TSTP Solution File: ALG045+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 : Thu Jul 14 15:33:53 EDT 2022
% Result : Unsatisfiable 4.29s 1.52s
% Output : Proof 10.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Wed Jun 8 13:08:06 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.48 ____ _
% 0.15/0.48 ___ / __ \_____(_)___ ________ __________
% 0.15/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.15/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.15/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.15/0.48
% 0.15/0.48 A Theorem Prover for First-Order Logic
% 0.15/0.49 (ePrincess v.1.0)
% 0.15/0.49
% 0.15/0.49 (c) Philipp Rümmer, 2009-2015
% 0.15/0.49 (c) Peter Backeman, 2014-2015
% 0.15/0.49 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.15/0.49 Free software under GNU Lesser General Public License (LGPL).
% 0.15/0.49 Bug reports to peter@backeman.se
% 0.15/0.49
% 0.15/0.49 For more information, visit http://user.uu.se/~petba168/breu/
% 0.15/0.49
% 0.15/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.15/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.88 Prover 0: Preprocessing ...
% 2.62/1.14 Prover 0: Constructing countermodel ...
% 4.29/1.52 Prover 0: proved (995ms)
% 4.29/1.52
% 4.29/1.52 No countermodel exists, formula is valid
% 4.29/1.52 % SZS status Unsatisfiable for theBenchmark
% 4.29/1.52
% 4.29/1.52 Generating proof ... found it (size 2548)
% 8.75/2.60
% 8.75/2.60 % SZS output start Proof for theBenchmark
% 8.75/2.60 Assumed formulas after preprocessing and simplification:
% 8.75/2.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e3, unit) = e3 & op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, unit) = e2 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, unit) = e1 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, unit) = e0 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (op(v19, v18) = v17) | ~ (op(v19, v18) = v16)) & ( ~ (v15 = e2) | ~ (v7 = e0)) & ( ~ (v15 = e2) | ~ (v3 = e1)) & ( ~ (v15 = e1) | ~ (v11 = e0)) & ( ~ (v15 = e1) | ~ (v3 = e2)) & ( ~ (v15 = e0) | ~ (v11 = e1)) & ( ~ (v15 = e0) | ~ (v7 = e2)) & ( ~ (v14 = e1) | ~ (v10 = e0)) & ( ~ (v14 = e0) | ~ (v10 = e1)) & ( ~ (v13 = e2) | ~ (v5 = e0)) & ( ~ (v13 = e0) | ~ (v5 = e2)) & ( ~ (v12 = e2) | ~ (v0 = e1)) & ( ~ (v12 = e1) | ~ (v0 = e2)) & ( ~ (v10 = e3) | ~ (v6 = e0)) & ( ~ (v10 = e3) | ~ (v2 = e1)) & ( ~ (v10 = e1) | ~ (v2 = e3)) & ( ~ (v10 = e0) | ~ (v6 = e3)) & ( ~ (v9 = e3) | ~ (v5 = e0)) & ( ~ (v9 = e0) | ~ (v5 = e3)) & ( ~ (v8 = e3) | ~ (v0 = e1)) & ( ~ (v8 = e1) | ~ (v0 = e3)) & ( ~ (v5 = e3) | ~ (v1 = e2)) & ( ~ (v5 = e2) | ~ (v1 = e3)) & ( ~ (v4 = e3) | ~ (v0 = e2)) & ( ~ (v4 = e2) | ~ (v0 = e3)) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v15 = e3 | v14 = e3 | v13 = e3 | v12 = e3) & (v15 = e3 | v11 = e3 | v7 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v12 = e2) & (v15 = e2 | v11 = e2 | v7 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v12 = e1) & (v15 = e1 | v11 = e1 | v7 = e1 | v3 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v12 = e0) & (v15 = e0 | v11 = e0 | v7 = e0 | v3 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v14 = e3 | v10 = e3 | v6 = e3 | v2 = e3) & (v14 = e2 | v10 = e2 | v6 = e2 | v2 = e2) & (v14 = e1 | v10 = e1 | v6 = e1 | v2 = e1) & (v14 = e0 | v10 = e0 | v6 = e0 | v2 = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v13 = e3 | v9 = e3 | v5 = e3 | v1 = e3) & (v13 = e2 | v9 = e2 | v5 = e2 | v1 = e2) & (v13 = e1 | v9 = e1 | v5 = e1 | v1 = e1) & (v13 = e0 | v9 = e0 | v5 = e0 | v1 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v12 = e3 | v8 = e3 | v4 = e3 | v0 = e3) & (v12 = e2 | v8 = e2 | v4 = e2 | v0 = e2) & (v12 = e1 | v8 = e1 | v4 = e1 | v0 = e1) & (v12 = e0 | v8 = e0 | v4 = e0 | v0 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v8 = e3) & (v11 = e2 | v10 = e2 | v9 = e2 | v8 = e2) & (v11 = e1 | v10 = e1 | v9 = e1 | v8 = e1) & (v11 = e0 | v10 = e0 | v9 = e0 | v8 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v7 = e3 | v6 = e3 | v5 = e3 | v4 = e3) & (v7 = e2 | v6 = e2 | v5 = e2 | v4 = e2) & (v7 = e1 | v6 = e1 | v5 = e1 | v4 = e1) & (v7 = e0 | v6 = e0 | v5 = e0 | v4 = e0) & (v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 = e0) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0) & (unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((v15 = e3 & v10 = e3 & v5 = e3 & v0 = e3) | (v15 = e2 & v10 = e2 & v5 = e2 & v0 = e2) | (v15 = e1 & v10 = e1 & v5 = e1 & v0 = e1) | (v15 = e0 & v10 = e0 & v5 = e0 & v0 = e0)))
% 9.15/2.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 9.15/2.64 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_0_0 = all_0_2_2) & ~ (all_0_0_0 = all_0_3_3) & ~ (all_0_0_0 = all_0_4_4) & ~ (all_0_0_0 = all_0_8_8) & ~ (all_0_0_0 = all_0_12_12) & ~ (all_0_1_1 = all_0_2_2) & ~ (all_0_1_1 = all_0_3_3) & ~ (all_0_1_1 = all_0_5_5) & ~ (all_0_1_1 = all_0_9_9) & ~ (all_0_1_1 = all_0_13_13) & ~ (all_0_2_2 = all_0_3_3) & ~ (all_0_2_2 = all_0_6_6) & ~ (all_0_2_2 = all_0_10_10) & ~ (all_0_2_2 = all_0_14_14) & ~ (all_0_3_3 = all_0_7_7) & ~ (all_0_3_3 = all_0_11_11) & ~ (all_0_3_3 = all_0_15_15) & ~ (all_0_4_4 = all_0_5_5) & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_4_4 = all_0_7_7) & ~ (all_0_4_4 = all_0_8_8) & ~ (all_0_4_4 = all_0_12_12) & ~ (all_0_5_5 = all_0_6_6) & ~ (all_0_5_5 = all_0_7_7) & ~ (all_0_5_5 = all_0_9_9) & ~ (all_0_5_5 = all_0_13_13) & ~ (all_0_6_6 = all_0_7_7) & ~ (all_0_6_6 = all_0_10_10) & ~ (all_0_6_6 = all_0_14_14) & ~ (all_0_7_7 = all_0_11_11) & ~ (all_0_7_7 = all_0_15_15) & ~ (all_0_8_8 = all_0_9_9) & ~ (all_0_8_8 = all_0_10_10) & ~ (all_0_8_8 = all_0_11_11) & ~ (all_0_8_8 = all_0_12_12) & ~ (all_0_9_9 = all_0_10_10) & ~ (all_0_9_9 = all_0_11_11) & ~ (all_0_9_9 = all_0_13_13) & ~ (all_0_10_10 = all_0_11_11) & ~ (all_0_10_10 = all_0_14_14) & ~ (all_0_11_11 = all_0_15_15) & ~ (all_0_12_12 = all_0_13_13) & ~ (all_0_12_12 = all_0_14_14) & ~ (all_0_12_12 = all_0_15_15) & ~ (all_0_13_13 = all_0_14_14) & ~ (all_0_13_13 = all_0_15_15) & ~ (all_0_14_14 = all_0_15_15) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(unit, e3) = e3 & op(unit, e2) = e2 & op(unit, e1) = e1 & op(unit, e0) = e0 & op(e3, unit) = e3 & op(e3, e3) = all_0_0_0 & op(e3, e2) = all_0_1_1 & op(e3, e1) = all_0_2_2 & op(e3, e0) = all_0_3_3 & op(e2, unit) = e2 & op(e2, e3) = all_0_4_4 & op(e2, e2) = all_0_5_5 & op(e2, e1) = all_0_6_6 & op(e2, e0) = all_0_7_7 & op(e1, unit) = e1 & op(e1, e3) = all_0_8_8 & op(e1, e2) = all_0_9_9 & op(e1, e1) = all_0_10_10 & op(e1, e0) = all_0_11_11 & op(e0, unit) = e0 & op(e0, e3) = all_0_12_12 & op(e0, e2) = all_0_13_13 & op(e0, e1) = all_0_14_14 & op(e0, e0) = all_0_15_15 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_8_8 = e0)) & ( ~ (all_0_0_0 = e2) | ~ (all_0_12_12 = e1)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_4_4 = e0)) & ( ~ (all_0_0_0 = e1) | ~ (all_0_12_12 = e2)) & ( ~ (all_0_0_0 = e0) | ~ (all_0_4_4 = e1)) & ( ~ (all_0_0_0 = e0) | ~ (all_0_8_8 = e2)) & ( ~ (all_0_1_1 = e1) | ~ (all_0_5_5 = e0)) & ( ~ (all_0_1_1 = e0) | ~ (all_0_5_5 = e1)) & ( ~ (all_0_2_2 = e2) | ~ (all_0_10_10 = e0)) & ( ~ (all_0_2_2 = e0) | ~ (all_0_10_10 = e2)) & ( ~ (all_0_3_3 = e2) | ~ (all_0_15_15 = e1)) & ( ~ (all_0_3_3 = e1) | ~ (all_0_15_15 = e2)) & ( ~ (all_0_5_5 = e3) | ~ (all_0_9_9 = e0)) & ( ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e1)) & ( ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e3)) & ( ~ (all_0_5_5 = e0) | ~ (all_0_9_9 = e3)) & ( ~ (all_0_6_6 = e3) | ~ (all_0_10_10 = e0)) & ( ~ (all_0_6_6 = e0) | ~ (all_0_10_10 = e3)) & ( ~ (all_0_7_7 = e3) | ~ (all_0_15_15 = e1)) & ( ~ (all_0_7_7 = e1) | ~ (all_0_15_15 = e3)) & ( ~ (all_0_10_10 = e3) | ~ (all_0_14_14 = e2)) & ( ~ (all_0_10_10 = e2) | ~ (all_0_14_14 = e3)) & ( ~ (all_0_11_11 = e3) | ~ (all_0_15_15 = e2)) & ( ~ (all_0_11_11 = e2) | ~ (all_0_15_15 = e3)) & (all_0_0_0 = e3 | all_0_0_0 = e2 | all_0_0_0 = e1 | all_0_0_0 = e0) & (all_0_0_0 = e3 | all_0_1_1 = e3 | all_0_2_2 = e3 | all_0_3_3 = e3) & (all_0_0_0 = e3 | all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3) & (all_0_0_0 = e2 | all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2) & (all_0_0_0 = e2 | all_0_4_4 = e2 | all_0_8_8 = e2 | all_0_12_12 = e2) & (all_0_0_0 = e1 | all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1) & (all_0_0_0 = e1 | all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1) & (all_0_0_0 = e0 | all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0) & (all_0_0_0 = e0 | all_0_4_4 = e0 | all_0_8_8 = e0 | all_0_12_12 = e0) & (all_0_1_1 = e3 | all_0_1_1 = e2 | all_0_1_1 = e1 | all_0_1_1 = e0) & (all_0_1_1 = e3 | all_0_5_5 = e3 | all_0_9_9 = e3 | all_0_13_13 = e3) & (all_0_1_1 = e2 | all_0_5_5 = e2 | all_0_9_9 = e2 | all_0_13_13 = e2) & (all_0_1_1 = e1 | all_0_5_5 = e1 | all_0_9_9 = e1 | all_0_13_13 = e1) & (all_0_1_1 = e0 | all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0) & (all_0_2_2 = e3 | all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0) & (all_0_2_2 = e3 | all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3) & (all_0_2_2 = e2 | all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2) & (all_0_2_2 = e1 | all_0_6_6 = e1 | all_0_10_10 = e1 | all_0_14_14 = e1) & (all_0_2_2 = e0 | all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0) & (all_0_3_3 = e3 | all_0_3_3 = e2 | all_0_3_3 = e1 | all_0_3_3 = e0) & (all_0_3_3 = e3 | all_0_7_7 = e3 | all_0_11_11 = e3 | all_0_15_15 = e3) & (all_0_3_3 = e2 | all_0_7_7 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2) & (all_0_3_3 = e1 | all_0_7_7 = e1 | all_0_11_11 = e1 | all_0_15_15 = e1) & (all_0_3_3 = e0 | all_0_7_7 = e0 | all_0_11_11 = e0 | all_0_15_15 = e0) & (all_0_4_4 = e3 | all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0) & (all_0_4_4 = e3 | all_0_5_5 = e3 | all_0_6_6 = e3 | all_0_7_7 = e3) & (all_0_4_4 = e2 | all_0_5_5 = e2 | all_0_6_6 = e2 | all_0_7_7 = e2) & (all_0_4_4 = e1 | all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1) & (all_0_4_4 = e0 | all_0_5_5 = e0 | all_0_6_6 = e0 | all_0_7_7 = e0) & (all_0_5_5 = e3 | all_0_5_5 = e2 | all_0_5_5 = e1 | all_0_5_5 = e0) & (all_0_6_6 = e3 | all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0) & (all_0_7_7 = e3 | all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0) & (all_0_8_8 = e3 | all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0) & (all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3) & (all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2) & (all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1) & (all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0) & (all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0) & (all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0) & (all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0) & (all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0) & (all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3) & (all_0_12_12 = e2 | all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2) & (all_0_12_12 = e1 | all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1) & (all_0_12_12 = e0 | all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0) & (all_0_13_13 = e3 | all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0) & (all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0) & (all_0_15_15 = e3 | all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0) & (unit = e3 | unit = e2 | unit = e1 | unit = e0) & ((all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1) | (all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0))
% 9.15/2.65 |
% 9.15/2.65 | Applying alpha-rule on (1) yields:
% 9.15/2.65 | (2) ~ (all_0_10_10 = all_0_11_11)
% 9.15/2.65 | (3) ~ (e1 = e0)
% 9.15/2.65 | (4) op(e1, e0) = all_0_11_11
% 9.15/2.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 9.15/2.66 | (6) ~ (all_0_3_3 = all_0_15_15)
% 9.15/2.66 | (7) all_0_2_2 = e0 | all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 9.15/2.66 | (8) ~ (all_0_3_3 = e2) | ~ (all_0_15_15 = e1)
% 9.15/2.66 | (9) all_0_2_2 = e3 | all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 9.15/2.66 | (10) ~ (all_0_2_2 = all_0_6_6)
% 9.15/2.66 | (11) op(e2, e3) = all_0_4_4
% 9.15/2.66 | (12) ~ (all_0_0_0 = all_0_2_2)
% 9.15/2.66 | (13) ~ (e2 = e0)
% 9.15/2.66 | (14) op(e1, e2) = all_0_9_9
% 9.15/2.66 | (15) ~ (all_0_6_6 = all_0_7_7)
% 9.15/2.66 | (16) all_0_12_12 = e0 | all_0_13_13 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 9.15/2.66 | (17) all_0_0_0 = e1 | all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 9.15/2.66 | (18) all_0_3_3 = e0 | all_0_7_7 = e0 | all_0_11_11 = e0 | all_0_15_15 = e0
% 9.15/2.66 | (19) op(e0, e1) = all_0_14_14
% 9.15/2.66 | (20) all_0_1_1 = e1 | all_0_5_5 = e1 | all_0_9_9 = e1 | all_0_13_13 = e1
% 9.15/2.66 | (21) ~ (all_0_7_7 = e3) | ~ (all_0_15_15 = e1)
% 9.15/2.66 | (22) ~ (all_0_0_0 = all_0_3_3)
% 9.15/2.66 | (23) ~ (all_0_13_13 = all_0_15_15)
% 9.15/2.66 | (24) op(unit, e1) = e1
% 9.15/2.66 | (25) op(e1, unit) = e1
% 9.15/2.66 | (26) all_0_1_1 = e2 | all_0_5_5 = e2 | all_0_9_9 = e2 | all_0_13_13 = e2
% 9.15/2.66 | (27) ~ (all_0_0_0 = e1) | ~ (all_0_12_12 = e2)
% 9.15/2.66 | (28) all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.15/2.66 | (29) ~ (e3 = e0)
% 9.15/2.66 | (30) ~ (all_0_1_1 = all_0_5_5)
% 9.15/2.66 | (31) all_0_0_0 = e3 | all_0_0_0 = e2 | all_0_0_0 = e1 | all_0_0_0 = e0
% 9.15/2.66 | (32) ~ (all_0_5_5 = e3) | ~ (all_0_9_9 = e0)
% 9.15/2.66 | (33) all_0_13_13 = e3 | all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 9.15/2.66 | (34) all_0_0_0 = e0 | all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0
% 9.15/2.66 | (35) ~ (all_0_6_6 = all_0_10_10)
% 9.15/2.66 | (36) ~ (all_0_4_4 = all_0_12_12)
% 9.15/2.66 | (37) ~ (all_0_0_0 = e1) | ~ (all_0_4_4 = e0)
% 9.15/2.66 | (38) all_0_2_2 = e3 | all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0
% 9.15/2.66 | (39) op(e2, e1) = all_0_6_6
% 9.15/2.66 | (40) ~ (all_0_10_10 = e2) | ~ (all_0_14_14 = e3)
% 9.15/2.66 | (41) ~ (all_0_14_14 = all_0_15_15)
% 9.15/2.66 | (42) ~ (all_0_1_1 = e0) | ~ (all_0_5_5 = e1)
% 9.15/2.66 | (43) all_0_0_0 = e3 | all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3
% 9.15/2.66 | (44) all_0_8_8 = e3 | all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 9.15/2.66 | (45) all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 9.15/2.66 | (46) op(e3, unit) = e3
% 9.15/2.66 | (47) ~ (all_0_1_1 = e1) | ~ (all_0_5_5 = e0)
% 9.15/2.66 | (48) ~ (all_0_11_11 = all_0_15_15)
% 9.15/2.66 | (49) all_0_11_11 = e3 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 9.15/2.66 | (50) ~ (all_0_2_2 = all_0_3_3)
% 9.15/2.66 | (51) ~ (all_0_12_12 = all_0_14_14)
% 9.15/2.66 | (52) all_0_0_0 = e2 | all_0_4_4 = e2 | all_0_8_8 = e2 | all_0_12_12 = e2
% 9.15/2.66 | (53) all_0_0_0 = e1 | all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 9.15/2.66 | (54) all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.15/2.66 | (55) unit = e3 | unit = e2 | unit = e1 | unit = e0
% 9.15/2.66 | (56) op(e1, e3) = all_0_8_8
% 9.15/2.66 | (57) op(unit, e2) = e2
% 9.15/2.66 | (58) op(e3, e2) = all_0_1_1
% 9.15/2.66 | (59) ~ (all_0_6_6 = e3) | ~ (all_0_10_10 = e0)
% 9.15/2.66 | (60) ~ (all_0_5_5 = all_0_9_9)
% 9.15/2.66 | (61) ~ (e3 = e1)
% 9.15/2.66 | (62) ~ (all_0_10_10 = all_0_14_14)
% 9.15/2.66 | (63) all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 9.15/2.66 | (64) ~ (all_0_4_4 = all_0_8_8)
% 9.15/2.66 | (65) op(e0, e0) = all_0_15_15
% 9.15/2.66 | (66) all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 9.15/2.66 | (67) ~ (all_0_5_5 = e0) | ~ (all_0_9_9 = e3)
% 9.15/2.66 | (68) ~ (all_0_3_3 = all_0_7_7)
% 9.15/2.66 | (69) ~ (all_0_3_3 = e1) | ~ (all_0_15_15 = e2)
% 9.15/2.66 | (70) all_0_1_1 = e0 | all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 9.15/2.66 | (71) all_0_2_2 = e1 | all_0_6_6 = e1 | all_0_10_10 = e1 | all_0_14_14 = e1
% 9.15/2.66 | (72) ~ (all_0_9_9 = all_0_13_13)
% 9.15/2.66 | (73) op(e0, e2) = all_0_13_13
% 9.15/2.66 | (74) all_0_1_1 = e3 | all_0_1_1 = e2 | all_0_1_1 = e1 | all_0_1_1 = e0
% 9.15/2.66 | (75) all_0_12_12 = e1 | all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 9.15/2.66 | (76) all_0_15_15 = e3 | all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 9.15/2.67 | (77) ~ (all_0_2_2 = all_0_14_14)
% 9.15/2.67 | (78) all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 9.15/2.67 | (79) all_0_4_4 = e3 | all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0
% 9.15/2.67 | (80) all_0_3_3 = e1 | all_0_7_7 = e1 | all_0_11_11 = e1 | all_0_15_15 = e1
% 9.15/2.67 | (81) ~ (all_0_8_8 = all_0_10_10)
% 9.15/2.67 | (82) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1) | (all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0)
% 9.15/2.67 | (83) ~ (all_0_2_2 = all_0_10_10)
% 9.15/2.67 | (84) op(e3, e3) = all_0_0_0
% 9.15/2.67 | (85) op(e3, e0) = all_0_3_3
% 9.15/2.67 | (86) ~ (e3 = e2)
% 9.15/2.67 | (87) all_0_4_4 = e0 | all_0_5_5 = e0 | all_0_6_6 = e0 | all_0_7_7 = e0
% 9.15/2.67 | (88) ~ (all_0_1_1 = all_0_13_13)
% 9.15/2.67 | (89) ~ (all_0_2_2 = e0) | ~ (all_0_10_10 = e2)
% 9.15/2.67 | (90) op(e2, e2) = all_0_5_5
% 9.15/2.67 | (91) all_0_1_1 = e3 | all_0_5_5 = e3 | all_0_9_9 = e3 | all_0_13_13 = e3
% 9.15/2.67 | (92) all_0_8_8 = e0 | all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 9.15/2.67 | (93) all_0_12_12 = e2 | all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 9.15/2.67 | (94) ~ (all_0_0_0 = e0) | ~ (all_0_4_4 = e1)
% 9.15/2.67 | (95) ~ (all_0_8_8 = all_0_11_11)
% 9.15/2.67 | (96) ~ (all_0_7_7 = e1) | ~ (all_0_15_15 = e3)
% 9.15/2.67 | (97) ~ (all_0_0_0 = e0) | ~ (all_0_8_8 = e2)
% 9.15/2.67 | (98) all_0_0_0 = e2 | all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2
% 9.15/2.67 | (99) ~ (all_0_0_0 = e2) | ~ (all_0_12_12 = e1)
% 9.15/2.67 | (100) ~ (all_0_7_7 = all_0_15_15)
% 9.15/2.67 | (101) op(unit, e0) = e0
% 9.15/2.67 | (102) ~ (all_0_6_6 = all_0_14_14)
% 9.15/2.67 | (103) ~ (all_0_5_5 = all_0_13_13)
% 9.15/2.67 | (104) ~ (all_0_8_8 = all_0_12_12)
% 9.15/2.67 | (105) ~ (all_0_1_1 = all_0_9_9)
% 9.15/2.67 | (106) all_0_4_4 = e1 | all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1
% 9.15/2.67 | (107) ~ (all_0_5_5 = all_0_7_7)
% 9.15/2.67 | (108) all_0_2_2 = e2 | all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2
% 9.15/2.67 | (109) ~ (all_0_6_6 = e0) | ~ (all_0_10_10 = e3)
% 9.15/2.67 | (110) ~ (all_0_0_0 = e2) | ~ (all_0_8_8 = e0)
% 9.15/2.67 | (111) ~ (all_0_0_0 = all_0_8_8)
% 9.15/2.67 | (112) all_0_3_3 = e3 | all_0_7_7 = e3 | all_0_11_11 = e3 | all_0_15_15 = e3
% 9.15/2.67 | (113) op(e2, unit) = e2
% 9.15/2.67 | (114) ~ (all_0_7_7 = all_0_11_11)
% 9.15/2.67 | (115) ~ (all_0_10_10 = e3) | ~ (all_0_14_14 = e2)
% 9.15/2.67 | (116) ~ (e2 = e1)
% 9.15/2.67 | (117) all_0_0_0 = e3 | all_0_1_1 = e3 | all_0_2_2 = e3 | all_0_3_3 = e3
% 9.15/2.67 | (118) ~ (all_0_1_1 = all_0_3_3)
% 9.15/2.67 | (119) all_0_0_0 = e0 | all_0_4_4 = e0 | all_0_8_8 = e0 | all_0_12_12 = e0
% 9.15/2.67 | (120) ~ (all_0_3_3 = all_0_11_11)
% 9.15/2.67 | (121) ~ (all_0_5_5 = e3) | ~ (all_0_13_13 = e1)
% 9.15/2.67 | (122) ~ (all_0_4_4 = all_0_7_7)
% 9.15/2.67 | (123) ~ (all_0_0_0 = all_0_12_12)
% 9.15/2.67 | (124) all_0_10_10 = e3 | all_0_10_10 = e2 | all_0_10_10 = e1 | all_0_10_10 = e0
% 9.15/2.67 | (125) ~ (all_0_11_11 = e2) | ~ (all_0_15_15 = e3)
% 9.15/2.67 | (126) ~ (all_0_4_4 = all_0_6_6)
% 9.15/2.67 | (127) ~ (all_0_13_13 = all_0_14_14)
% 9.15/2.67 | (128) all_0_6_6 = e3 | all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0
% 9.15/2.67 | (129) ~ (all_0_5_5 = e1) | ~ (all_0_13_13 = e3)
% 9.15/2.67 | (130) op(e1, e1) = all_0_10_10
% 9.15/2.67 | (131) all_0_7_7 = e3 | all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0
% 9.15/2.67 | (132) ~ (all_0_0_0 = all_0_4_4)
% 9.15/2.67 | (133) op(e0, unit) = e0
% 9.15/2.67 | (134) ~ (all_0_1_1 = all_0_2_2)
% 9.15/2.67 | (135) all_0_4_4 = e2 | all_0_5_5 = e2 | all_0_6_6 = e2 | all_0_7_7 = e2
% 9.15/2.67 | (136) ~ (all_0_0_0 = all_0_1_1)
% 9.15/2.68 | (137) ~ (all_0_9_9 = all_0_11_11)
% 9.15/2.68 | (138) all_0_4_4 = e3 | all_0_5_5 = e3 | all_0_6_6 = e3 | all_0_7_7 = e3
% 9.15/2.68 | (139) ~ (all_0_5_5 = all_0_6_6)
% 9.15/2.68 | (140) ~ (all_0_8_8 = all_0_9_9)
% 9.15/2.68 | (141) ~ (all_0_12_12 = all_0_13_13)
% 9.15/2.68 | (142) ~ (all_0_2_2 = e2) | ~ (all_0_10_10 = e0)
% 9.15/2.68 | (143) op(unit, e3) = e3
% 9.15/2.68 | (144) op(e2, e0) = all_0_7_7
% 9.15/2.68 | (145) all_0_3_3 = e2 | all_0_7_7 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2
% 9.15/2.68 | (146) ~ (all_0_4_4 = all_0_5_5)
% 9.15/2.68 | (147) op(e0, e3) = all_0_12_12
% 9.15/2.68 | (148) ~ (all_0_12_12 = all_0_15_15)
% 9.15/2.68 | (149) ~ (all_0_9_9 = all_0_10_10)
% 9.15/2.68 | (150) all_0_3_3 = e3 | all_0_3_3 = e2 | all_0_3_3 = e1 | all_0_3_3 = e0
% 9.15/2.68 | (151) all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.15/2.68 | (152) op(e3, e1) = all_0_2_2
% 9.15/2.68 | (153) all_0_5_5 = e3 | all_0_5_5 = e2 | all_0_5_5 = e1 | all_0_5_5 = e0
% 9.15/2.68 | (154) ~ (all_0_11_11 = e3) | ~ (all_0_15_15 = e2)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (40), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (155) ~ (all_0_10_10 = e2)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (125), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (156) ~ (all_0_11_11 = e2)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (115), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (157) ~ (all_0_10_10 = e3)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (96), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (158) ~ (all_0_7_7 = e1)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (67), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (159) ~ (all_0_5_5 = e0)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (82), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (160), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 9.15/2.68 |
% 9.15/2.68 +-Applying beta-rule and splitting (161), into two cases.
% 9.15/2.68 |-Branch one:
% 9.15/2.68 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 9.15/2.68 |
% 9.15/2.68 | Applying alpha-rule on (162) yields:
% 9.15/2.68 | (163) all_0_0_0 = e3
% 9.15/2.68 | (164) all_0_5_5 = e3
% 9.15/2.68 | (165) all_0_10_10 = e3
% 9.15/2.68 | (166) all_0_15_15 = e3
% 9.15/2.68 |
% 9.15/2.68 | Equations (165) can reduce 157 to:
% 9.15/2.68 | (167) $false
% 9.15/2.68 |
% 9.15/2.68 |-The branch is then unsatisfiable
% 9.15/2.68 |-Branch two:
% 9.15/2.68 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 9.15/2.68 |
% 9.15/2.68 | Applying alpha-rule on (168) yields:
% 9.15/2.68 | (169) all_0_0_0 = e2
% 9.15/2.68 | (170) all_0_5_5 = e2
% 9.15/2.68 | (171) all_0_10_10 = e2
% 9.15/2.68 | (172) all_0_15_15 = e2
% 9.15/2.68 |
% 9.15/2.68 | Equations (171) can reduce 155 to:
% 9.15/2.68 | (167) $false
% 9.15/2.68 |
% 9.15/2.68 |-The branch is then unsatisfiable
% 9.15/2.68 |-Branch two:
% 9.15/2.68 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 9.15/2.68 |
% 9.15/2.68 | Applying alpha-rule on (174) yields:
% 9.15/2.68 | (175) all_0_0_0 = e1
% 9.15/2.68 | (176) all_0_5_5 = e1
% 9.15/2.68 | (177) all_0_10_10 = e1
% 9.15/2.68 | (178) all_0_15_15 = e1
% 9.15/2.68 |
% 9.15/2.68 | Equations (176) can reduce 30 to:
% 9.15/2.68 | (179) ~ (all_0_1_1 = e1)
% 9.15/2.68 |
% 9.15/2.68 | Equations (177) can reduce 83 to:
% 9.15/2.68 | (180) ~ (all_0_2_2 = e1)
% 9.15/2.68 |
% 9.15/2.68 | Equations (178) can reduce 6 to:
% 9.15/2.69 | (181) ~ (all_0_3_3 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (176) can reduce 146 to:
% 9.15/2.69 | (182) ~ (all_0_4_4 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (177) can reduce 35 to:
% 9.15/2.69 | (183) ~ (all_0_6_6 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (177) can reduce 81 to:
% 9.15/2.69 | (184) ~ (all_0_8_8 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (177) can reduce 149 to:
% 9.15/2.69 | (185) ~ (all_0_9_9 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (177) can reduce 155 to:
% 9.15/2.69 | (186) ~ (e2 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Simplifying 186 yields:
% 9.15/2.69 | (116) ~ (e2 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (178) can reduce 148 to:
% 9.15/2.69 | (188) ~ (all_0_12_12 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (178) can reduce 23 to:
% 9.15/2.69 | (189) ~ (all_0_13_13 = e1)
% 9.15/2.69 |
% 9.15/2.69 | From (175) and (84) follows:
% 9.15/2.69 | (190) op(e3, e3) = e1
% 9.15/2.69 |
% 9.15/2.69 | From (176) and (90) follows:
% 9.15/2.69 | (191) op(e2, e2) = e1
% 9.15/2.69 |
% 9.15/2.69 +-Applying beta-rule and splitting (37), into two cases.
% 9.15/2.69 |-Branch one:
% 9.15/2.69 | (192) ~ (all_0_0_0 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (175) can reduce 192 to:
% 9.15/2.69 | (167) $false
% 9.15/2.69 |
% 9.15/2.69 |-The branch is then unsatisfiable
% 9.15/2.69 |-Branch two:
% 9.15/2.69 | (175) all_0_0_0 = e1
% 9.15/2.69 | (195) ~ (all_0_4_4 = e0)
% 9.15/2.69 |
% 9.15/2.69 +-Applying beta-rule and splitting (8), into two cases.
% 9.15/2.69 |-Branch one:
% 9.15/2.69 | (196) ~ (all_0_3_3 = e2)
% 9.15/2.69 |
% 9.15/2.69 +-Applying beta-rule and splitting (129), into two cases.
% 9.15/2.69 |-Branch one:
% 9.15/2.69 | (197) ~ (all_0_5_5 = e1)
% 9.15/2.69 |
% 9.15/2.69 | Equations (176) can reduce 197 to:
% 9.57/2.69 | (167) $false
% 9.57/2.69 |
% 9.57/2.69 |-The branch is then unsatisfiable
% 9.57/2.69 |-Branch two:
% 9.57/2.69 | (176) all_0_5_5 = e1
% 9.57/2.69 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.69 |
% 9.57/2.69 +-Applying beta-rule and splitting (145), into two cases.
% 9.57/2.69 |-Branch one:
% 9.57/2.69 | (201) all_0_3_3 = e2
% 9.57/2.69 |
% 9.57/2.69 | Equations (201) can reduce 196 to:
% 9.57/2.69 | (167) $false
% 9.57/2.69 |
% 9.57/2.69 |-The branch is then unsatisfiable
% 9.57/2.69 |-Branch two:
% 9.57/2.69 | (196) ~ (all_0_3_3 = e2)
% 9.57/2.69 | (204) all_0_7_7 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2
% 9.57/2.69 |
% 9.57/2.69 +-Applying beta-rule and splitting (27), into two cases.
% 9.57/2.69 |-Branch one:
% 9.57/2.69 | (192) ~ (all_0_0_0 = e1)
% 9.57/2.69 |
% 9.57/2.69 | Equations (175) can reduce 192 to:
% 9.57/2.69 | (167) $false
% 9.57/2.69 |
% 9.57/2.69 |-The branch is then unsatisfiable
% 9.57/2.69 |-Branch two:
% 9.57/2.69 | (175) all_0_0_0 = e1
% 9.57/2.69 | (208) ~ (all_0_12_12 = e2)
% 9.57/2.69 |
% 9.57/2.69 +-Applying beta-rule and splitting (204), into two cases.
% 9.57/2.69 |-Branch one:
% 9.57/2.69 | (209) all_0_7_7 = e2
% 9.57/2.69 |
% 9.57/2.69 | Equations (209) can reduce 68 to:
% 9.57/2.69 | (196) ~ (all_0_3_3 = e2)
% 9.57/2.69 |
% 9.57/2.69 | Equations (209) can reduce 122 to:
% 9.57/2.69 | (211) ~ (all_0_4_4 = e2)
% 9.57/2.69 |
% 9.57/2.69 | Equations (209) can reduce 114 to:
% 9.57/2.69 | (212) ~ (all_0_11_11 = e2)
% 9.57/2.69 |
% 9.57/2.69 | Simplifying 212 yields:
% 9.57/2.69 | (156) ~ (all_0_11_11 = e2)
% 9.57/2.69 |
% 9.57/2.69 +-Applying beta-rule and splitting (79), into two cases.
% 9.57/2.69 |-Branch one:
% 9.57/2.69 | (214) all_0_4_4 = e3
% 9.57/2.69 |
% 9.57/2.69 | Equations (214) can reduce 36 to:
% 9.57/2.69 | (215) ~ (all_0_12_12 = e3)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 215 yields:
% 9.57/2.70 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.70 |
% 9.57/2.70 | Equations (214) can reduce 182 to:
% 9.57/2.70 | (61) ~ (e3 = e1)
% 9.57/2.70 |
% 9.57/2.70 | From (214) and (11) follows:
% 9.57/2.70 | (218) op(e2, e3) = e3
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (54), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (219) all_0_12_12 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (219) can reduce 216 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.70 | (222) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (222), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (223) all_0_13_13 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (223) can reduce 200 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.70 | (226) all_0_14_14 = e3 | all_0_15_15 = e3
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (42), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (28), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (219) all_0_12_12 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (219) can reduce 216 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.70 | (231) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (231), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (232) all_0_12_12 = e2
% 9.57/2.70 |
% 9.57/2.70 | Equations (232) can reduce 208 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (208) ~ (all_0_12_12 = e2)
% 9.57/2.70 | (235) all_0_12_12 = e1 | all_0_12_12 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (235), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (236) all_0_12_12 = e1
% 9.57/2.70 |
% 9.57/2.70 | Equations (236) can reduce 188 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (188) ~ (all_0_12_12 = e1)
% 9.57/2.70 | (239) all_0_12_12 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (239) can reduce 104 to:
% 9.57/2.70 | (240) ~ (all_0_8_8 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Equations (239) can reduce 141 to:
% 9.57/2.70 | (241) ~ (all_0_13_13 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 241 yields:
% 9.57/2.70 | (242) ~ (all_0_13_13 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Equations (239) can reduce 216 to:
% 9.57/2.70 | (243) ~ (e3 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 243 yields:
% 9.57/2.70 | (29) ~ (e3 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Equations (239) can reduce 188 to:
% 9.57/2.70 | (245) ~ (e1 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 245 yields:
% 9.57/2.70 | (3) ~ (e1 = e0)
% 9.57/2.70 |
% 9.57/2.70 | From (239) and (147) follows:
% 9.57/2.70 | (247) op(e0, e3) = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (33), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (223) all_0_13_13 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (223) can reduce 200 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.70 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (251), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (252) all_0_13_13 = e2
% 9.57/2.70 |
% 9.57/2.70 | Equations (252) can reduce 88 to:
% 9.57/2.70 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.70 |
% 9.57/2.70 | Equations (252) can reduce 72 to:
% 9.57/2.70 | (254) ~ (all_0_9_9 = e2)
% 9.57/2.70 |
% 9.57/2.70 | Equations (252) can reduce 189 to:
% 9.57/2.70 | (116) ~ (e2 = e1)
% 9.57/2.70 |
% 9.57/2.70 | From (252) and (73) follows:
% 9.57/2.70 | (256) op(e0, e2) = e2
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (151), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (257) all_0_8_8 = e2
% 9.57/2.70 |
% 9.57/2.70 | Equations (257) can reduce 140 to:
% 9.57/2.70 | (258) ~ (all_0_9_9 = e2)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 258 yields:
% 9.57/2.70 | (254) ~ (all_0_9_9 = e2)
% 9.57/2.70 |
% 9.57/2.70 | Equations (257) can reduce 184 to:
% 9.57/2.70 | (116) ~ (e2 = e1)
% 9.57/2.70 |
% 9.57/2.70 | Equations (257) can reduce 240 to:
% 9.57/2.70 | (13) ~ (e2 = e0)
% 9.57/2.70 |
% 9.57/2.70 | From (257) and (56) follows:
% 9.57/2.70 | (262) op(e1, e3) = e2
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (87), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (263) all_0_4_4 = e0
% 9.57/2.70 |
% 9.57/2.70 | Combining equations (263,214) yields a new equation:
% 9.57/2.70 | (264) e3 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (264) can reduce 29 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (195) ~ (all_0_4_4 = e0)
% 9.57/2.70 | (267) all_0_5_5 = e0 | all_0_6_6 = e0 | all_0_7_7 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (226), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (268) all_0_14_14 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (268) can reduce 77 to:
% 9.57/2.70 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.70 |
% 9.57/2.70 | From (268) and (19) follows:
% 9.57/2.70 | (270) op(e0, e1) = e3
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (267), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (271) all_0_5_5 = e0
% 9.57/2.70 |
% 9.57/2.70 | Combining equations (176,271) yields a new equation:
% 9.57/2.70 | (272) e1 = e0
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 272 yields:
% 9.57/2.70 | (273) e1 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (273) can reduce 3 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (159) ~ (all_0_5_5 = e0)
% 9.57/2.70 | (276) all_0_6_6 = e0 | all_0_7_7 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (276), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (277) all_0_6_6 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (277) can reduce 10 to:
% 9.57/2.70 | (278) ~ (all_0_2_2 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Equations (277) can reduce 183 to:
% 9.57/2.70 | (245) ~ (e1 = e0)
% 9.57/2.70 |
% 9.57/2.70 | Simplifying 245 yields:
% 9.57/2.70 | (3) ~ (e1 = e0)
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (38), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (281) all_0_2_2 = e3
% 9.57/2.70 |
% 9.57/2.70 | Equations (281) can reduce 269 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.70 | (284) all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (34), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (285) all_0_0_0 = e0
% 9.57/2.70 |
% 9.57/2.70 | Combining equations (285,175) yields a new equation:
% 9.57/2.70 | (273) e1 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (273) can reduce 3 to:
% 9.57/2.70 | (167) $false
% 9.57/2.70 |
% 9.57/2.70 |-The branch is then unsatisfiable
% 9.57/2.70 |-Branch two:
% 9.57/2.70 | (288) ~ (all_0_0_0 = e0)
% 9.57/2.70 | (289) all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0
% 9.57/2.70 |
% 9.57/2.70 | Equations (175) can reduce 288 to:
% 9.57/2.70 | (3) ~ (e1 = e0)
% 9.57/2.70 |
% 9.57/2.70 +-Applying beta-rule and splitting (284), into two cases.
% 9.57/2.70 |-Branch one:
% 9.57/2.70 | (291) all_0_2_2 = e2
% 9.57/2.70 |
% 9.57/2.70 | Equations (291) can reduce 134 to:
% 9.57/2.70 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.71 |
% 9.57/2.71 | Equations (291) can reduce 50 to:
% 9.57/2.71 | (293) ~ (all_0_3_3 = e2)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 293 yields:
% 9.57/2.71 | (196) ~ (all_0_3_3 = e2)
% 9.57/2.71 |
% 9.57/2.71 | Equations (291) can reduce 180 to:
% 9.57/2.71 | (116) ~ (e2 = e1)
% 9.57/2.71 |
% 9.57/2.71 | Equations (291) can reduce 278 to:
% 9.57/2.71 | (13) ~ (e2 = e0)
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (289), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (297) all_0_1_1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (297) can reduce 227 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.71 | (300) all_0_2_2 = e0 | all_0_3_3 = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (74), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (301) all_0_1_1 = e3
% 9.57/2.71 |
% 9.57/2.71 | Equations (301) can reduce 227 to:
% 9.57/2.71 | (29) ~ (e3 = e0)
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (70), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (297) all_0_1_1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (297,301) yields a new equation:
% 9.57/2.71 | (264) e3 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (264) can reduce 29 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.71 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (307), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (271) all_0_5_5 = e0
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (271,176) yields a new equation:
% 9.57/2.71 | (273) e1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (273) can reduce 3 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (159) ~ (all_0_5_5 = e0)
% 9.57/2.71 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (312), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (313) all_0_9_9 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (313) can reduce 137 to:
% 9.57/2.71 | (314) ~ (all_0_11_11 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 314 yields:
% 9.57/2.71 | (315) ~ (all_0_11_11 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Equations (313) can reduce 254 to:
% 9.57/2.71 | (316) ~ (e2 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 316 yields:
% 9.57/2.71 | (13) ~ (e2 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Equations (313) can reduce 185 to:
% 9.57/2.71 | (245) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 245 yields:
% 9.57/2.71 | (3) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (18), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (320) all_0_3_3 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (320) can reduce 196 to:
% 9.57/2.71 | (316) ~ (e2 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 316 yields:
% 9.57/2.71 | (13) ~ (e2 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Equations (320) can reduce 181 to:
% 9.57/2.71 | (245) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 245 yields:
% 9.57/2.71 | (3) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (55), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (325) unit = e3
% 9.57/2.71 |
% 9.57/2.71 | From (325) and (46) follows:
% 9.57/2.71 | (326) op(e3, e3) = e3
% 9.57/2.71 |
% 9.57/2.71 | From (325) and (113) follows:
% 9.57/2.71 | (327) op(e2, e3) = e2
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e3, e3, e3, e1 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e1, yields:
% 9.57/2.71 | (328) e3 = e1
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e2, e3, e2, e3 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e2, yields:
% 9.57/2.71 | (329) e3 = e2
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (328,329) yields a new equation:
% 9.57/2.71 | (330) e2 = e1
% 9.57/2.71 |
% 9.57/2.71 | Equations (330) can reduce 116 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (332) ~ (unit = e3)
% 9.57/2.71 | (333) unit = e2 | unit = e1 | unit = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (333), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (334) unit = e2
% 9.57/2.71 |
% 9.57/2.71 | From (334) and (113) follows:
% 9.57/2.71 | (335) op(e2, e2) = e2
% 9.57/2.71 |
% 9.57/2.71 | From (334) and (133) follows:
% 9.57/2.71 | (336) op(e0, e2) = e0
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e2, e2, e2, e1 and discharging atoms op(e2, e2) = e2, op(e2, e2) = e1, yields:
% 9.57/2.71 | (330) e2 = e1
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e0, e2, e0, e2 and discharging atoms op(e0, e2) = e2, op(e0, e2) = e0, yields:
% 9.57/2.71 | (338) e2 = e0
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (330,338) yields a new equation:
% 9.57/2.71 | (272) e1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 272 yields:
% 9.57/2.71 | (273) e1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (273) can reduce 3 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (342) ~ (unit = e2)
% 9.57/2.71 | (343) unit = e1 | unit = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (343), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (344) unit = e1
% 9.57/2.71 |
% 9.57/2.71 | From (344) and (143) follows:
% 9.57/2.71 | (345) op(e1, e3) = e3
% 9.57/2.71 |
% 9.57/2.71 | From (344) and (133) follows:
% 9.57/2.71 | (346) op(e0, e1) = e0
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e1, e3, e3, e2 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e2, yields:
% 9.57/2.71 | (329) e3 = e2
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e0, e1, e0, e3 and discharging atoms op(e0, e1) = e3, op(e0, e1) = e0, yields:
% 9.57/2.71 | (264) e3 = e0
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (329,264) yields a new equation:
% 9.57/2.71 | (349) e2 = e0
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 349 yields:
% 9.57/2.71 | (338) e2 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (338) can reduce 13 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (352) ~ (unit = e1)
% 9.57/2.71 | (353) unit = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (353) can reduce 352 to:
% 9.57/2.71 | (245) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 245 yields:
% 9.57/2.71 | (3) ~ (e1 = e0)
% 9.57/2.71 |
% 9.57/2.71 | From (353) and (143) follows:
% 9.57/2.71 | (356) op(e0, e3) = e3
% 9.57/2.71 |
% 9.57/2.71 | From (353) and (24) follows:
% 9.57/2.71 | (357) op(e0, e1) = e1
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e0, e3, e3, e0 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e0, yields:
% 9.57/2.71 | (264) e3 = e0
% 9.57/2.71 |
% 9.57/2.71 | Instantiating formula (5) with e0, e1, e1, e3 and discharging atoms op(e0, e1) = e3, op(e0, e1) = e1, yields:
% 9.57/2.71 | (328) e3 = e1
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (264,328) yields a new equation:
% 9.57/2.71 | (273) e1 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (273) can reduce 3 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (362) ~ (all_0_3_3 = e0)
% 9.57/2.71 | (363) all_0_7_7 = e0 | all_0_11_11 = e0 | all_0_15_15 = e0
% 9.57/2.71 |
% 9.57/2.71 +-Applying beta-rule and splitting (363), into two cases.
% 9.57/2.71 |-Branch one:
% 9.57/2.71 | (364) all_0_7_7 = e0
% 9.57/2.71 |
% 9.57/2.71 | Combining equations (209,364) yields a new equation:
% 9.57/2.71 | (349) e2 = e0
% 9.57/2.71 |
% 9.57/2.71 | Simplifying 349 yields:
% 9.57/2.71 | (338) e2 = e0
% 9.57/2.71 |
% 9.57/2.71 | Equations (338) can reduce 13 to:
% 9.57/2.71 | (167) $false
% 9.57/2.71 |
% 9.57/2.71 |-The branch is then unsatisfiable
% 9.57/2.71 |-Branch two:
% 9.57/2.71 | (368) ~ (all_0_7_7 = e0)
% 9.57/2.71 | (369) all_0_11_11 = e0 | all_0_15_15 = e0
% 9.57/2.71 |
% 9.57/2.72 +-Applying beta-rule and splitting (369), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (370) all_0_11_11 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (370) can reduce 315 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (315) ~ (all_0_11_11 = e0)
% 9.57/2.72 | (373) all_0_15_15 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (178,373) yields a new equation:
% 9.57/2.72 | (272) e1 = e0
% 9.57/2.72 |
% 9.57/2.72 | Simplifying 272 yields:
% 9.57/2.72 | (273) e1 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (273) can reduce 3 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (377) ~ (all_0_9_9 = e0)
% 9.57/2.72 | (378) all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (252,378) yields a new equation:
% 9.57/2.72 | (349) e2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Simplifying 349 yields:
% 9.57/2.72 | (338) e2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (338) can reduce 13 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (382) ~ (all_0_1_1 = e3)
% 9.57/2.72 | (383) all_0_1_1 = e2 | all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (70), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (297) all_0_1_1 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (297) can reduce 227 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.72 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (307), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (271) all_0_5_5 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (271,176) yields a new equation:
% 9.57/2.72 | (273) e1 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (273) can reduce 3 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (159) ~ (all_0_5_5 = e0)
% 9.57/2.72 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (312), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (313) all_0_9_9 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (313) can reduce 254 to:
% 9.57/2.72 | (316) ~ (e2 = e0)
% 9.57/2.72 |
% 9.57/2.72 | Simplifying 316 yields:
% 9.57/2.72 | (13) ~ (e2 = e0)
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (383), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (396) all_0_1_1 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (396) can reduce 253 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.72 | (399) all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (300), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (400) all_0_2_2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (400,291) yields a new equation:
% 9.57/2.72 | (338) e2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (338) can reduce 13 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (278) ~ (all_0_2_2 = e0)
% 9.57/2.72 | (320) all_0_3_3 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (320) can reduce 118 to:
% 9.57/2.72 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (399), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (406) all_0_1_1 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (406) can reduce 179 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.72 | (297) all_0_1_1 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (297) can reduce 227 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (377) ~ (all_0_9_9 = e0)
% 9.57/2.72 | (378) all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (378,252) yields a new equation:
% 9.57/2.72 | (338) e2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (338) can reduce 13 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.72 | (416) all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (108), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (291) all_0_2_2 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (291) can reduce 415 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.72 | (420) all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (98), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (169) all_0_0_0 = e2
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (169,175) yields a new equation:
% 9.57/2.72 | (422) e2 = e1
% 9.57/2.72 |
% 9.57/2.72 | Simplifying 422 yields:
% 9.57/2.72 | (330) e2 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (330) can reduce 116 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (425) ~ (all_0_0_0 = e2)
% 9.57/2.72 | (426) all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (426), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (396) all_0_1_1 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (396) can reduce 253 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.72 | (430) all_0_2_2 = e2 | all_0_3_3 = e2
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (430), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (291) all_0_2_2 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (291) can reduce 415 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.72 | (201) all_0_3_3 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (201) can reduce 196 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (436) ~ (all_0_6_6 = e0)
% 9.57/2.72 | (364) all_0_7_7 = e0
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (364,209) yields a new equation:
% 9.57/2.72 | (338) e2 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (338) can reduce 13 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (440) ~ (all_0_14_14 = e3)
% 9.57/2.72 | (166) all_0_15_15 = e3
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (166,178) yields a new equation:
% 9.57/2.72 | (442) e3 = e1
% 9.57/2.72 |
% 9.57/2.72 | Simplifying 442 yields:
% 9.57/2.72 | (328) e3 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (328) can reduce 61 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.72 | (446) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (446), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (447) all_0_9_9 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (447) can reduce 254 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (254) ~ (all_0_9_9 = e2)
% 9.57/2.72 | (450) all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (450), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (171) all_0_10_10 = e2
% 9.57/2.72 |
% 9.57/2.72 | Combining equations (177,171) yields a new equation:
% 9.57/2.72 | (330) e2 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (330) can reduce 116 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (155) ~ (all_0_10_10 = e2)
% 9.57/2.72 | (455) all_0_11_11 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (455) can reduce 156 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.72 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (458), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (459) all_0_13_13 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (459) can reduce 189 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (189) ~ (all_0_13_13 = e1)
% 9.57/2.72 | (378) all_0_13_13 = e0
% 9.57/2.72 |
% 9.57/2.72 | Equations (378) can reduce 242 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (297) all_0_1_1 = e0
% 9.57/2.72 | (197) ~ (all_0_5_5 = e1)
% 9.57/2.72 |
% 9.57/2.72 | Equations (176) can reduce 197 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (467) ~ (all_0_4_4 = e3)
% 9.57/2.72 | (468) all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (468), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (469) all_0_4_4 = e2
% 9.57/2.72 |
% 9.57/2.72 | Equations (469) can reduce 211 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (211) ~ (all_0_4_4 = e2)
% 9.57/2.72 | (472) all_0_4_4 = e1 | all_0_4_4 = e0
% 9.57/2.72 |
% 9.57/2.72 +-Applying beta-rule and splitting (472), into two cases.
% 9.57/2.72 |-Branch one:
% 9.57/2.72 | (473) all_0_4_4 = e1
% 9.57/2.72 |
% 9.57/2.72 | Equations (473) can reduce 182 to:
% 9.57/2.72 | (167) $false
% 9.57/2.72 |
% 9.57/2.72 |-The branch is then unsatisfiable
% 9.57/2.72 |-Branch two:
% 9.57/2.72 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.73 | (263) all_0_4_4 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (263) can reduce 195 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (478) ~ (all_0_7_7 = e2)
% 9.57/2.73 | (479) all_0_11_11 = e2 | all_0_15_15 = e2
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (479), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (455) all_0_11_11 = e2
% 9.57/2.73 |
% 9.57/2.73 | Equations (455) can reduce 156 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (156) ~ (all_0_11_11 = e2)
% 9.57/2.73 | (172) all_0_15_15 = e2
% 9.57/2.73 |
% 9.57/2.73 | Combining equations (172,178) yields a new equation:
% 9.57/2.73 | (422) e2 = e1
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 422 yields:
% 9.57/2.73 | (330) e2 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (330) can reduce 116 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (201) all_0_3_3 = e2
% 9.57/2.73 | (488) ~ (all_0_15_15 = e1)
% 9.57/2.73 |
% 9.57/2.73 | Equations (178) can reduce 488 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 9.57/2.73 |
% 9.57/2.73 | Applying alpha-rule on (490) yields:
% 9.57/2.73 | (285) all_0_0_0 = e0
% 9.57/2.73 | (271) all_0_5_5 = e0
% 9.57/2.73 | (493) all_0_10_10 = e0
% 9.57/2.73 | (373) all_0_15_15 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (271) can reduce 159 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (271) all_0_5_5 = e0
% 9.57/2.73 | (497) ~ (all_0_9_9 = e3)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (47), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (82), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (160), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (161), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 9.57/2.73 |
% 9.57/2.73 | Applying alpha-rule on (162) yields:
% 9.57/2.73 | (163) all_0_0_0 = e3
% 9.57/2.73 | (164) all_0_5_5 = e3
% 9.57/2.73 | (165) all_0_10_10 = e3
% 9.57/2.73 | (166) all_0_15_15 = e3
% 9.57/2.73 |
% 9.57/2.73 | Combining equations (164,271) yields a new equation:
% 9.57/2.73 | (506) e3 = e0
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 506 yields:
% 9.57/2.73 | (264) e3 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (264) can reduce 29 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 9.57/2.73 |
% 9.57/2.73 | Applying alpha-rule on (168) yields:
% 9.57/2.73 | (169) all_0_0_0 = e2
% 9.57/2.73 | (170) all_0_5_5 = e2
% 9.57/2.73 | (171) all_0_10_10 = e2
% 9.57/2.73 | (172) all_0_15_15 = e2
% 9.57/2.73 |
% 9.57/2.73 | Combining equations (170,271) yields a new equation:
% 9.57/2.73 | (349) e2 = e0
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 349 yields:
% 9.57/2.73 | (338) e2 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (338) can reduce 13 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 9.57/2.73 |
% 9.57/2.73 | Applying alpha-rule on (174) yields:
% 9.57/2.73 | (175) all_0_0_0 = e1
% 9.57/2.73 | (176) all_0_5_5 = e1
% 9.57/2.73 | (177) all_0_10_10 = e1
% 9.57/2.73 | (178) all_0_15_15 = e1
% 9.57/2.73 |
% 9.57/2.73 | Combining equations (176,271) yields a new equation:
% 9.57/2.73 | (272) e1 = e0
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 272 yields:
% 9.57/2.73 | (273) e1 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (273) can reduce 3 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 9.57/2.73 |
% 9.57/2.73 | Applying alpha-rule on (490) yields:
% 9.57/2.73 | (285) all_0_0_0 = e0
% 9.57/2.73 | (271) all_0_5_5 = e0
% 9.57/2.73 | (493) all_0_10_10 = e0
% 9.57/2.73 | (373) all_0_15_15 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (285) can reduce 136 to:
% 9.57/2.73 | (530) ~ (all_0_1_1 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 530 yields:
% 9.57/2.73 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Equations (493) can reduce 83 to:
% 9.57/2.73 | (278) ~ (all_0_2_2 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Equations (493) can reduce 155 to:
% 9.57/2.73 | (316) ~ (e2 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 316 yields:
% 9.57/2.73 | (13) ~ (e2 = e0)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (97), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (288) ~ (all_0_0_0 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Equations (285) can reduce 288 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (285) all_0_0_0 = e0
% 9.57/2.73 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (151), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (257) all_0_8_8 = e2
% 9.57/2.73 |
% 9.57/2.73 | Equations (257) can reduce 445 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.73 | (446) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (446), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (447) all_0_9_9 = e2
% 9.57/2.73 |
% 9.57/2.73 | Equations (447) can reduce 105 to:
% 9.57/2.73 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (142), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (94), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (288) ~ (all_0_0_0 = e0)
% 9.57/2.73 |
% 9.57/2.73 | Equations (285) can reduce 288 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (285) all_0_0_0 = e0
% 9.57/2.73 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (20), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (406) all_0_1_1 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (406) can reduce 179 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.73 | (553) all_0_5_5 = e1 | all_0_9_9 = e1 | all_0_13_13 = e1
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (74), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (301) all_0_1_1 = e3
% 9.57/2.73 |
% 9.57/2.73 | Equations (301) can reduce 134 to:
% 9.57/2.73 | (555) ~ (all_0_2_2 = e3)
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 555 yields:
% 9.57/2.73 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (38), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (281) all_0_2_2 = e3
% 9.57/2.73 |
% 9.57/2.73 | Equations (281) can reduce 269 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.73 | (284) all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (284), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (291) all_0_2_2 = e2
% 9.57/2.73 |
% 9.57/2.73 | Equations (291) can reduce 415 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.73 | (416) all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (416), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (565) all_0_2_2 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (565) can reduce 10 to:
% 9.57/2.73 | (566) ~ (all_0_6_6 = e1)
% 9.57/2.73 |
% 9.57/2.73 | Simplifying 566 yields:
% 9.57/2.73 | (183) ~ (all_0_6_6 = e1)
% 9.57/2.73 |
% 9.57/2.73 | Equations (565) can reduce 278 to:
% 9.57/2.73 | (3) ~ (e1 = e0)
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (106), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (473) all_0_4_4 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (473) can reduce 182 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.73 | (572) all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (572), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (176) all_0_5_5 = e1
% 9.57/2.73 |
% 9.57/2.73 | Combining equations (271,176) yields a new equation:
% 9.57/2.73 | (273) e1 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (273) can reduce 3 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (197) ~ (all_0_5_5 = e1)
% 9.57/2.73 | (577) all_0_6_6 = e1 | all_0_7_7 = e1
% 9.57/2.73 |
% 9.57/2.73 +-Applying beta-rule and splitting (577), into two cases.
% 9.57/2.73 |-Branch one:
% 9.57/2.73 | (578) all_0_6_6 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (578) can reduce 183 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (183) ~ (all_0_6_6 = e1)
% 9.57/2.73 | (581) all_0_7_7 = e1
% 9.57/2.73 |
% 9.57/2.73 | Equations (581) can reduce 158 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.73 | (180) ~ (all_0_2_2 = e1)
% 9.57/2.73 | (400) all_0_2_2 = e0
% 9.57/2.73 |
% 9.57/2.73 | Equations (400) can reduce 278 to:
% 9.57/2.73 | (167) $false
% 9.57/2.73 |
% 9.57/2.73 |-The branch is then unsatisfiable
% 9.57/2.73 |-Branch two:
% 9.57/2.74 | (382) ~ (all_0_1_1 = e3)
% 9.57/2.74 | (383) all_0_1_1 = e2 | all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (383), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (396) all_0_1_1 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (396) can reduce 253 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.74 | (399) all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (399), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (406) all_0_1_1 = e1
% 9.57/2.74 |
% 9.57/2.74 | Equations (406) can reduce 179 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.74 | (297) all_0_1_1 = e0
% 9.57/2.74 |
% 9.57/2.74 | Equations (297) can reduce 227 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (291) all_0_2_2 = e2
% 9.57/2.74 | (598) ~ (all_0_10_10 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 598 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (254) ~ (all_0_9_9 = e2)
% 9.57/2.74 | (450) all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (450), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (171) all_0_10_10 = e2
% 9.57/2.74 |
% 9.57/2.74 | Combining equations (493,171) yields a new equation:
% 9.57/2.74 | (338) e2 = e0
% 9.57/2.74 |
% 9.57/2.74 | Equations (338) can reduce 13 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (155) ~ (all_0_10_10 = e2)
% 9.57/2.74 | (455) all_0_11_11 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (455) can reduce 156 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (406) all_0_1_1 = e1
% 9.57/2.74 | (159) ~ (all_0_5_5 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (271) can reduce 159 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (581) all_0_7_7 = e1
% 9.57/2.74 | (612) ~ (all_0_15_15 = e3)
% 9.57/2.74 |
% 9.57/2.74 | Equations (581) can reduce 15 to:
% 9.57/2.74 | (183) ~ (all_0_6_6 = e1)
% 9.57/2.74 |
% 9.57/2.74 | Equations (581) can reduce 114 to:
% 9.57/2.74 | (614) ~ (all_0_11_11 = e1)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 614 yields:
% 9.57/2.74 | (615) ~ (all_0_11_11 = e1)
% 9.57/2.74 |
% 9.57/2.74 | Equations (581) can reduce 100 to:
% 9.57/2.74 | (616) ~ (all_0_15_15 = e1)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 616 yields:
% 9.57/2.74 | (488) ~ (all_0_15_15 = e1)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (82), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (160), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (161), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 9.57/2.74 |
% 9.57/2.74 | Applying alpha-rule on (162) yields:
% 9.57/2.74 | (163) all_0_0_0 = e3
% 9.57/2.74 | (164) all_0_5_5 = e3
% 9.57/2.74 | (165) all_0_10_10 = e3
% 9.57/2.74 | (166) all_0_15_15 = e3
% 9.57/2.74 |
% 9.57/2.74 | Equations (166) can reduce 612 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 9.57/2.74 |
% 9.57/2.74 | Applying alpha-rule on (168) yields:
% 9.57/2.74 | (169) all_0_0_0 = e2
% 9.57/2.74 | (170) all_0_5_5 = e2
% 9.57/2.74 | (171) all_0_10_10 = e2
% 9.57/2.74 | (172) all_0_15_15 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (171) can reduce 155 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 9.57/2.74 |
% 9.57/2.74 | Applying alpha-rule on (174) yields:
% 9.57/2.74 | (175) all_0_0_0 = e1
% 9.57/2.74 | (176) all_0_5_5 = e1
% 9.57/2.74 | (177) all_0_10_10 = e1
% 9.57/2.74 | (178) all_0_15_15 = e1
% 9.57/2.74 |
% 9.57/2.74 | Equations (178) can reduce 488 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 9.57/2.74 |
% 9.57/2.74 | Applying alpha-rule on (490) yields:
% 9.57/2.74 | (285) all_0_0_0 = e0
% 9.57/2.74 | (271) all_0_5_5 = e0
% 9.57/2.74 | (493) all_0_10_10 = e0
% 9.57/2.74 | (373) all_0_15_15 = e0
% 9.57/2.74 |
% 9.57/2.74 | Equations (271) can reduce 30 to:
% 9.57/2.74 | (227) ~ (all_0_1_1 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 83 to:
% 9.57/2.74 | (278) ~ (all_0_2_2 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (271) can reduce 146 to:
% 9.57/2.74 | (195) ~ (all_0_4_4 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 35 to:
% 9.57/2.74 | (436) ~ (all_0_6_6 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 81 to:
% 9.57/2.74 | (240) ~ (all_0_8_8 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 149 to:
% 9.57/2.74 | (377) ~ (all_0_9_9 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (493) can reduce 155 to:
% 9.57/2.74 | (316) ~ (e2 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 316 yields:
% 9.57/2.74 | (13) ~ (e2 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (373) can reduce 48 to:
% 9.57/2.74 | (315) ~ (all_0_11_11 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (373) can reduce 148 to:
% 9.57/2.74 | (652) ~ (all_0_12_12 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (373) can reduce 23 to:
% 9.57/2.74 | (242) ~ (all_0_13_13 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (373) can reduce 488 to:
% 9.57/2.74 | (245) ~ (e1 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 245 yields:
% 9.57/2.74 | (3) ~ (e1 = e0)
% 9.57/2.74 |
% 9.57/2.74 | From (285) and (84) follows:
% 9.57/2.74 | (656) op(e3, e3) = e0
% 9.57/2.74 |
% 9.57/2.74 | From (271) and (90) follows:
% 9.57/2.74 | (657) op(e2, e2) = e0
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (145), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (201) all_0_3_3 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (201) can reduce 118 to:
% 9.57/2.74 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Equations (201) can reduce 120 to:
% 9.57/2.74 | (212) ~ (all_0_11_11 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 212 yields:
% 9.57/2.74 | (156) ~ (all_0_11_11 = e2)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (47), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (97), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (288) ~ (all_0_0_0 = e0)
% 9.57/2.74 |
% 9.57/2.74 | Equations (285) can reduce 288 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (285) all_0_0_0 = e0
% 9.57/2.74 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (59), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (667) ~ (all_0_6_6 = e3)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (49), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (668) all_0_11_11 = e3
% 9.57/2.74 |
% 9.57/2.74 | Equations (668) can reduce 95 to:
% 9.57/2.74 | (669) ~ (all_0_8_8 = e3)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (128), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (670) all_0_6_6 = e3
% 9.57/2.74 |
% 9.57/2.74 | Equations (670) can reduce 667 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (667) ~ (all_0_6_6 = e3)
% 9.57/2.74 | (673) all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (673), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (674) all_0_6_6 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (674) can reduce 10 to:
% 9.57/2.74 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Equations (674) can reduce 126 to:
% 9.57/2.74 | (211) ~ (all_0_4_4 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Equations (674) can reduce 102 to:
% 9.57/2.74 | (677) ~ (all_0_14_14 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Simplifying 677 yields:
% 9.57/2.74 | (678) ~ (all_0_14_14 = e2)
% 9.57/2.74 |
% 9.57/2.74 | Equations (674) can reduce 183 to:
% 9.57/2.74 | (116) ~ (e2 = e1)
% 9.57/2.74 |
% 9.57/2.74 | Equations (674) can reduce 436 to:
% 9.57/2.74 | (13) ~ (e2 = e0)
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (151), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (257) all_0_8_8 = e2
% 9.57/2.74 |
% 9.57/2.74 | Equations (257) can reduce 445 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.74 | (446) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (44), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.74 | (685) all_0_8_8 = e3
% 9.57/2.74 |
% 9.57/2.74 | Equations (685) can reduce 669 to:
% 9.57/2.74 | (167) $false
% 9.57/2.74 |
% 9.57/2.74 |-The branch is then unsatisfiable
% 9.57/2.74 |-Branch two:
% 9.57/2.74 | (669) ~ (all_0_8_8 = e3)
% 9.57/2.74 | (688) all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 9.57/2.74 |
% 9.57/2.74 +-Applying beta-rule and splitting (688), into two cases.
% 9.57/2.74 |-Branch one:
% 9.57/2.75 | (257) all_0_8_8 = e2
% 9.57/2.75 |
% 9.57/2.75 | Equations (257) can reduce 445 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.75 | (692) all_0_8_8 = e1 | all_0_8_8 = e0
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (17), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (175) all_0_0_0 = e1
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (175,285) yields a new equation:
% 9.57/2.75 | (272) e1 = e0
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 272 yields:
% 9.57/2.75 | (273) e1 = e0
% 9.57/2.75 |
% 9.57/2.75 | Equations (273) can reduce 3 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (192) ~ (all_0_0_0 = e1)
% 9.57/2.75 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (698), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (406) all_0_1_1 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (406) can reduce 179 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.75 | (702) all_0_2_2 = e1 | all_0_3_3 = e1
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (52), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (169) all_0_0_0 = e2
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (169,285) yields a new equation:
% 9.57/2.75 | (349) e2 = e0
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 349 yields:
% 9.57/2.75 | (338) e2 = e0
% 9.57/2.75 |
% 9.57/2.75 | Equations (338) can reduce 13 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (425) ~ (all_0_0_0 = e2)
% 9.57/2.75 | (708) all_0_4_4 = e2 | all_0_8_8 = e2 | all_0_12_12 = e2
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (74), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (301) all_0_1_1 = e3
% 9.57/2.75 |
% 9.57/2.75 | Equations (301) can reduce 134 to:
% 9.57/2.75 | (555) ~ (all_0_2_2 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 555 yields:
% 9.57/2.75 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Equations (301) can reduce 105 to:
% 9.57/2.75 | (712) ~ (all_0_9_9 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 712 yields:
% 9.57/2.75 | (497) ~ (all_0_9_9 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Equations (301) can reduce 253 to:
% 9.57/2.75 | (86) ~ (e3 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (301) can reduce 227 to:
% 9.57/2.75 | (29) ~ (e3 = e0)
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (138), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (214) all_0_4_4 = e3
% 9.57/2.75 |
% 9.57/2.75 | Equations (214) can reduce 211 to:
% 9.57/2.75 | (86) ~ (e3 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (214) can reduce 195 to:
% 9.57/2.75 | (29) ~ (e3 = e0)
% 9.57/2.75 |
% 9.57/2.75 | From (214) and (11) follows:
% 9.57/2.75 | (218) op(e2, e3) = e3
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (9), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (281) all_0_2_2 = e3
% 9.57/2.75 |
% 9.57/2.75 | Equations (281) can reduce 269 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.75 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (702), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (565) all_0_2_2 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (565) can reduce 77 to:
% 9.57/2.75 | (725) ~ (all_0_14_14 = e1)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 725 yields:
% 9.57/2.75 | (726) ~ (all_0_14_14 = e1)
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (66), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (268) all_0_14_14 = e3
% 9.57/2.75 |
% 9.57/2.75 | Equations (268) can reduce 51 to:
% 9.57/2.75 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Equations (268) can reduce 127 to:
% 9.57/2.75 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.75 |
% 9.57/2.75 | Equations (268) can reduce 678 to:
% 9.57/2.75 | (86) ~ (e3 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (268) can reduce 726 to:
% 9.57/2.75 | (61) ~ (e3 = e1)
% 9.57/2.75 |
% 9.57/2.75 | From (268) and (19) follows:
% 9.57/2.75 | (270) op(e0, e1) = e3
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (708), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (469) all_0_4_4 = e2
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (469,214) yields a new equation:
% 9.57/2.75 | (329) e3 = e2
% 9.57/2.75 |
% 9.57/2.75 | Equations (329) can reduce 86 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (211) ~ (all_0_4_4 = e2)
% 9.57/2.75 | (737) all_0_8_8 = e2 | all_0_12_12 = e2
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (446), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (447) all_0_9_9 = e2
% 9.57/2.75 |
% 9.57/2.75 | Equations (447) can reduce 72 to:
% 9.57/2.75 | (739) ~ (all_0_13_13 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 739 yields:
% 9.57/2.75 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (447) can reduce 497 to:
% 9.57/2.75 | (741) ~ (e3 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 741 yields:
% 9.57/2.75 | (86) ~ (e3 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (447) can reduce 377 to:
% 9.57/2.75 | (13) ~ (e2 = e0)
% 9.57/2.75 |
% 9.57/2.75 | From (447) and (14) follows:
% 9.57/2.75 | (744) op(e1, e2) = e2
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (20), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (406) all_0_1_1 = e1
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (406,301) yields a new equation:
% 9.57/2.75 | (328) e3 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (328) can reduce 61 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.75 | (553) all_0_5_5 = e1 | all_0_9_9 = e1 | all_0_13_13 = e1
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (45), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (750) all_0_8_8 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (750) can reduce 104 to:
% 9.57/2.75 | (751) ~ (all_0_12_12 = e1)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 751 yields:
% 9.57/2.75 | (188) ~ (all_0_12_12 = e1)
% 9.57/2.75 |
% 9.57/2.75 | Equations (750) can reduce 240 to:
% 9.57/2.75 | (3) ~ (e1 = e0)
% 9.57/2.75 |
% 9.57/2.75 | From (750) and (56) follows:
% 9.57/2.75 | (754) op(e1, e3) = e1
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (28), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (219) all_0_12_12 = e3
% 9.57/2.75 |
% 9.57/2.75 | Equations (219) can reduce 216 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.75 | (231) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (231), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (232) all_0_12_12 = e2
% 9.57/2.75 |
% 9.57/2.75 | Equations (232) can reduce 141 to:
% 9.57/2.75 | (739) ~ (all_0_13_13 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 739 yields:
% 9.57/2.75 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.75 |
% 9.57/2.75 | Equations (232) can reduce 188 to:
% 9.57/2.75 | (116) ~ (e2 = e1)
% 9.57/2.75 |
% 9.57/2.75 | Equations (232) can reduce 652 to:
% 9.57/2.75 | (13) ~ (e2 = e0)
% 9.57/2.75 |
% 9.57/2.75 | From (232) and (147) follows:
% 9.57/2.75 | (764) op(e0, e3) = e2
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (75), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (236) all_0_12_12 = e1
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (236,232) yields a new equation:
% 9.57/2.75 | (330) e2 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (330) can reduce 116 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (188) ~ (all_0_12_12 = e1)
% 9.57/2.75 | (769) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (232) can reduce 188 to:
% 9.57/2.75 | (116) ~ (e2 = e1)
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (553), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (176) all_0_5_5 = e1
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (271,176) yields a new equation:
% 9.57/2.75 | (273) e1 = e0
% 9.57/2.75 |
% 9.57/2.75 | Equations (273) can reduce 3 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (197) ~ (all_0_5_5 = e1)
% 9.57/2.75 | (775) all_0_9_9 = e1 | all_0_13_13 = e1
% 9.57/2.75 |
% 9.57/2.75 +-Applying beta-rule and splitting (775), into two cases.
% 9.57/2.75 |-Branch one:
% 9.57/2.75 | (776) all_0_9_9 = e1
% 9.57/2.75 |
% 9.57/2.75 | Combining equations (447,776) yields a new equation:
% 9.57/2.75 | (422) e2 = e1
% 9.57/2.75 |
% 9.57/2.75 | Simplifying 422 yields:
% 9.57/2.75 | (330) e2 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (330) can reduce 116 to:
% 9.57/2.75 | (167) $false
% 9.57/2.75 |
% 9.57/2.75 |-The branch is then unsatisfiable
% 9.57/2.75 |-Branch two:
% 9.57/2.75 | (185) ~ (all_0_9_9 = e1)
% 9.57/2.75 | (459) all_0_13_13 = e1
% 9.57/2.75 |
% 9.57/2.75 | Equations (459) can reduce 457 to:
% 9.57/2.75 | (186) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 186 yields:
% 9.57/2.76 | (116) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Equations (459) can reduce 242 to:
% 9.57/2.76 | (3) ~ (e1 = e0)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (55), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (325) unit = e3
% 9.57/2.76 |
% 9.57/2.76 | From (325) and (46) follows:
% 9.57/2.76 | (326) op(e3, e3) = e3
% 9.57/2.76 |
% 9.57/2.76 | From (325) and (113) follows:
% 9.57/2.76 | (327) op(e2, e3) = e2
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e3, e3, e3, e0 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e0, yields:
% 9.57/2.76 | (264) e3 = e0
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e2, e3, e2, e3 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e2, yields:
% 9.57/2.76 | (329) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (264,329) yields a new equation:
% 9.57/2.76 | (338) e2 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (338) can reduce 13 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (332) ~ (unit = e3)
% 9.57/2.76 | (333) unit = e2 | unit = e1 | unit = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (333), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (334) unit = e2
% 9.57/2.76 |
% 9.57/2.76 | From (334) and (113) follows:
% 9.57/2.76 | (335) op(e2, e2) = e2
% 9.57/2.76 |
% 9.57/2.76 | From (334) and (25) follows:
% 9.57/2.76 | (796) op(e1, e2) = e1
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e2, e2, e2, e0 and discharging atoms op(e2, e2) = e2, op(e2, e2) = e0, yields:
% 9.57/2.76 | (338) e2 = e0
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e1, e2, e1, e2 and discharging atoms op(e1, e2) = e2, op(e1, e2) = e1, yields:
% 9.57/2.76 | (330) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (338,330) yields a new equation:
% 9.57/2.76 | (273) e1 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (273) can reduce 3 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (342) ~ (unit = e2)
% 9.57/2.76 | (343) unit = e1 | unit = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (343), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (344) unit = e1
% 9.57/2.76 |
% 9.57/2.76 | From (344) and (143) follows:
% 9.57/2.76 | (345) op(e1, e3) = e3
% 9.57/2.76 |
% 9.57/2.76 | From (344) and (133) follows:
% 9.57/2.76 | (346) op(e0, e1) = e0
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e1, e3, e3, e1 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e1, yields:
% 9.57/2.76 | (328) e3 = e1
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e0, e1, e0, e3 and discharging atoms op(e0, e1) = e3, op(e0, e1) = e0, yields:
% 9.57/2.76 | (264) e3 = e0
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (328,264) yields a new equation:
% 9.57/2.76 | (272) e1 = e0
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 272 yields:
% 9.57/2.76 | (273) e1 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (273) can reduce 3 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (352) ~ (unit = e1)
% 9.57/2.76 | (353) unit = e0
% 9.57/2.76 |
% 9.57/2.76 | From (353) and (143) follows:
% 9.57/2.76 | (356) op(e0, e3) = e3
% 9.57/2.76 |
% 9.57/2.76 | From (353) and (24) follows:
% 9.57/2.76 | (357) op(e0, e1) = e1
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e0, e3, e3, e2 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e2, yields:
% 9.57/2.76 | (329) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Instantiating formula (5) with e0, e1, e1, e3 and discharging atoms op(e0, e1) = e3, op(e0, e1) = e1, yields:
% 9.57/2.76 | (328) e3 = e1
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (329,328) yields a new equation:
% 9.57/2.76 | (422) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 422 yields:
% 9.57/2.76 | (330) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (330) can reduce 116 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (208) ~ (all_0_12_12 = e2)
% 9.57/2.76 | (235) all_0_12_12 = e1 | all_0_12_12 = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (235), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (236) all_0_12_12 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (236) can reduce 188 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (188) ~ (all_0_12_12 = e1)
% 9.57/2.76 | (239) all_0_12_12 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (239) can reduce 652 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (184) ~ (all_0_8_8 = e1)
% 9.57/2.76 | (828) all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (33), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (223) all_0_13_13 = e3
% 9.57/2.76 |
% 9.57/2.76 | Equations (223) can reduce 200 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.76 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (93), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (232) all_0_12_12 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (232) can reduce 141 to:
% 9.57/2.76 | (739) ~ (all_0_13_13 = e2)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 739 yields:
% 9.57/2.76 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (251), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (252) all_0_13_13 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (252) can reduce 457 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.76 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (458), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (459) all_0_13_13 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (459) can reduce 200 to:
% 9.57/2.76 | (841) ~ (e3 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 841 yields:
% 9.57/2.76 | (61) ~ (e3 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Equations (459) can reduce 457 to:
% 9.57/2.76 | (186) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 186 yields:
% 9.57/2.76 | (116) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Equations (459) can reduce 242 to:
% 9.57/2.76 | (3) ~ (e1 = e0)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (828), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (776) all_0_9_9 = e1
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (447,776) yields a new equation:
% 9.57/2.76 | (422) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 422 yields:
% 9.57/2.76 | (330) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (330) can reduce 116 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (185) ~ (all_0_9_9 = e1)
% 9.57/2.76 | (851) all_0_10_10 = e1 | all_0_11_11 = e1
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (851), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (177) all_0_10_10 = e1
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (493,177) yields a new equation:
% 9.57/2.76 | (273) e1 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (273) can reduce 3 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (855) ~ (all_0_10_10 = e1)
% 9.57/2.76 | (856) all_0_11_11 = e1
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (668,856) yields a new equation:
% 9.57/2.76 | (442) e3 = e1
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 442 yields:
% 9.57/2.76 | (328) e3 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (328) can reduce 61 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (189) ~ (all_0_13_13 = e1)
% 9.57/2.76 | (378) all_0_13_13 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (378) can reduce 242 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (208) ~ (all_0_12_12 = e2)
% 9.57/2.76 | (864) all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (251), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (252) all_0_13_13 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (252) can reduce 457 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.76 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (458), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (459) all_0_13_13 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (459) can reduce 457 to:
% 9.57/2.76 | (186) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 186 yields:
% 9.57/2.76 | (116) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (864), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (252) all_0_13_13 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (459,252) yields a new equation:
% 9.57/2.76 | (330) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (330) can reduce 116 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (457) ~ (all_0_13_13 = e2)
% 9.57/2.76 | (876) all_0_14_14 = e2 | all_0_15_15 = e2
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (876), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (877) all_0_14_14 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (268,877) yields a new equation:
% 9.57/2.76 | (878) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 878 yields:
% 9.57/2.76 | (329) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (329) can reduce 86 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (678) ~ (all_0_14_14 = e2)
% 9.57/2.76 | (172) all_0_15_15 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (373,172) yields a new equation:
% 9.57/2.76 | (338) e2 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (338) can reduce 13 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (189) ~ (all_0_13_13 = e1)
% 9.57/2.76 | (378) all_0_13_13 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (378) can reduce 242 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (254) ~ (all_0_9_9 = e2)
% 9.57/2.76 | (450) all_0_10_10 = e2 | all_0_11_11 = e2
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (692), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (750) all_0_8_8 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (750) can reduce 445 to:
% 9.57/2.76 | (186) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 186 yields:
% 9.57/2.76 | (116) ~ (e2 = e1)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (737), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (257) all_0_8_8 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (750,257) yields a new equation:
% 9.57/2.76 | (330) e2 = e1
% 9.57/2.76 |
% 9.57/2.76 | Equations (330) can reduce 116 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (445) ~ (all_0_8_8 = e2)
% 9.57/2.76 | (232) all_0_12_12 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (232) can reduce 216 to:
% 9.57/2.76 | (741) ~ (e3 = e2)
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 741 yields:
% 9.57/2.76 | (86) ~ (e3 = e2)
% 9.57/2.76 |
% 9.57/2.76 | Equations (232) can reduce 652 to:
% 9.57/2.76 | (13) ~ (e2 = e0)
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (450), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (171) all_0_10_10 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (493,171) yields a new equation:
% 9.57/2.76 | (338) e2 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (338) can reduce 13 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (155) ~ (all_0_10_10 = e2)
% 9.57/2.76 | (455) all_0_11_11 = e2
% 9.57/2.76 |
% 9.57/2.76 | Combining equations (668,455) yields a new equation:
% 9.57/2.76 | (878) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Simplifying 878 yields:
% 9.57/2.76 | (329) e3 = e2
% 9.57/2.76 |
% 9.57/2.76 | Equations (329) can reduce 86 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (184) ~ (all_0_8_8 = e1)
% 9.57/2.76 | (910) all_0_8_8 = e0
% 9.57/2.76 |
% 9.57/2.76 | Equations (910) can reduce 240 to:
% 9.57/2.76 | (167) $false
% 9.57/2.76 |
% 9.57/2.76 |-The branch is then unsatisfiable
% 9.57/2.76 |-Branch two:
% 9.57/2.76 | (440) ~ (all_0_14_14 = e3)
% 9.57/2.76 | (913) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 9.57/2.76 |
% 9.57/2.76 +-Applying beta-rule and splitting (723), into two cases.
% 9.57/2.76 |-Branch one:
% 9.57/2.76 | (670) all_0_6_6 = e3
% 9.57/2.76 |
% 9.57/2.77 | Combining equations (674,670) yields a new equation:
% 9.57/2.77 | (329) e3 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (329) can reduce 86 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (667) ~ (all_0_6_6 = e3)
% 9.57/2.77 | (918) all_0_10_10 = e3 | all_0_14_14 = e3
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (918), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (165) all_0_10_10 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (165,493) yields a new equation:
% 9.57/2.77 | (506) e3 = e0
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 506 yields:
% 9.57/2.77 | (264) e3 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (264) can reduce 29 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (157) ~ (all_0_10_10 = e3)
% 9.57/2.77 | (268) all_0_14_14 = e3
% 9.57/2.77 |
% 9.57/2.77 | Equations (268) can reduce 440 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (180) ~ (all_0_2_2 = e1)
% 9.57/2.77 | (927) all_0_3_3 = e1
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (201,927) yields a new equation:
% 9.57/2.77 | (422) e2 = e1
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 422 yields:
% 9.57/2.77 | (330) e2 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (330) can reduce 116 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (467) ~ (all_0_4_4 = e3)
% 9.57/2.77 | (932) all_0_5_5 = e3 | all_0_6_6 = e3 | all_0_7_7 = e3
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (38), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (281) all_0_2_2 = e3
% 9.57/2.77 |
% 9.57/2.77 | Equations (281) can reduce 269 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.77 | (284) all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (284), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (291) all_0_2_2 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (291) can reduce 415 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (415) ~ (all_0_2_2 = e2)
% 9.57/2.77 | (416) all_0_2_2 = e1 | all_0_2_2 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (416), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (565) all_0_2_2 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (565) can reduce 269 to:
% 9.57/2.77 | (841) ~ (e3 = e1)
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 841 yields:
% 9.57/2.77 | (61) ~ (e3 = e1)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (9), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (281) all_0_2_2 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (565,281) yields a new equation:
% 9.57/2.77 | (328) e3 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (328) can reduce 61 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (269) ~ (all_0_2_2 = e3)
% 9.57/2.77 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 9.57/2.77 |
% 9.57/2.77 | Equations (565) can reduce 269 to:
% 9.57/2.77 | (841) ~ (e3 = e1)
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 841 yields:
% 9.57/2.77 | (61) ~ (e3 = e1)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (43), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (163) all_0_0_0 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (163,285) yields a new equation:
% 9.57/2.77 | (506) e3 = e0
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 506 yields:
% 9.57/2.77 | (264) e3 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (264) can reduce 29 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (955) ~ (all_0_0_0 = e3)
% 9.57/2.77 | (956) all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3
% 9.57/2.77 |
% 9.57/2.77 | Equations (285) can reduce 955 to:
% 9.57/2.77 | (243) ~ (e3 = e0)
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 243 yields:
% 9.57/2.77 | (29) ~ (e3 = e0)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (932), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (164) all_0_5_5 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (271,164) yields a new equation:
% 9.57/2.77 | (264) e3 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (264) can reduce 29 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (962) ~ (all_0_5_5 = e3)
% 9.57/2.77 | (963) all_0_6_6 = e3 | all_0_7_7 = e3
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (963), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (670) all_0_6_6 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (674,670) yields a new equation:
% 9.57/2.77 | (329) e3 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (329) can reduce 86 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (667) ~ (all_0_6_6 = e3)
% 9.57/2.77 | (968) all_0_7_7 = e3
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (581,968) yields a new equation:
% 9.57/2.77 | (328) e3 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (328) can reduce 61 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (180) ~ (all_0_2_2 = e1)
% 9.57/2.77 | (400) all_0_2_2 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (400) can reduce 278 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (382) ~ (all_0_1_1 = e3)
% 9.57/2.77 | (383) all_0_1_1 = e2 | all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (383), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (396) all_0_1_1 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (396) can reduce 253 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (253) ~ (all_0_1_1 = e2)
% 9.57/2.77 | (399) all_0_1_1 = e1 | all_0_1_1 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (399), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (406) all_0_1_1 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (406) can reduce 179 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.77 | (297) all_0_1_1 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (297) can reduce 227 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (985) ~ (all_0_6_6 = e2)
% 9.57/2.77 | (986) all_0_6_6 = e1 | all_0_6_6 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (986), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (578) all_0_6_6 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (578) can reduce 183 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (183) ~ (all_0_6_6 = e1)
% 9.57/2.77 | (277) all_0_6_6 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (277) can reduce 436 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (992) ~ (all_0_11_11 = e3)
% 9.57/2.77 | (993) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (993), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (455) all_0_11_11 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (455) can reduce 156 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (156) ~ (all_0_11_11 = e2)
% 9.57/2.77 | (997) all_0_11_11 = e1 | all_0_11_11 = e0
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (997), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (856) all_0_11_11 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (856) can reduce 615 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (615) ~ (all_0_11_11 = e1)
% 9.57/2.77 | (370) all_0_11_11 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (370) can reduce 315 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (670) all_0_6_6 = e3
% 9.57/2.77 | (598) ~ (all_0_10_10 = e0)
% 9.57/2.77 |
% 9.57/2.77 | Equations (493) can reduce 598 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (406) all_0_1_1 = e1
% 9.57/2.77 | (159) ~ (all_0_5_5 = e0)
% 9.57/2.77 |
% 9.57/2.77 | Equations (271) can reduce 159 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (196) ~ (all_0_3_3 = e2)
% 9.57/2.77 | (204) all_0_7_7 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (204), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (209) all_0_7_7 = e2
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (581,209) yields a new equation:
% 9.57/2.77 | (330) e2 = e1
% 9.57/2.77 |
% 9.57/2.77 | Equations (330) can reduce 116 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (478) ~ (all_0_7_7 = e2)
% 9.57/2.77 | (479) all_0_11_11 = e2 | all_0_15_15 = e2
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (479), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (455) all_0_11_11 = e2
% 9.57/2.77 |
% 9.57/2.77 | Equations (455) can reduce 156 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (156) ~ (all_0_11_11 = e2)
% 9.57/2.77 | (172) all_0_15_15 = e2
% 9.57/2.77 |
% 9.57/2.77 | Combining equations (172,373) yields a new equation:
% 9.57/2.77 | (349) e2 = e0
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 349 yields:
% 9.57/2.77 | (338) e2 = e0
% 9.57/2.77 |
% 9.57/2.77 | Equations (338) can reduce 13 to:
% 9.57/2.77 | (167) $false
% 9.57/2.77 |
% 9.57/2.77 |-The branch is then unsatisfiable
% 9.57/2.77 |-Branch two:
% 9.57/2.77 | (165) all_0_10_10 = e3
% 9.57/2.77 | (678) ~ (all_0_14_14 = e2)
% 9.57/2.77 |
% 9.57/2.77 | Equations (165) can reduce 155 to:
% 9.57/2.77 | (86) ~ (e3 = e2)
% 9.57/2.77 |
% 9.57/2.77 | From (165) and (130) follows:
% 9.57/2.77 | (1026) op(e1, e1) = e3
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (109), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (436) ~ (all_0_6_6 = e0)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (82), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (160), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 9.57/2.77 |
% 9.57/2.77 +-Applying beta-rule and splitting (161), into two cases.
% 9.57/2.77 |-Branch one:
% 9.57/2.77 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 9.57/2.77 |
% 9.57/2.77 | Applying alpha-rule on (162) yields:
% 9.57/2.77 | (163) all_0_0_0 = e3
% 9.57/2.77 | (164) all_0_5_5 = e3
% 9.57/2.77 | (165) all_0_10_10 = e3
% 9.57/2.77 | (166) all_0_15_15 = e3
% 9.57/2.77 |
% 9.57/2.77 | Equations (166) can reduce 6 to:
% 9.57/2.77 | (1035) ~ (all_0_3_3 = e3)
% 9.57/2.77 |
% 9.57/2.77 | Equations (164) can reduce 146 to:
% 9.57/2.77 | (467) ~ (all_0_4_4 = e3)
% 9.57/2.77 |
% 9.57/2.77 | Equations (164) can reduce 139 to:
% 9.57/2.77 | (1037) ~ (all_0_6_6 = e3)
% 9.57/2.77 |
% 9.57/2.77 | Simplifying 1037 yields:
% 9.57/2.77 | (667) ~ (all_0_6_6 = e3)
% 9.57/2.77 |
% 9.57/2.77 | Equations (166) can reduce 100 to:
% 9.57/2.77 | (1039) ~ (all_0_7_7 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (166) can reduce 48 to:
% 9.57/2.78 | (992) ~ (all_0_11_11 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (166) can reduce 148 to:
% 9.57/2.78 | (216) ~ (all_0_12_12 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (166) can reduce 23 to:
% 9.57/2.78 | (200) ~ (all_0_13_13 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (166) can reduce 41 to:
% 9.57/2.78 | (440) ~ (all_0_14_14 = e3)
% 9.57/2.78 |
% 9.57/2.78 | From (164) and (90) follows:
% 9.57/2.78 | (1044) op(e2, e2) = e3
% 9.57/2.78 |
% 9.57/2.78 | From (166) and (65) follows:
% 9.57/2.78 | (1045) op(e0, e0) = e3
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (121), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (962) ~ (all_0_5_5 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (164) can reduce 962 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (164) all_0_5_5 = e3
% 9.57/2.78 | (189) ~ (all_0_13_13 = e1)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (32), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (962) ~ (all_0_5_5 = e3)
% 9.57/2.78 |
% 9.57/2.78 | Equations (164) can reduce 962 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (164) all_0_5_5 = e3
% 9.57/2.78 | (377) ~ (all_0_9_9 = e0)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (96), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (158) ~ (all_0_7_7 = e1)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (75), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (236) all_0_12_12 = e1
% 9.57/2.78 |
% 9.57/2.78 | Equations (236) can reduce 36 to:
% 9.57/2.78 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Equations (236) can reduce 141 to:
% 9.57/2.78 | (1057) ~ (all_0_13_13 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 1057 yields:
% 9.57/2.78 | (189) ~ (all_0_13_13 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Equations (236) can reduce 216 to:
% 9.57/2.78 | (841) ~ (e3 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 841 yields:
% 9.57/2.78 | (61) ~ (e3 = e1)
% 9.57/2.78 |
% 9.57/2.78 | From (236) and (147) follows:
% 9.57/2.78 | (1061) op(e0, e3) = e1
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (106), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (473) all_0_4_4 = e1
% 9.57/2.78 |
% 9.57/2.78 | Equations (473) can reduce 182 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.78 | (572) all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (572), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (176) all_0_5_5 = e1
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (176,164) yields a new equation:
% 9.57/2.78 | (328) e3 = e1
% 9.57/2.78 |
% 9.57/2.78 | Equations (328) can reduce 61 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (197) ~ (all_0_5_5 = e1)
% 9.57/2.78 | (577) all_0_6_6 = e1 | all_0_7_7 = e1
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (577), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (578) all_0_6_6 = e1
% 9.57/2.78 |
% 9.57/2.78 | Equations (578) can reduce 126 to:
% 9.57/2.78 | (182) ~ (all_0_4_4 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Equations (578) can reduce 102 to:
% 9.57/2.78 | (725) ~ (all_0_14_14 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 725 yields:
% 9.57/2.78 | (726) ~ (all_0_14_14 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Equations (578) can reduce 667 to:
% 9.57/2.78 | (841) ~ (e3 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 841 yields:
% 9.57/2.78 | (61) ~ (e3 = e1)
% 9.57/2.78 |
% 9.57/2.78 | Equations (578) can reduce 436 to:
% 9.57/2.78 | (3) ~ (e1 = e0)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (108), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (291) all_0_2_2 = e2
% 9.57/2.78 |
% 9.57/2.78 | Equations (291) can reduce 50 to:
% 9.57/2.78 | (293) ~ (all_0_3_3 = e2)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 293 yields:
% 9.57/2.78 | (196) ~ (all_0_3_3 = e2)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (7), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (400) all_0_2_2 = e0
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (400,291) yields a new equation:
% 9.57/2.78 | (338) e2 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (338) can reduce 13 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (278) ~ (all_0_2_2 = e0)
% 9.57/2.78 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (1085), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (277) all_0_6_6 = e0
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (578,277) yields a new equation:
% 9.57/2.78 | (272) e1 = e0
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 272 yields:
% 9.57/2.78 | (273) e1 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (273) can reduce 3 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (436) ~ (all_0_6_6 = e0)
% 9.57/2.78 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (1091), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (493) all_0_10_10 = e0
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (493,165) yields a new equation:
% 9.57/2.78 | (264) e3 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (264) can reduce 29 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (598) ~ (all_0_10_10 = e0)
% 9.57/2.78 | (1096) all_0_14_14 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (1096) can reduce 127 to:
% 9.57/2.78 | (242) ~ (all_0_13_13 = e0)
% 9.57/2.78 |
% 9.57/2.78 | Equations (1096) can reduce 440 to:
% 9.57/2.78 | (243) ~ (e3 = e0)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 243 yields:
% 9.57/2.78 | (29) ~ (e3 = e0)
% 9.57/2.78 |
% 9.57/2.78 | Equations (1096) can reduce 726 to:
% 9.57/2.78 | (245) ~ (e1 = e0)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 245 yields:
% 9.57/2.78 | (3) ~ (e1 = e0)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (70), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (297) all_0_1_1 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (297) can reduce 118 to:
% 9.57/2.78 | (1103) ~ (all_0_3_3 = e0)
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 1103 yields:
% 9.57/2.78 | (362) ~ (all_0_3_3 = e0)
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (20), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (406) all_0_1_1 = e1
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (406,297) yields a new equation:
% 9.57/2.78 | (272) e1 = e0
% 9.57/2.78 |
% 9.57/2.78 | Simplifying 272 yields:
% 9.57/2.78 | (273) e1 = e0
% 9.57/2.78 |
% 9.57/2.78 | Equations (273) can reduce 3 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (179) ~ (all_0_1_1 = e1)
% 9.57/2.78 | (553) all_0_5_5 = e1 | all_0_9_9 = e1 | all_0_13_13 = e1
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (150), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (1111) all_0_3_3 = e3
% 9.57/2.78 |
% 9.57/2.78 | Equations (1111) can reduce 1035 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (1035) ~ (all_0_3_3 = e3)
% 9.57/2.78 | (1114) all_0_3_3 = e2 | all_0_3_3 = e1 | all_0_3_3 = e0
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (553), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (176) all_0_5_5 = e1
% 9.57/2.78 |
% 9.57/2.78 | Combining equations (176,164) yields a new equation:
% 9.57/2.78 | (328) e3 = e1
% 9.57/2.78 |
% 9.57/2.78 | Equations (328) can reduce 61 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (197) ~ (all_0_5_5 = e1)
% 9.57/2.78 | (775) all_0_9_9 = e1 | all_0_13_13 = e1
% 9.57/2.78 |
% 9.57/2.78 +-Applying beta-rule and splitting (1114), into two cases.
% 9.57/2.78 |-Branch one:
% 9.57/2.78 | (201) all_0_3_3 = e2
% 9.57/2.78 |
% 9.57/2.78 | Equations (201) can reduce 196 to:
% 9.57/2.78 | (167) $false
% 9.57/2.78 |
% 9.57/2.78 |-The branch is then unsatisfiable
% 9.57/2.78 |-Branch two:
% 9.57/2.78 | (196) ~ (all_0_3_3 = e2)
% 9.97/2.78 | (1123) all_0_3_3 = e1 | all_0_3_3 = e0
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (1123), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (927) all_0_3_3 = e1
% 9.97/2.78 |
% 9.97/2.78 | Equations (927) can reduce 68 to:
% 9.97/2.78 | (1125) ~ (all_0_7_7 = e1)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 1125 yields:
% 9.97/2.78 | (158) ~ (all_0_7_7 = e1)
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (775), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (776) all_0_9_9 = e1
% 9.97/2.78 |
% 9.97/2.78 | Equations (776) can reduce 137 to:
% 9.97/2.78 | (614) ~ (all_0_11_11 = e1)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 614 yields:
% 9.97/2.78 | (615) ~ (all_0_11_11 = e1)
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (49), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (668) all_0_11_11 = e3
% 9.97/2.78 |
% 9.97/2.78 | Equations (668) can reduce 992 to:
% 9.97/2.78 | (167) $false
% 9.97/2.78 |
% 9.97/2.78 |-The branch is then unsatisfiable
% 9.97/2.78 |-Branch two:
% 9.97/2.78 | (992) ~ (all_0_11_11 = e3)
% 9.97/2.78 | (993) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (151), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (257) all_0_8_8 = e2
% 9.97/2.78 |
% 9.97/2.78 | Equations (257) can reduce 95 to:
% 9.97/2.78 | (212) ~ (all_0_11_11 = e2)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 212 yields:
% 9.97/2.78 | (156) ~ (all_0_11_11 = e2)
% 9.97/2.78 |
% 9.97/2.78 | From (257) and (56) follows:
% 9.97/2.78 | (262) op(e1, e3) = e2
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (993), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (455) all_0_11_11 = e2
% 9.97/2.78 |
% 9.97/2.78 | Equations (455) can reduce 156 to:
% 9.97/2.78 | (167) $false
% 9.97/2.78 |
% 9.97/2.78 |-The branch is then unsatisfiable
% 9.97/2.78 |-Branch two:
% 9.97/2.78 | (156) ~ (all_0_11_11 = e2)
% 9.97/2.78 | (997) all_0_11_11 = e1 | all_0_11_11 = e0
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (997), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (856) all_0_11_11 = e1
% 9.97/2.78 |
% 9.97/2.78 | Equations (856) can reduce 615 to:
% 9.97/2.78 | (167) $false
% 9.97/2.78 |
% 9.97/2.78 |-The branch is then unsatisfiable
% 9.97/2.78 |-Branch two:
% 9.97/2.78 | (615) ~ (all_0_11_11 = e1)
% 9.97/2.78 | (370) all_0_11_11 = e0
% 9.97/2.78 |
% 9.97/2.78 | Equations (370) can reduce 114 to:
% 9.97/2.78 | (368) ~ (all_0_7_7 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Equations (370) can reduce 992 to:
% 9.97/2.78 | (243) ~ (e3 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 243 yields:
% 9.97/2.78 | (29) ~ (e3 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Equations (370) can reduce 615 to:
% 9.97/2.78 | (245) ~ (e1 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 245 yields:
% 9.97/2.78 | (3) ~ (e1 = e0)
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (87), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (263) all_0_4_4 = e0
% 9.97/2.78 |
% 9.97/2.78 | Equations (263) can reduce 122 to:
% 9.97/2.78 | (1152) ~ (all_0_7_7 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 1152 yields:
% 9.97/2.78 | (368) ~ (all_0_7_7 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Equations (263) can reduce 182 to:
% 9.97/2.78 | (245) ~ (e1 = e0)
% 9.97/2.78 |
% 9.97/2.78 | Simplifying 245 yields:
% 9.97/2.78 | (3) ~ (e1 = e0)
% 9.97/2.78 |
% 9.97/2.78 | From (263) and (11) follows:
% 9.97/2.78 | (1156) op(e2, e3) = e0
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (131), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (968) all_0_7_7 = e3
% 9.97/2.78 |
% 9.97/2.78 | Equations (968) can reduce 1039 to:
% 9.97/2.78 | (167) $false
% 9.97/2.78 |
% 9.97/2.78 |-The branch is then unsatisfiable
% 9.97/2.78 |-Branch two:
% 9.97/2.78 | (1039) ~ (all_0_7_7 = e3)
% 9.97/2.78 | (1160) all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (1160), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (209) all_0_7_7 = e2
% 9.97/2.78 |
% 9.97/2.78 | Equations (209) can reduce 368 to:
% 9.97/2.78 | (13) ~ (e2 = e0)
% 9.97/2.78 |
% 9.97/2.78 +-Applying beta-rule and splitting (55), into two cases.
% 9.97/2.78 |-Branch one:
% 9.97/2.78 | (325) unit = e3
% 9.97/2.78 |
% 9.97/2.78 | From (325) and (113) follows:
% 9.97/2.78 | (327) op(e2, e3) = e2
% 9.97/2.78 |
% 9.97/2.78 | From (325) and (25) follows:
% 9.97/2.78 | (754) op(e1, e3) = e1
% 9.97/2.78 |
% 9.97/2.78 | Instantiating formula (5) with e2, e3, e2, e0 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e0, yields:
% 9.97/2.78 | (338) e2 = e0
% 9.97/2.78 |
% 9.97/2.78 | Instantiating formula (5) with e1, e3, e1, e2 and discharging atoms op(e1, e3) = e2, op(e1, e3) = e1, yields:
% 9.97/2.79 | (330) e2 = e1
% 9.97/2.79 |
% 9.97/2.79 | Combining equations (338,330) yields a new equation:
% 9.97/2.79 | (273) e1 = e0
% 9.97/2.79 |
% 9.97/2.79 | Equations (273) can reduce 3 to:
% 9.97/2.79 | (167) $false
% 9.97/2.79 |
% 9.97/2.79 |-The branch is then unsatisfiable
% 9.97/2.79 |-Branch two:
% 9.97/2.79 | (332) ~ (unit = e3)
% 9.97/2.79 | (333) unit = e2 | unit = e1 | unit = e0
% 9.97/2.79 |
% 9.97/2.79 +-Applying beta-rule and splitting (333), into two cases.
% 9.97/2.79 |-Branch one:
% 9.97/2.79 | (334) unit = e2
% 9.97/2.79 |
% 9.97/2.79 | From (334) and (143) follows:
% 9.97/2.79 | (218) op(e2, e3) = e3
% 9.97/2.79 |
% 9.97/2.79 | From (334) and (113) follows:
% 9.97/2.79 | (335) op(e2, e2) = e2
% 9.97/2.79 |
% 9.97/2.79 | Instantiating formula (5) with e2, e3, e3, e0 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e0, yields:
% 9.97/2.79 | (264) e3 = e0
% 9.97/2.79 |
% 9.97/2.79 | Instantiating formula (5) with e2, e2, e2, e3 and discharging atoms op(e2, e2) = e3, op(e2, e2) = e2, yields:
% 9.97/2.79 | (329) e3 = e2
% 9.97/2.79 |
% 9.97/2.79 | Combining equations (264,329) yields a new equation:
% 9.97/2.79 | (338) e2 = e0
% 9.97/2.79 |
% 9.97/2.79 | Equations (338) can reduce 13 to:
% 9.97/2.79 | (167) $false
% 9.97/2.79 |
% 9.97/2.79 |-The branch is then unsatisfiable
% 9.97/2.79 |-Branch two:
% 9.97/2.79 | (342) ~ (unit = e2)
% 9.97/2.79 | (343) unit = e1 | unit = e0
% 9.97/2.79 |
% 9.97/2.79 +-Applying beta-rule and splitting (343), into two cases.
% 9.97/2.79 |-Branch one:
% 9.97/2.79 | (344) unit = e1
% 9.97/2.79 |
% 9.97/2.79 | Equations (344) can reduce 342 to:
% 9.97/2.79 | (186) ~ (e2 = e1)
% 9.97/2.79 |
% 9.97/2.79 | Simplifying 186 yields:
% 9.97/2.79 | (116) ~ (e2 = e1)
% 9.97/2.79 |
% 9.97/2.79 | From (344) and (143) follows:
% 9.97/2.79 | (345) op(e1, e3) = e3
% 9.97/2.79 |
% 9.97/2.79 | From (344) and (25) follows:
% 9.97/2.79 | (1185) op(e1, e1) = e1
% 9.97/2.79 |
% 9.97/2.79 | Instantiating formula (5) with e1, e3, e3, e2 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e2, yields:
% 9.97/2.79 | (329) e3 = e2
% 9.97/2.79 |
% 9.97/2.79 | Instantiating formula (5) with e1, e1, e1, e3 and discharging atoms op(e1, e1) = e3, op(e1, e1) = e1, yields:
% 9.97/2.79 | (328) e3 = e1
% 9.97/2.79 |
% 9.97/2.79 | Combining equations (329,328) yields a new equation:
% 9.97/2.79 | (422) e2 = e1
% 9.97/2.79 |
% 9.97/2.79 | Simplifying 422 yields:
% 9.97/2.79 | (330) e2 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (330) can reduce 116 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (352) ~ (unit = e1)
% 10.00/2.79 | (353) unit = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (353) can reduce 352 to:
% 10.00/2.79 | (245) ~ (e1 = e0)
% 10.00/2.79 |
% 10.00/2.79 | Simplifying 245 yields:
% 10.00/2.79 | (3) ~ (e1 = e0)
% 10.00/2.79 |
% 10.00/2.79 | From (353) and (143) follows:
% 10.00/2.79 | (356) op(e0, e3) = e3
% 10.00/2.79 |
% 10.00/2.79 | From (353) and (133) follows:
% 10.00/2.79 | (1196) op(e0, e0) = e0
% 10.00/2.79 |
% 10.00/2.79 | Instantiating formula (5) with e0, e3, e3, e1 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e1, yields:
% 10.00/2.79 | (328) e3 = e1
% 10.00/2.79 |
% 10.00/2.79 | Instantiating formula (5) with e0, e0, e0, e3 and discharging atoms op(e0, e0) = e3, op(e0, e0) = e0, yields:
% 10.00/2.79 | (264) e3 = e0
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (328,264) yields a new equation:
% 10.00/2.79 | (272) e1 = e0
% 10.00/2.79 |
% 10.00/2.79 | Simplifying 272 yields:
% 10.00/2.79 | (273) e1 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (273) can reduce 3 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.79 | (1203) all_0_7_7 = e1 | all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (1203), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (581) all_0_7_7 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (581) can reduce 158 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (158) ~ (all_0_7_7 = e1)
% 10.00/2.79 | (364) all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (364) can reduce 368 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (195) ~ (all_0_4_4 = e0)
% 10.00/2.79 | (267) all_0_5_5 = e0 | all_0_6_6 = e0 | all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (267), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (271) all_0_5_5 = e0
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (271,164) yields a new equation:
% 10.00/2.79 | (264) e3 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (264) can reduce 29 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (159) ~ (all_0_5_5 = e0)
% 10.00/2.79 | (276) all_0_6_6 = e0 | all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (276), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (277) all_0_6_6 = e0
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (277,578) yields a new equation:
% 10.00/2.79 | (273) e1 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (273) can reduce 3 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (436) ~ (all_0_6_6 = e0)
% 10.00/2.79 | (364) all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (364) can reduce 368 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (445) ~ (all_0_8_8 = e2)
% 10.00/2.79 | (446) all_0_9_9 = e2 | all_0_10_10 = e2 | all_0_11_11 = e2
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (993), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (455) all_0_11_11 = e2
% 10.00/2.79 |
% 10.00/2.79 | Equations (455) can reduce 156 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (156) ~ (all_0_11_11 = e2)
% 10.00/2.79 | (997) all_0_11_11 = e1 | all_0_11_11 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (997), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (856) all_0_11_11 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (856) can reduce 615 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (615) ~ (all_0_11_11 = e1)
% 10.00/2.79 | (370) all_0_11_11 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (370) can reduce 114 to:
% 10.00/2.79 | (368) ~ (all_0_7_7 = e0)
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (131), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (968) all_0_7_7 = e3
% 10.00/2.79 |
% 10.00/2.79 | Equations (968) can reduce 1039 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (1039) ~ (all_0_7_7 = e3)
% 10.00/2.79 | (1160) all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (1160), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (209) all_0_7_7 = e2
% 10.00/2.79 |
% 10.00/2.79 | Equations (209) can reduce 122 to:
% 10.00/2.79 | (211) ~ (all_0_4_4 = e2)
% 10.00/2.79 |
% 10.00/2.79 | Equations (209) can reduce 1039 to:
% 10.00/2.79 | (741) ~ (e3 = e2)
% 10.00/2.79 |
% 10.00/2.79 | Simplifying 741 yields:
% 10.00/2.79 | (86) ~ (e3 = e2)
% 10.00/2.79 |
% 10.00/2.79 | Equations (209) can reduce 158 to:
% 10.00/2.79 | (116) ~ (e2 = e1)
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (52), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (169) all_0_0_0 = e2
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (169,163) yields a new equation:
% 10.00/2.79 | (329) e3 = e2
% 10.00/2.79 |
% 10.00/2.79 | Equations (329) can reduce 86 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (425) ~ (all_0_0_0 = e2)
% 10.00/2.79 | (708) all_0_4_4 = e2 | all_0_8_8 = e2 | all_0_12_12 = e2
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (708), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (469) all_0_4_4 = e2
% 10.00/2.79 |
% 10.00/2.79 | Equations (469) can reduce 211 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (211) ~ (all_0_4_4 = e2)
% 10.00/2.79 | (737) all_0_8_8 = e2 | all_0_12_12 = e2
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (737), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (257) all_0_8_8 = e2
% 10.00/2.79 |
% 10.00/2.79 | Equations (257) can reduce 445 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (445) ~ (all_0_8_8 = e2)
% 10.00/2.79 | (232) all_0_12_12 = e2
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (236,232) yields a new equation:
% 10.00/2.79 | (330) e2 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (330) can reduce 116 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.79 | (1203) all_0_7_7 = e1 | all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (1203), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (581) all_0_7_7 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (581) can reduce 158 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (158) ~ (all_0_7_7 = e1)
% 10.00/2.79 | (364) all_0_7_7 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (364) can reduce 368 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (185) ~ (all_0_9_9 = e1)
% 10.00/2.79 | (459) all_0_13_13 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (459) can reduce 189 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (181) ~ (all_0_3_3 = e1)
% 10.00/2.79 | (320) all_0_3_3 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (320) can reduce 362 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (227) ~ (all_0_1_1 = e0)
% 10.00/2.79 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (307), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (271) all_0_5_5 = e0
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (164,271) yields a new equation:
% 10.00/2.79 | (506) e3 = e0
% 10.00/2.79 |
% 10.00/2.79 | Simplifying 506 yields:
% 10.00/2.79 | (264) e3 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (264) can reduce 29 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (159) ~ (all_0_5_5 = e0)
% 10.00/2.79 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (312), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (313) all_0_9_9 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (313) can reduce 377 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (377) ~ (all_0_9_9 = e0)
% 10.00/2.79 | (378) all_0_13_13 = e0
% 10.00/2.79 |
% 10.00/2.79 | Equations (378) can reduce 242 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (415) ~ (all_0_2_2 = e2)
% 10.00/2.79 | (420) all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (420), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (674) all_0_6_6 = e2
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (578,674) yields a new equation:
% 10.00/2.79 | (330) e2 = e1
% 10.00/2.79 |
% 10.00/2.79 | Equations (330) can reduce 116 to:
% 10.00/2.79 | (167) $false
% 10.00/2.79 |
% 10.00/2.79 |-The branch is then unsatisfiable
% 10.00/2.79 |-Branch two:
% 10.00/2.79 | (985) ~ (all_0_6_6 = e2)
% 10.00/2.79 | (1289) all_0_10_10 = e2 | all_0_14_14 = e2
% 10.00/2.79 |
% 10.00/2.79 +-Applying beta-rule and splitting (1289), into two cases.
% 10.00/2.79 |-Branch one:
% 10.00/2.79 | (171) all_0_10_10 = e2
% 10.00/2.79 |
% 10.00/2.79 | Combining equations (165,171) yields a new equation:
% 10.00/2.79 | (878) e3 = e2
% 10.00/2.79 |
% 10.00/2.79 | Simplifying 878 yields:
% 10.00/2.79 | (329) e3 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (329) can reduce 86 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (155) ~ (all_0_10_10 = e2)
% 10.00/2.80 | (877) all_0_14_14 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (877) can reduce 678 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (183) ~ (all_0_6_6 = e1)
% 10.00/2.80 | (581) all_0_7_7 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (581) can reduce 158 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (188) ~ (all_0_12_12 = e1)
% 10.00/2.80 | (769) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (769), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (459) all_0_13_13 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (459) can reduce 189 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (189) ~ (all_0_13_13 = e1)
% 10.00/2.80 | (1305) all_0_14_14 = e1 | all_0_15_15 = e1
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (1305), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (1306) all_0_14_14 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (1306) can reduce 51 to:
% 10.00/2.80 | (188) ~ (all_0_12_12 = e1)
% 10.00/2.80 |
% 10.00/2.80 | Equations (1306) can reduce 678 to:
% 10.00/2.80 | (186) ~ (e2 = e1)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 186 yields:
% 10.00/2.80 | (116) ~ (e2 = e1)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (7), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (400) all_0_2_2 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (400) can reduce 134 to:
% 10.00/2.80 | (227) ~ (all_0_1_1 = e0)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (108), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (291) all_0_2_2 = e2
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (291,400) yields a new equation:
% 10.00/2.80 | (349) e2 = e0
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 349 yields:
% 10.00/2.80 | (338) e2 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (338) can reduce 13 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (415) ~ (all_0_2_2 = e2)
% 10.00/2.80 | (420) all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (128), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (670) all_0_6_6 = e3
% 10.00/2.80 |
% 10.00/2.80 | Equations (670) can reduce 667 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (667) ~ (all_0_6_6 = e3)
% 10.00/2.80 | (673) all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (673), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (674) all_0_6_6 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (674) can reduce 15 to:
% 10.00/2.80 | (1323) ~ (all_0_7_7 = e2)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 1323 yields:
% 10.00/2.80 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.80 |
% 10.00/2.80 | Equations (674) can reduce 667 to:
% 10.00/2.80 | (741) ~ (e3 = e2)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 741 yields:
% 10.00/2.80 | (86) ~ (e3 = e2)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (145), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (201) all_0_3_3 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (201) can reduce 68 to:
% 10.00/2.80 | (1323) ~ (all_0_7_7 = e2)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 1323 yields:
% 10.00/2.80 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (70), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (297) all_0_1_1 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (297) can reduce 227 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (227) ~ (all_0_1_1 = e0)
% 10.00/2.80 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (131), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (968) all_0_7_7 = e3
% 10.00/2.80 |
% 10.00/2.80 | Equations (968) can reduce 1039 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (1039) ~ (all_0_7_7 = e3)
% 10.00/2.80 | (1160) all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (1160), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (209) all_0_7_7 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (209) can reduce 478 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.80 | (1203) all_0_7_7 = e1 | all_0_7_7 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (1203), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (581) all_0_7_7 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (581) can reduce 158 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (158) ~ (all_0_7_7 = e1)
% 10.00/2.80 | (364) all_0_7_7 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (364) can reduce 122 to:
% 10.00/2.80 | (195) ~ (all_0_4_4 = e0)
% 10.00/2.80 |
% 10.00/2.80 | Equations (364) can reduce 1039 to:
% 10.00/2.80 | (243) ~ (e3 = e0)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 243 yields:
% 10.00/2.80 | (29) ~ (e3 = e0)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (307), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (271) all_0_5_5 = e0
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (271,164) yields a new equation:
% 10.00/2.80 | (264) e3 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (264) can reduce 29 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (159) ~ (all_0_5_5 = e0)
% 10.00/2.80 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (312), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (313) all_0_9_9 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (313) can reduce 377 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (377) ~ (all_0_9_9 = e0)
% 10.00/2.80 | (378) all_0_13_13 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (378) can reduce 141 to:
% 10.00/2.80 | (652) ~ (all_0_12_12 = e0)
% 10.00/2.80 |
% 10.00/2.80 | Equations (378) can reduce 200 to:
% 10.00/2.80 | (243) ~ (e3 = e0)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 243 yields:
% 10.00/2.80 | (29) ~ (e3 = e0)
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (28), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (219) all_0_12_12 = e3
% 10.00/2.80 |
% 10.00/2.80 | Equations (219) can reduce 216 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (216) ~ (all_0_12_12 = e3)
% 10.00/2.80 | (231) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (231), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (232) all_0_12_12 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (232) can reduce 36 to:
% 10.00/2.80 | (211) ~ (all_0_4_4 = e2)
% 10.00/2.80 |
% 10.00/2.80 | Equations (232) can reduce 652 to:
% 10.00/2.80 | (13) ~ (e2 = e0)
% 10.00/2.80 |
% 10.00/2.80 | From (232) and (147) follows:
% 10.00/2.80 | (764) op(e0, e3) = e2
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (119), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (285) all_0_0_0 = e0
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (285,163) yields a new equation:
% 10.00/2.80 | (264) e3 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (264) can reduce 29 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (288) ~ (all_0_0_0 = e0)
% 10.00/2.80 | (1373) all_0_4_4 = e0 | all_0_8_8 = e0 | all_0_12_12 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (1373), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (263) all_0_4_4 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (263) can reduce 195 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (195) ~ (all_0_4_4 = e0)
% 10.00/2.80 | (1377) all_0_8_8 = e0 | all_0_12_12 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (1377), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (910) all_0_8_8 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (910) can reduce 64 to:
% 10.00/2.80 | (195) ~ (all_0_4_4 = e0)
% 10.00/2.80 |
% 10.00/2.80 | From (910) and (56) follows:
% 10.00/2.80 | (1380) op(e1, e3) = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (79), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (214) all_0_4_4 = e3
% 10.00/2.80 |
% 10.00/2.80 | Equations (214) can reduce 467 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (467) ~ (all_0_4_4 = e3)
% 10.00/2.80 | (468) all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (468), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (469) all_0_4_4 = e2
% 10.00/2.80 |
% 10.00/2.80 | Equations (469) can reduce 211 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (211) ~ (all_0_4_4 = e2)
% 10.00/2.80 | (472) all_0_4_4 = e1 | all_0_4_4 = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (472), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (473) all_0_4_4 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (473) can reduce 211 to:
% 10.00/2.80 | (186) ~ (e2 = e1)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 186 yields:
% 10.00/2.80 | (116) ~ (e2 = e1)
% 10.00/2.80 |
% 10.00/2.80 | Equations (473) can reduce 195 to:
% 10.00/2.80 | (3) ~ (e1 = e0)
% 10.00/2.80 |
% 10.00/2.80 | From (473) and (11) follows:
% 10.00/2.80 | (1393) op(e2, e3) = e1
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (55), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (325) unit = e3
% 10.00/2.80 |
% 10.00/2.80 | From (325) and (113) follows:
% 10.00/2.80 | (327) op(e2, e3) = e2
% 10.00/2.80 |
% 10.00/2.80 | From (325) and (133) follows:
% 10.00/2.80 | (247) op(e0, e3) = e0
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e2, e3, e2, e1 and discharging atoms op(e2, e3) = e2, op(e2, e3) = e1, yields:
% 10.00/2.80 | (330) e2 = e1
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e0, e3, e0, e2 and discharging atoms op(e0, e3) = e2, op(e0, e3) = e0, yields:
% 10.00/2.80 | (338) e2 = e0
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (330,338) yields a new equation:
% 10.00/2.80 | (272) e1 = e0
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 272 yields:
% 10.00/2.80 | (273) e1 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (273) can reduce 3 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (332) ~ (unit = e3)
% 10.00/2.80 | (333) unit = e2 | unit = e1 | unit = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (333), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (334) unit = e2
% 10.00/2.80 |
% 10.00/2.80 | From (334) and (143) follows:
% 10.00/2.80 | (218) op(e2, e3) = e3
% 10.00/2.80 |
% 10.00/2.80 | From (334) and (113) follows:
% 10.00/2.80 | (335) op(e2, e2) = e2
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e2, e3, e3, e1 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e1, yields:
% 10.00/2.80 | (328) e3 = e1
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e2, e2, e2, e3 and discharging atoms op(e2, e2) = e3, op(e2, e2) = e2, yields:
% 10.00/2.80 | (329) e3 = e2
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (328,329) yields a new equation:
% 10.00/2.80 | (330) e2 = e1
% 10.00/2.80 |
% 10.00/2.80 | Equations (330) can reduce 116 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (342) ~ (unit = e2)
% 10.00/2.80 | (343) unit = e1 | unit = e0
% 10.00/2.80 |
% 10.00/2.80 +-Applying beta-rule and splitting (343), into two cases.
% 10.00/2.80 |-Branch one:
% 10.00/2.80 | (344) unit = e1
% 10.00/2.80 |
% 10.00/2.80 | From (344) and (143) follows:
% 10.00/2.80 | (345) op(e1, e3) = e3
% 10.00/2.80 |
% 10.00/2.80 | From (344) and (25) follows:
% 10.00/2.80 | (1185) op(e1, e1) = e1
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e1, e3, e3, e0 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e0, yields:
% 10.00/2.80 | (264) e3 = e0
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e1, e1, e1, e3 and discharging atoms op(e1, e1) = e3, op(e1, e1) = e1, yields:
% 10.00/2.80 | (328) e3 = e1
% 10.00/2.80 |
% 10.00/2.80 | Combining equations (264,328) yields a new equation:
% 10.00/2.80 | (273) e1 = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (273) can reduce 3 to:
% 10.00/2.80 | (167) $false
% 10.00/2.80 |
% 10.00/2.80 |-The branch is then unsatisfiable
% 10.00/2.80 |-Branch two:
% 10.00/2.80 | (352) ~ (unit = e1)
% 10.00/2.80 | (353) unit = e0
% 10.00/2.80 |
% 10.00/2.80 | Equations (353) can reduce 342 to:
% 10.00/2.80 | (316) ~ (e2 = e0)
% 10.00/2.80 |
% 10.00/2.80 | Simplifying 316 yields:
% 10.00/2.80 | (13) ~ (e2 = e0)
% 10.00/2.80 |
% 10.00/2.80 | From (353) and (143) follows:
% 10.00/2.80 | (356) op(e0, e3) = e3
% 10.00/2.80 |
% 10.00/2.80 | From (353) and (133) follows:
% 10.00/2.80 | (1196) op(e0, e0) = e0
% 10.00/2.80 |
% 10.00/2.80 | Instantiating formula (5) with e0, e3, e3, e2 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e2, yields:
% 10.00/2.81 | (329) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Instantiating formula (5) with e0, e0, e0, e3 and discharging atoms op(e0, e0) = e3, op(e0, e0) = e0, yields:
% 10.00/2.81 | (264) e3 = e0
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (329,264) yields a new equation:
% 10.00/2.81 | (349) e2 = e0
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 349 yields:
% 10.00/2.81 | (338) e2 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (338) can reduce 13 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (182) ~ (all_0_4_4 = e1)
% 10.00/2.81 | (263) all_0_4_4 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (263) can reduce 195 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (240) ~ (all_0_8_8 = e0)
% 10.00/2.81 | (239) all_0_12_12 = e0
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (232,239) yields a new equation:
% 10.00/2.81 | (349) e2 = e0
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 349 yields:
% 10.00/2.81 | (338) e2 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (338) can reduce 13 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (208) ~ (all_0_12_12 = e2)
% 10.00/2.81 | (235) all_0_12_12 = e1 | all_0_12_12 = e0
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (235), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (236) all_0_12_12 = e1
% 10.00/2.81 |
% 10.00/2.81 | Equations (236) can reduce 188 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (188) ~ (all_0_12_12 = e1)
% 10.00/2.81 | (239) all_0_12_12 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (239) can reduce 652 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (196) ~ (all_0_3_3 = e2)
% 10.00/2.81 | (204) all_0_7_7 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (98), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (169) all_0_0_0 = e2
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (169,163) yields a new equation:
% 10.00/2.81 | (329) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (329) can reduce 86 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (425) ~ (all_0_0_0 = e2)
% 10.00/2.81 | (426) all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (163) can reduce 425 to:
% 10.00/2.81 | (86) ~ (e3 = e2)
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (204), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (209) all_0_7_7 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (209) can reduce 478 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.81 | (479) all_0_11_11 = e2 | all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (479), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (455) all_0_11_11 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (455) can reduce 156 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (156) ~ (all_0_11_11 = e2)
% 10.00/2.81 | (172) all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (166,172) yields a new equation:
% 10.00/2.81 | (878) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 878 yields:
% 10.00/2.81 | (329) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (329) can reduce 86 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (985) ~ (all_0_6_6 = e2)
% 10.00/2.81 | (986) all_0_6_6 = e1 | all_0_6_6 = e0
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (420), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (674) all_0_6_6 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (674) can reduce 985 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (985) ~ (all_0_6_6 = e2)
% 10.00/2.81 | (1289) all_0_10_10 = e2 | all_0_14_14 = e2
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (1289), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (171) all_0_10_10 = e2
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (165,171) yields a new equation:
% 10.00/2.81 | (878) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 878 yields:
% 10.00/2.81 | (329) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (329) can reduce 86 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (155) ~ (all_0_10_10 = e2)
% 10.00/2.81 | (877) all_0_14_14 = e2
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (1306,877) yields a new equation:
% 10.00/2.81 | (330) e2 = e1
% 10.00/2.81 |
% 10.00/2.81 | Equations (330) can reduce 116 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (278) ~ (all_0_2_2 = e0)
% 10.00/2.81 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (1085), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (277) all_0_6_6 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (277) can reduce 436 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (436) ~ (all_0_6_6 = e0)
% 10.00/2.81 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (1091), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (493) all_0_10_10 = e0
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (165,493) yields a new equation:
% 10.00/2.81 | (506) e3 = e0
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 506 yields:
% 10.00/2.81 | (264) e3 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (264) can reduce 29 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (598) ~ (all_0_10_10 = e0)
% 10.00/2.81 | (1096) all_0_14_14 = e0
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (1096,1306) yields a new equation:
% 10.00/2.81 | (273) e1 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (273) can reduce 3 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (726) ~ (all_0_14_14 = e1)
% 10.00/2.81 | (178) all_0_15_15 = e1
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (178,166) yields a new equation:
% 10.00/2.81 | (328) e3 = e1
% 10.00/2.81 |
% 10.00/2.81 | Equations (328) can reduce 61 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (581) all_0_7_7 = e1
% 10.00/2.81 | (612) ~ (all_0_15_15 = e3)
% 10.00/2.81 |
% 10.00/2.81 | Equations (166) can reduce 612 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (168) yields:
% 10.00/2.81 | (169) all_0_0_0 = e2
% 10.00/2.81 | (170) all_0_5_5 = e2
% 10.00/2.81 | (171) all_0_10_10 = e2
% 10.00/2.81 | (172) all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (165,171) yields a new equation:
% 10.00/2.81 | (878) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 878 yields:
% 10.00/2.81 | (329) e3 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (329) can reduce 86 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (174) yields:
% 10.00/2.81 | (175) all_0_0_0 = e1
% 10.00/2.81 | (176) all_0_5_5 = e1
% 10.00/2.81 | (177) all_0_10_10 = e1
% 10.00/2.81 | (178) all_0_15_15 = e1
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (165,177) yields a new equation:
% 10.00/2.81 | (442) e3 = e1
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 442 yields:
% 10.00/2.81 | (328) e3 = e1
% 10.00/2.81 |
% 10.00/2.81 | Equations (328) can reduce 61 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (490) yields:
% 10.00/2.81 | (285) all_0_0_0 = e0
% 10.00/2.81 | (271) all_0_5_5 = e0
% 10.00/2.81 | (493) all_0_10_10 = e0
% 10.00/2.81 | (373) all_0_15_15 = e0
% 10.00/2.81 |
% 10.00/2.81 | Combining equations (165,493) yields a new equation:
% 10.00/2.81 | (506) e3 = e0
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 506 yields:
% 10.00/2.81 | (264) e3 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (264) can reduce 29 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (277) all_0_6_6 = e0
% 10.00/2.81 | (157) ~ (all_0_10_10 = e3)
% 10.00/2.81 |
% 10.00/2.81 | Equations (165) can reduce 157 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (455) all_0_11_11 = e2
% 10.00/2.81 | (612) ~ (all_0_15_15 = e3)
% 10.00/2.81 |
% 10.00/2.81 | Equations (455) can reduce 120 to:
% 10.00/2.81 | (196) ~ (all_0_3_3 = e2)
% 10.00/2.81 |
% 10.00/2.81 | Equations (455) can reduce 114 to:
% 10.00/2.81 | (478) ~ (all_0_7_7 = e2)
% 10.00/2.81 |
% 10.00/2.81 | Equations (455) can reduce 48 to:
% 10.00/2.81 | (1531) ~ (all_0_15_15 = e2)
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 1531 yields:
% 10.00/2.81 | (1532) ~ (all_0_15_15 = e2)
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (27), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (192) ~ (all_0_0_0 = e1)
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (82), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (160), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 10.00/2.81 |
% 10.00/2.81 +-Applying beta-rule and splitting (161), into two cases.
% 10.00/2.81 |-Branch one:
% 10.00/2.81 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (162) yields:
% 10.00/2.81 | (163) all_0_0_0 = e3
% 10.00/2.81 | (164) all_0_5_5 = e3
% 10.00/2.81 | (165) all_0_10_10 = e3
% 10.00/2.81 | (166) all_0_15_15 = e3
% 10.00/2.81 |
% 10.00/2.81 | Equations (166) can reduce 612 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (168) yields:
% 10.00/2.81 | (169) all_0_0_0 = e2
% 10.00/2.81 | (170) all_0_5_5 = e2
% 10.00/2.81 | (171) all_0_10_10 = e2
% 10.00/2.81 | (172) all_0_15_15 = e2
% 10.00/2.81 |
% 10.00/2.81 | Equations (172) can reduce 1532 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (174) yields:
% 10.00/2.81 | (175) all_0_0_0 = e1
% 10.00/2.81 | (176) all_0_5_5 = e1
% 10.00/2.81 | (177) all_0_10_10 = e1
% 10.00/2.81 | (178) all_0_15_15 = e1
% 10.00/2.81 |
% 10.00/2.81 | Equations (175) can reduce 192 to:
% 10.00/2.81 | (167) $false
% 10.00/2.81 |
% 10.00/2.81 |-The branch is then unsatisfiable
% 10.00/2.81 |-Branch two:
% 10.00/2.81 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 10.00/2.81 |
% 10.00/2.81 | Applying alpha-rule on (490) yields:
% 10.00/2.81 | (285) all_0_0_0 = e0
% 10.00/2.81 | (271) all_0_5_5 = e0
% 10.00/2.81 | (493) all_0_10_10 = e0
% 10.00/2.81 | (373) all_0_15_15 = e0
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 6 to:
% 10.00/2.81 | (362) ~ (all_0_3_3 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (271) can reduce 146 to:
% 10.00/2.81 | (195) ~ (all_0_4_4 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (493) can reduce 35 to:
% 10.00/2.81 | (436) ~ (all_0_6_6 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 100 to:
% 10.00/2.81 | (368) ~ (all_0_7_7 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (493) can reduce 149 to:
% 10.00/2.81 | (377) ~ (all_0_9_9 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 148 to:
% 10.00/2.81 | (652) ~ (all_0_12_12 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 23 to:
% 10.00/2.81 | (242) ~ (all_0_13_13 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 41 to:
% 10.00/2.81 | (1566) ~ (all_0_14_14 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Equations (373) can reduce 612 to:
% 10.00/2.81 | (243) ~ (e3 = e0)
% 10.00/2.81 |
% 10.00/2.81 | Simplifying 243 yields:
% 10.00/2.81 | (29) ~ (e3 = e0)
% 10.00/2.82 |
% 10.00/2.82 | Equations (373) can reduce 1532 to:
% 10.00/2.82 | (316) ~ (e2 = e0)
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 316 yields:
% 10.00/2.82 | (13) ~ (e2 = e0)
% 10.00/2.82 |
% 10.00/2.82 | From (285) and (84) follows:
% 10.00/2.82 | (656) op(e3, e3) = e0
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (94), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (288) ~ (all_0_0_0 = e0)
% 10.00/2.82 |
% 10.00/2.82 | Equations (285) can reduce 288 to:
% 10.00/2.82 | (167) $false
% 10.00/2.82 |
% 10.00/2.82 |-The branch is then unsatisfiable
% 10.00/2.82 |-Branch two:
% 10.00/2.82 | (285) all_0_0_0 = e0
% 10.00/2.82 | (182) ~ (all_0_4_4 = e1)
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (59), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (667) ~ (all_0_6_6 = e3)
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (142), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (415) ~ (all_0_2_2 = e2)
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (98), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (169) all_0_0_0 = e2
% 10.00/2.82 |
% 10.00/2.82 | Combining equations (169,285) yields a new equation:
% 10.00/2.82 | (349) e2 = e0
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 349 yields:
% 10.00/2.82 | (338) e2 = e0
% 10.00/2.82 |
% 10.00/2.82 | Equations (338) can reduce 13 to:
% 10.00/2.82 | (167) $false
% 10.00/2.82 |
% 10.00/2.82 |-The branch is then unsatisfiable
% 10.00/2.82 |-Branch two:
% 10.00/2.82 | (425) ~ (all_0_0_0 = e2)
% 10.00/2.82 | (426) all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (426), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (396) all_0_1_1 = e2
% 10.00/2.82 |
% 10.00/2.82 | Equations (396) can reduce 134 to:
% 10.00/2.82 | (1585) ~ (all_0_2_2 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 1585 yields:
% 10.00/2.82 | (415) ~ (all_0_2_2 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Equations (396) can reduce 118 to:
% 10.00/2.82 | (293) ~ (all_0_3_3 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 293 yields:
% 10.00/2.82 | (196) ~ (all_0_3_3 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Equations (396) can reduce 105 to:
% 10.00/2.82 | (258) ~ (all_0_9_9 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 258 yields:
% 10.00/2.82 | (254) ~ (all_0_9_9 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Equations (396) can reduce 88 to:
% 10.00/2.82 | (739) ~ (all_0_13_13 = e2)
% 10.00/2.82 |
% 10.00/2.82 | Simplifying 739 yields:
% 10.00/2.82 | (457) ~ (all_0_13_13 = e2)
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (67), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (159) ~ (all_0_5_5 = e0)
% 10.00/2.82 |
% 10.00/2.82 | Equations (271) can reduce 159 to:
% 10.00/2.82 | (167) $false
% 10.00/2.82 |
% 10.00/2.82 |-The branch is then unsatisfiable
% 10.00/2.82 |-Branch two:
% 10.00/2.82 | (271) all_0_5_5 = e0
% 10.00/2.82 | (497) ~ (all_0_9_9 = e3)
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (63), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (1597) all_0_9_9 = e3
% 10.00/2.82 |
% 10.00/2.82 | Equations (1597) can reduce 497 to:
% 10.00/2.82 | (167) $false
% 10.00/2.82 |
% 10.00/2.82 |-The branch is then unsatisfiable
% 10.00/2.82 |-Branch two:
% 10.00/2.82 | (497) ~ (all_0_9_9 = e3)
% 10.00/2.82 | (1600) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.00/2.82 |
% 10.00/2.82 +-Applying beta-rule and splitting (1600), into two cases.
% 10.00/2.82 |-Branch one:
% 10.00/2.82 | (447) all_0_9_9 = e2
% 10.00/2.82 |
% 10.11/2.82 | Equations (447) can reduce 254 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (254) ~ (all_0_9_9 = e2)
% 10.11/2.82 | (1604) all_0_9_9 = e1 | all_0_9_9 = e0
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (1604), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (776) all_0_9_9 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (776) can reduce 140 to:
% 10.11/2.82 | (184) ~ (all_0_8_8 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (776) can reduce 72 to:
% 10.11/2.82 | (1057) ~ (all_0_13_13 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 1057 yields:
% 10.11/2.82 | (189) ~ (all_0_13_13 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (776) can reduce 497 to:
% 10.11/2.82 | (841) ~ (e3 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 841 yields:
% 10.11/2.82 | (61) ~ (e3 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (776) can reduce 377 to:
% 10.11/2.82 | (3) ~ (e1 = e0)
% 10.11/2.82 |
% 10.11/2.82 | From (776) and (14) follows:
% 10.11/2.82 | (796) op(e1, e2) = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (78), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (685) all_0_8_8 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (685) can reduce 64 to:
% 10.11/2.82 | (467) ~ (all_0_4_4 = e3)
% 10.11/2.82 |
% 10.11/2.82 | From (685) and (56) follows:
% 10.11/2.82 | (345) op(e1, e3) = e3
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (138), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (214) all_0_4_4 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (214) can reduce 467 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (467) ~ (all_0_4_4 = e3)
% 10.11/2.82 | (932) all_0_5_5 = e3 | all_0_6_6 = e3 | all_0_7_7 = e3
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (79), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (214) all_0_4_4 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (214) can reduce 467 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (467) ~ (all_0_4_4 = e3)
% 10.11/2.82 | (468) all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (33), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (223) all_0_13_13 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (223) can reduce 141 to:
% 10.11/2.82 | (216) ~ (all_0_12_12 = e3)
% 10.11/2.82 |
% 10.11/2.82 | Equations (223) can reduce 127 to:
% 10.11/2.82 | (1626) ~ (all_0_14_14 = e3)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 1626 yields:
% 10.11/2.82 | (440) ~ (all_0_14_14 = e3)
% 10.11/2.82 |
% 10.11/2.82 | Equations (223) can reduce 189 to:
% 10.11/2.82 | (61) ~ (e3 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (223) can reduce 242 to:
% 10.11/2.82 | (29) ~ (e3 = e0)
% 10.11/2.82 |
% 10.11/2.82 | From (223) and (73) follows:
% 10.11/2.82 | (1630) op(e0, e2) = e3
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (468), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (469) all_0_4_4 = e2
% 10.11/2.82 |
% 10.11/2.82 | Equations (469) can reduce 126 to:
% 10.11/2.82 | (1632) ~ (all_0_6_6 = e2)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 1632 yields:
% 10.11/2.82 | (985) ~ (all_0_6_6 = e2)
% 10.11/2.82 |
% 10.11/2.82 | Equations (469) can reduce 122 to:
% 10.11/2.82 | (1323) ~ (all_0_7_7 = e2)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 1323 yields:
% 10.11/2.82 | (478) ~ (all_0_7_7 = e2)
% 10.11/2.82 |
% 10.11/2.82 | Equations (469) can reduce 182 to:
% 10.11/2.82 | (116) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (469) can reduce 195 to:
% 10.11/2.82 | (13) ~ (e2 = e0)
% 10.11/2.82 |
% 10.11/2.82 | From (469) and (11) follows:
% 10.11/2.82 | (327) op(e2, e3) = e2
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (128), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (670) all_0_6_6 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (670) can reduce 667 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (667) ~ (all_0_6_6 = e3)
% 10.11/2.82 | (673) all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (53), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (175) all_0_0_0 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (175,285) yields a new equation:
% 10.11/2.82 | (272) e1 = e0
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 272 yields:
% 10.11/2.82 | (273) e1 = e0
% 10.11/2.82 |
% 10.11/2.82 | Equations (273) can reduce 3 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (192) ~ (all_0_0_0 = e1)
% 10.11/2.82 | (1648) all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (9), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (281) all_0_2_2 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (281) can reduce 415 to:
% 10.11/2.82 | (86) ~ (e3 = e2)
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (1648), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (473) all_0_4_4 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (473,469) yields a new equation:
% 10.11/2.82 | (330) e2 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (330) can reduce 116 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (182) ~ (all_0_4_4 = e1)
% 10.11/2.82 | (1655) all_0_8_8 = e1 | all_0_12_12 = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (1655), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (750) all_0_8_8 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (685,750) yields a new equation:
% 10.11/2.82 | (442) e3 = e1
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 442 yields:
% 10.11/2.82 | (328) e3 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (328) can reduce 61 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (184) ~ (all_0_8_8 = e1)
% 10.11/2.82 | (236) all_0_12_12 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (236) can reduce 652 to:
% 10.11/2.82 | (3) ~ (e1 = e0)
% 10.11/2.82 |
% 10.11/2.82 | From (236) and (147) follows:
% 10.11/2.82 | (1061) op(e0, e3) = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (108), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (291) all_0_2_2 = e2
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (291,281) yields a new equation:
% 10.11/2.82 | (329) e3 = e2
% 10.11/2.82 |
% 10.11/2.82 | Equations (329) can reduce 86 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (415) ~ (all_0_2_2 = e2)
% 10.11/2.82 | (420) all_0_6_6 = e2 | all_0_10_10 = e2 | all_0_14_14 = e2
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (17), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (175) all_0_0_0 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (175,285) yields a new equation:
% 10.11/2.82 | (272) e1 = e0
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 272 yields:
% 10.11/2.82 | (273) e1 = e0
% 10.11/2.82 |
% 10.11/2.82 | Equations (273) can reduce 3 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (192) ~ (all_0_0_0 = e1)
% 10.11/2.82 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (673), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (674) all_0_6_6 = e2
% 10.11/2.82 |
% 10.11/2.82 | Equations (674) can reduce 985 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (985) ~ (all_0_6_6 = e2)
% 10.11/2.82 | (986) all_0_6_6 = e1 | all_0_6_6 = e0
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (986), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (578) all_0_6_6 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (578) can reduce 15 to:
% 10.11/2.82 | (1125) ~ (all_0_7_7 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 1125 yields:
% 10.11/2.82 | (158) ~ (all_0_7_7 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (578) can reduce 102 to:
% 10.11/2.82 | (725) ~ (all_0_14_14 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 725 yields:
% 10.11/2.82 | (726) ~ (all_0_14_14 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (578) can reduce 985 to:
% 10.11/2.82 | (186) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 186 yields:
% 10.11/2.82 | (116) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (131), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (968) all_0_7_7 = e3
% 10.11/2.82 |
% 10.11/2.82 | Equations (968) can reduce 158 to:
% 10.11/2.82 | (61) ~ (e3 = e1)
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (420), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (674) all_0_6_6 = e2
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (674,578) yields a new equation:
% 10.11/2.82 | (422) e2 = e1
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 422 yields:
% 10.11/2.82 | (330) e2 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (330) can reduce 116 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (985) ~ (all_0_6_6 = e2)
% 10.11/2.82 | (1289) all_0_10_10 = e2 | all_0_14_14 = e2
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (1289), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (171) all_0_10_10 = e2
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (493,171) yields a new equation:
% 10.11/2.82 | (338) e2 = e0
% 10.11/2.82 |
% 10.11/2.82 | Equations (338) can reduce 13 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (155) ~ (all_0_10_10 = e2)
% 10.11/2.82 | (877) all_0_14_14 = e2
% 10.11/2.82 |
% 10.11/2.82 | Equations (877) can reduce 726 to:
% 10.11/2.82 | (116) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Equations (877) can reduce 1566 to:
% 10.11/2.82 | (13) ~ (e2 = e0)
% 10.11/2.82 |
% 10.11/2.82 | From (877) and (19) follows:
% 10.11/2.82 | (1701) op(e0, e1) = e2
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (698), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (406) all_0_1_1 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (406,396) yields a new equation:
% 10.11/2.82 | (330) e2 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (330) can reduce 116 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (179) ~ (all_0_1_1 = e1)
% 10.11/2.82 | (702) all_0_2_2 = e1 | all_0_3_3 = e1
% 10.11/2.82 |
% 10.11/2.82 +-Applying beta-rule and splitting (702), into two cases.
% 10.11/2.82 |-Branch one:
% 10.11/2.82 | (565) all_0_2_2 = e1
% 10.11/2.82 |
% 10.11/2.82 | Combining equations (281,565) yields a new equation:
% 10.11/2.82 | (442) e3 = e1
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 442 yields:
% 10.11/2.82 | (328) e3 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (328) can reduce 61 to:
% 10.11/2.82 | (167) $false
% 10.11/2.82 |
% 10.11/2.82 |-The branch is then unsatisfiable
% 10.11/2.82 |-Branch two:
% 10.11/2.82 | (180) ~ (all_0_2_2 = e1)
% 10.11/2.82 | (927) all_0_3_3 = e1
% 10.11/2.82 |
% 10.11/2.82 | Equations (927) can reduce 196 to:
% 10.11/2.82 | (186) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.82 | Simplifying 186 yields:
% 10.11/2.82 | (116) ~ (e2 = e1)
% 10.11/2.82 |
% 10.11/2.83 | Equations (927) can reduce 362 to:
% 10.11/2.83 | (3) ~ (e1 = e0)
% 10.11/2.83 |
% 10.11/2.83 +-Applying beta-rule and splitting (55), into two cases.
% 10.11/2.83 |-Branch one:
% 10.11/2.83 | (325) unit = e3
% 10.11/2.83 |
% 10.11/2.83 | From (325) and (46) follows:
% 10.11/2.83 | (326) op(e3, e3) = e3
% 10.11/2.83 |
% 10.11/2.83 | From (325) and (25) follows:
% 10.11/2.83 | (754) op(e1, e3) = e1
% 10.11/2.83 |
% 10.11/2.83 | Instantiating formula (5) with e3, e3, e3, e0 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e0, yields:
% 10.11/2.83 | (264) e3 = e0
% 10.11/2.83 |
% 10.11/2.83 | Instantiating formula (5) with e1, e3, e1, e3 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e1, yields:
% 10.11/2.83 | (328) e3 = e1
% 10.11/2.83 |
% 10.11/2.83 | Combining equations (264,328) yields a new equation:
% 10.11/2.83 | (273) e1 = e0
% 10.11/2.83 |
% 10.11/2.83 | Equations (273) can reduce 3 to:
% 10.11/2.83 | (167) $false
% 10.11/2.83 |
% 10.11/2.83 |-The branch is then unsatisfiable
% 10.11/2.83 |-Branch two:
% 10.11/2.83 | (332) ~ (unit = e3)
% 10.11/2.83 | (333) unit = e2 | unit = e1 | unit = e0
% 10.11/2.83 |
% 10.11/2.83 +-Applying beta-rule and splitting (333), into two cases.
% 10.11/2.83 |-Branch one:
% 10.11/2.83 | (334) unit = e2
% 10.11/2.83 |
% 10.11/2.83 | From (334) and (143) follows:
% 10.11/2.83 | (218) op(e2, e3) = e3
% 10.11/2.83 |
% 10.11/2.83 | From (334) and (133) follows:
% 10.11/2.83 | (336) op(e0, e2) = e0
% 10.11/2.83 |
% 10.11/2.83 | Instantiating formula (5) with e2, e3, e3, e2 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e2, yields:
% 10.11/2.83 | (329) e3 = e2
% 10.11/2.83 |
% 10.11/2.83 | Instantiating formula (5) with e0, e2, e0, e3 and discharging atoms op(e0, e2) = e3, op(e0, e2) = e0, yields:
% 10.15/2.83 | (264) e3 = e0
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (329,264) yields a new equation:
% 10.15/2.83 | (349) e2 = e0
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 349 yields:
% 10.15/2.83 | (338) e2 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (338) can reduce 13 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (342) ~ (unit = e2)
% 10.15/2.83 | (343) unit = e1 | unit = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (343), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (344) unit = e1
% 10.15/2.83 |
% 10.15/2.83 | From (344) and (57) follows:
% 10.15/2.83 | (744) op(e1, e2) = e2
% 10.15/2.83 |
% 10.15/2.83 | From (344) and (133) follows:
% 10.15/2.83 | (346) op(e0, e1) = e0
% 10.15/2.83 |
% 10.15/2.83 | Instantiating formula (5) with e1, e2, e2, e1 and discharging atoms op(e1, e2) = e2, op(e1, e2) = e1, yields:
% 10.15/2.83 | (330) e2 = e1
% 10.15/2.83 |
% 10.15/2.83 | Instantiating formula (5) with e0, e1, e0, e2 and discharging atoms op(e0, e1) = e2, op(e0, e1) = e0, yields:
% 10.15/2.83 | (338) e2 = e0
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (330,338) yields a new equation:
% 10.15/2.83 | (272) e1 = e0
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 272 yields:
% 10.15/2.83 | (273) e1 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (273) can reduce 3 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (352) ~ (unit = e1)
% 10.15/2.83 | (353) unit = e0
% 10.15/2.83 |
% 10.15/2.83 | From (353) and (143) follows:
% 10.15/2.83 | (356) op(e0, e3) = e3
% 10.15/2.83 |
% 10.15/2.83 | From (353) and (57) follows:
% 10.15/2.83 | (256) op(e0, e2) = e2
% 10.15/2.83 |
% 10.15/2.83 | Instantiating formula (5) with e0, e3, e3, e1 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e1, yields:
% 10.15/2.83 | (328) e3 = e1
% 10.15/2.83 |
% 10.15/2.83 | Instantiating formula (5) with e0, e2, e2, e3 and discharging atoms op(e0, e2) = e3, op(e0, e2) = e2, yields:
% 10.15/2.83 | (329) e3 = e2
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (328,329) yields a new equation:
% 10.15/2.83 | (330) e2 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (330) can reduce 116 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.83 | (1160) all_0_7_7 = e2 | all_0_7_7 = e1 | all_0_7_7 = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1160), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (209) all_0_7_7 = e2
% 10.15/2.83 |
% 10.15/2.83 | Equations (209) can reduce 478 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (478) ~ (all_0_7_7 = e2)
% 10.15/2.83 | (1203) all_0_7_7 = e1 | all_0_7_7 = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1203), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (581) all_0_7_7 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (581) can reduce 158 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (158) ~ (all_0_7_7 = e1)
% 10.15/2.83 | (364) all_0_7_7 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (364) can reduce 368 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.83 | (277) all_0_6_6 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (277) can reduce 436 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.83 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (723), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (670) all_0_6_6 = e3
% 10.15/2.83 |
% 10.15/2.83 | Equations (670) can reduce 667 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (667) ~ (all_0_6_6 = e3)
% 10.15/2.83 | (918) all_0_10_10 = e3 | all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (918), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (165) all_0_10_10 = e3
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (493,165) yields a new equation:
% 10.15/2.83 | (264) e3 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (264) can reduce 29 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.83 | (268) all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 | Equations (268) can reduce 440 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (211) ~ (all_0_4_4 = e2)
% 10.15/2.83 | (472) all_0_4_4 = e1 | all_0_4_4 = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (53), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (175) all_0_0_0 = e1
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (175,285) yields a new equation:
% 10.15/2.83 | (272) e1 = e0
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 272 yields:
% 10.15/2.83 | (273) e1 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (273) can reduce 3 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.83 | (1648) all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (9), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (281) all_0_2_2 = e3
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1648), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (473) all_0_4_4 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (473) can reduce 182 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.83 | (1655) all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1655), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (750) all_0_8_8 = e1
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (685,750) yields a new equation:
% 10.15/2.83 | (442) e3 = e1
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 442 yields:
% 10.15/2.83 | (328) e3 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (328) can reduce 61 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.83 | (236) all_0_12_12 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (236) can reduce 51 to:
% 10.15/2.83 | (725) ~ (all_0_14_14 = e1)
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 725 yields:
% 10.15/2.83 | (726) ~ (all_0_14_14 = e1)
% 10.15/2.83 |
% 10.15/2.83 | Equations (236) can reduce 216 to:
% 10.15/2.83 | (841) ~ (e3 = e1)
% 10.15/2.83 |
% 10.15/2.83 | Simplifying 841 yields:
% 10.15/2.83 | (61) ~ (e3 = e1)
% 10.15/2.83 |
% 10.15/2.83 | Equations (236) can reduce 652 to:
% 10.15/2.83 | (3) ~ (e1 = e0)
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (71), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (565) all_0_2_2 = e1
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (565,281) yields a new equation:
% 10.15/2.83 | (328) e3 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (328) can reduce 61 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.83 | (1805) all_0_6_6 = e1 | all_0_10_10 = e1 | all_0_14_14 = e1
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1805), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (578) all_0_6_6 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (578) can reduce 126 to:
% 10.15/2.83 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (472), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (473) all_0_4_4 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (473) can reduce 182 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.83 | (263) all_0_4_4 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (263) can reduce 195 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.83 | (1814) all_0_10_10 = e1 | all_0_14_14 = e1
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (1814), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (177) all_0_10_10 = e1
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (493,177) yields a new equation:
% 10.15/2.83 | (273) e1 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (273) can reduce 3 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (855) ~ (all_0_10_10 = e1)
% 10.15/2.83 | (1306) all_0_14_14 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (1306) can reduce 726 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.83 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (723), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (670) all_0_6_6 = e3
% 10.15/2.83 |
% 10.15/2.83 | Equations (670) can reduce 667 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (667) ~ (all_0_6_6 = e3)
% 10.15/2.83 | (918) all_0_10_10 = e3 | all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (918), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (165) all_0_10_10 = e3
% 10.15/2.83 |
% 10.15/2.83 | Combining equations (493,165) yields a new equation:
% 10.15/2.83 | (264) e3 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (264) can reduce 29 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.83 | (268) all_0_14_14 = e3
% 10.15/2.83 |
% 10.15/2.83 | Equations (268) can reduce 440 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.83 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (251), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (252) all_0_13_13 = e2
% 10.15/2.83 |
% 10.15/2.83 | Equations (252) can reduce 457 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.83 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.83 |
% 10.15/2.83 +-Applying beta-rule and splitting (458), into two cases.
% 10.15/2.83 |-Branch one:
% 10.15/2.83 | (459) all_0_13_13 = e1
% 10.15/2.83 |
% 10.15/2.83 | Equations (459) can reduce 189 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.83 |-Branch two:
% 10.15/2.83 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.83 | (378) all_0_13_13 = e0
% 10.15/2.83 |
% 10.15/2.83 | Equations (378) can reduce 242 to:
% 10.15/2.83 | (167) $false
% 10.15/2.83 |
% 10.15/2.83 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.84 | (1845) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (91), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (301) all_0_1_1 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (301,396) yields a new equation:
% 10.15/2.84 | (878) e3 = e2
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 878 yields:
% 10.15/2.84 | (329) e3 = e2
% 10.15/2.84 |
% 10.15/2.84 | Equations (329) can reduce 86 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.84 | (1851) all_0_5_5 = e3 | all_0_9_9 = e3 | all_0_13_13 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (33), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (223) all_0_13_13 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (223) can reduce 457 to:
% 10.15/2.84 | (86) ~ (e3 = e2)
% 10.15/2.84 |
% 10.15/2.84 | Equations (223) can reduce 189 to:
% 10.15/2.84 | (61) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (223) can reduce 242 to:
% 10.15/2.84 | (29) ~ (e3 = e0)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1845), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (1597) all_0_9_9 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (776,1597) yields a new equation:
% 10.15/2.84 | (328) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (328) can reduce 61 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.84 | (1860) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1860), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (165) all_0_10_10 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (493,165) yields a new equation:
% 10.15/2.84 | (264) e3 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (264) can reduce 29 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.84 | (668) all_0_11_11 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (455,668) yields a new equation:
% 10.15/2.84 | (329) e3 = e2
% 10.15/2.84 |
% 10.15/2.84 | Equations (329) can reduce 86 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.84 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (53), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (175) all_0_0_0 = e1
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (175,285) yields a new equation:
% 10.15/2.84 | (272) e1 = e0
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 272 yields:
% 10.15/2.84 | (273) e1 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (273) can reduce 3 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.84 | (1648) all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1648), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (473) all_0_4_4 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (473) can reduce 182 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.84 | (1655) all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1655), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (750) all_0_8_8 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (750) can reduce 184 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.84 | (236) all_0_12_12 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (236) can reduce 36 to:
% 10.15/2.84 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (43), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (163) all_0_0_0 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (163,285) yields a new equation:
% 10.15/2.84 | (506) e3 = e0
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 506 yields:
% 10.15/2.84 | (264) e3 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (264) can reduce 29 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (955) ~ (all_0_0_0 = e3)
% 10.15/2.84 | (956) all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (956), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (214) all_0_4_4 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (214) can reduce 182 to:
% 10.15/2.84 | (61) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (214) can reduce 195 to:
% 10.15/2.84 | (29) ~ (e3 = e0)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (54), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (219) all_0_12_12 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (236,219) yields a new equation:
% 10.15/2.84 | (328) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (328) can reduce 61 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (216) ~ (all_0_12_12 = e3)
% 10.15/2.84 | (222) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (236) can reduce 216 to:
% 10.15/2.84 | (841) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 841 yields:
% 10.15/2.84 | (61) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1851), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (164) all_0_5_5 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (164,271) yields a new equation:
% 10.15/2.84 | (506) e3 = e0
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 506 yields:
% 10.15/2.84 | (264) e3 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (264) can reduce 29 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (962) ~ (all_0_5_5 = e3)
% 10.15/2.84 | (1906) all_0_9_9 = e3 | all_0_13_13 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1906), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (1597) all_0_9_9 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (776,1597) yields a new equation:
% 10.15/2.84 | (328) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (328) can reduce 61 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.84 | (223) all_0_13_13 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (223) can reduce 200 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.84 | (1914) all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (1914), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (685) all_0_8_8 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (685) can reduce 669 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.84 | (219) all_0_12_12 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (236,219) yields a new equation:
% 10.15/2.84 | (328) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (328) can reduce 61 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (185) ~ (all_0_9_9 = e1)
% 10.15/2.84 | (313) all_0_9_9 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (313) can reduce 377 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (253) ~ (all_0_1_1 = e2)
% 10.15/2.84 | (430) all_0_2_2 = e2 | all_0_3_3 = e2
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (430), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (291) all_0_2_2 = e2
% 10.15/2.84 |
% 10.15/2.84 | Equations (291) can reduce 415 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (415) ~ (all_0_2_2 = e2)
% 10.15/2.84 | (201) all_0_3_3 = e2
% 10.15/2.84 |
% 10.15/2.84 | Equations (201) can reduce 196 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (291) all_0_2_2 = e2
% 10.15/2.84 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.84 |
% 10.15/2.84 | Equations (493) can reduce 598 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (670) all_0_6_6 = e3
% 10.15/2.84 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.84 |
% 10.15/2.84 | Equations (493) can reduce 598 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (175) all_0_0_0 = e1
% 10.15/2.84 | (208) ~ (all_0_12_12 = e2)
% 10.15/2.84 |
% 10.15/2.84 | From (175) and (84) follows:
% 10.15/2.84 | (190) op(e3, e3) = e1
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (37), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (175) can reduce 192 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (175) all_0_0_0 = e1
% 10.15/2.84 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (52), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (169) all_0_0_0 = e2
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (169,175) yields a new equation:
% 10.15/2.84 | (422) e2 = e1
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 422 yields:
% 10.15/2.84 | (330) e2 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (330) can reduce 116 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (425) ~ (all_0_0_0 = e2)
% 10.15/2.84 | (708) all_0_4_4 = e2 | all_0_8_8 = e2 | all_0_12_12 = e2
% 10.15/2.84 |
% 10.15/2.84 | Equations (175) can reduce 425 to:
% 10.15/2.84 | (186) ~ (e2 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 186 yields:
% 10.15/2.84 | (116) ~ (e2 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (82), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (160), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (161), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 10.15/2.84 |
% 10.15/2.84 | Applying alpha-rule on (162) yields:
% 10.15/2.84 | (163) all_0_0_0 = e3
% 10.15/2.84 | (164) all_0_5_5 = e3
% 10.15/2.84 | (165) all_0_10_10 = e3
% 10.15/2.84 | (166) all_0_15_15 = e3
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (163,175) yields a new equation:
% 10.15/2.84 | (442) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 442 yields:
% 10.15/2.84 | (328) e3 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (328) can reduce 61 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 10.15/2.84 |
% 10.15/2.84 | Applying alpha-rule on (168) yields:
% 10.15/2.84 | (169) all_0_0_0 = e2
% 10.15/2.84 | (170) all_0_5_5 = e2
% 10.15/2.84 | (171) all_0_10_10 = e2
% 10.15/2.84 | (172) all_0_15_15 = e2
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (169,175) yields a new equation:
% 10.15/2.84 | (422) e2 = e1
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 422 yields:
% 10.15/2.84 | (330) e2 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (330) can reduce 116 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 10.15/2.84 |
% 10.15/2.84 | Applying alpha-rule on (174) yields:
% 10.15/2.84 | (175) all_0_0_0 = e1
% 10.15/2.84 | (176) all_0_5_5 = e1
% 10.15/2.84 | (177) all_0_10_10 = e1
% 10.15/2.84 | (178) all_0_15_15 = e1
% 10.15/2.84 |
% 10.15/2.84 | Equations (176) can reduce 30 to:
% 10.15/2.84 | (179) ~ (all_0_1_1 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 6 to:
% 10.15/2.84 | (181) ~ (all_0_3_3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (176) can reduce 146 to:
% 10.15/2.84 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 100 to:
% 10.15/2.84 | (158) ~ (all_0_7_7 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (177) can reduce 81 to:
% 10.15/2.84 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 148 to:
% 10.15/2.84 | (188) ~ (all_0_12_12 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 23 to:
% 10.15/2.84 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 41 to:
% 10.15/2.84 | (726) ~ (all_0_14_14 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 612 to:
% 10.15/2.84 | (841) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 841 yields:
% 10.15/2.84 | (61) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (178) can reduce 1532 to:
% 10.15/2.84 | (186) ~ (e2 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 186 yields:
% 10.15/2.84 | (116) ~ (e2 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (129), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (197) ~ (all_0_5_5 = e1)
% 10.15/2.84 |
% 10.15/2.84 | Equations (176) can reduce 197 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (176) all_0_5_5 = e1
% 10.15/2.84 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (42), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (21), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (112), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (1111) all_0_3_3 = e3
% 10.15/2.84 |
% 10.15/2.84 | Equations (1111) can reduce 118 to:
% 10.15/2.84 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.84 |
% 10.15/2.84 | Equations (1111) can reduce 68 to:
% 10.15/2.84 | (1995) ~ (all_0_7_7 = e3)
% 10.15/2.84 |
% 10.15/2.84 | Simplifying 1995 yields:
% 10.15/2.84 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.84 |
% 10.15/2.84 | Equations (1111) can reduce 196 to:
% 10.15/2.84 | (86) ~ (e3 = e2)
% 10.15/2.84 |
% 10.15/2.84 | Equations (1111) can reduce 181 to:
% 10.15/2.84 | (61) ~ (e3 = e1)
% 10.15/2.84 |
% 10.15/2.84 +-Applying beta-rule and splitting (34), into two cases.
% 10.15/2.84 |-Branch one:
% 10.15/2.84 | (285) all_0_0_0 = e0
% 10.15/2.84 |
% 10.15/2.84 | Combining equations (285,175) yields a new equation:
% 10.15/2.84 | (273) e1 = e0
% 10.15/2.84 |
% 10.15/2.84 | Equations (273) can reduce 3 to:
% 10.15/2.84 | (167) $false
% 10.15/2.84 |
% 10.15/2.84 |-The branch is then unsatisfiable
% 10.15/2.84 |-Branch two:
% 10.15/2.84 | (288) ~ (all_0_0_0 = e0)
% 10.15/2.84 | (289) all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.84 |
% 10.15/2.85 +-Applying beta-rule and splitting (289), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (297) all_0_1_1 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (297) can reduce 227 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.85 | (300) all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (300), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (400) all_0_2_2 = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (98), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (169) all_0_0_0 = e2
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (169,175) yields a new equation:
% 10.15/2.85 | (422) e2 = e1
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 422 yields:
% 10.15/2.85 | (330) e2 = e1
% 10.15/2.85 |
% 10.15/2.85 | Equations (330) can reduce 116 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (425) ~ (all_0_0_0 = e2)
% 10.15/2.85 | (426) all_0_1_1 = e2 | all_0_2_2 = e2 | all_0_3_3 = e2
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (426), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (396) all_0_1_1 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (396) can reduce 88 to:
% 10.15/2.85 | (739) ~ (all_0_13_13 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 739 yields:
% 10.15/2.85 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (396) can reduce 382 to:
% 10.15/2.85 | (741) ~ (e3 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 741 yields:
% 10.15/2.85 | (86) ~ (e3 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (396) can reduce 179 to:
% 10.15/2.85 | (116) ~ (e2 = e1)
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (93), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (232) all_0_12_12 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (232) can reduce 208 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (208) ~ (all_0_12_12 = e2)
% 10.15/2.85 | (864) all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (864), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (252) all_0_13_13 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (252) can reduce 457 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.85 | (876) all_0_14_14 = e2 | all_0_15_15 = e2
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (876), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (877) all_0_14_14 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (877) can reduce 102 to:
% 10.15/2.85 | (985) ~ (all_0_6_6 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (877) can reduce 127 to:
% 10.15/2.85 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (877) can reduce 726 to:
% 10.15/2.85 | (116) ~ (e2 = e1)
% 10.15/2.85 |
% 10.15/2.85 | From (877) and (19) follows:
% 10.15/2.85 | (1701) op(e0, e1) = e2
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (135), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (469) all_0_4_4 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (469) can reduce 122 to:
% 10.15/2.85 | (1323) ~ (all_0_7_7 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 1323 yields:
% 10.15/2.85 | (478) ~ (all_0_7_7 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (469) can reduce 64 to:
% 10.15/2.85 | (2037) ~ (all_0_8_8 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 2037 yields:
% 10.15/2.85 | (445) ~ (all_0_8_8 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (469) can reduce 36 to:
% 10.15/2.85 | (2039) ~ (all_0_12_12 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 2039 yields:
% 10.15/2.85 | (208) ~ (all_0_12_12 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (469) can reduce 182 to:
% 10.15/2.85 | (116) ~ (e2 = e1)
% 10.15/2.85 |
% 10.15/2.85 | From (469) and (11) follows:
% 10.15/2.85 | (327) op(e2, e3) = e2
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (33), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (223) all_0_13_13 = e3
% 10.15/2.85 |
% 10.15/2.85 | Equations (223) can reduce 200 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.85 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (251), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (252) all_0_13_13 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (252) can reduce 457 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.85 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (458), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (459) all_0_13_13 = e1
% 10.15/2.85 |
% 10.15/2.85 | Equations (459) can reduce 189 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.85 | (378) all_0_13_13 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (378) can reduce 72 to:
% 10.15/2.85 | (377) ~ (all_0_9_9 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (378) can reduce 200 to:
% 10.15/2.85 | (243) ~ (e3 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 243 yields:
% 10.15/2.85 | (29) ~ (e3 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (378) can reduce 457 to:
% 10.15/2.85 | (316) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 316 yields:
% 10.15/2.85 | (13) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (378) can reduce 189 to:
% 10.15/2.85 | (245) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 245 yields:
% 10.15/2.85 | (3) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | From (378) and (73) follows:
% 10.15/2.85 | (336) op(e0, e2) = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (92), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (910) all_0_8_8 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (910) can reduce 104 to:
% 10.15/2.85 | (2064) ~ (all_0_12_12 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 2064 yields:
% 10.15/2.85 | (652) ~ (all_0_12_12 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (910) can reduce 445 to:
% 10.15/2.85 | (316) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 316 yields:
% 10.15/2.85 | (13) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (910) can reduce 184 to:
% 10.15/2.85 | (245) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 245 yields:
% 10.15/2.85 | (3) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | From (910) and (56) follows:
% 10.15/2.85 | (1380) op(e1, e3) = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (43), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (163) all_0_0_0 = e3
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (163,175) yields a new equation:
% 10.15/2.85 | (442) e3 = e1
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 442 yields:
% 10.15/2.85 | (328) e3 = e1
% 10.15/2.85 |
% 10.15/2.85 | Equations (328) can reduce 61 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (955) ~ (all_0_0_0 = e3)
% 10.15/2.85 | (956) all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (956), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (214) all_0_4_4 = e3
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (214,469) yields a new equation:
% 10.15/2.85 | (878) e3 = e2
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 878 yields:
% 10.15/2.85 | (329) e3 = e2
% 10.15/2.85 |
% 10.15/2.85 | Equations (329) can reduce 86 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.85 | (1914) all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (1914), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (685) all_0_8_8 = e3
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (910,685) yields a new equation:
% 10.15/2.85 | (264) e3 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (264) can reduce 29 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.85 | (219) all_0_12_12 = e3
% 10.15/2.85 |
% 10.15/2.85 | Equations (219) can reduce 208 to:
% 10.15/2.85 | (86) ~ (e3 = e2)
% 10.15/2.85 |
% 10.15/2.85 | Equations (219) can reduce 188 to:
% 10.15/2.85 | (61) ~ (e3 = e1)
% 10.15/2.85 |
% 10.15/2.85 | Equations (219) can reduce 652 to:
% 10.15/2.85 | (29) ~ (e3 = e0)
% 10.15/2.85 |
% 10.15/2.85 | From (219) and (147) follows:
% 10.15/2.85 | (356) op(e0, e3) = e3
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (18), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (320) all_0_3_3 = e0
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (320,1111) yields a new equation:
% 10.15/2.85 | (264) e3 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (264) can reduce 29 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (362) ~ (all_0_3_3 = e0)
% 10.15/2.85 | (363) all_0_7_7 = e0 | all_0_11_11 = e0 | all_0_15_15 = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (363), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (364) all_0_7_7 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (364) can reduce 1039 to:
% 10.15/2.85 | (243) ~ (e3 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 243 yields:
% 10.15/2.85 | (29) ~ (e3 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (364) can reduce 478 to:
% 10.15/2.85 | (316) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 316 yields:
% 10.15/2.85 | (13) ~ (e2 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Equations (364) can reduce 158 to:
% 10.15/2.85 | (245) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 245 yields:
% 10.15/2.85 | (3) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (63), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (1597) all_0_9_9 = e3
% 10.15/2.85 |
% 10.15/2.85 | From (1597) and (14) follows:
% 10.15/2.85 | (2105) op(e1, e2) = e3
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (55), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (325) unit = e3
% 10.15/2.85 |
% 10.15/2.85 | From (325) and (46) follows:
% 10.15/2.85 | (326) op(e3, e3) = e3
% 10.15/2.85 |
% 10.15/2.85 | From (325) and (133) follows:
% 10.15/2.85 | (247) op(e0, e3) = e0
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e3, e3, e3, e1 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e1, yields:
% 10.15/2.85 | (328) e3 = e1
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e0, e3, e0, e3 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e0, yields:
% 10.15/2.85 | (264) e3 = e0
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (328,264) yields a new equation:
% 10.15/2.85 | (272) e1 = e0
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 272 yields:
% 10.15/2.85 | (273) e1 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (273) can reduce 3 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (332) ~ (unit = e3)
% 10.15/2.85 | (333) unit = e2 | unit = e1 | unit = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (333), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (334) unit = e2
% 10.15/2.85 |
% 10.15/2.85 | From (334) and (143) follows:
% 10.15/2.85 | (218) op(e2, e3) = e3
% 10.15/2.85 |
% 10.15/2.85 | From (334) and (25) follows:
% 10.15/2.85 | (796) op(e1, e2) = e1
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e2, e3, e3, e2 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e2, yields:
% 10.15/2.85 | (329) e3 = e2
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e1, e2, e1, e3 and discharging atoms op(e1, e2) = e3, op(e1, e2) = e1, yields:
% 10.15/2.85 | (328) e3 = e1
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (329,328) yields a new equation:
% 10.15/2.85 | (422) e2 = e1
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 422 yields:
% 10.15/2.85 | (330) e2 = e1
% 10.15/2.85 |
% 10.15/2.85 | Equations (330) can reduce 116 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (342) ~ (unit = e2)
% 10.15/2.85 | (343) unit = e1 | unit = e0
% 10.15/2.85 |
% 10.15/2.85 +-Applying beta-rule and splitting (343), into two cases.
% 10.15/2.85 |-Branch one:
% 10.15/2.85 | (344) unit = e1
% 10.15/2.85 |
% 10.15/2.85 | From (344) and (143) follows:
% 10.15/2.85 | (345) op(e1, e3) = e3
% 10.15/2.85 |
% 10.15/2.85 | From (344) and (57) follows:
% 10.15/2.85 | (744) op(e1, e2) = e2
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e1, e3, e3, e0 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e0, yields:
% 10.15/2.85 | (264) e3 = e0
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e1, e2, e2, e3 and discharging atoms op(e1, e2) = e3, op(e1, e2) = e2, yields:
% 10.15/2.85 | (329) e3 = e2
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (264,329) yields a new equation:
% 10.15/2.85 | (338) e2 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (338) can reduce 13 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (352) ~ (unit = e1)
% 10.15/2.85 | (353) unit = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (353) can reduce 352 to:
% 10.15/2.85 | (245) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | Simplifying 245 yields:
% 10.15/2.85 | (3) ~ (e1 = e0)
% 10.15/2.85 |
% 10.15/2.85 | From (353) and (57) follows:
% 10.15/2.85 | (256) op(e0, e2) = e2
% 10.15/2.85 |
% 10.15/2.85 | From (353) and (24) follows:
% 10.15/2.85 | (357) op(e0, e1) = e1
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e0, e2, e2, e0 and discharging atoms op(e0, e2) = e2, op(e0, e2) = e0, yields:
% 10.15/2.85 | (338) e2 = e0
% 10.15/2.85 |
% 10.15/2.85 | Instantiating formula (5) with e0, e1, e1, e2 and discharging atoms op(e0, e1) = e2, op(e0, e1) = e1, yields:
% 10.15/2.85 | (330) e2 = e1
% 10.15/2.85 |
% 10.15/2.85 | Combining equations (338,330) yields a new equation:
% 10.15/2.85 | (273) e1 = e0
% 10.15/2.85 |
% 10.15/2.85 | Equations (273) can reduce 3 to:
% 10.15/2.85 | (167) $false
% 10.15/2.85 |
% 10.15/2.85 |-The branch is then unsatisfiable
% 10.15/2.85 |-Branch two:
% 10.15/2.85 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.86 | (1600) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (9), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (281) all_0_2_2 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (281,400) yields a new equation:
% 10.15/2.86 | (506) e3 = e0
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 506 yields:
% 10.15/2.86 | (264) e3 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (264) can reduce 29 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.86 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 10.15/2.86 |
% 10.15/2.86 | Equations (400) can reduce 269 to:
% 10.15/2.86 | (243) ~ (e3 = e0)
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 243 yields:
% 10.15/2.86 | (29) ~ (e3 = e0)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (78), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (685) all_0_8_8 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (910,685) yields a new equation:
% 10.15/2.86 | (264) e3 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (264) can reduce 29 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.86 | (1845) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (91), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (301) all_0_1_1 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (301,396) yields a new equation:
% 10.15/2.86 | (878) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 878 yields:
% 10.15/2.86 | (329) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (329) can reduce 86 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.86 | (1851) all_0_5_5 = e3 | all_0_9_9 = e3 | all_0_13_13 = e3
% 10.15/2.86 |
% 10.15/2.86 | Equations (396) can reduce 382 to:
% 10.15/2.86 | (741) ~ (e3 = e2)
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 741 yields:
% 10.15/2.86 | (86) ~ (e3 = e2)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (1845), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (1597) all_0_9_9 = e3
% 10.15/2.86 |
% 10.15/2.86 | Equations (1597) can reduce 497 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.86 | (1860) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (1860), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (165) all_0_10_10 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (165,177) yields a new equation:
% 10.15/2.86 | (442) e3 = e1
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 442 yields:
% 10.15/2.86 | (328) e3 = e1
% 10.15/2.86 |
% 10.15/2.86 | Equations (328) can reduce 61 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.86 | (668) all_0_11_11 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (455,668) yields a new equation:
% 10.15/2.86 | (329) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (329) can reduce 86 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (368) ~ (all_0_7_7 = e0)
% 10.15/2.86 | (369) all_0_11_11 = e0 | all_0_15_15 = e0
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (369), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (370) all_0_11_11 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (455,370) yields a new equation:
% 10.15/2.86 | (349) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 349 yields:
% 10.15/2.86 | (338) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (338) can reduce 13 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (315) ~ (all_0_11_11 = e0)
% 10.15/2.86 | (373) all_0_15_15 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (373,178) yields a new equation:
% 10.15/2.86 | (273) e1 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (273) can reduce 3 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.86 | (2189) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (119), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (285) all_0_0_0 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (285,175) yields a new equation:
% 10.15/2.86 | (273) e1 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (273) can reduce 3 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (288) ~ (all_0_0_0 = e0)
% 10.15/2.86 | (1373) all_0_4_4 = e0 | all_0_8_8 = e0 | all_0_12_12 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (175) can reduce 288 to:
% 10.15/2.86 | (3) ~ (e1 = e0)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2189), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (313) all_0_9_9 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (313) can reduce 377 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (377) ~ (all_0_9_9 = e0)
% 10.15/2.86 | (2199) all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (1373), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (263) all_0_4_4 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (263,469) yields a new equation:
% 10.15/2.86 | (338) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (338) can reduce 13 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.86 | (1377) all_0_8_8 = e0 | all_0_12_12 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (469) can reduce 195 to:
% 10.15/2.86 | (13) ~ (e2 = e0)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2199), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (493) all_0_10_10 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (177,493) yields a new equation:
% 10.15/2.86 | (272) e1 = e0
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 272 yields:
% 10.15/2.86 | (273) e1 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (273) can reduce 3 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.86 | (370) all_0_11_11 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (455,370) yields a new equation:
% 10.15/2.86 | (349) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 349 yields:
% 10.15/2.86 | (338) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (338) can reduce 13 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (211) ~ (all_0_4_4 = e2)
% 10.15/2.86 | (2216) all_0_5_5 = e2 | all_0_6_6 = e2 | all_0_7_7 = e2
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2216), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (170) all_0_5_5 = e2
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (170,176) yields a new equation:
% 10.15/2.86 | (422) e2 = e1
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 422 yields:
% 10.15/2.86 | (330) e2 = e1
% 10.15/2.86 |
% 10.15/2.86 | Equations (330) can reduce 116 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (2221) ~ (all_0_5_5 = e2)
% 10.15/2.86 | (2222) all_0_6_6 = e2 | all_0_7_7 = e2
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2222), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (674) all_0_6_6 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (674) can reduce 985 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (985) ~ (all_0_6_6 = e2)
% 10.15/2.86 | (209) all_0_7_7 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (209) can reduce 478 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (678) ~ (all_0_14_14 = e2)
% 10.15/2.86 | (172) all_0_15_15 = e2
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (172,178) yields a new equation:
% 10.15/2.86 | (422) e2 = e1
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 422 yields:
% 10.15/2.86 | (330) e2 = e1
% 10.15/2.86 |
% 10.15/2.86 | Equations (330) can reduce 116 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (253) ~ (all_0_1_1 = e2)
% 10.15/2.86 | (430) all_0_2_2 = e2 | all_0_3_3 = e2
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (430), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (291) all_0_2_2 = e2
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (291,400) yields a new equation:
% 10.15/2.86 | (349) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 349 yields:
% 10.15/2.86 | (338) e2 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (338) can reduce 13 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (415) ~ (all_0_2_2 = e2)
% 10.15/2.86 | (201) all_0_3_3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (1111,201) yields a new equation:
% 10.15/2.86 | (878) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 878 yields:
% 10.15/2.86 | (329) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (329) can reduce 86 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.86 | (320) all_0_3_3 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (320,1111) yields a new equation:
% 10.15/2.86 | (264) e3 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (264) can reduce 29 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (1035) ~ (all_0_3_3 = e3)
% 10.15/2.86 | (2249) all_0_7_7 = e3 | all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2249), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (968) all_0_7_7 = e3
% 10.15/2.86 |
% 10.15/2.86 | Equations (968) can reduce 1039 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.86 | (2253) all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (2253), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (668) all_0_11_11 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (455,668) yields a new equation:
% 10.15/2.86 | (329) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (329) can reduce 86 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.86 | (166) all_0_15_15 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (166,178) yields a new equation:
% 10.15/2.86 | (442) e3 = e1
% 10.15/2.86 |
% 10.15/2.86 | Simplifying 442 yields:
% 10.15/2.86 | (328) e3 = e1
% 10.15/2.86 |
% 10.15/2.86 | Equations (328) can reduce 61 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (968) all_0_7_7 = e3
% 10.15/2.86 | (488) ~ (all_0_15_15 = e1)
% 10.15/2.86 |
% 10.15/2.86 | Equations (178) can reduce 488 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (297) all_0_1_1 = e0
% 10.15/2.86 | (197) ~ (all_0_5_5 = e1)
% 10.15/2.86 |
% 10.15/2.86 | Equations (176) can reduce 197 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 10.15/2.86 |
% 10.15/2.86 | Applying alpha-rule on (490) yields:
% 10.15/2.86 | (285) all_0_0_0 = e0
% 10.15/2.86 | (271) all_0_5_5 = e0
% 10.15/2.86 | (493) all_0_10_10 = e0
% 10.15/2.86 | (373) all_0_15_15 = e0
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (285,175) yields a new equation:
% 10.15/2.86 | (273) e1 = e0
% 10.15/2.86 |
% 10.15/2.86 | Equations (273) can reduce 3 to:
% 10.15/2.86 | (167) $false
% 10.15/2.86 |
% 10.15/2.86 |-The branch is then unsatisfiable
% 10.15/2.86 |-Branch two:
% 10.15/2.86 | (171) all_0_10_10 = e2
% 10.15/2.86 | (440) ~ (all_0_14_14 = e3)
% 10.15/2.86 |
% 10.15/2.86 | From (171) and (130) follows:
% 10.15/2.86 | (2277) op(e1, e1) = e2
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (82), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (160) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2) | (all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (160), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (161) (all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3) | (all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2)
% 10.15/2.86 |
% 10.15/2.86 +-Applying beta-rule and splitting (161), into two cases.
% 10.15/2.86 |-Branch one:
% 10.15/2.86 | (162) all_0_0_0 = e3 & all_0_5_5 = e3 & all_0_10_10 = e3 & all_0_15_15 = e3
% 10.15/2.86 |
% 10.15/2.86 | Applying alpha-rule on (162) yields:
% 10.15/2.86 | (163) all_0_0_0 = e3
% 10.15/2.86 | (164) all_0_5_5 = e3
% 10.15/2.86 | (165) all_0_10_10 = e3
% 10.15/2.86 | (166) all_0_15_15 = e3
% 10.15/2.86 |
% 10.15/2.86 | Combining equations (171,165) yields a new equation:
% 10.15/2.86 | (329) e3 = e2
% 10.15/2.86 |
% 10.15/2.86 | Equations (329) can reduce 86 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (168) all_0_0_0 = e2 & all_0_5_5 = e2 & all_0_10_10 = e2 & all_0_15_15 = e2
% 10.15/2.87 |
% 10.15/2.87 | Applying alpha-rule on (168) yields:
% 10.15/2.87 | (169) all_0_0_0 = e2
% 10.15/2.87 | (170) all_0_5_5 = e2
% 10.15/2.87 | (171) all_0_10_10 = e2
% 10.15/2.87 | (172) all_0_15_15 = e2
% 10.15/2.87 |
% 10.15/2.87 | Equations (169) can reduce 12 to:
% 10.15/2.87 | (1585) ~ (all_0_2_2 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 1585 yields:
% 10.15/2.87 | (415) ~ (all_0_2_2 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (169) can reduce 111 to:
% 10.15/2.87 | (2037) ~ (all_0_8_8 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 2037 yields:
% 10.15/2.87 | (445) ~ (all_0_8_8 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (170) can reduce 30 to:
% 10.15/2.87 | (253) ~ (all_0_1_1 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 6 to:
% 10.15/2.87 | (196) ~ (all_0_3_3 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (170) can reduce 146 to:
% 10.15/2.87 | (211) ~ (all_0_4_4 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (170) can reduce 139 to:
% 10.15/2.87 | (1632) ~ (all_0_6_6 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 1632 yields:
% 10.15/2.87 | (985) ~ (all_0_6_6 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (170) can reduce 60 to:
% 10.15/2.87 | (258) ~ (all_0_9_9 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 258 yields:
% 10.15/2.87 | (254) ~ (all_0_9_9 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 100 to:
% 10.15/2.87 | (478) ~ (all_0_7_7 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 48 to:
% 10.15/2.87 | (156) ~ (all_0_11_11 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 148 to:
% 10.15/2.87 | (208) ~ (all_0_12_12 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 23 to:
% 10.15/2.87 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (172) can reduce 41 to:
% 10.15/2.87 | (678) ~ (all_0_14_14 = e2)
% 10.15/2.87 |
% 10.15/2.87 | From (169) and (84) follows:
% 10.15/2.87 | (2308) op(e3, e3) = e2
% 10.15/2.87 |
% 10.15/2.87 | From (172) and (65) follows:
% 10.15/2.87 | (2309) op(e0, e0) = e2
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (110), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (425) ~ (all_0_0_0 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (169) can reduce 425 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (169) all_0_0_0 = e2
% 10.15/2.87 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (154), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (99), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (425) ~ (all_0_0_0 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (169) can reduce 425 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (169) all_0_0_0 = e2
% 10.15/2.87 | (188) ~ (all_0_12_12 = e1)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (89), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (69), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (181) ~ (all_0_3_3 = e1)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (80), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (927) all_0_3_3 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (927) can reduce 181 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (181) ~ (all_0_3_3 = e1)
% 10.15/2.87 | (2324) all_0_7_7 = e1 | all_0_11_11 = e1 | all_0_15_15 = e1
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (28), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (219) all_0_12_12 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 36 to:
% 10.15/2.87 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 104 to:
% 10.15/2.87 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 141 to:
% 10.15/2.87 | (2328) ~ (all_0_13_13 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 2328 yields:
% 10.15/2.87 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 51 to:
% 10.15/2.87 | (1626) ~ (all_0_14_14 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 1626 yields:
% 10.15/2.87 | (440) ~ (all_0_14_14 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 208 to:
% 10.15/2.87 | (86) ~ (e3 = e2)
% 10.15/2.87 |
% 10.15/2.87 | Equations (219) can reduce 188 to:
% 10.15/2.87 | (61) ~ (e3 = e1)
% 10.15/2.87 |
% 10.15/2.87 | From (219) and (147) follows:
% 10.15/2.87 | (356) op(e0, e3) = e3
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (78), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (685) all_0_8_8 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (685) can reduce 669 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.87 | (1845) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (44), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (685) all_0_8_8 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (685) can reduce 669 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.87 | (688) all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (119), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (285) all_0_0_0 = e0
% 10.15/2.87 |
% 10.15/2.87 | Combining equations (285,169) yields a new equation:
% 10.15/2.87 | (338) e2 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (338) can reduce 13 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (288) ~ (all_0_0_0 = e0)
% 10.15/2.87 | (1373) all_0_4_4 = e0 | all_0_8_8 = e0 | all_0_12_12 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (169) can reduce 288 to:
% 10.15/2.87 | (13) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (1373), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (263) all_0_4_4 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (263) can reduce 126 to:
% 10.15/2.87 | (2350) ~ (all_0_6_6 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 2350 yields:
% 10.15/2.87 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (263) can reduce 64 to:
% 10.15/2.87 | (2352) ~ (all_0_8_8 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 2352 yields:
% 10.15/2.87 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (263) can reduce 211 to:
% 10.15/2.87 | (316) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 316 yields:
% 10.15/2.87 | (13) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 | From (263) and (11) follows:
% 10.15/2.87 | (1156) op(e2, e3) = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (53), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (175) all_0_0_0 = e1
% 10.15/2.87 |
% 10.15/2.87 | Combining equations (175,169) yields a new equation:
% 10.15/2.87 | (330) e2 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (330) can reduce 116 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.87 | (1648) all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (1648), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (473) all_0_4_4 = e1
% 10.15/2.87 |
% 10.15/2.87 | Combining equations (473,263) yields a new equation:
% 10.15/2.87 | (272) e1 = e0
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 272 yields:
% 10.15/2.87 | (273) e1 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (273) can reduce 3 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.87 | (1655) all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (1655), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (750) all_0_8_8 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (750) can reduce 95 to:
% 10.15/2.87 | (614) ~ (all_0_11_11 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 614 yields:
% 10.15/2.87 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Equations (750) can reduce 445 to:
% 10.15/2.87 | (186) ~ (e2 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 186 yields:
% 10.15/2.87 | (116) ~ (e2 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Equations (750) can reduce 240 to:
% 10.15/2.87 | (3) ~ (e1 = e0)
% 10.15/2.87 |
% 10.15/2.87 | From (750) and (56) follows:
% 10.15/2.87 | (754) op(e1, e3) = e1
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (7), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (400) all_0_2_2 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (400) can reduce 278 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.87 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (1085), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (277) all_0_6_6 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (277) can reduce 436 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.87 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (1091), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (493) all_0_10_10 = e0
% 10.15/2.87 |
% 10.15/2.87 | Combining equations (493,171) yields a new equation:
% 10.15/2.87 | (338) e2 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (338) can reduce 13 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.87 | (1096) all_0_14_14 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (1096) can reduce 102 to:
% 10.15/2.87 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (1096) can reduce 127 to:
% 10.15/2.87 | (242) ~ (all_0_13_13 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (1096) can reduce 440 to:
% 10.15/2.87 | (243) ~ (e3 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 243 yields:
% 10.15/2.87 | (29) ~ (e3 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (1096) can reduce 678 to:
% 10.15/2.87 | (316) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 316 yields:
% 10.15/2.87 | (13) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (49), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (668) all_0_11_11 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (668) can reduce 992 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.87 | (993) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (2324), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (581) all_0_7_7 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (581) can reduce 15 to:
% 10.15/2.87 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Equations (581) can reduce 114 to:
% 10.15/2.87 | (614) ~ (all_0_11_11 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 614 yields:
% 10.15/2.87 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (71), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (565) all_0_2_2 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (565) can reduce 10 to:
% 10.15/2.87 | (566) ~ (all_0_6_6 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 566 yields:
% 10.15/2.87 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (128), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (670) all_0_6_6 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (670) can reduce 985 to:
% 10.15/2.87 | (86) ~ (e3 = e2)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (33), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (223) all_0_13_13 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (223) can reduce 200 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.87 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (251), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (252) all_0_13_13 = e2
% 10.15/2.87 |
% 10.15/2.87 | Equations (252) can reduce 457 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.87 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (458), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (459) all_0_13_13 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (459) can reduce 200 to:
% 10.15/2.87 | (841) ~ (e3 = e1)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 841 yields:
% 10.15/2.87 | (61) ~ (e3 = e1)
% 10.15/2.87 |
% 10.15/2.87 | From (459) and (73) follows:
% 10.15/2.87 | (2418) op(e0, e2) = e1
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (112), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (1111) all_0_3_3 = e3
% 10.15/2.87 |
% 10.15/2.87 | Equations (1111) can reduce 120 to:
% 10.15/2.87 | (2420) ~ (all_0_11_11 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 2420 yields:
% 10.15/2.87 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.87 |
% 10.15/2.87 | Equations (1111) can reduce 196 to:
% 10.15/2.87 | (86) ~ (e3 = e2)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (993), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (455) all_0_11_11 = e2
% 10.15/2.87 |
% 10.15/2.87 | Equations (455) can reduce 156 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (156) ~ (all_0_11_11 = e2)
% 10.15/2.87 | (997) all_0_11_11 = e1 | all_0_11_11 = e0
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (997), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (856) all_0_11_11 = e1
% 10.15/2.87 |
% 10.15/2.87 | Equations (856) can reduce 615 to:
% 10.15/2.87 | (167) $false
% 10.15/2.87 |
% 10.15/2.87 |-The branch is then unsatisfiable
% 10.15/2.87 |-Branch two:
% 10.15/2.87 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.87 | (370) all_0_11_11 = e0
% 10.15/2.87 |
% 10.15/2.87 | Equations (370) can reduce 992 to:
% 10.15/2.87 | (243) ~ (e3 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 243 yields:
% 10.15/2.87 | (29) ~ (e3 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (370) can reduce 156 to:
% 10.15/2.87 | (316) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 316 yields:
% 10.15/2.87 | (13) ~ (e2 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Equations (370) can reduce 615 to:
% 10.15/2.87 | (245) ~ (e1 = e0)
% 10.15/2.87 |
% 10.15/2.87 | Simplifying 245 yields:
% 10.15/2.87 | (3) ~ (e1 = e0)
% 10.15/2.87 |
% 10.15/2.87 +-Applying beta-rule and splitting (63), into two cases.
% 10.15/2.87 |-Branch one:
% 10.15/2.87 | (1597) all_0_9_9 = e3
% 10.15/2.87 |
% 10.15/2.87 | From (1597) and (14) follows:
% 10.15/2.88 | (2105) op(e1, e2) = e3
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (55), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (325) unit = e3
% 10.15/2.88 |
% 10.15/2.88 | From (325) and (46) follows:
% 10.15/2.88 | (326) op(e3, e3) = e3
% 10.15/2.88 |
% 10.15/2.88 | From (325) and (133) follows:
% 10.15/2.88 | (247) op(e0, e3) = e0
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e3, e3, e3, e2 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e2, yields:
% 10.15/2.88 | (329) e3 = e2
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e0, e3, e0, e3 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e0, yields:
% 10.15/2.88 | (264) e3 = e0
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (329,264) yields a new equation:
% 10.15/2.88 | (349) e2 = e0
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 349 yields:
% 10.15/2.88 | (338) e2 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (338) can reduce 13 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (332) ~ (unit = e3)
% 10.15/2.88 | (333) unit = e2 | unit = e1 | unit = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (333), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (334) unit = e2
% 10.15/2.88 |
% 10.15/2.88 | From (334) and (143) follows:
% 10.15/2.88 | (218) op(e2, e3) = e3
% 10.15/2.88 |
% 10.15/2.88 | From (334) and (25) follows:
% 10.15/2.88 | (796) op(e1, e2) = e1
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e2, e3, e3, e0 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e0, yields:
% 10.15/2.88 | (264) e3 = e0
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e1, e2, e1, e3 and discharging atoms op(e1, e2) = e3, op(e1, e2) = e1, yields:
% 10.15/2.88 | (328) e3 = e1
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (264,328) yields a new equation:
% 10.15/2.88 | (273) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (273) can reduce 3 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (342) ~ (unit = e2)
% 10.15/2.88 | (343) unit = e1 | unit = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (343), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (344) unit = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (344) can reduce 342 to:
% 10.15/2.88 | (186) ~ (e2 = e1)
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 186 yields:
% 10.15/2.88 | (116) ~ (e2 = e1)
% 10.15/2.88 |
% 10.15/2.88 | From (344) and (143) follows:
% 10.15/2.88 | (345) op(e1, e3) = e3
% 10.15/2.88 |
% 10.15/2.88 | From (344) and (57) follows:
% 10.15/2.88 | (744) op(e1, e2) = e2
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e1, e3, e3, e1 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e1, yields:
% 10.15/2.88 | (328) e3 = e1
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e1, e2, e2, e3 and discharging atoms op(e1, e2) = e3, op(e1, e2) = e2, yields:
% 10.15/2.88 | (329) e3 = e2
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (328,329) yields a new equation:
% 10.15/2.88 | (330) e2 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (330) can reduce 116 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (352) ~ (unit = e1)
% 10.15/2.88 | (353) unit = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (353) can reduce 352 to:
% 10.15/2.88 | (245) ~ (e1 = e0)
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 245 yields:
% 10.15/2.88 | (3) ~ (e1 = e0)
% 10.15/2.88 |
% 10.15/2.88 | From (353) and (57) follows:
% 10.15/2.88 | (256) op(e0, e2) = e2
% 10.15/2.88 |
% 10.15/2.88 | From (353) and (133) follows:
% 10.15/2.88 | (1196) op(e0, e0) = e0
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e0, e2, e2, e1 and discharging atoms op(e0, e2) = e2, op(e0, e2) = e1, yields:
% 10.15/2.88 | (330) e2 = e1
% 10.15/2.88 |
% 10.15/2.88 | Instantiating formula (5) with e0, e0, e0, e2 and discharging atoms op(e0, e0) = e2, op(e0, e0) = e0, yields:
% 10.15/2.88 | (338) e2 = e0
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (330,338) yields a new equation:
% 10.15/2.88 | (272) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 272 yields:
% 10.15/2.88 | (273) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (273) can reduce 3 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.88 | (1600) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (1845), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (1597) all_0_9_9 = e3
% 10.15/2.88 |
% 10.15/2.88 | Equations (1597) can reduce 497 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.88 | (1860) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (1860), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (165) all_0_10_10 = e3
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (171,165) yields a new equation:
% 10.15/2.88 | (329) e3 = e2
% 10.15/2.88 |
% 10.15/2.88 | Equations (329) can reduce 86 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.88 | (668) all_0_11_11 = e3
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (370,668) yields a new equation:
% 10.15/2.88 | (264) e3 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (264) can reduce 29 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (1035) ~ (all_0_3_3 = e3)
% 10.15/2.88 | (2249) all_0_7_7 = e3 | all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (2249), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (968) all_0_7_7 = e3
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (581,968) yields a new equation:
% 10.15/2.88 | (328) e3 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (328) can reduce 61 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.88 | (2253) all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (2253), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (668) all_0_11_11 = e3
% 10.15/2.88 |
% 10.15/2.88 | Equations (668) can reduce 992 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.88 | (166) all_0_15_15 = e3
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (172,166) yields a new equation:
% 10.15/2.88 | (329) e3 = e2
% 10.15/2.88 |
% 10.15/2.88 | Equations (329) can reduce 86 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.88 | (378) all_0_13_13 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (378) can reduce 242 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (667) ~ (all_0_6_6 = e3)
% 10.15/2.88 | (673) all_0_6_6 = e2 | all_0_6_6 = e1 | all_0_6_6 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (673), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (674) all_0_6_6 = e2
% 10.15/2.88 |
% 10.15/2.88 | Equations (674) can reduce 985 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (985) ~ (all_0_6_6 = e2)
% 10.15/2.88 | (986) all_0_6_6 = e1 | all_0_6_6 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (986), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (578) all_0_6_6 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (578) can reduce 183 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.88 | (277) all_0_6_6 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (277) can reduce 436 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.88 | (1805) all_0_6_6 = e1 | all_0_10_10 = e1 | all_0_14_14 = e1
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (33), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (223) all_0_13_13 = e3
% 10.15/2.88 |
% 10.15/2.88 | Equations (223) can reduce 200 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (200) ~ (all_0_13_13 = e3)
% 10.15/2.88 | (251) all_0_13_13 = e2 | all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (251), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (252) all_0_13_13 = e2
% 10.15/2.88 |
% 10.15/2.88 | Equations (252) can reduce 457 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (457) ~ (all_0_13_13 = e2)
% 10.15/2.88 | (458) all_0_13_13 = e1 | all_0_13_13 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (458), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (459) all_0_13_13 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (459) can reduce 457 to:
% 10.15/2.88 | (186) ~ (e2 = e1)
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 186 yields:
% 10.15/2.88 | (116) ~ (e2 = e1)
% 10.15/2.88 |
% 10.15/2.88 | Equations (459) can reduce 242 to:
% 10.15/2.88 | (3) ~ (e1 = e0)
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (1805), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (578) all_0_6_6 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (578) can reduce 183 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.88 | (1814) all_0_10_10 = e1 | all_0_14_14 = e1
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (17), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (175) all_0_0_0 = e1
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (175,169) yields a new equation:
% 10.15/2.88 | (330) e2 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (330) can reduce 116 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.88 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (169) can reduce 192 to:
% 10.15/2.88 | (116) ~ (e2 = e1)
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (1814), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (177) all_0_10_10 = e1
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (171,177) yields a new equation:
% 10.15/2.88 | (422) e2 = e1
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 422 yields:
% 10.15/2.88 | (330) e2 = e1
% 10.15/2.88 |
% 10.15/2.88 | Equations (330) can reduce 116 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (855) ~ (all_0_10_10 = e1)
% 10.15/2.88 | (1306) all_0_14_14 = e1
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (1306,1096) yields a new equation:
% 10.15/2.88 | (272) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 272 yields:
% 10.15/2.88 | (273) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (273) can reduce 3 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.88 | (378) all_0_13_13 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (378) can reduce 242 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (158) ~ (all_0_7_7 = e1)
% 10.15/2.88 | (2555) all_0_11_11 = e1 | all_0_15_15 = e1
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (1845), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (1597) all_0_9_9 = e3
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (92), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (910) all_0_8_8 = e0
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (910,750) yields a new equation:
% 10.15/2.88 | (273) e1 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (273) can reduce 3 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.88 | (2189) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (2189), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (313) all_0_9_9 = e0
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (1597,313) yields a new equation:
% 10.15/2.88 | (506) e3 = e0
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 506 yields:
% 10.15/2.88 | (264) e3 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (264) can reduce 29 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (377) ~ (all_0_9_9 = e0)
% 10.15/2.88 | (2199) all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.88 |
% 10.15/2.88 +-Applying beta-rule and splitting (2199), into two cases.
% 10.15/2.88 |-Branch one:
% 10.15/2.88 | (493) all_0_10_10 = e0
% 10.15/2.88 |
% 10.15/2.88 | Combining equations (171,493) yields a new equation:
% 10.15/2.88 | (349) e2 = e0
% 10.15/2.88 |
% 10.15/2.88 | Simplifying 349 yields:
% 10.15/2.88 | (338) e2 = e0
% 10.15/2.88 |
% 10.15/2.88 | Equations (338) can reduce 13 to:
% 10.15/2.88 | (167) $false
% 10.15/2.88 |
% 10.15/2.88 |-The branch is then unsatisfiable
% 10.15/2.88 |-Branch two:
% 10.15/2.88 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.89 | (370) all_0_11_11 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (370) can reduce 615 to:
% 10.15/2.89 | (245) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 245 yields:
% 10.15/2.89 | (3) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (106), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (473) all_0_4_4 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (473,263) yields a new equation:
% 10.15/2.89 | (272) e1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 272 yields:
% 10.15/2.89 | (273) e1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (273) can reduce 3 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.89 | (572) all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (263) can reduce 182 to:
% 10.15/2.89 | (245) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 245 yields:
% 10.15/2.89 | (3) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2555), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (856) all_0_11_11 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (370,856) yields a new equation:
% 10.15/2.89 | (273) e1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (273) can reduce 3 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.89 | (178) all_0_15_15 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (172,178) yields a new equation:
% 10.15/2.89 | (422) e2 = e1
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 422 yields:
% 10.15/2.89 | (330) e2 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (330) can reduce 116 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.89 | (1860) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (63), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (1597) all_0_9_9 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (1597) can reduce 497 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.89 | (1600) all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (91), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (301) all_0_1_1 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (301) can reduce 253 to:
% 10.15/2.89 | (86) ~ (e3 = e2)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (1860), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (165) all_0_10_10 = e3
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (171,165) yields a new equation:
% 10.15/2.89 | (329) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Equations (329) can reduce 86 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.89 | (668) all_0_11_11 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (668) can reduce 992 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.89 | (1851) all_0_5_5 = e3 | all_0_9_9 = e3 | all_0_13_13 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (1851), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (164) all_0_5_5 = e3
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (170,164) yields a new equation:
% 10.15/2.89 | (329) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Equations (329) can reduce 86 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (962) ~ (all_0_5_5 = e3)
% 10.15/2.89 | (1906) all_0_9_9 = e3 | all_0_13_13 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (1906), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (1597) all_0_9_9 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (1597) can reduce 497 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.89 | (223) all_0_13_13 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (223) can reduce 200 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.89 | (236) all_0_12_12 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (219,236) yields a new equation:
% 10.15/2.89 | (442) e3 = e1
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 442 yields:
% 10.15/2.89 | (328) e3 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (328) can reduce 61 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.89 | (1377) all_0_8_8 = e0 | all_0_12_12 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (1845), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (1597) all_0_9_9 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (1597) can reduce 105 to:
% 10.15/2.89 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Equations (1597) can reduce 140 to:
% 10.15/2.89 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Equations (1597) can reduce 254 to:
% 10.15/2.89 | (86) ~ (e3 = e2)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (92), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (910) all_0_8_8 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (910) can reduce 240 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.89 | (2189) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (688), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (257) all_0_8_8 = e2
% 10.15/2.89 |
% 10.15/2.89 | Equations (257) can reduce 445 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (445) ~ (all_0_8_8 = e2)
% 10.15/2.89 | (692) all_0_8_8 = e1 | all_0_8_8 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (692), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (750) all_0_8_8 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (750) can reduce 95 to:
% 10.15/2.89 | (614) ~ (all_0_11_11 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 614 yields:
% 10.15/2.89 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Equations (750) can reduce 669 to:
% 10.15/2.89 | (841) ~ (e3 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 841 yields:
% 10.15/2.89 | (61) ~ (e3 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Equations (750) can reduce 445 to:
% 10.15/2.89 | (186) ~ (e2 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 186 yields:
% 10.15/2.89 | (116) ~ (e2 = e1)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2189), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (313) all_0_9_9 = e0
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (1597,313) yields a new equation:
% 10.15/2.89 | (506) e3 = e0
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 506 yields:
% 10.15/2.89 | (264) e3 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (264) can reduce 29 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (377) ~ (all_0_9_9 = e0)
% 10.15/2.89 | (2199) all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2199), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (493) all_0_10_10 = e0
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (493,171) yields a new equation:
% 10.15/2.89 | (338) e2 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (338) can reduce 13 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.89 | (370) all_0_11_11 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (370) can reduce 120 to:
% 10.15/2.89 | (362) ~ (all_0_3_3 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Equations (370) can reduce 114 to:
% 10.15/2.89 | (368) ~ (all_0_7_7 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Equations (370) can reduce 156 to:
% 10.15/2.89 | (316) ~ (e2 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 316 yields:
% 10.15/2.89 | (13) ~ (e2 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Equations (370) can reduce 615 to:
% 10.15/2.89 | (245) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 245 yields:
% 10.15/2.89 | (3) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (34), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (285) all_0_0_0 = e0
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (285,169) yields a new equation:
% 10.15/2.89 | (338) e2 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (338) can reduce 13 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (288) ~ (all_0_0_0 = e0)
% 10.15/2.89 | (289) all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (169) can reduce 288 to:
% 10.15/2.89 | (13) ~ (e2 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (79), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (214) all_0_4_4 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (214) can reduce 467 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.89 | (468) all_0_4_4 = e2 | all_0_4_4 = e1 | all_0_4_4 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2324), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (581) all_0_7_7 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (581) can reduce 478 to:
% 10.15/2.89 | (186) ~ (e2 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 186 yields:
% 10.15/2.89 | (116) ~ (e2 = e1)
% 10.15/2.89 |
% 10.15/2.89 | Equations (581) can reduce 368 to:
% 10.15/2.89 | (3) ~ (e1 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (138), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (214) all_0_4_4 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (214) can reduce 467 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.89 | (932) all_0_5_5 = e3 | all_0_6_6 = e3 | all_0_7_7 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (932), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (164) all_0_5_5 = e3
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (164,170) yields a new equation:
% 10.15/2.89 | (878) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 878 yields:
% 10.15/2.89 | (329) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Equations (329) can reduce 86 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (962) ~ (all_0_5_5 = e3)
% 10.15/2.89 | (963) all_0_6_6 = e3 | all_0_7_7 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (963), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (670) all_0_6_6 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (670) can reduce 10 to:
% 10.15/2.89 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Equations (670) can reduce 102 to:
% 10.15/2.89 | (1626) ~ (all_0_14_14 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 1626 yields:
% 10.15/2.89 | (440) ~ (all_0_14_14 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Equations (670) can reduce 985 to:
% 10.15/2.89 | (86) ~ (e3 = e2)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (7), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (400) all_0_2_2 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (400) can reduce 278 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.89 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (117), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (163) all_0_0_0 = e3
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (163,169) yields a new equation:
% 10.15/2.89 | (878) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 878 yields:
% 10.15/2.89 | (329) e3 = e2
% 10.15/2.89 |
% 10.15/2.89 | Equations (329) can reduce 86 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (955) ~ (all_0_0_0 = e3)
% 10.15/2.89 | (2699) all_0_1_1 = e3 | all_0_2_2 = e3 | all_0_3_3 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2699), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (301) all_0_1_1 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (301) can reduce 382 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.89 | (2703) all_0_2_2 = e3 | all_0_3_3 = e3
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (2703), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (281) all_0_2_2 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (281) can reduce 269 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.89 | (1111) all_0_3_3 = e3
% 10.15/2.89 |
% 10.15/2.89 | Equations (1111) can reduce 118 to:
% 10.15/2.89 | (382) ~ (all_0_1_1 = e3)
% 10.15/2.89 |
% 10.15/2.89 | Equations (1111) can reduce 362 to:
% 10.15/2.89 | (29) ~ (e3 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (289), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (297) all_0_1_1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (297) can reduce 382 to:
% 10.15/2.89 | (243) ~ (e3 = e0)
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 243 yields:
% 10.15/2.89 | (29) ~ (e3 = e0)
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (17), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (175) all_0_0_0 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (175,169) yields a new equation:
% 10.15/2.89 | (330) e2 = e1
% 10.15/2.89 |
% 10.15/2.89 | Equations (330) can reduce 116 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.89 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.89 |
% 10.15/2.89 +-Applying beta-rule and splitting (698), into two cases.
% 10.15/2.89 |-Branch one:
% 10.15/2.89 | (406) all_0_1_1 = e1
% 10.15/2.89 |
% 10.15/2.89 | Combining equations (406,297) yields a new equation:
% 10.15/2.89 | (272) e1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Simplifying 272 yields:
% 10.15/2.89 | (273) e1 = e0
% 10.15/2.89 |
% 10.15/2.89 | Equations (273) can reduce 3 to:
% 10.15/2.89 | (167) $false
% 10.15/2.89 |
% 10.15/2.89 |-The branch is then unsatisfiable
% 10.15/2.89 |-Branch two:
% 10.15/2.89 | (179) ~ (all_0_1_1 = e1)
% 10.15/2.89 | (702) all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (297) can reduce 179 to:
% 10.15/2.90 | (245) ~ (e1 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 245 yields:
% 10.15/2.90 | (3) ~ (e1 = e0)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (1377), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (910) all_0_8_8 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (750,910) yields a new equation:
% 10.15/2.90 | (272) e1 = e0
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 272 yields:
% 10.15/2.90 | (273) e1 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (273) can reduce 3 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.90 | (239) all_0_12_12 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (239,219) yields a new equation:
% 10.15/2.90 | (264) e3 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (264) can reduce 29 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.90 | (300) all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (1085), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (277) all_0_6_6 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (277,670) yields a new equation:
% 10.15/2.90 | (264) e3 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (264) can reduce 29 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.90 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (1091), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (493) all_0_10_10 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (171,493) yields a new equation:
% 10.15/2.90 | (349) e2 = e0
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 349 yields:
% 10.15/2.90 | (338) e2 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (338) can reduce 13 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (598) ~ (all_0_10_10 = e0)
% 10.15/2.90 | (1096) all_0_14_14 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (1096) can reduce 77 to:
% 10.15/2.90 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (1096) can reduce 440 to:
% 10.15/2.90 | (243) ~ (e3 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 243 yields:
% 10.15/2.90 | (29) ~ (e3 = e0)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (300), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (400) all_0_2_2 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (400) can reduce 278 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.90 | (320) all_0_3_3 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (320,1111) yields a new equation:
% 10.15/2.90 | (264) e3 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (264) can reduce 29 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (667) ~ (all_0_6_6 = e3)
% 10.15/2.90 | (968) all_0_7_7 = e3
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (581,968) yields a new equation:
% 10.15/2.90 | (328) e3 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (328) can reduce 61 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (158) ~ (all_0_7_7 = e1)
% 10.15/2.90 | (2555) all_0_11_11 = e1 | all_0_15_15 = e1
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (2555), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (856) all_0_11_11 = e1
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (370,856) yields a new equation:
% 10.15/2.90 | (273) e1 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (273) can reduce 3 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.90 | (178) all_0_15_15 = e1
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (178,172) yields a new equation:
% 10.15/2.90 | (330) e2 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (330) can reduce 116 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.90 | (910) all_0_8_8 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (910) can reduce 240 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (497) ~ (all_0_9_9 = e3)
% 10.15/2.90 | (1860) all_0_10_10 = e3 | all_0_11_11 = e3
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (1860), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (165) all_0_10_10 = e3
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (171,165) yields a new equation:
% 10.15/2.90 | (329) e3 = e2
% 10.15/2.90 |
% 10.15/2.90 | Equations (329) can reduce 86 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (157) ~ (all_0_10_10 = e3)
% 10.15/2.90 | (668) all_0_11_11 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (668) can reduce 992 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (216) ~ (all_0_12_12 = e3)
% 10.15/2.90 | (231) all_0_12_12 = e2 | all_0_12_12 = e1 | all_0_12_12 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (54), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (219) all_0_12_12 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (219) can reduce 216 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (216) ~ (all_0_12_12 = e3)
% 10.15/2.90 | (222) all_0_13_13 = e3 | all_0_14_14 = e3 | all_0_15_15 = e3
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (231), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (232) all_0_12_12 = e2
% 10.15/2.90 |
% 10.15/2.90 | Equations (232) can reduce 208 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (208) ~ (all_0_12_12 = e2)
% 10.15/2.90 | (235) all_0_12_12 = e1 | all_0_12_12 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (222), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (223) all_0_13_13 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (223) can reduce 127 to:
% 10.15/2.90 | (1626) ~ (all_0_14_14 = e3)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 1626 yields:
% 10.15/2.90 | (440) ~ (all_0_14_14 = e3)
% 10.15/2.90 |
% 10.15/2.90 | From (223) and (73) follows:
% 10.15/2.90 | (1630) op(e0, e2) = e3
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (75), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (236) all_0_12_12 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (236) can reduce 188 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (188) ~ (all_0_12_12 = e1)
% 10.15/2.90 | (769) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (235), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (236) all_0_12_12 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (236) can reduce 188 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (188) ~ (all_0_12_12 = e1)
% 10.15/2.90 | (239) all_0_12_12 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (239) can reduce 36 to:
% 10.15/2.90 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (239) can reduce 104 to:
% 10.15/2.90 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (239) can reduce 51 to:
% 10.15/2.90 | (2804) ~ (all_0_14_14 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 2804 yields:
% 10.15/2.90 | (1566) ~ (all_0_14_14 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (239) can reduce 208 to:
% 10.15/2.90 | (316) ~ (e2 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 316 yields:
% 10.15/2.90 | (13) ~ (e2 = e0)
% 10.15/2.90 |
% 10.15/2.90 | From (239) and (147) follows:
% 10.15/2.90 | (247) op(e0, e3) = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (7), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (400) all_0_2_2 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (400) can reduce 278 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.90 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (1085), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (277) all_0_6_6 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (277) can reduce 10 to:
% 10.15/2.90 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (277) can reduce 126 to:
% 10.15/2.90 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (277) can reduce 15 to:
% 10.15/2.90 | (1152) ~ (all_0_7_7 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 1152 yields:
% 10.15/2.90 | (368) ~ (all_0_7_7 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (277) can reduce 102 to:
% 10.15/2.90 | (2804) ~ (all_0_14_14 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 2804 yields:
% 10.15/2.90 | (1566) ~ (all_0_14_14 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Equations (277) can reduce 985 to:
% 10.15/2.90 | (316) ~ (e2 = e0)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 316 yields:
% 10.15/2.90 | (13) ~ (e2 = e0)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (66), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (268) all_0_14_14 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (268) can reduce 440 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (440) ~ (all_0_14_14 = e3)
% 10.15/2.90 | (913) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (913), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (877) all_0_14_14 = e2
% 10.15/2.90 |
% 10.15/2.90 | Equations (877) can reduce 678 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (678) ~ (all_0_14_14 = e2)
% 10.15/2.90 | (2829) all_0_14_14 = e1 | all_0_14_14 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (2829), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (1306) all_0_14_14 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (1306) can reduce 77 to:
% 10.15/2.90 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Equations (1306) can reduce 678 to:
% 10.15/2.90 | (186) ~ (e2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 186 yields:
% 10.15/2.90 | (116) ~ (e2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Equations (1306) can reduce 1566 to:
% 10.15/2.90 | (3) ~ (e1 = e0)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (17), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (175) all_0_0_0 = e1
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (175,169) yields a new equation:
% 10.15/2.90 | (330) e2 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (330) can reduce 116 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.90 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (698), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (406) all_0_1_1 = e1
% 10.15/2.90 |
% 10.15/2.90 | Equations (406) can reduce 134 to:
% 10.15/2.90 | (2841) ~ (all_0_2_2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 2841 yields:
% 10.15/2.90 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Equations (406) can reduce 253 to:
% 10.15/2.90 | (186) ~ (e2 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 186 yields:
% 10.15/2.90 | (116) ~ (e2 = e1)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (38), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (281) all_0_2_2 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (281) can reduce 50 to:
% 10.15/2.90 | (2846) ~ (all_0_3_3 = e3)
% 10.15/2.90 |
% 10.15/2.90 | Simplifying 2846 yields:
% 10.15/2.90 | (1035) ~ (all_0_3_3 = e3)
% 10.15/2.90 |
% 10.15/2.90 | Equations (281) can reduce 415 to:
% 10.15/2.90 | (86) ~ (e3 = e2)
% 10.15/2.90 |
% 10.15/2.90 | Equations (281) can reduce 180 to:
% 10.15/2.90 | (61) ~ (e3 = e1)
% 10.15/2.90 |
% 10.15/2.90 | Equations (281) can reduce 278 to:
% 10.15/2.90 | (29) ~ (e3 = e0)
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (112), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (1111) all_0_3_3 = e3
% 10.15/2.90 |
% 10.15/2.90 | Equations (1111) can reduce 1035 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (1035) ~ (all_0_3_3 = e3)
% 10.15/2.90 | (2249) all_0_7_7 = e3 | all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (70), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (297) all_0_1_1 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (297,406) yields a new equation:
% 10.15/2.90 | (273) e1 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (273) can reduce 3 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.90 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (307), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (271) all_0_5_5 = e0
% 10.15/2.90 |
% 10.15/2.90 | Combining equations (271,170) yields a new equation:
% 10.15/2.90 | (338) e2 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (338) can reduce 13 to:
% 10.15/2.90 | (167) $false
% 10.15/2.90 |
% 10.15/2.90 |-The branch is then unsatisfiable
% 10.15/2.90 |-Branch two:
% 10.15/2.90 | (159) ~ (all_0_5_5 = e0)
% 10.15/2.90 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 10.15/2.90 |
% 10.15/2.90 +-Applying beta-rule and splitting (312), into two cases.
% 10.15/2.90 |-Branch one:
% 10.15/2.90 | (313) all_0_9_9 = e0
% 10.15/2.90 |
% 10.15/2.90 | Equations (313) can reduce 140 to:
% 10.15/2.91 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Equations (313) can reduce 137 to:
% 10.15/2.91 | (314) ~ (all_0_11_11 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 314 yields:
% 10.15/2.91 | (315) ~ (all_0_11_11 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Equations (313) can reduce 254 to:
% 10.15/2.91 | (316) ~ (e2 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 316 yields:
% 10.15/2.91 | (13) ~ (e2 = e0)
% 10.15/2.91 |
% 10.15/2.91 | From (313) and (14) follows:
% 10.15/2.91 | (2871) op(e1, e2) = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (49), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (668) all_0_11_11 = e3
% 10.15/2.91 |
% 10.15/2.91 | Equations (668) can reduce 992 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.91 | (993) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (2249), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (968) all_0_7_7 = e3
% 10.15/2.91 |
% 10.15/2.91 | Equations (968) can reduce 122 to:
% 10.15/2.91 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.91 |
% 10.15/2.91 | Equations (968) can reduce 478 to:
% 10.15/2.91 | (86) ~ (e3 = e2)
% 10.15/2.91 |
% 10.15/2.91 | Equations (968) can reduce 368 to:
% 10.15/2.91 | (29) ~ (e3 = e0)
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (43), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (163) all_0_0_0 = e3
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (163,169) yields a new equation:
% 10.15/2.91 | (878) e3 = e2
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 878 yields:
% 10.15/2.91 | (329) e3 = e2
% 10.15/2.91 |
% 10.15/2.91 | Equations (329) can reduce 86 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (955) ~ (all_0_0_0 = e3)
% 10.15/2.91 | (956) all_0_4_4 = e3 | all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (2324), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (581) all_0_7_7 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (968,581) yields a new equation:
% 10.15/2.91 | (442) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 442 yields:
% 10.15/2.91 | (328) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (328) can reduce 61 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (158) ~ (all_0_7_7 = e1)
% 10.15/2.91 | (2555) all_0_11_11 = e1 | all_0_15_15 = e1
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (956), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (214) all_0_4_4 = e3
% 10.15/2.91 |
% 10.15/2.91 | Equations (214) can reduce 467 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (467) ~ (all_0_4_4 = e3)
% 10.15/2.91 | (1914) all_0_8_8 = e3 | all_0_12_12 = e3
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (2555), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (856) all_0_11_11 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (856) can reduce 120 to:
% 10.15/2.91 | (181) ~ (all_0_3_3 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Equations (856) can reduce 95 to:
% 10.15/2.91 | (184) ~ (all_0_8_8 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Equations (856) can reduce 156 to:
% 10.15/2.91 | (186) ~ (e2 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 186 yields:
% 10.15/2.91 | (116) ~ (e2 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Equations (856) can reduce 315 to:
% 10.15/2.91 | (3) ~ (e1 = e0)
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (1914), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (685) all_0_8_8 = e3
% 10.15/2.91 |
% 10.15/2.91 | Equations (685) can reduce 184 to:
% 10.15/2.91 | (61) ~ (e3 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Equations (685) can reduce 240 to:
% 10.15/2.91 | (29) ~ (e3 = e0)
% 10.15/2.91 |
% 10.15/2.91 | From (685) and (56) follows:
% 10.15/2.91 | (345) op(e1, e3) = e3
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (34), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (285) all_0_0_0 = e0
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (285,169) yields a new equation:
% 10.15/2.91 | (338) e2 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (338) can reduce 13 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (288) ~ (all_0_0_0 = e0)
% 10.15/2.91 | (289) all_0_1_1 = e0 | all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (289), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (297) all_0_1_1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (297,406) yields a new equation:
% 10.15/2.91 | (273) e1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (273) can reduce 3 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.91 | (300) all_0_2_2 = e0 | all_0_3_3 = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (300), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (400) all_0_2_2 = e0
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (400,281) yields a new equation:
% 10.15/2.91 | (264) e3 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (264) can reduce 29 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (278) ~ (all_0_2_2 = e0)
% 10.15/2.91 | (320) all_0_3_3 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (320) can reduce 181 to:
% 10.15/2.91 | (245) ~ (e1 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 245 yields:
% 10.15/2.91 | (3) ~ (e1 = e0)
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (53), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (175) all_0_0_0 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (175,169) yields a new equation:
% 10.15/2.91 | (330) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (330) can reduce 116 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.91 | (1648) all_0_4_4 = e1 | all_0_8_8 = e1 | all_0_12_12 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (169) can reduce 192 to:
% 10.15/2.91 | (116) ~ (e2 = e1)
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (106), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (473) all_0_4_4 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (473) can reduce 211 to:
% 10.15/2.91 | (186) ~ (e2 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 186 yields:
% 10.15/2.91 | (116) ~ (e2 = e1)
% 10.15/2.91 |
% 10.15/2.91 | Equations (473) can reduce 195 to:
% 10.15/2.91 | (3) ~ (e1 = e0)
% 10.15/2.91 |
% 10.15/2.91 | From (473) and (11) follows:
% 10.15/2.91 | (1393) op(e2, e3) = e1
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (55), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (325) unit = e3
% 10.15/2.91 |
% 10.15/2.91 | From (325) and (46) follows:
% 10.15/2.91 | (326) op(e3, e3) = e3
% 10.15/2.91 |
% 10.15/2.91 | From (325) and (25) follows:
% 10.15/2.91 | (754) op(e1, e3) = e1
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e3, e3, e3, e2 and discharging atoms op(e3, e3) = e3, op(e3, e3) = e2, yields:
% 10.15/2.91 | (329) e3 = e2
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e1, e3, e1, e3 and discharging atoms op(e1, e3) = e3, op(e1, e3) = e1, yields:
% 10.15/2.91 | (328) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (329,328) yields a new equation:
% 10.15/2.91 | (422) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 422 yields:
% 10.15/2.91 | (330) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (330) can reduce 116 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (332) ~ (unit = e3)
% 10.15/2.91 | (333) unit = e2 | unit = e1 | unit = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (333), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (334) unit = e2
% 10.15/2.91 |
% 10.15/2.91 | From (334) and (143) follows:
% 10.15/2.91 | (218) op(e2, e3) = e3
% 10.15/2.91 |
% 10.15/2.91 | From (334) and (133) follows:
% 10.15/2.91 | (336) op(e0, e2) = e0
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e2, e3, e3, e1 and discharging atoms op(e2, e3) = e3, op(e2, e3) = e1, yields:
% 10.15/2.91 | (328) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e0, e2, e0, e3 and discharging atoms op(e0, e2) = e3, op(e0, e2) = e0, yields:
% 10.15/2.91 | (264) e3 = e0
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (328,264) yields a new equation:
% 10.15/2.91 | (272) e1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 272 yields:
% 10.15/2.91 | (273) e1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (273) can reduce 3 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (342) ~ (unit = e2)
% 10.15/2.91 | (343) unit = e1 | unit = e0
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (343), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (344) unit = e1
% 10.15/2.91 |
% 10.15/2.91 | From (344) and (57) follows:
% 10.15/2.91 | (744) op(e1, e2) = e2
% 10.15/2.91 |
% 10.15/2.91 | From (344) and (25) follows:
% 10.15/2.91 | (1185) op(e1, e1) = e1
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e1, e2, e2, e0 and discharging atoms op(e1, e2) = e2, op(e1, e2) = e0, yields:
% 10.15/2.91 | (338) e2 = e0
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e1, e1, e1, e2 and discharging atoms op(e1, e1) = e2, op(e1, e1) = e1, yields:
% 10.15/2.91 | (330) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (338,330) yields a new equation:
% 10.15/2.91 | (273) e1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (273) can reduce 3 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (352) ~ (unit = e1)
% 10.15/2.91 | (353) unit = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (353) can reduce 342 to:
% 10.15/2.91 | (316) ~ (e2 = e0)
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 316 yields:
% 10.15/2.91 | (13) ~ (e2 = e0)
% 10.15/2.91 |
% 10.15/2.91 | From (353) and (143) follows:
% 10.15/2.91 | (356) op(e0, e3) = e3
% 10.15/2.91 |
% 10.15/2.91 | From (353) and (57) follows:
% 10.15/2.91 | (256) op(e0, e2) = e2
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e0, e3, e3, e0 and discharging atoms op(e0, e3) = e3, op(e0, e3) = e0, yields:
% 10.15/2.91 | (264) e3 = e0
% 10.15/2.91 |
% 10.15/2.91 | Instantiating formula (5) with e0, e2, e2, e3 and discharging atoms op(e0, e2) = e3, op(e0, e2) = e2, yields:
% 10.15/2.91 | (329) e3 = e2
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (264,329) yields a new equation:
% 10.15/2.91 | (338) e2 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (338) can reduce 13 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (182) ~ (all_0_4_4 = e1)
% 10.15/2.91 | (572) all_0_5_5 = e1 | all_0_6_6 = e1 | all_0_7_7 = e1
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (572), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (176) all_0_5_5 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (170,176) yields a new equation:
% 10.15/2.91 | (422) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 422 yields:
% 10.15/2.91 | (330) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (330) can reduce 116 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (197) ~ (all_0_5_5 = e1)
% 10.15/2.91 | (577) all_0_6_6 = e1 | all_0_7_7 = e1
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (577), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (578) all_0_6_6 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (277,578) yields a new equation:
% 10.15/2.91 | (273) e1 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (273) can reduce 3 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (183) ~ (all_0_6_6 = e1)
% 10.15/2.91 | (581) all_0_7_7 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (968,581) yields a new equation:
% 10.15/2.91 | (442) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 442 yields:
% 10.15/2.91 | (328) e3 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (328) can reduce 61 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (669) ~ (all_0_8_8 = e3)
% 10.15/2.91 | (219) all_0_12_12 = e3
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (239,219) yields a new equation:
% 10.15/2.91 | (264) e3 = e0
% 10.15/2.91 |
% 10.15/2.91 | Equations (264) can reduce 29 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (615) ~ (all_0_11_11 = e1)
% 10.15/2.91 | (178) all_0_15_15 = e1
% 10.15/2.91 |
% 10.15/2.91 | Combining equations (172,178) yields a new equation:
% 10.15/2.91 | (422) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Simplifying 422 yields:
% 10.15/2.91 | (330) e2 = e1
% 10.15/2.91 |
% 10.15/2.91 | Equations (330) can reduce 116 to:
% 10.15/2.91 | (167) $false
% 10.15/2.91 |
% 10.15/2.91 |-The branch is then unsatisfiable
% 10.15/2.91 |-Branch two:
% 10.15/2.91 | (1039) ~ (all_0_7_7 = e3)
% 10.15/2.91 | (2253) all_0_11_11 = e3 | all_0_15_15 = e3
% 10.15/2.91 |
% 10.15/2.91 +-Applying beta-rule and splitting (2253), into two cases.
% 10.15/2.91 |-Branch one:
% 10.15/2.91 | (668) all_0_11_11 = e3
% 10.15/2.91 |
% 10.15/2.92 | Equations (668) can reduce 992 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (992) ~ (all_0_11_11 = e3)
% 10.15/2.92 | (166) all_0_15_15 = e3
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (172,166) yields a new equation:
% 10.15/2.92 | (329) e3 = e2
% 10.15/2.92 |
% 10.15/2.92 | Equations (329) can reduce 86 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (377) ~ (all_0_9_9 = e0)
% 10.15/2.92 | (378) all_0_13_13 = e0
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (378,223) yields a new equation:
% 10.15/2.92 | (264) e3 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (264) can reduce 29 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (269) ~ (all_0_2_2 = e3)
% 10.15/2.92 | (284) all_0_2_2 = e2 | all_0_2_2 = e1 | all_0_2_2 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (284), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (291) all_0_2_2 = e2
% 10.15/2.92 |
% 10.15/2.92 | Equations (291) can reduce 415 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (415) ~ (all_0_2_2 = e2)
% 10.15/2.92 | (416) all_0_2_2 = e1 | all_0_2_2 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (416), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (565) all_0_2_2 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (565) can reduce 180 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.92 | (400) all_0_2_2 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (400) can reduce 278 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (179) ~ (all_0_1_1 = e1)
% 10.15/2.92 | (702) all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (702), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (565) all_0_2_2 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (565) can reduce 180 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.92 | (927) all_0_3_3 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (927) can reduce 181 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (726) ~ (all_0_14_14 = e1)
% 10.15/2.92 | (1096) all_0_14_14 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (1096) can reduce 1566 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.92 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (78), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (685) all_0_8_8 = e3
% 10.15/2.92 |
% 10.15/2.92 | Equations (685) can reduce 240 to:
% 10.15/2.92 | (29) ~ (e3 = e0)
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (87), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (263) all_0_4_4 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (263) can reduce 195 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (195) ~ (all_0_4_4 = e0)
% 10.15/2.92 | (267) all_0_5_5 = e0 | all_0_6_6 = e0 | all_0_7_7 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (769), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (459) all_0_13_13 = e1
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (223,459) yields a new equation:
% 10.15/2.92 | (442) e3 = e1
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 442 yields:
% 10.15/2.92 | (328) e3 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (328) can reduce 61 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (189) ~ (all_0_13_13 = e1)
% 10.15/2.92 | (1305) all_0_14_14 = e1 | all_0_15_15 = e1
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (1305), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (1306) all_0_14_14 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (1306) can reduce 77 to:
% 10.15/2.92 | (180) ~ (all_0_2_2 = e1)
% 10.15/2.92 |
% 10.15/2.92 | Equations (1306) can reduce 678 to:
% 10.15/2.92 | (186) ~ (e2 = e1)
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 186 yields:
% 10.15/2.92 | (116) ~ (e2 = e1)
% 10.15/2.92 |
% 10.15/2.92 | Equations (1306) can reduce 1566 to:
% 10.15/2.92 | (3) ~ (e1 = e0)
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (17), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (175) all_0_0_0 = e1
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (175,169) yields a new equation:
% 10.15/2.92 | (330) e2 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (330) can reduce 116 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (192) ~ (all_0_0_0 = e1)
% 10.15/2.92 | (698) all_0_1_1 = e1 | all_0_2_2 = e1 | all_0_3_3 = e1
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (267), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (271) all_0_5_5 = e0
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (271,170) yields a new equation:
% 10.15/2.92 | (338) e2 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (338) can reduce 13 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (159) ~ (all_0_5_5 = e0)
% 10.15/2.92 | (276) all_0_6_6 = e0 | all_0_7_7 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (698), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (406) all_0_1_1 = e1
% 10.15/2.92 |
% 10.15/2.92 | Equations (406) can reduce 105 to:
% 10.15/2.92 | (3059) ~ (all_0_9_9 = e1)
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 3059 yields:
% 10.15/2.92 | (185) ~ (all_0_9_9 = e1)
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (276), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (277) all_0_6_6 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (277) can reduce 436 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (436) ~ (all_0_6_6 = e0)
% 10.15/2.92 | (364) all_0_7_7 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (364) can reduce 478 to:
% 10.15/2.92 | (316) ~ (e2 = e0)
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 316 yields:
% 10.15/2.92 | (13) ~ (e2 = e0)
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (92), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (910) all_0_8_8 = e0
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (685,910) yields a new equation:
% 10.15/2.92 | (506) e3 = e0
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 506 yields:
% 10.15/2.92 | (264) e3 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (264) can reduce 29 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (240) ~ (all_0_8_8 = e0)
% 10.15/2.92 | (2189) all_0_9_9 = e0 | all_0_10_10 = e0 | all_0_11_11 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (685) can reduce 240 to:
% 10.15/2.92 | (29) ~ (e3 = e0)
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (70), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (297) all_0_1_1 = e0
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (297,406) yields a new equation:
% 10.15/2.92 | (273) e1 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (273) can reduce 3 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (227) ~ (all_0_1_1 = e0)
% 10.15/2.92 | (307) all_0_5_5 = e0 | all_0_9_9 = e0 | all_0_13_13 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (307), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (271) all_0_5_5 = e0
% 10.15/2.92 |
% 10.15/2.92 | Combining equations (170,271) yields a new equation:
% 10.15/2.92 | (349) e2 = e0
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 349 yields:
% 10.15/2.92 | (338) e2 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (338) can reduce 13 to:
% 10.15/2.92 | (167) $false
% 10.15/2.92 |
% 10.15/2.92 |-The branch is then unsatisfiable
% 10.15/2.92 |-Branch two:
% 10.15/2.92 | (159) ~ (all_0_5_5 = e0)
% 10.15/2.92 | (312) all_0_9_9 = e0 | all_0_13_13 = e0
% 10.15/2.92 |
% 10.15/2.92 +-Applying beta-rule and splitting (312), into two cases.
% 10.15/2.92 |-Branch one:
% 10.15/2.92 | (313) all_0_9_9 = e0
% 10.15/2.92 |
% 10.15/2.92 | Equations (313) can reduce 254 to:
% 10.15/2.92 | (316) ~ (e2 = e0)
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 316 yields:
% 10.15/2.92 | (13) ~ (e2 = e0)
% 10.15/2.92 |
% 10.15/2.92 | Equations (313) can reduce 185 to:
% 10.15/2.92 | (245) ~ (e1 = e0)
% 10.15/2.92 |
% 10.15/2.92 | Simplifying 245 yields:
% 10.15/2.92 | (3) ~ (e1 = e0)
% 10.15/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (1091), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (493) all_0_10_10 = e0
% 10.55/2.92 |
% 10.55/2.92 | Combining equations (171,493) yields a new equation:
% 10.55/2.92 | (349) e2 = e0
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 349 yields:
% 10.55/2.92 | (338) e2 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (338) can reduce 13 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (598) ~ (all_0_10_10 = e0)
% 10.55/2.92 | (1096) all_0_14_14 = e0
% 10.55/2.92 |
% 10.55/2.92 | Combining equations (1306,1096) yields a new equation:
% 10.55/2.92 | (272) e1 = e0
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 272 yields:
% 10.55/2.92 | (273) e1 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (273) can reduce 3 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (377) ~ (all_0_9_9 = e0)
% 10.55/2.92 | (378) all_0_13_13 = e0
% 10.55/2.92 |
% 10.55/2.92 | Combining equations (378,223) yields a new equation:
% 10.55/2.92 | (264) e3 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (264) can reduce 29 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (179) ~ (all_0_1_1 = e1)
% 10.55/2.92 | (702) all_0_2_2 = e1 | all_0_3_3 = e1
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (702), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (565) all_0_2_2 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (565) can reduce 180 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (180) ~ (all_0_2_2 = e1)
% 10.55/2.92 | (927) all_0_3_3 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (927) can reduce 181 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (726) ~ (all_0_14_14 = e1)
% 10.55/2.92 | (178) all_0_15_15 = e1
% 10.55/2.92 |
% 10.55/2.92 | Combining equations (172,178) yields a new equation:
% 10.55/2.92 | (422) e2 = e1
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 422 yields:
% 10.55/2.92 | (330) e2 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (330) can reduce 116 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (669) ~ (all_0_8_8 = e3)
% 10.55/2.92 | (1845) all_0_9_9 = e3 | all_0_10_10 = e3 | all_0_11_11 = e3
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (44), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (685) all_0_8_8 = e3
% 10.55/2.92 |
% 10.55/2.92 | Equations (685) can reduce 669 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (669) ~ (all_0_8_8 = e3)
% 10.55/2.92 | (688) all_0_8_8 = e2 | all_0_8_8 = e1 | all_0_8_8 = e0
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (688), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (257) all_0_8_8 = e2
% 10.55/2.92 |
% 10.55/2.92 | Equations (257) can reduce 445 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (445) ~ (all_0_8_8 = e2)
% 10.55/2.92 | (692) all_0_8_8 = e1 | all_0_8_8 = e0
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (692), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (750) all_0_8_8 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (750) can reduce 95 to:
% 10.55/2.92 | (614) ~ (all_0_11_11 = e1)
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 614 yields:
% 10.55/2.92 | (615) ~ (all_0_11_11 = e1)
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (49), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (668) all_0_11_11 = e3
% 10.55/2.92 |
% 10.55/2.92 | Equations (668) can reduce 992 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (992) ~ (all_0_11_11 = e3)
% 10.55/2.92 | (993) all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (993), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (455) all_0_11_11 = e2
% 10.55/2.92 |
% 10.55/2.92 | Equations (455) can reduce 156 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (156) ~ (all_0_11_11 = e2)
% 10.55/2.92 | (997) all_0_11_11 = e1 | all_0_11_11 = e0
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (997), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (856) all_0_11_11 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (856) can reduce 615 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (615) ~ (all_0_11_11 = e1)
% 10.55/2.92 | (370) all_0_11_11 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (370) can reduce 156 to:
% 10.55/2.92 | (316) ~ (e2 = e0)
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 316 yields:
% 10.55/2.92 | (13) ~ (e2 = e0)
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (1091), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (493) all_0_10_10 = e0
% 10.55/2.92 |
% 10.55/2.92 | Combining equations (171,493) yields a new equation:
% 10.55/2.92 | (349) e2 = e0
% 10.55/2.92 |
% 10.55/2.92 | Simplifying 349 yields:
% 10.55/2.92 | (338) e2 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (338) can reduce 13 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (598) ~ (all_0_10_10 = e0)
% 10.55/2.92 | (1096) all_0_14_14 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (1096) can reduce 1566 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (184) ~ (all_0_8_8 = e1)
% 10.55/2.92 | (910) all_0_8_8 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (910) can reduce 240 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (200) ~ (all_0_13_13 = e3)
% 10.55/2.92 | (226) all_0_14_14 = e3 | all_0_15_15 = e3
% 10.55/2.92 |
% 10.55/2.92 +-Applying beta-rule and splitting (235), into two cases.
% 10.55/2.92 |-Branch one:
% 10.55/2.92 | (236) all_0_12_12 = e1
% 10.55/2.92 |
% 10.55/2.92 | Equations (236) can reduce 188 to:
% 10.55/2.92 | (167) $false
% 10.55/2.92 |
% 10.55/2.92 |-The branch is then unsatisfiable
% 10.55/2.92 |-Branch two:
% 10.55/2.92 | (188) ~ (all_0_12_12 = e1)
% 10.55/2.92 | (239) all_0_12_12 = e0
% 10.55/2.92 |
% 10.55/2.92 | Equations (239) can reduce 51 to:
% 10.55/2.92 | (2804) ~ (all_0_14_14 = e0)
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 2804 yields:
% 10.55/2.93 | (1566) ~ (all_0_14_14 = e0)
% 10.55/2.93 |
% 10.55/2.93 | Equations (239) can reduce 216 to:
% 10.55/2.93 | (243) ~ (e3 = e0)
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 243 yields:
% 10.55/2.93 | (29) ~ (e3 = e0)
% 10.55/2.93 |
% 10.55/2.93 | Equations (239) can reduce 208 to:
% 10.55/2.93 | (316) ~ (e2 = e0)
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 316 yields:
% 10.55/2.93 | (13) ~ (e2 = e0)
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (66), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (268) all_0_14_14 = e3
% 10.55/2.93 |
% 10.55/2.93 | Equations (268) can reduce 440 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (440) ~ (all_0_14_14 = e3)
% 10.55/2.93 | (913) all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (913), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (877) all_0_14_14 = e2
% 10.55/2.93 |
% 10.55/2.93 | Equations (877) can reduce 678 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (678) ~ (all_0_14_14 = e2)
% 10.55/2.93 | (2829) all_0_14_14 = e1 | all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (2829), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (1306) all_0_14_14 = e1
% 10.55/2.93 |
% 10.55/2.93 | Equations (1306) can reduce 77 to:
% 10.55/2.93 | (180) ~ (all_0_2_2 = e1)
% 10.55/2.93 |
% 10.55/2.93 | Equations (1306) can reduce 440 to:
% 10.55/2.93 | (841) ~ (e3 = e1)
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 841 yields:
% 10.55/2.93 | (61) ~ (e3 = e1)
% 10.55/2.93 |
% 10.55/2.93 | Equations (1306) can reduce 1566 to:
% 10.55/2.93 | (3) ~ (e1 = e0)
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (7), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (400) all_0_2_2 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (400) can reduce 278 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (278) ~ (all_0_2_2 = e0)
% 10.55/2.93 | (1085) all_0_6_6 = e0 | all_0_10_10 = e0 | all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (1085), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (277) all_0_6_6 = e0
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (9), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (281) all_0_2_2 = e3
% 10.55/2.93 |
% 10.55/2.93 | Equations (281) can reduce 415 to:
% 10.55/2.93 | (86) ~ (e3 = e2)
% 10.55/2.93 |
% 10.55/2.93 | Equations (281) can reduce 180 to:
% 10.55/2.93 | (61) ~ (e3 = e1)
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (226), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (268) all_0_14_14 = e3
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (1306,268) yields a new equation:
% 10.55/2.93 | (328) e3 = e1
% 10.55/2.93 |
% 10.55/2.93 | Equations (328) can reduce 61 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (440) ~ (all_0_14_14 = e3)
% 10.55/2.93 | (166) all_0_15_15 = e3
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (166,172) yields a new equation:
% 10.55/2.93 | (878) e3 = e2
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 878 yields:
% 10.55/2.93 | (329) e3 = e2
% 10.55/2.93 |
% 10.55/2.93 | Equations (329) can reduce 86 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (269) ~ (all_0_2_2 = e3)
% 10.55/2.93 | (723) all_0_6_6 = e3 | all_0_10_10 = e3 | all_0_14_14 = e3
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (723), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (670) all_0_6_6 = e3
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (277,670) yields a new equation:
% 10.55/2.93 | (264) e3 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (264) can reduce 29 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (667) ~ (all_0_6_6 = e3)
% 10.55/2.93 | (918) all_0_10_10 = e3 | all_0_14_14 = e3
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (918), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (165) all_0_10_10 = e3
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (171,165) yields a new equation:
% 10.55/2.93 | (329) e3 = e2
% 10.55/2.93 |
% 10.55/2.93 | Equations (329) can reduce 86 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (157) ~ (all_0_10_10 = e3)
% 10.55/2.93 | (268) all_0_14_14 = e3
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (1306,268) yields a new equation:
% 10.55/2.93 | (328) e3 = e1
% 10.55/2.93 |
% 10.55/2.93 | Equations (328) can reduce 61 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (436) ~ (all_0_6_6 = e0)
% 10.55/2.93 | (1091) all_0_10_10 = e0 | all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 +-Applying beta-rule and splitting (1091), into two cases.
% 10.55/2.93 |-Branch one:
% 10.55/2.93 | (493) all_0_10_10 = e0
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (171,493) yields a new equation:
% 10.55/2.93 | (349) e2 = e0
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 349 yields:
% 10.55/2.93 | (338) e2 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (338) can reduce 13 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (598) ~ (all_0_10_10 = e0)
% 10.55/2.93 | (1096) all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (1306,1096) yields a new equation:
% 10.55/2.93 | (272) e1 = e0
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 272 yields:
% 10.55/2.93 | (273) e1 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (273) can reduce 3 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (726) ~ (all_0_14_14 = e1)
% 10.55/2.93 | (1096) all_0_14_14 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (1096) can reduce 1566 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (927) all_0_3_3 = e1
% 10.55/2.93 | (1532) ~ (all_0_15_15 = e2)
% 10.55/2.93 |
% 10.55/2.93 | Equations (172) can reduce 1532 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (400) all_0_2_2 = e0
% 10.55/2.93 | (155) ~ (all_0_10_10 = e2)
% 10.55/2.93 |
% 10.55/2.93 | Equations (171) can reduce 155 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (668) all_0_11_11 = e3
% 10.55/2.93 | (1532) ~ (all_0_15_15 = e2)
% 10.55/2.93 |
% 10.55/2.93 | Equations (172) can reduce 1532 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (174) all_0_0_0 = e1 & all_0_5_5 = e1 & all_0_10_10 = e1 & all_0_15_15 = e1
% 10.55/2.93 |
% 10.55/2.93 | Applying alpha-rule on (174) yields:
% 10.55/2.93 | (175) all_0_0_0 = e1
% 10.55/2.93 | (176) all_0_5_5 = e1
% 10.55/2.93 | (177) all_0_10_10 = e1
% 10.55/2.93 | (178) all_0_15_15 = e1
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (171,177) yields a new equation:
% 10.55/2.93 | (422) e2 = e1
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 422 yields:
% 10.55/2.93 | (330) e2 = e1
% 10.55/2.93 |
% 10.55/2.93 | Equations (330) can reduce 116 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 |-Branch two:
% 10.55/2.93 | (490) all_0_0_0 = e0 & all_0_5_5 = e0 & all_0_10_10 = e0 & all_0_15_15 = e0
% 10.55/2.93 |
% 10.55/2.93 | Applying alpha-rule on (490) yields:
% 10.55/2.93 | (285) all_0_0_0 = e0
% 10.55/2.93 | (271) all_0_5_5 = e0
% 10.55/2.93 | (493) all_0_10_10 = e0
% 10.55/2.93 | (373) all_0_15_15 = e0
% 10.55/2.93 |
% 10.55/2.93 | Combining equations (171,493) yields a new equation:
% 10.55/2.93 | (349) e2 = e0
% 10.55/2.93 |
% 10.55/2.93 | Simplifying 349 yields:
% 10.55/2.93 | (338) e2 = e0
% 10.55/2.93 |
% 10.55/2.93 | Equations (338) can reduce 13 to:
% 10.55/2.93 | (167) $false
% 10.55/2.93 |
% 10.55/2.93 |-The branch is then unsatisfiable
% 10.55/2.93 % SZS output end Proof for theBenchmark
% 10.55/2.93
% 10.55/2.93 2437ms
%------------------------------------------------------------------------------