TSTP Solution File: SET765+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET765+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:21:55 EDT 2022
% Result : Theorem 4.54s 1.63s
% Output : Proof 6.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET765+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 01:04:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.58 ____ _
% 0.57/0.58 ___ / __ \_____(_)___ ________ __________
% 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.58
% 0.57/0.58 A Theorem Prover for First-Order Logic
% 0.57/0.58 (ePrincess v.1.0)
% 0.57/0.58
% 0.57/0.58 (c) Philipp Rümmer, 2009-2015
% 0.57/0.58 (c) Peter Backeman, 2014-2015
% 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58 Bug reports to peter@backeman.se
% 0.57/0.58
% 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58
% 0.57/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.92 Prover 0: Preprocessing ...
% 2.55/1.16 Prover 0: Warning: ignoring some quantifiers
% 2.66/1.19 Prover 0: Constructing countermodel ...
% 3.10/1.34 Prover 0: gave up
% 3.10/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.36/1.38 Prover 1: Preprocessing ...
% 4.17/1.55 Prover 1: Constructing countermodel ...
% 4.54/1.63 Prover 1: proved (290ms)
% 4.54/1.63
% 4.54/1.63 No countermodel exists, formula is valid
% 4.54/1.63 % SZS status Theorem for theBenchmark
% 4.54/1.63
% 4.54/1.63 Generating proof ... found it (size 77)
% 6.14/2.03
% 6.14/2.03 % SZS output start Proof for theBenchmark
% 6.14/2.03 Assumed formulas after preprocessing and simplification:
% 6.14/2.03 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & equivalence(v1, v2) = v3 & equivalence(v1, v0) = 0 & subset(v2, v0) = 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] : (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] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) & ! [v4] : ~ (member(v4, empty_set) = 0))
% 6.53/2.08 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 6.53/2.08 | (1) ~ (all_0_0_0 = 0) & equivalence(all_0_2_2, all_0_1_1) = all_0_0_0 & equivalence(all_0_2_2, all_0_3_3) = 0 & subset(all_0_1_1, all_0_3_3) = 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] : (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] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.58/2.11 |
% 6.58/2.11 | Applying alpha-rule on (1) yields:
% 6.58/2.11 | (2) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 6.58/2.11 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.58/2.11 | (4) subset(all_0_1_1, all_0_3_3) = 0
% 6.58/2.11 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 6.58/2.11 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 6.58/2.11 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.58/2.11 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 6.58/2.11 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.58/2.11 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.58/2.11 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 6.58/2.11 | (12) equivalence(all_0_2_2, all_0_1_1) = all_0_0_0
% 6.58/2.11 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 6.58/2.11 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 6.58/2.11 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.58/2.11 | (16) ~ (all_0_0_0 = 0)
% 6.58/2.11 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0))
% 6.58/2.11 | (18) ! [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)))
% 6.58/2.11 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.71/2.11 | (20) ! [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)))
% 6.71/2.12 | (21) ! [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))))
% 6.71/2.12 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 6.71/2.12 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.71/2.12 | (24) equivalence(all_0_2_2, all_0_3_3) = 0
% 6.71/2.12 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.71/2.12 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 6.71/2.12 | (27) ! [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))))
% 6.71/2.12 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 6.71/2.12 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.71/2.12 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 6.71/2.12 | (31) ! [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)))
% 6.71/2.12 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 6.71/2.12 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 6.71/2.12 | (34) ! [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))))
% 6.71/2.12 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 6.71/2.13 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 6.71/2.13 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 6.71/2.13 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 6.71/2.13 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 6.71/2.13 | (40) ! [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))
% 6.71/2.13 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 6.71/2.13 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.71/2.13 | (43) ! [v0] : ~ (member(v0, empty_set) = 0)
% 6.71/2.13 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0))
% 6.71/2.13 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 6.71/2.13 | (46) ! [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)))))
% 6.71/2.13 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 6.71/2.13 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 6.71/2.13 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 6.71/2.13 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 6.71/2.13 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 6.71/2.13 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 6.71/2.13 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 6.71/2.13 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 6.71/2.13 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0))
% 6.71/2.13 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.71/2.13 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 6.71/2.13 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0))
% 6.71/2.13 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 6.71/2.13 |
% 6.71/2.13 | Instantiating formula (31) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms equivalence(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 6.71/2.13 | (60) 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_2_2, v1, v2) = 0 & apply(all_0_2_2, v0, v2) = v8 & apply(all_0_2_2, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_2_2, v1, v0) = v5 & apply(all_0_2_2, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_2_2, v0, v0) = v2 & member(v0, all_0_1_1) = 0))
% 6.71/2.13 |
% 6.71/2.13 +-Applying beta-rule and splitting (60), into two cases.
% 6.71/2.13 |-Branch one:
% 6.71/2.13 | (61) all_0_0_0 = 0
% 6.71/2.13 |
% 6.71/2.14 | Equations (61) can reduce 16 to:
% 6.71/2.14 | (62) $false
% 6.71/2.14 |
% 6.71/2.14 |-The branch is then unsatisfiable
% 6.71/2.14 |-Branch two:
% 6.71/2.14 | (16) ~ (all_0_0_0 = 0)
% 6.71/2.14 | (64) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_2_2, v1, v2) = 0 & apply(all_0_2_2, v0, v2) = v8 & apply(all_0_2_2, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(all_0_2_2, v1, v0) = v5 & apply(all_0_2_2, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_2_2, v0, v0) = v2 & member(v0, all_0_1_1) = 0))
% 6.71/2.14 |
% 6.71/2.14 | Instantiating (64) with all_14_0_4, all_14_1_5, all_14_2_6, all_14_3_7, all_14_4_8, all_14_5_9, all_14_6_10, all_14_7_11, all_14_8_12 yields:
% 6.71/2.14 | (65) (all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0 & apply(all_0_2_2, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_3_7 = 0) & apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_14_3_7 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_7_11 = 0 & ~ (all_14_6_10 = 0) & apply(all_0_2_2, all_14_8_12, all_14_8_12) = all_14_6_10 & member(all_14_8_12, all_0_1_1) = 0)
% 6.71/2.14 |
% 6.71/2.14 +-Applying beta-rule and splitting (65), into two cases.
% 6.71/2.14 |-Branch one:
% 6.71/2.14 | (66) (all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0 & apply(all_0_2_2, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_3_7 = 0) & apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_14_3_7 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0)
% 6.71/2.14 |
% 6.71/2.14 +-Applying beta-rule and splitting (66), into two cases.
% 6.71/2.14 |-Branch one:
% 6.71/2.14 | (67) all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0 & apply(all_0_2_2, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.14 |
% 6.83/2.14 | Applying alpha-rule on (67) yields:
% 6.83/2.14 | (68) all_14_3_7 = 0
% 6.83/2.14 | (69) all_14_2_6 = 0
% 6.83/2.14 | (70) all_14_5_9 = 0
% 6.83/2.14 | (71) all_14_1_5 = 0
% 6.83/2.14 | (72) member(all_14_7_11, all_0_1_1) = 0
% 6.83/2.14 | (73) ~ (all_14_0_4 = 0)
% 6.83/2.14 | (74) apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0
% 6.83/2.14 | (75) member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.14 | (76) apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0
% 6.83/2.14 | (77) all_14_4_8 = 0
% 6.83/2.14 | (78) apply(all_0_2_2, all_14_8_12, all_14_6_10) = all_14_0_4
% 6.83/2.14 | (79) member(all_14_6_10, all_0_1_1) = 0
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (18) with all_14_6_10, all_14_7_11, all_0_2_2, all_0_3_3 and discharging atoms equivalence(all_0_2_2, all_0_3_3) = 0, apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0, yields:
% 6.83/2.14 | (80) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_2_2, all_14_6_10, all_14_7_11) = v2 & member(all_14_6_10, all_0_3_3) = v1 & member(all_14_7_11, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (21) with all_14_0_4, all_14_6_10, all_14_7_11, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms equivalence(all_0_2_2, all_0_3_3) = 0, apply(all_0_2_2, all_14_8_12, all_14_6_10) = all_14_0_4, apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0, yields:
% 6.83/2.14 | (81) all_14_0_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_2_2, all_14_7_11, all_14_6_10) = v3 & member(all_14_6_10, all_0_3_3) = v2 & member(all_14_7_11, all_0_3_3) = v1 & member(all_14_8_12, all_0_3_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (18) with all_14_7_11, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms equivalence(all_0_2_2, all_0_3_3) = 0, apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0, yields:
% 6.83/2.14 | (82) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_2_2, all_14_7_11, all_14_8_12) = v2 & member(all_14_7_11, all_0_3_3) = v1 & member(all_14_8_12, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (57) with all_14_6_10, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_6_10, all_0_1_1) = 0, yields:
% 6.83/2.14 | (83) member(all_14_6_10, all_0_3_3) = 0
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (57) with all_14_7_11, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_7_11, all_0_1_1) = 0, yields:
% 6.83/2.14 | (84) member(all_14_7_11, all_0_3_3) = 0
% 6.83/2.14 |
% 6.83/2.14 | Instantiating formula (57) with all_14_8_12, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_8_12, all_0_1_1) = 0, yields:
% 6.83/2.14 | (85) member(all_14_8_12, all_0_3_3) = 0
% 6.83/2.14 |
% 6.83/2.14 | Instantiating (82) with all_40_0_13, all_40_1_14, all_40_2_15 yields:
% 6.83/2.14 | (86) apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_40_0_13 & member(all_14_7_11, all_0_3_3) = all_40_1_14 & member(all_14_8_12, all_0_3_3) = all_40_2_15 & ( ~ (all_40_1_14 = 0) | ~ (all_40_2_15 = 0) | all_40_0_13 = 0)
% 6.83/2.14 |
% 6.83/2.14 | Applying alpha-rule on (86) yields:
% 6.83/2.14 | (87) apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_40_0_13
% 6.83/2.14 | (88) member(all_14_7_11, all_0_3_3) = all_40_1_14
% 6.83/2.14 | (89) member(all_14_8_12, all_0_3_3) = all_40_2_15
% 6.83/2.14 | (90) ~ (all_40_1_14 = 0) | ~ (all_40_2_15 = 0) | all_40_0_13 = 0
% 6.83/2.14 |
% 6.83/2.14 | Instantiating (80) with all_42_0_16, all_42_1_17, all_42_2_18 yields:
% 6.83/2.14 | (91) apply(all_0_2_2, all_14_6_10, all_14_7_11) = all_42_0_16 & member(all_14_6_10, all_0_3_3) = all_42_1_17 & member(all_14_7_11, all_0_3_3) = all_42_2_18 & ( ~ (all_42_1_17 = 0) | ~ (all_42_2_18 = 0) | all_42_0_16 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Applying alpha-rule on (91) yields:
% 6.83/2.15 | (92) apply(all_0_2_2, all_14_6_10, all_14_7_11) = all_42_0_16
% 6.83/2.15 | (93) member(all_14_6_10, all_0_3_3) = all_42_1_17
% 6.83/2.15 | (94) member(all_14_7_11, all_0_3_3) = all_42_2_18
% 6.83/2.15 | (95) ~ (all_42_1_17 = 0) | ~ (all_42_2_18 = 0) | all_42_0_16 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_6_10, all_0_3_3, 0, all_42_1_17 and discharging atoms member(all_14_6_10, all_0_3_3) = all_42_1_17, member(all_14_6_10, all_0_3_3) = 0, yields:
% 6.83/2.15 | (96) all_42_1_17 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_7_11, all_0_3_3, all_42_2_18, 0 and discharging atoms member(all_14_7_11, all_0_3_3) = all_42_2_18, member(all_14_7_11, all_0_3_3) = 0, yields:
% 6.83/2.15 | (97) all_42_2_18 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_7_11, all_0_3_3, all_40_1_14, all_42_2_18 and discharging atoms member(all_14_7_11, all_0_3_3) = all_42_2_18, member(all_14_7_11, all_0_3_3) = all_40_1_14, yields:
% 6.83/2.15 | (98) all_42_2_18 = all_40_1_14
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_8_12, all_0_3_3, all_40_2_15, 0 and discharging atoms member(all_14_8_12, all_0_3_3) = all_40_2_15, member(all_14_8_12, all_0_3_3) = 0, yields:
% 6.83/2.15 | (99) all_40_2_15 = 0
% 6.83/2.15 |
% 6.83/2.15 | Combining equations (97,98) yields a new equation:
% 6.83/2.15 | (100) all_40_1_14 = 0
% 6.83/2.15 |
% 6.83/2.15 | From (96) and (93) follows:
% 6.83/2.15 | (83) member(all_14_6_10, all_0_3_3) = 0
% 6.83/2.15 |
% 6.83/2.15 | From (100) and (88) follows:
% 6.83/2.15 | (84) member(all_14_7_11, all_0_3_3) = 0
% 6.83/2.15 |
% 6.83/2.15 | From (99) and (89) follows:
% 6.83/2.15 | (85) member(all_14_8_12, all_0_3_3) = 0
% 6.83/2.15 |
% 6.83/2.15 +-Applying beta-rule and splitting (81), into two cases.
% 6.83/2.15 |-Branch one:
% 6.83/2.15 | (104) all_14_0_4 = 0
% 6.83/2.15 |
% 6.83/2.15 | Equations (104) can reduce 73 to:
% 6.83/2.15 | (62) $false
% 6.83/2.15 |
% 6.83/2.15 |-The branch is then unsatisfiable
% 6.83/2.15 |-Branch two:
% 6.83/2.15 | (73) ~ (all_14_0_4 = 0)
% 6.83/2.15 | (107) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_2_2, all_14_7_11, all_14_6_10) = v3 & member(all_14_6_10, all_0_3_3) = v2 & member(all_14_7_11, all_0_3_3) = v1 & member(all_14_8_12, all_0_3_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 6.83/2.15 |
% 6.83/2.15 | Instantiating (107) with all_56_0_19, all_56_1_20, all_56_2_21, all_56_3_22 yields:
% 6.83/2.15 | (108) apply(all_0_2_2, all_14_7_11, all_14_6_10) = all_56_0_19 & member(all_14_6_10, all_0_3_3) = all_56_1_20 & member(all_14_7_11, all_0_3_3) = all_56_2_21 & member(all_14_8_12, all_0_3_3) = all_56_3_22 & ( ~ (all_56_0_19 = 0) | ~ (all_56_1_20 = 0) | ~ (all_56_2_21 = 0) | ~ (all_56_3_22 = 0))
% 6.83/2.15 |
% 6.83/2.15 | Applying alpha-rule on (108) yields:
% 6.83/2.15 | (109) member(all_14_6_10, all_0_3_3) = all_56_1_20
% 6.83/2.15 | (110) member(all_14_7_11, all_0_3_3) = all_56_2_21
% 6.83/2.15 | (111) member(all_14_8_12, all_0_3_3) = all_56_3_22
% 6.83/2.15 | (112) ~ (all_56_0_19 = 0) | ~ (all_56_1_20 = 0) | ~ (all_56_2_21 = 0) | ~ (all_56_3_22 = 0)
% 6.83/2.15 | (113) apply(all_0_2_2, all_14_7_11, all_14_6_10) = all_56_0_19
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (49) with all_0_2_2, all_14_7_11, all_14_6_10, all_56_0_19, 0 and discharging atoms apply(all_0_2_2, all_14_7_11, all_14_6_10) = all_56_0_19, apply(all_0_2_2, all_14_7_11, all_14_6_10) = 0, yields:
% 6.83/2.15 | (114) all_56_0_19 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_6_10, all_0_3_3, all_56_1_20, 0 and discharging atoms member(all_14_6_10, all_0_3_3) = all_56_1_20, member(all_14_6_10, all_0_3_3) = 0, yields:
% 6.83/2.15 | (115) all_56_1_20 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_7_11, all_0_3_3, all_56_2_21, 0 and discharging atoms member(all_14_7_11, all_0_3_3) = all_56_2_21, member(all_14_7_11, all_0_3_3) = 0, yields:
% 6.83/2.15 | (116) all_56_2_21 = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (56) with all_14_8_12, all_0_3_3, all_56_3_22, 0 and discharging atoms member(all_14_8_12, all_0_3_3) = all_56_3_22, member(all_14_8_12, all_0_3_3) = 0, yields:
% 6.83/2.15 | (117) all_56_3_22 = 0
% 6.83/2.15 |
% 6.83/2.15 +-Applying beta-rule and splitting (112), into two cases.
% 6.83/2.15 |-Branch one:
% 6.83/2.15 | (118) ~ (all_56_0_19 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Equations (114) can reduce 118 to:
% 6.83/2.15 | (62) $false
% 6.83/2.15 |
% 6.83/2.15 |-The branch is then unsatisfiable
% 6.83/2.15 |-Branch two:
% 6.83/2.15 | (114) all_56_0_19 = 0
% 6.83/2.15 | (121) ~ (all_56_1_20 = 0) | ~ (all_56_2_21 = 0) | ~ (all_56_3_22 = 0)
% 6.83/2.15 |
% 6.83/2.15 +-Applying beta-rule and splitting (121), into two cases.
% 6.83/2.15 |-Branch one:
% 6.83/2.15 | (122) ~ (all_56_1_20 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Equations (115) can reduce 122 to:
% 6.83/2.15 | (62) $false
% 6.83/2.15 |
% 6.83/2.15 |-The branch is then unsatisfiable
% 6.83/2.15 |-Branch two:
% 6.83/2.15 | (115) all_56_1_20 = 0
% 6.83/2.15 | (125) ~ (all_56_2_21 = 0) | ~ (all_56_3_22 = 0)
% 6.83/2.15 |
% 6.83/2.15 +-Applying beta-rule and splitting (125), into two cases.
% 6.83/2.15 |-Branch one:
% 6.83/2.15 | (126) ~ (all_56_2_21 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Equations (116) can reduce 126 to:
% 6.83/2.15 | (62) $false
% 6.83/2.15 |
% 6.83/2.15 |-The branch is then unsatisfiable
% 6.83/2.15 |-Branch two:
% 6.83/2.15 | (116) all_56_2_21 = 0
% 6.83/2.15 | (129) ~ (all_56_3_22 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Equations (117) can reduce 129 to:
% 6.83/2.15 | (62) $false
% 6.83/2.15 |
% 6.83/2.15 |-The branch is then unsatisfiable
% 6.83/2.15 |-Branch two:
% 6.83/2.15 | (131) all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_3_7 = 0) & apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_14_3_7 & apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.15 |
% 6.83/2.15 | Applying alpha-rule on (131) yields:
% 6.83/2.15 | (132) ~ (all_14_3_7 = 0)
% 6.83/2.15 | (133) all_14_6_10 = 0
% 6.83/2.15 | (70) all_14_5_9 = 0
% 6.83/2.15 | (72) member(all_14_7_11, all_0_1_1) = 0
% 6.83/2.15 | (75) member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.15 | (76) apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0
% 6.83/2.15 | (77) all_14_4_8 = 0
% 6.83/2.15 | (139) apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_14_3_7
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (18) with all_14_7_11, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms equivalence(all_0_2_2, all_0_3_3) = 0, apply(all_0_2_2, all_14_8_12, all_14_7_11) = 0, yields:
% 6.83/2.15 | (82) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_2_2, all_14_7_11, all_14_8_12) = v2 & member(all_14_7_11, all_0_3_3) = v1 & member(all_14_8_12, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (57) with all_14_7_11, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_7_11, all_0_1_1) = 0, yields:
% 6.83/2.15 | (84) member(all_14_7_11, all_0_3_3) = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating formula (57) with all_14_8_12, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_8_12, all_0_1_1) = 0, yields:
% 6.83/2.15 | (85) member(all_14_8_12, all_0_3_3) = 0
% 6.83/2.15 |
% 6.83/2.15 | Instantiating (82) with all_40_0_23, all_40_1_24, all_40_2_25 yields:
% 6.83/2.15 | (143) apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_40_0_23 & member(all_14_7_11, all_0_3_3) = all_40_1_24 & member(all_14_8_12, all_0_3_3) = all_40_2_25 & ( ~ (all_40_1_24 = 0) | ~ (all_40_2_25 = 0) | all_40_0_23 = 0)
% 6.83/2.15 |
% 6.83/2.15 | Applying alpha-rule on (143) yields:
% 6.83/2.15 | (144) apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_40_0_23
% 6.83/2.15 | (145) member(all_14_7_11, all_0_3_3) = all_40_1_24
% 6.83/2.15 | (146) member(all_14_8_12, all_0_3_3) = all_40_2_25
% 6.83/2.16 | (147) ~ (all_40_1_24 = 0) | ~ (all_40_2_25 = 0) | all_40_0_23 = 0
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (49) with all_0_2_2, all_14_7_11, all_14_8_12, all_40_0_23, all_14_3_7 and discharging atoms apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_40_0_23, apply(all_0_2_2, all_14_7_11, all_14_8_12) = all_14_3_7, yields:
% 6.83/2.16 | (148) all_40_0_23 = all_14_3_7
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (56) with all_14_7_11, all_0_3_3, 0, all_40_1_24 and discharging atoms member(all_14_7_11, all_0_3_3) = all_40_1_24, member(all_14_7_11, all_0_3_3) = 0, yields:
% 6.83/2.16 | (149) all_40_1_24 = 0
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (56) with all_14_8_12, all_0_3_3, all_40_2_25, 0 and discharging atoms member(all_14_8_12, all_0_3_3) = all_40_2_25, member(all_14_8_12, all_0_3_3) = 0, yields:
% 6.83/2.16 | (150) all_40_2_25 = 0
% 6.83/2.16 |
% 6.83/2.16 +-Applying beta-rule and splitting (147), into two cases.
% 6.83/2.16 |-Branch one:
% 6.83/2.16 | (151) ~ (all_40_1_24 = 0)
% 6.83/2.16 |
% 6.83/2.16 | Equations (149) can reduce 151 to:
% 6.83/2.16 | (62) $false
% 6.83/2.16 |
% 6.83/2.16 |-The branch is then unsatisfiable
% 6.83/2.16 |-Branch two:
% 6.83/2.16 | (149) all_40_1_24 = 0
% 6.83/2.16 | (154) ~ (all_40_2_25 = 0) | all_40_0_23 = 0
% 6.83/2.16 |
% 6.83/2.16 +-Applying beta-rule and splitting (154), into two cases.
% 6.83/2.16 |-Branch one:
% 6.83/2.16 | (155) ~ (all_40_2_25 = 0)
% 6.83/2.16 |
% 6.83/2.16 | Equations (150) can reduce 155 to:
% 6.83/2.16 | (62) $false
% 6.83/2.16 |
% 6.83/2.16 |-The branch is then unsatisfiable
% 6.83/2.16 |-Branch two:
% 6.83/2.16 | (150) all_40_2_25 = 0
% 6.83/2.16 | (158) all_40_0_23 = 0
% 6.83/2.16 |
% 6.83/2.16 | Combining equations (158,148) yields a new equation:
% 6.83/2.16 | (68) all_14_3_7 = 0
% 6.83/2.16 |
% 6.83/2.16 | Equations (68) can reduce 132 to:
% 6.83/2.16 | (62) $false
% 6.83/2.16 |
% 6.83/2.16 |-The branch is then unsatisfiable
% 6.83/2.16 |-Branch two:
% 6.83/2.16 | (161) all_14_7_11 = 0 & ~ (all_14_6_10 = 0) & apply(all_0_2_2, all_14_8_12, all_14_8_12) = all_14_6_10 & member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.16 |
% 6.83/2.16 | Applying alpha-rule on (161) yields:
% 6.83/2.16 | (162) all_14_7_11 = 0
% 6.83/2.16 | (163) ~ (all_14_6_10 = 0)
% 6.83/2.16 | (164) apply(all_0_2_2, all_14_8_12, all_14_8_12) = all_14_6_10
% 6.83/2.16 | (75) member(all_14_8_12, all_0_1_1) = 0
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (37) with all_14_6_10, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms equivalence(all_0_2_2, all_0_3_3) = 0, apply(all_0_2_2, all_14_8_12, all_14_8_12) = all_14_6_10, yields:
% 6.83/2.16 | (166) all_14_6_10 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_14_8_12, all_0_3_3) = v0)
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (57) with all_14_8_12, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = 0, member(all_14_8_12, all_0_1_1) = 0, yields:
% 6.83/2.16 | (85) member(all_14_8_12, all_0_3_3) = 0
% 6.83/2.16 |
% 6.83/2.16 +-Applying beta-rule and splitting (166), into two cases.
% 6.83/2.16 |-Branch one:
% 6.83/2.16 | (133) all_14_6_10 = 0
% 6.83/2.16 |
% 6.83/2.16 | Equations (133) can reduce 163 to:
% 6.83/2.16 | (62) $false
% 6.83/2.16 |
% 6.83/2.16 |-The branch is then unsatisfiable
% 6.83/2.16 |-Branch two:
% 6.83/2.16 | (163) ~ (all_14_6_10 = 0)
% 6.83/2.16 | (171) ? [v0] : ( ~ (v0 = 0) & member(all_14_8_12, all_0_3_3) = v0)
% 6.83/2.16 |
% 6.83/2.16 | Instantiating (171) with all_44_0_26 yields:
% 6.83/2.16 | (172) ~ (all_44_0_26 = 0) & member(all_14_8_12, all_0_3_3) = all_44_0_26
% 6.83/2.16 |
% 6.83/2.16 | Applying alpha-rule on (172) yields:
% 6.83/2.16 | (173) ~ (all_44_0_26 = 0)
% 6.83/2.16 | (174) member(all_14_8_12, all_0_3_3) = all_44_0_26
% 6.83/2.16 |
% 6.83/2.16 | Instantiating formula (56) with all_14_8_12, all_0_3_3, 0, all_44_0_26 and discharging atoms member(all_14_8_12, all_0_3_3) = all_44_0_26, member(all_14_8_12, all_0_3_3) = 0, yields:
% 6.83/2.16 | (175) all_44_0_26 = 0
% 6.83/2.16 |
% 6.83/2.16 | Equations (175) can reduce 173 to:
% 6.83/2.16 | (62) $false
% 6.83/2.16 |
% 6.83/2.16 |-The branch is then unsatisfiable
% 6.83/2.16 % SZS output end Proof for theBenchmark
% 6.83/2.16
% 6.83/2.16 1571ms
%------------------------------------------------------------------------------