TSTP Solution File: SET791+4 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 00:22:06 EDT 2022
% Result : Theorem 4.44s 1.67s
% Output : Proof 6.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.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 : Sun Jul 10 12:08:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.60/0.90 Prover 0: Preprocessing ...
% 1.94/1.07 Prover 0: Warning: ignoring some quantifiers
% 2.14/1.09 Prover 0: Constructing countermodel ...
% 3.35/1.45 Prover 0: gave up
% 3.35/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.67/1.48 Prover 1: Preprocessing ...
% 4.44/1.63 Prover 1: Constructing countermodel ...
% 4.44/1.67 Prover 1: proved (219ms)
% 4.44/1.67
% 4.44/1.67 No countermodel exists, formula is valid
% 4.44/1.67 % SZS status Theorem for theBenchmark
% 4.44/1.67
% 4.44/1.67 Generating proof ... found it (size 38)
% 5.72/1.93
% 5.72/1.93 % SZS output start Proof for theBenchmark
% 5.72/1.93 Assumed formulas after preprocessing and simplification:
% 5.72/1.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & max(v2, v0, v1) = v3 & greatest(v2, v0, v1) = 0 & order(v0, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (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] : (v5 = v4 | ~ (greatest_lower_bound(v9, v8, v7, v6) = v5) | ~ (greatest_lower_bound(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (least_upper_bound(v9, v8, v7, v6) = v5) | ~ (least_upper_bound(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (greatest_lower_bound(v4, v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & ~ (v12 = 0) & lower_bound(v9, v6, v5) = 0 & apply(v6, v9, v4) = v12 & member(v9, v7) = 0) | (lower_bound(v4, v6, v5) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (least_upper_bound(v4, v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & ~ (v12 = 0) & upper_bound(v9, v6, v5) = 0 & apply(v6, v4, v9) = v12 & member(v9, v7) = 0) | (upper_bound(v4, v6, v5) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (least(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (greatest(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (lower_bound(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (upper_bound(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (total_order(v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (apply(v4, v7, v6) = v11 & member(v7, v5) = v10 & member(v6, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (min(v8, v7, v6) = v5) | ~ (min(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (max(v8, v7, v6) = v5) | ~ (max(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (least(v8, v7, v6) = v5) | ~ (least(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (greatest(v8, v7, v6) = v5) | ~ (greatest(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (lower_bound(v8, v7, v6) = v5) | ~ (lower_bound(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (upper_bound(v8, v7, v6) = v5) | ~ (upper_bound(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] : ( ~ (greatest_lower_bound(v4, v5, v6, v7) = 0) | ~ (lower_bound(v8, v6, v5) = 0) | ? [v9] : ? [v10] : (apply(v6, v8, v4) = v10 & member(v8, v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (least_upper_bound(v4, v5, v6, v7) = 0) | ~ (upper_bound(v8, v6, v5) = 0) | ? [v9] : ? [v10] : (apply(v6, v4, v8) = v10 & member(v8, v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (min(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (max(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (order(v4, v5) = 0) | ~ (apply(v4, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (apply(v4, v7, v6) = v10 & member(v7, v5) = v9 & member(v6, v5) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (min(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & apply(v4, v8, v6) = 0 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (max(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & apply(v4, v6, v8) = 0 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (least(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & apply(v4, v6, v8) = v10 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (greatest(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & apply(v4, v8, v6) = v10 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lower_bound(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v4, v6, v8) = v9 & member(v8, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (upper_bound(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v4, v8, v6) = v9 & member(v8, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (order(v4, v5) = 0) | ~ (apply(v4, v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (total_order(v7, v6) = v5) | ~ (total_order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (order(v7, v6) = v5) | ~ (order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (greatest_lower_bound(v4, v5, v6, v7) = 0) | (lower_bound(v4, v6, v5) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (least_upper_bound(v4, v5, v6, v7) = 0) | (upper_bound(v4, v6, v5) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (total_order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & v9 = 0 & ~ (v12 = 0) & ~ (v11 = 0) & apply(v4, v8, v7) = v12 & apply(v4, v7, v8) = v11 & member(v8, v5) = 0 & member(v7, v5) = 0) | ( ~ (v7 = 0) & order(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (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) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v8 = v7) & apply(v4, v8, v7) = 0 & apply(v4, v7, v8) = 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] : ( ~ (min(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (max(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (least(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (greatest(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ( ~ (total_order(v4, v5) = 0) | order(v4, v5) = 0))
% 5.72/1.98 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 5.72/1.98 | (1) ~ (all_0_0_0 = 0) & max(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 & greatest(all_0_1_1, all_0_3_3, all_0_2_2) = 0 & order(all_0_3_3, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (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] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(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] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (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) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 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] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0)
% 6.08/2.00 |
% 6.08/2.00 | Applying alpha-rule on (1) yields:
% 6.08/2.00 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0))
% 6.08/2.00 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 6.08/2.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 6.08/2.00 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 6.08/2.00 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0))
% 6.08/2.00 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 6.08/2.00 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.08/2.00 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 6.08/2.00 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 6.08/2.00 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.08/2.00 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 6.08/2.00 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 6.08/2.00 | (14) greatest(all_0_1_1, all_0_3_3, all_0_2_2) = 0
% 6.08/2.00 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 6.08/2.01 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 6.08/2.01 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.08/2.01 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 6.08/2.01 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0))
% 6.08/2.01 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4))
% 6.08/2.01 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 6.08/2.01 | (22) order(all_0_3_3, all_0_2_2) = 0
% 6.08/2.01 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 6.08/2.01 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (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))))
% 6.08/2.01 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0))
% 6.08/2.01 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 6.08/2.01 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 6.08/2.01 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 6.08/2.01 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0))
% 6.08/2.01 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0))
% 6.08/2.01 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4))
% 6.08/2.01 | (32) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0)
% 6.08/2.01 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 6.08/2.01 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 6.08/2.01 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 6.08/2.01 | (36) max(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0
% 6.08/2.01 | (37) ~ (all_0_0_0 = 0)
% 6.08/2.01 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0))
% 6.08/2.01 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0))
% 6.08/2.01 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0))
% 6.08/2.02 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 6.08/2.02 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0))
% 6.08/2.02 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0))
% 6.08/2.02 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0))
% 6.08/2.02 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (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) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0)))
% 6.08/2.02 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3)))
% 6.08/2.02 |
% 6.08/2.02 | Instantiating formula (26) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms max(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 6.08/2.02 | (47) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & ~ (v0 = all_0_1_1) & apply(all_0_3_3, all_0_1_1, v0) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0))
% 6.08/2.02 |
% 6.08/2.02 | Instantiating formula (12) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms greatest(all_0_1_1, all_0_3_3, all_0_2_2) = 0, yields:
% 6.08/2.02 | (48) member(all_0_1_1, all_0_2_2) = 0
% 6.08/2.02 |
% 6.08/2.02 +-Applying beta-rule and splitting (47), into two cases.
% 6.08/2.02 |-Branch one:
% 6.08/2.02 | (49) all_0_0_0 = 0
% 6.08/2.02 |
% 6.08/2.02 | Equations (49) can reduce 37 to:
% 6.08/2.02 | (50) $false
% 6.08/2.02 |
% 6.08/2.02 |-The branch is then unsatisfiable
% 6.08/2.02 |-Branch two:
% 6.08/2.02 | (37) ~ (all_0_0_0 = 0)
% 6.08/2.02 | (52) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & ~ (v0 = all_0_1_1) & apply(all_0_3_3, all_0_1_1, v0) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0))
% 6.08/2.02 |
% 6.08/2.02 | Instantiating (52) with all_13_0_4, all_13_1_5, all_13_2_6 yields:
% 6.08/2.02 | (53) (all_13_0_4 = 0 & all_13_1_5 = 0 & ~ (all_13_2_6 = all_0_1_1) & apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0 & member(all_13_2_6, all_0_2_2) = 0) | ( ~ (all_13_2_6 = 0) & member(all_0_1_1, all_0_2_2) = all_13_2_6)
% 6.08/2.02 |
% 6.08/2.02 +-Applying beta-rule and splitting (53), into two cases.
% 6.08/2.02 |-Branch one:
% 6.08/2.02 | (54) all_13_0_4 = 0 & all_13_1_5 = 0 & ~ (all_13_2_6 = all_0_1_1) & apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0 & member(all_13_2_6, all_0_2_2) = 0
% 6.08/2.02 |
% 6.08/2.02 | Applying alpha-rule on (54) yields:
% 6.08/2.02 | (55) member(all_13_2_6, all_0_2_2) = 0
% 6.08/2.02 | (56) ~ (all_13_2_6 = all_0_1_1)
% 6.08/2.02 | (57) apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0
% 6.08/2.02 | (58) all_13_0_4 = 0
% 6.08/2.02 | (59) all_13_1_5 = 0
% 6.08/2.02 |
% 6.08/2.02 | Instantiating formula (13) with all_13_2_6, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0, yields:
% 6.08/2.02 | (60) all_13_2_6 = all_0_1_1 | ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_13_2_6, all_0_1_1) = v2 & member(all_13_2_6, all_0_2_2) = v1 & member(all_0_1_1, all_0_2_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 6.08/2.03 |
% 6.08/2.03 +-Applying beta-rule and splitting (60), into two cases.
% 6.08/2.03 |-Branch one:
% 6.08/2.03 | (61) all_13_2_6 = all_0_1_1
% 6.08/2.03 |
% 6.08/2.03 | Equations (61) can reduce 56 to:
% 6.08/2.03 | (50) $false
% 6.08/2.03 |
% 6.08/2.03 |-The branch is then unsatisfiable
% 6.08/2.03 |-Branch two:
% 6.08/2.03 | (56) ~ (all_13_2_6 = all_0_1_1)
% 6.08/2.03 | (64) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_13_2_6, all_0_1_1) = v2 & member(all_13_2_6, all_0_2_2) = v1 & member(all_0_1_1, all_0_2_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 6.08/2.03 |
% 6.08/2.03 | Instantiating (64) with all_25_0_7, all_25_1_8, all_25_2_9 yields:
% 6.08/2.03 | (65) apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_25_0_7 & member(all_13_2_6, all_0_2_2) = all_25_1_8 & member(all_0_1_1, all_0_2_2) = all_25_2_9 & ( ~ (all_25_0_7 = 0) | ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0))
% 6.08/2.03 |
% 6.08/2.03 | Applying alpha-rule on (65) yields:
% 6.08/2.03 | (66) apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_25_0_7
% 6.08/2.03 | (67) member(all_13_2_6, all_0_2_2) = all_25_1_8
% 6.08/2.03 | (68) member(all_0_1_1, all_0_2_2) = all_25_2_9
% 6.08/2.03 | (69) ~ (all_25_0_7 = 0) | ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0)
% 6.08/2.03 |
% 6.08/2.03 | Instantiating formula (34) with all_13_2_6, all_0_2_2, all_25_1_8, 0 and discharging atoms member(all_13_2_6, all_0_2_2) = all_25_1_8, member(all_13_2_6, all_0_2_2) = 0, yields:
% 6.08/2.03 | (70) all_25_1_8 = 0
% 6.08/2.03 |
% 6.08/2.03 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_25_2_9, 0 and discharging atoms member(all_0_1_1, all_0_2_2) = all_25_2_9, member(all_0_1_1, all_0_2_2) = 0, yields:
% 6.08/2.03 | (71) all_25_2_9 = 0
% 6.08/2.03 |
% 6.08/2.03 | From (70) and (67) follows:
% 6.08/2.03 | (55) member(all_13_2_6, all_0_2_2) = 0
% 6.08/2.03 |
% 6.08/2.03 +-Applying beta-rule and splitting (69), into two cases.
% 6.08/2.03 |-Branch one:
% 6.08/2.03 | (73) ~ (all_25_0_7 = 0)
% 6.08/2.03 |
% 6.08/2.03 | Instantiating formula (33) with all_25_0_7, all_13_2_6, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms greatest(all_0_1_1, all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_25_0_7, yields:
% 6.08/2.03 | (74) all_25_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0)
% 6.08/2.03 |
% 6.08/2.03 +-Applying beta-rule and splitting (74), into two cases.
% 6.08/2.03 |-Branch one:
% 6.08/2.03 | (75) all_25_0_7 = 0
% 6.08/2.03 |
% 6.08/2.03 | Equations (75) can reduce 73 to:
% 6.08/2.03 | (50) $false
% 6.08/2.03 |
% 6.08/2.03 |-The branch is then unsatisfiable
% 6.08/2.03 |-Branch two:
% 6.08/2.03 | (73) ~ (all_25_0_7 = 0)
% 6.08/2.03 | (78) ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0)
% 6.08/2.03 |
% 6.08/2.03 | Instantiating (78) with all_42_0_10 yields:
% 6.08/2.03 | (79) ~ (all_42_0_10 = 0) & member(all_13_2_6, all_0_2_2) = all_42_0_10
% 6.08/2.03 |
% 6.08/2.03 | Applying alpha-rule on (79) yields:
% 6.08/2.03 | (80) ~ (all_42_0_10 = 0)
% 6.08/2.03 | (81) member(all_13_2_6, all_0_2_2) = all_42_0_10
% 6.08/2.03 |
% 6.08/2.03 | Instantiating formula (34) with all_13_2_6, all_0_2_2, all_42_0_10, 0 and discharging atoms member(all_13_2_6, all_0_2_2) = all_42_0_10, member(all_13_2_6, all_0_2_2) = 0, yields:
% 6.08/2.03 | (82) all_42_0_10 = 0
% 6.08/2.03 |
% 6.08/2.03 | Equations (82) can reduce 80 to:
% 6.08/2.03 | (50) $false
% 6.08/2.03 |
% 6.08/2.03 |-The branch is then unsatisfiable
% 6.08/2.03 |-Branch two:
% 6.08/2.03 | (75) all_25_0_7 = 0
% 6.08/2.03 | (85) ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0)
% 6.08/2.03 |
% 6.08/2.03 +-Applying beta-rule and splitting (85), into two cases.
% 6.08/2.03 |-Branch one:
% 6.08/2.03 | (86) ~ (all_25_1_8 = 0)
% 6.08/2.03 |
% 6.08/2.03 | Equations (70) can reduce 86 to:
% 6.08/2.04 | (50) $false
% 6.08/2.04 |
% 6.08/2.04 |-The branch is then unsatisfiable
% 6.08/2.04 |-Branch two:
% 6.08/2.04 | (70) all_25_1_8 = 0
% 6.08/2.04 | (89) ~ (all_25_2_9 = 0)
% 6.08/2.04 |
% 6.08/2.04 | Equations (71) can reduce 89 to:
% 6.08/2.04 | (50) $false
% 6.08/2.04 |
% 6.08/2.04 |-The branch is then unsatisfiable
% 6.08/2.04 |-Branch two:
% 6.08/2.04 | (91) ~ (all_13_2_6 = 0) & member(all_0_1_1, all_0_2_2) = all_13_2_6
% 6.08/2.04 |
% 6.08/2.04 | Applying alpha-rule on (91) yields:
% 6.08/2.04 | (92) ~ (all_13_2_6 = 0)
% 6.08/2.04 | (93) member(all_0_1_1, all_0_2_2) = all_13_2_6
% 6.08/2.04 |
% 6.08/2.04 | Instantiating formula (34) with all_0_1_1, all_0_2_2, 0, all_13_2_6 and discharging atoms member(all_0_1_1, all_0_2_2) = all_13_2_6, member(all_0_1_1, all_0_2_2) = 0, yields:
% 6.08/2.04 | (94) all_13_2_6 = 0
% 6.08/2.04 |
% 6.08/2.04 | Equations (94) can reduce 92 to:
% 6.08/2.04 | (50) $false
% 6.08/2.04 |
% 6.08/2.04 |-The branch is then unsatisfiable
% 6.08/2.04 % SZS output end Proof for theBenchmark
% 6.08/2.04
% 6.08/2.04 1448ms
%------------------------------------------------------------------------------