/3.41 | From (299) and (383) follows:
% 12.15/3.41 | (384) member(all_10_7_11, all_31_0_68) = all_79_0_80
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_7_11, all_31_0_68, 0, all_79_0_80 and discharging atoms member(all_10_7_11, all_31_0_68) = all_79_0_80, member(all_10_7_11, all_31_0_68) = 0, yields:
% 12.15/3.41 | (385) all_79_0_80 = 0
% 12.15/3.41 |
% 12.15/3.41 | Equations (385) can reduce 382 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (387) ~ (all_35_3_73 = all_31_0_68)
% 12.15/3.41 | (388) ? [v0] : ( ~ (v0 = 0) & member(all_10_8_12, all_35_3_73) = v0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating (388) with all_71_0_88 yields:
% 12.15/3.41 | (389) ~ (all_71_0_88 = 0) & member(all_10_8_12, all_35_3_73) = all_71_0_88
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (389) yields:
% 12.15/3.41 | (390) ~ (all_71_0_88 = 0)
% 12.15/3.41 | (391) member(all_10_8_12, all_35_3_73) = all_71_0_88
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_8_12, all_35_3_73, all_71_0_88, 0 and discharging atoms member(all_10_8_12, all_35_3_73) = all_71_0_88, member(all_10_8_12, all_35_3_73) = 0, yields:
% 12.15/3.41 | (392) all_71_0_88 = 0
% 12.15/3.41 |
% 12.15/3.41 | Equations (392) can reduce 390 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (394) member(all_10_7_11, all_0_2_2) = all_35_2_72 & member(all_10_8_12, all_0_2_2) = all_35_3_73 & ( ~ (all_35_2_72 = 0) | ~ (all_35_3_73 = 0))
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (394) yields:
% 12.15/3.41 | (395) member(all_10_7_11, all_0_2_2) = all_35_2_72
% 12.15/3.41 | (396) member(all_10_8_12, all_0_2_2) = all_35_3_73
% 12.15/3.41 | (397) ~ (all_35_2_72 = 0) | ~ (all_35_3_73 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_7_11, all_0_2_2, all_35_2_72, 0 and discharging atoms member(all_10_7_11, all_0_2_2) = all_35_2_72, member(all_10_7_11, all_0_2_2) = 0, yields:
% 12.15/3.41 | (267) all_35_2_72 = 0
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_35_3_73, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_35_3_73, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.41 | (399) all_35_3_73 = 0
% 12.15/3.41 |
% 12.15/3.41 +-Applying beta-rule and splitting (397), into two cases.
% 12.15/3.41 |-Branch one:
% 12.15/3.41 | (400) ~ (all_35_2_72 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (267) can reduce 400 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (267) all_35_2_72 = 0
% 12.15/3.41 | (403) ~ (all_35_3_73 = 0)
% 12.15/3.41 |
% 12.15/3.41 | Equations (399) can reduce 403 to:
% 12.15/3.41 | (63) $false
% 12.15/3.41 |
% 12.15/3.41 |-The branch is then unsatisfiable
% 12.15/3.41 |-Branch two:
% 12.15/3.41 | (405) all_10_7_11 = 0 & ~ (all_10_6_10 = 0) & apply(all_0_1_1, all_10_8_12, all_10_8_12) = all_10_6_10 & member(all_10_8_12, all_0_2_2) = 0
% 12.15/3.41 |
% 12.15/3.41 | Applying alpha-rule on (405) yields:
% 12.15/3.41 | (406) all_10_7_11 = 0
% 12.15/3.41 | (407) ~ (all_10_6_10 = 0)
% 12.15/3.41 | (408) apply(all_0_1_1, all_10_8_12, all_10_8_12) = all_10_6_10
% 12.15/3.41 | (69) member(all_10_8_12, all_0_2_2) = 0
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (12) with all_10_8_12, all_0_2_2, all_0_3_3 and discharging atoms partition(all_0_3_3, all_0_2_2) = 0, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.41 | (86) ? [v0] : (member(v0, all_0_3_3) = 0 & member(all_10_8_12, v0) = 0)
% 12.15/3.41 |
% 12.15/3.41 | Instantiating formula (46) with all_0_2_2, all_10_6_10, all_10_8_12, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_8_12) = all_10_6_10, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.15/3.41 | (411) all_10_6_10 = 0 | ? [v0] : ? [v1] : ((member(all_10_8_12, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.30/3.41 |
% 12.30/3.41 | Instantiating (86) with all_31_0_99 yields:
% 12.30/3.41 | (412) member(all_31_0_99, all_0_3_3) = 0 & member(all_10_8_12, all_31_0_99) = 0
% 12.30/3.41 |
% 12.30/3.41 | Applying alpha-rule on (412) yields:
% 12.30/3.41 | (413) member(all_31_0_99, all_0_3_3) = 0
% 12.30/3.41 | (414) member(all_10_8_12, all_31_0_99) = 0
% 12.30/3.41 |
% 12.30/3.41 +-Applying beta-rule and splitting (411), into two cases.
% 12.30/3.41 |-Branch one:
% 12.30/3.41 | (251) all_10_6_10 = 0
% 12.30/3.41 |
% 12.30/3.41 | Equations (251) can reduce 407 to:
% 12.30/3.41 | (63) $false
% 12.30/3.41 |
% 12.30/3.41 |-The branch is then unsatisfiable
% 12.30/3.41 |-Branch two:
% 12.30/3.41 | (407) ~ (all_10_6_10 = 0)
% 12.30/3.41 | (418) ? [v0] : ? [v1] : ((member(all_10_8_12, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_0_2_2, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.30/3.41 |
% 12.30/3.41 | Instantiating (418) with all_37_0_100, all_37_1_101 yields:
% 12.30/3.41 | (419) (member(all_10_8_12, all_0_2_2) = all_37_0_100 & member(all_10_8_12, all_0_2_2) = all_37_1_101 & ( ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0))) | (member(all_10_8_12, all_0_2_2) = all_37_0_100 & member(all_0_2_2, all_0_3_3) = all_37_1_101 & ( ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0)))
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (419), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (420) member(all_10_8_12, all_0_2_2) = all_37_0_100 & member(all_10_8_12, all_0_2_2) = all_37_1_101 & ( ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0))
% 12.30/3.42 |
% 12.30/3.42 | Applying alpha-rule on (420) yields:
% 12.30/3.42 | (421) member(all_10_8_12, all_0_2_2) = all_37_0_100
% 12.30/3.42 | (422) member(all_10_8_12, all_0_2_2) = all_37_1_101
% 12.30/3.42 | (423) ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_37_0_100, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_37_0_100, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.30/3.42 | (424) all_37_0_100 = 0
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_37_1_101, all_37_0_100 and discharging atoms member(all_10_8_12, all_0_2_2) = all_37_0_100, member(all_10_8_12, all_0_2_2) = all_37_1_101, yields:
% 12.30/3.42 | (425) all_37_0_100 = all_37_1_101
% 12.30/3.42 |
% 12.30/3.42 | Combining equations (424,425) yields a new equation:
% 12.30/3.42 | (426) all_37_1_101 = 0
% 12.30/3.42 |
% 12.30/3.42 | Combining equations (426,425) yields a new equation:
% 12.30/3.42 | (424) all_37_0_100 = 0
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (423), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (428) ~ (all_37_0_100 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (424) can reduce 428 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (424) all_37_0_100 = 0
% 12.30/3.42 | (431) ~ (all_37_1_101 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (426) can reduce 431 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (433) member(all_10_8_12, all_0_2_2) = all_37_0_100 & member(all_0_2_2, all_0_3_3) = all_37_1_101 & ( ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0))
% 12.30/3.42 |
% 12.30/3.42 | Applying alpha-rule on (433) yields:
% 12.30/3.42 | (421) member(all_10_8_12, all_0_2_2) = all_37_0_100
% 12.30/3.42 | (435) member(all_0_2_2, all_0_3_3) = all_37_1_101
% 12.30/3.42 | (423) ~ (all_37_0_100 = 0) | ~ (all_37_1_101 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_37_0_100, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_37_0_100, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.30/3.42 | (424) all_37_0_100 = 0
% 12.30/3.42 |
% 12.30/3.42 | From (424) and (421) follows:
% 12.30/3.42 | (69) member(all_10_8_12, all_0_2_2) = 0
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (46) with all_31_0_99, all_10_6_10, all_10_8_12, all_10_8_12 and discharging atoms apply(all_0_1_1, all_10_8_12, all_10_8_12) = all_10_6_10, member(all_10_8_12, all_31_0_99) = 0, yields:
% 12.30/3.42 | (439) all_10_6_10 = 0 | ? [v0] : ? [v1] : ((member(all_31_0_99, all_0_3_3) = v0 & member(all_10_8_12, all_31_0_99) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (439), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (251) all_10_6_10 = 0
% 12.30/3.42 |
% 12.30/3.42 | Equations (251) can reduce 407 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (407) ~ (all_10_6_10 = 0)
% 12.30/3.42 | (443) ? [v0] : ? [v1] : ((member(all_31_0_99, all_0_3_3) = v0 & member(all_10_8_12, all_31_0_99) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_10_8_12, all_0_2_2) = v1 & member(all_10_8_12, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 12.30/3.42 |
% 12.30/3.42 | Instantiating (443) with all_65_0_102, all_65_1_103 yields:
% 12.30/3.42 | (444) (member(all_31_0_99, all_0_3_3) = all_65_1_103 & member(all_10_8_12, all_31_0_99) = all_65_0_102 & ( ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0))) | (member(all_10_8_12, all_0_2_2) = all_65_0_102 & member(all_10_8_12, all_0_2_2) = all_65_1_103 & ( ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0)))
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (444), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (445) member(all_31_0_99, all_0_3_3) = all_65_1_103 & member(all_10_8_12, all_31_0_99) = all_65_0_102 & ( ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0))
% 12.30/3.42 |
% 12.30/3.42 | Applying alpha-rule on (445) yields:
% 12.30/3.42 | (446) member(all_31_0_99, all_0_3_3) = all_65_1_103
% 12.30/3.42 | (447) member(all_10_8_12, all_31_0_99) = all_65_0_102
% 12.30/3.42 | (448) ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_31_0_99, all_0_3_3, all_65_1_103, 0 and discharging atoms member(all_31_0_99, all_0_3_3) = all_65_1_103, member(all_31_0_99, all_0_3_3) = 0, yields:
% 12.30/3.42 | (449) all_65_1_103 = 0
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_31_0_99, all_65_0_102, 0 and discharging atoms member(all_10_8_12, all_31_0_99) = all_65_0_102, member(all_10_8_12, all_31_0_99) = 0, yields:
% 12.30/3.42 | (450) all_65_0_102 = 0
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (448), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (451) ~ (all_65_0_102 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (450) can reduce 451 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (450) all_65_0_102 = 0
% 12.30/3.42 | (454) ~ (all_65_1_103 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (449) can reduce 454 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (456) member(all_10_8_12, all_0_2_2) = all_65_0_102 & member(all_10_8_12, all_0_2_2) = all_65_1_103 & ( ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0))
% 12.30/3.42 |
% 12.30/3.42 | Applying alpha-rule on (456) yields:
% 12.30/3.42 | (457) member(all_10_8_12, all_0_2_2) = all_65_0_102
% 12.30/3.42 | (458) member(all_10_8_12, all_0_2_2) = all_65_1_103
% 12.30/3.42 | (448) ~ (all_65_0_102 = 0) | ~ (all_65_1_103 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_65_0_102, 0 and discharging atoms member(all_10_8_12, all_0_2_2) = all_65_0_102, member(all_10_8_12, all_0_2_2) = 0, yields:
% 12.30/3.42 | (450) all_65_0_102 = 0
% 12.30/3.42 |
% 12.30/3.42 | Instantiating formula (14) with all_10_8_12, all_0_2_2, all_65_1_103, all_65_0_102 and discharging atoms member(all_10_8_12, all_0_2_2) = all_65_0_102, member(all_10_8_12, all_0_2_2) = all_65_1_103, yields:
% 12.30/3.42 | (461) all_65_0_102 = all_65_1_103
% 12.30/3.42 |
% 12.30/3.42 | Combining equations (450,461) yields a new equation:
% 12.30/3.42 | (449) all_65_1_103 = 0
% 12.30/3.42 |
% 12.30/3.42 | Combining equations (449,461) yields a new equation:
% 12.30/3.42 | (450) all_65_0_102 = 0
% 12.30/3.42 |
% 12.30/3.42 +-Applying beta-rule and splitting (448), into two cases.
% 12.30/3.42 |-Branch one:
% 12.30/3.42 | (451) ~ (all_65_0_102 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (450) can reduce 451 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 |-Branch two:
% 12.30/3.42 | (450) all_65_0_102 = 0
% 12.30/3.42 | (454) ~ (all_65_1_103 = 0)
% 12.30/3.42 |
% 12.30/3.42 | Equations (449) can reduce 454 to:
% 12.30/3.42 | (63) $false
% 12.30/3.42 |
% 12.30/3.42 |-The branch is then unsatisfiable
% 12.30/3.42 % SZS output end Proof for theBenchmark
% 12.30/3.42
% 12.30/3.42 2796ms
%------------------------------------------------------------------------------