TSTP Solution File: ALG170+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : ALG170+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 15:37:04 EDT 2022
% Result : Theorem 5.28s 1.81s
% Output : Proof 8.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG170+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 19:17:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.62 ____ _
% 0.49/0.62 ___ / __ \_____(_)___ ________ __________
% 0.49/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.62
% 0.49/0.62 A Theorem Prover for First-Order Logic
% 0.49/0.62 (ePrincess v.1.0)
% 0.49/0.62
% 0.49/0.62 (c) Philipp Rümmer, 2009-2015
% 0.49/0.62 (c) Peter Backeman, 2014-2015
% 0.49/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.62 Bug reports to peter@backeman.se
% 0.49/0.62
% 0.49/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.62
% 0.49/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.66/1.18 Prover 0: Preprocessing ...
% 4.05/1.51 Prover 0: Constructing countermodel ...
% 5.28/1.80 Prover 0: proved (1137ms)
% 5.28/1.81
% 5.28/1.81 No countermodel exists, formula is valid
% 5.28/1.81 % SZS status Theorem for theBenchmark
% 5.28/1.81
% 5.28/1.81 Generating proof ... found it (size 478)
% 7.51/2.43
% 7.51/2.43 % SZS output start Proof for theBenchmark
% 7.51/2.43 Assumed formulas after preprocessing and simplification:
% 7.51/2.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = v10) & ~ (v18 = v5) & ~ (v18 = v1) & ~ (v18 = e1) & ~ (v18 = e0) & ~ (v17 = v16) & ~ (v17 = v14) & ~ (v17 = v9) & ~ (v17 = v4) & ~ (v17 = v0) & ~ (v17 = e1) & ~ (v17 = e0) & ~ (v16 = v12) & ~ (v16 = v7) & ~ (v16 = v3) & ~ (v16 = e3) & ~ (v16 = e1) & ~ (v16 = e0) & ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v6) & ~ (v15 = v2) & ~ (v15 = e1) & ~ (v15 = e0) & ~ (v14 = v13) & ~ (v14 = v12) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v14 = v0) & ~ (v14 = e0) & ~ (v13 = v12) & ~ (v13 = v8) & ~ (v13 = e4) & ~ (v13 = e2) & ~ (v13 = e0) & ~ (v12 = v7) & ~ (v12 = v3) & ~ (v12 = e3) & ~ (v12 = e0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v6) & ~ (v11 = v2) & ~ (v11 = e1) & ~ (v10 = v9) & ~ (v10 = v8) & ~ (v10 = v7) & ~ (v10 = v5) & ~ (v10 = v1) & ~ (v10 = e0) & ~ (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v4) & ~ (v9 = v0) & ~ (v8 = v7) & ~ (v8 = e4) & ~ (v8 = e2) & ~ (v8 = e0) & ~ (v7 = v3) & ~ (v7 = e3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v3) & ~ (v6 = v2) & ~ (v6 = e4) & ~ (v6 = e1) & ~ (v5 = v4) & ~ (v5 = v3) & ~ (v5 = v1) & ~ (v5 = e4) & ~ (v5 = e0) & ~ (v4 = v3) & ~ (v4 = v0) & ~ (v4 = e4) & ~ (v3 = e4) & ~ (v3 = e3) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v2 = e3) & ~ (v2 = e2) & ~ (v2 = e1) & ~ (v1 = v0) & ~ (v1 = e3) & ~ (v1 = e2) & ~ (v1 = e0) & ~ (v0 = e3) & ~ (v0 = e2) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(v18, v15) = e3 & op(v17, v11) = e2 & op(v16, v2) = e0 & op(v15, v18) = e4 & op(v14, v10) = e2 & op(v13, v5) = e1 & op(v12, v1) = e0 & op(v11, v17) = e4 & op(v10, v14) = e3 & op(v9, v9) = e2 & op(v8, v4) = e1 & op(v7, v0) = e0 & op(v6, e0) = e4 & op(v5, v13) = e3 & op(v4, v8) = e2 & op(v3, e2) = e0 & op(v2, v16) = e4 & op(v1, v12) = e3 & op(v0, v7) = e2 & op(e4, e4) = e1 & op(e4, e3) = v18 & op(e4, e2) = v17 & op(e4, e1) = e0 & op(e4, e0) = v16 & op(e3, e4) = v15 & op(e3, e3) = e0 & op(e3, e2) = v14 & op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, v3) = e1 & op(e2, e4) = v11 & op(e2, e3) = v10 & op(e2, e2) = v9 & op(e2, e1) = v8 & op(e2, e0) = v7 & op(e1, e4) = v6 & op(e1, e3) = v5 & op(e1, e2) = v4 & op(e1, e1) = e4 & op(e1, e0) = v3 & op(e0, v6) = e1 & op(e0, e4) = v2 & op(e0, e3) = v1 & op(e0, e2) = v0 & op(e0, e1) = e2 & op(e0, e0) = e3 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (op(v22, v21) = v20) | ~ (op(v22, v21) = v19)) & ( ~ (v13 = e3) | ( ~ (v18 = e4) & ~ (v10 = e2) & ~ (v5 = e1)) | ( ~ (v17 = e4) & ~ (v14 = e3) & ~ (v9 = e2) & ~ (v4 = e1) & ~ (v0 = e0)) | ( ~ (v16 = e4) & ~ (v7 = e2) & ~ (v3 = e1)) | ( ~ (v15 = e3) & ~ (v11 = e2) & ~ (v2 = e0))) & ( ~ (v2 = e4) | ( ~ (v18 = e3) & ~ (v17 = e2)) | ( ~ (v15 = e4) & ~ (v14 = e2) & ~ (v13 = e1)) | ( ~ (v11 = e4) & ~ (v10 = e3) & ~ (v9 = e2) & ~ (v8 = e1) & ~ (v7 = e0)) | ( ~ (v5 = e3) & ~ (v4 = e2) & ~ (v3 = e0))) & (v18 = e4 | v18 = e3 | v18 = e2) & (v18 = e4 | v17 = e4 | v16 = e4) & (v18 = e4 | v10 = e4 | v1 = e4) & (v18 = e3 | v17 = e3) & (v18 = e3 | v10 = e3 | v5 = e3) & (v18 = e2 | v17 = e2 | v16 = e2) & (v18 = e2 | v10 = e2 | v5 = e2) & (v17 = e4 | v17 = e3 | v17 = e2) & (v17 = e4 | v14 = e4 | v9 = e4 | v0 = e4) & (v17 = e3 | v14 = e3 | v9 = e3 | v4 = e3) & (v17 = e2 | v14 = e2 | v9 = e2 | v4 = e2) & (v16 = e4 | v16 = e2) & (v16 = e4 | v12 = e4 | v7 = e4) & (v16 = e2 | v12 = e2 | v7 = e2 | v3 = e2) & (v15 = e4 | v15 = e3 | v15 = e2) & (v15 = e4 | v14 = e4 | v12 = e4) & (v15 = e4 | v11 = e4 | v2 = e4) & (v15 = e3 | v14 = e3 | v13 = e3) & (v15 = e3 | v11 = e3 | v6 = e3) & (v15 = e2 | v14 = e2 | v12 = e2) & (v15 = e2 | v11 = e2 | v6 = e2) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1) & (v14 = e1 | v13 = e1 | v12 = e1) & (v14 = e1 | v9 = e1 | v4 = e1 | v0 = e1) & (v13 = e3 | v13 = e1) & (v13 = e3 | v8 = e3) & (v13 = e1 | v8 = e1) & (v12 = e4 | v12 = e2 | v12 = e1) & (v12 = e1 | v7 = e1 | v3 = e1) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e0) & (v11 = e4 | v10 = e4 | v9 = e4 | v7 = e4) & (v11 = e3 | v10 = e3 | v9 = e3 | v8 = e3) & (v11 = e2 | v10 = e2 | v9 = e2 | v7 = e2) & (v11 = e0 | v9 = e0 | v7 = e0) & (v11 = e0 | v6 = e0 | v2 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1) & (v10 = e1 | v9 = e1 | v8 = e1 | v7 = e1) & (v10 = e1 | v5 = e1 | v1 = e1) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v9 = e0 | v4 = e0 | v0 = e0) & (v8 = e3 | v8 = e1) & (v7 = e4 | v7 = e2 | v7 = e1 | v7 = e0) & (v7 = e0 | v3 = e0) & (v6 = e3 | v6 = e2 | v6 = e0) & (v6 = e3 | v5 = e3 | v4 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v3 = e2) & (v6 = e0 | v4 = e0 | v3 = e0) & (v5 = e3 | v5 = e2 | v5 = e1) & (v5 = e1 | v4 = e1 | v3 = e1) & (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e0) & (v2 = e4 | v1 = e4 | v0 = e4) & (v2 = e0 | v0 = e0) & (v1 = e4 | v1 = e1) & (v1 = e1 | v0 = e1) & (v0 = e4 | v0 = e1 | v0 = e0))
% 7.95/2.48 | 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, all_0_16_16, all_0_17_17, all_0_18_18 yields:
% 7.95/2.48 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_0_0 = all_0_2_2) & ~ (all_0_0_0 = all_0_8_8) & ~ (all_0_0_0 = all_0_13_13) & ~ (all_0_0_0 = all_0_17_17) & ~ (all_0_0_0 = e1) & ~ (all_0_0_0 = e0) & ~ (all_0_1_1 = all_0_2_2) & ~ (all_0_1_1 = all_0_4_4) & ~ (all_0_1_1 = all_0_9_9) & ~ (all_0_1_1 = all_0_14_14) & ~ (all_0_1_1 = all_0_18_18) & ~ (all_0_1_1 = e1) & ~ (all_0_1_1 = e0) & ~ (all_0_2_2 = all_0_6_6) & ~ (all_0_2_2 = all_0_11_11) & ~ (all_0_2_2 = all_0_15_15) & ~ (all_0_2_2 = e3) & ~ (all_0_2_2 = e1) & ~ (all_0_2_2 = e0) & ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = all_0_5_5) & ~ (all_0_3_3 = all_0_6_6) & ~ (all_0_3_3 = all_0_7_7) & ~ (all_0_3_3 = all_0_12_12) & ~ (all_0_3_3 = all_0_16_16) & ~ (all_0_3_3 = e1) & ~ (all_0_3_3 = e0) & ~ (all_0_4_4 = all_0_5_5) & ~ (all_0_4_4 = all_0_6_6) & ~ (all_0_4_4 = all_0_9_9) & ~ (all_0_4_4 = all_0_14_14) & ~ (all_0_4_4 = all_0_18_18) & ~ (all_0_4_4 = e0) & ~ (all_0_5_5 = all_0_6_6) & ~ (all_0_5_5 = all_0_10_10) & ~ (all_0_5_5 = e4) & ~ (all_0_5_5 = e2) & ~ (all_0_5_5 = e0) & ~ (all_0_6_6 = all_0_11_11) & ~ (all_0_6_6 = all_0_15_15) & ~ (all_0_6_6 = e3) & ~ (all_0_6_6 = e0) & ~ (all_0_7_7 = all_0_8_8) & ~ (all_0_7_7 = all_0_9_9) & ~ (all_0_7_7 = all_0_10_10) & ~ (all_0_7_7 = all_0_11_11) & ~ (all_0_7_7 = all_0_12_12) & ~ (all_0_7_7 = all_0_16_16) & ~ (all_0_7_7 = e1) & ~ (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_13_13) & ~ (all_0_8_8 = all_0_17_17) & ~ (all_0_8_8 = e0) & ~ (all_0_9_9 = all_0_10_10) & ~ (all_0_9_9 = all_0_11_11) & ~ (all_0_9_9 = all_0_14_14) & ~ (all_0_9_9 = all_0_18_18) & ~ (all_0_10_10 = all_0_11_11) & ~ (all_0_10_10 = e4) & ~ (all_0_10_10 = e2) & ~ (all_0_10_10 = e0) & ~ (all_0_11_11 = all_0_15_15) & ~ (all_0_11_11 = e3) & ~ (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_12_12 = all_0_16_16) & ~ (all_0_12_12 = e4) & ~ (all_0_12_12 = e1) & ~ (all_0_13_13 = all_0_14_14) & ~ (all_0_13_13 = all_0_15_15) & ~ (all_0_13_13 = all_0_17_17) & ~ (all_0_13_13 = e4) & ~ (all_0_13_13 = e0) & ~ (all_0_14_14 = all_0_15_15) & ~ (all_0_14_14 = all_0_18_18) & ~ (all_0_14_14 = e4) & ~ (all_0_15_15 = e4) & ~ (all_0_15_15 = e3) & ~ (all_0_16_16 = all_0_17_17) & ~ (all_0_16_16 = all_0_18_18) & ~ (all_0_16_16 = e3) & ~ (all_0_16_16 = e2) & ~ (all_0_16_16 = e1) & ~ (all_0_17_17 = all_0_18_18) & ~ (all_0_17_17 = e3) & ~ (all_0_17_17 = e2) & ~ (all_0_17_17 = e0) & ~ (all_0_18_18 = e3) & ~ (all_0_18_18 = e2) & ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & op(all_0_0_0, all_0_3_3) = e3 & op(all_0_1_1, all_0_7_7) = e2 & op(all_0_2_2, all_0_16_16) = e0 & op(all_0_3_3, all_0_0_0) = e4 & op(all_0_4_4, all_0_8_8) = e2 & op(all_0_5_5, all_0_13_13) = e1 & op(all_0_6_6, all_0_17_17) = e0 & op(all_0_7_7, all_0_1_1) = e4 & op(all_0_8_8, all_0_4_4) = e3 & op(all_0_9_9, all_0_9_9) = e2 & op(all_0_10_10, all_0_14_14) = e1 & op(all_0_11_11, all_0_18_18) = e0 & op(all_0_12_12, e0) = e4 & op(all_0_13_13, all_0_5_5) = e3 & op(all_0_14_14, all_0_10_10) = e2 & op(all_0_15_15, e2) = e0 & op(all_0_16_16, all_0_2_2) = e4 & op(all_0_17_17, all_0_6_6) = e3 & op(all_0_18_18, all_0_11_11) = e2 & op(e4, e4) = e1 & op(e4, e3) = all_0_0_0 & op(e4, e2) = all_0_1_1 & op(e4, e1) = e0 & op(e4, e0) = all_0_2_2 & op(e3, e4) = all_0_3_3 & op(e3, e3) = e0 & op(e3, e2) = all_0_4_4 & op(e3, e1) = all_0_5_5 & op(e3, e0) = all_0_6_6 & op(e2, all_0_15_15) = e1 & op(e2, e4) = all_0_7_7 & op(e2, e3) = all_0_8_8 & op(e2, e2) = all_0_9_9 & op(e2, e1) = all_0_10_10 & op(e2, e0) = all_0_11_11 & op(e1, e4) = all_0_12_12 & op(e1, e3) = all_0_13_13 & op(e1, e2) = all_0_14_14 & op(e1, e1) = e4 & op(e1, e0) = all_0_15_15 & op(e0, all_0_12_12) = e1 & op(e0, e4) = all_0_16_16 & op(e0, e3) = all_0_17_17 & op(e0, e2) = all_0_18_18 & op(e0, e1) = e2 & op(e0, e0) = e3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) & ( ~ (all_0_5_5 = e3) | ( ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)) | ( ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0)) | ( ~ (all_0_2_2 = e4) & ~ (all_0_11_11 = e2) & ~ (all_0_15_15 = e1)) | ( ~ (all_0_3_3 = e3) & ~ (all_0_7_7 = e2) & ~ (all_0_16_16 = e0))) & ( ~ (all_0_16_16 = e4) | ( ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)) | ( ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1)) | ( ~ (all_0_7_7 = e4) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_10_10 = e1) & ~ (all_0_11_11 = e0)) | ( ~ (all_0_13_13 = e3) & ~ (all_0_14_14 = e2) & ~ (all_0_15_15 = e0))) & (all_0_0_0 = e4 | all_0_0_0 = e3 | all_0_0_0 = e2) & (all_0_0_0 = e4 | all_0_1_1 = e4 | all_0_2_2 = e4) & (all_0_0_0 = e4 | all_0_8_8 = e4 | all_0_17_17 = e4) & (all_0_0_0 = e3 | all_0_1_1 = e3) & (all_0_0_0 = e3 | all_0_8_8 = e3 | all_0_13_13 = e3) & (all_0_0_0 = e2 | all_0_1_1 = e2 | all_0_2_2 = e2) & (all_0_0_0 = e2 | all_0_8_8 = e2 | all_0_13_13 = e2) & (all_0_1_1 = e4 | all_0_1_1 = e3 | all_0_1_1 = e2) & (all_0_1_1 = e4 | all_0_4_4 = e4 | all_0_9_9 = e4 | all_0_18_18 = e4) & (all_0_1_1 = e3 | all_0_4_4 = e3 | all_0_9_9 = e3 | all_0_14_14 = e3) & (all_0_1_1 = e2 | all_0_4_4 = e2 | all_0_9_9 = e2 | all_0_14_14 = e2) & (all_0_2_2 = e4 | all_0_2_2 = e2) & (all_0_2_2 = e4 | all_0_6_6 = e4 | all_0_11_11 = e4) & (all_0_2_2 = e2 | all_0_6_6 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2) & (all_0_3_3 = e4 | all_0_3_3 = e3 | all_0_3_3 = e2) & (all_0_3_3 = e4 | all_0_4_4 = e4 | all_0_6_6 = e4) & (all_0_3_3 = e4 | all_0_7_7 = e4 | all_0_16_16 = e4) & (all_0_3_3 = e3 | all_0_4_4 = e3 | all_0_5_5 = e3) & (all_0_3_3 = e3 | all_0_7_7 = e3 | all_0_12_12 = e3) & (all_0_3_3 = e2 | all_0_4_4 = e2 | all_0_6_6 = e2) & (all_0_3_3 = e2 | all_0_7_7 = e2 | all_0_12_12 = e2) & (all_0_4_4 = e4 | all_0_4_4 = e3 | all_0_4_4 = e2 | all_0_4_4 = e1) & (all_0_4_4 = e1 | all_0_5_5 = e1 | all_0_6_6 = e1) & (all_0_4_4 = e1 | all_0_9_9 = e1 | all_0_14_14 = e1 | all_0_18_18 = e1) & (all_0_5_5 = e3 | all_0_5_5 = e1) & (all_0_5_5 = e3 | all_0_10_10 = e3) & (all_0_5_5 = e1 | all_0_10_10 = e1) & (all_0_6_6 = e4 | all_0_6_6 = e2 | all_0_6_6 = e1) & (all_0_6_6 = e1 | all_0_11_11 = e1 | all_0_15_15 = e1) & (all_0_7_7 = e4 | all_0_7_7 = e3 | all_0_7_7 = e2 | all_0_7_7 = e0) & (all_0_7_7 = e4 | all_0_8_8 = e4 | all_0_9_9 = e4 | all_0_11_11 = e4) & (all_0_7_7 = e3 | all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3) & (all_0_7_7 = e2 | all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_11_11 = e2) & (all_0_7_7 = e0 | all_0_9_9 = e0 | all_0_11_11 = e0) & (all_0_7_7 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0) & (all_0_8_8 = e4 | all_0_8_8 = e3 | all_0_8_8 = e2 | all_0_8_8 = e1) & (all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1) & (all_0_8_8 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1) & (all_0_9_9 = e4 | all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0) & (all_0_9_9 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0) & (all_0_10_10 = e3 | all_0_10_10 = e1) & (all_0_11_11 = e4 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0) & (all_0_11_11 = e0 | all_0_15_15 = e0) & (all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e0) & (all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = 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 = 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 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1) & (all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0) & (all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0) & (all_0_16_16 = e4 | all_0_16_16 = e0) & (all_0_16_16 = e4 | all_0_17_17 = e4 | all_0_18_18 = e4) & (all_0_16_16 = e0 | all_0_18_18 = e0) & (all_0_17_17 = e4 | all_0_17_17 = e1) & (all_0_17_17 = e1 | all_0_18_18 = e1) & (all_0_18_18 = e4 | all_0_18_18 = e1 | all_0_18_18 = e0)
% 8.20/2.50 |
% 8.20/2.50 | Applying alpha-rule on (1) yields:
% 8.20/2.50 | (2) all_0_2_2 = e2 | all_0_6_6 = e2 | all_0_11_11 = e2 | all_0_15_15 = e2
% 8.20/2.50 | (3) ~ (all_0_2_2 = e0)
% 8.20/2.50 | (4) ~ (all_0_6_6 = all_0_15_15)
% 8.20/2.50 | (5) ~ (e4 = e0)
% 8.20/2.50 | (6) ~ (all_0_15_15 = e3)
% 8.20/2.50 | (7) ~ (all_0_2_2 = all_0_15_15)
% 8.20/2.50 | (8) op(all_0_8_8, all_0_4_4) = e3
% 8.20/2.50 | (9) all_0_0_0 = e4 | all_0_8_8 = e4 | all_0_17_17 = e4
% 8.20/2.50 | (10) all_0_4_4 = e4 | all_0_4_4 = e3 | all_0_4_4 = e2 | all_0_4_4 = e1
% 8.20/2.50 | (11) all_0_17_17 = e4 | all_0_17_17 = e1
% 8.20/2.50 | (12) ~ (all_0_17_17 = all_0_18_18)
% 8.20/2.50 | (13) ~ (all_0_16_16 = all_0_18_18)
% 8.20/2.50 | (14) all_0_16_16 = e4 | all_0_17_17 = e4 | all_0_18_18 = e4
% 8.20/2.50 | (15) ~ (all_0_5_5 = e4)
% 8.20/2.50 | (16) all_0_13_13 = e3 | all_0_13_13 = e2 | all_0_13_13 = e1
% 8.20/2.50 | (17) op(e0, e3) = all_0_17_17
% 8.20/2.50 | (18) all_0_3_3 = e4 | all_0_7_7 = e4 | all_0_16_16 = e4
% 8.20/2.50 | (19) ~ (all_0_8_8 = all_0_17_17)
% 8.20/2.50 | (20) ~ (all_0_11_11 = e3)
% 8.20/2.50 | (21) ~ (all_0_13_13 = all_0_17_17)
% 8.20/2.50 | (22) op(all_0_3_3, all_0_0_0) = e4
% 8.20/2.50 | (23) ~ (all_0_8_8 = e0)
% 8.20/2.50 | (24) all_0_2_2 = e4 | all_0_2_2 = e2
% 8.20/2.50 | (25) op(e4, e1) = e0
% 8.20/2.50 | (26) ~ (all_0_9_9 = all_0_11_11)
% 8.20/2.50 | (27) ~ (all_0_0_0 = e1)
% 8.20/2.50 | (28) ~ (e4 = e3)
% 8.20/2.50 | (29) op(e1, e1) = e4
% 8.20/2.50 | (30) op(all_0_0_0, all_0_3_3) = e3
% 8.20/2.50 | (31) ~ (all_0_7_7 = all_0_8_8)
% 8.20/2.50 | (32) ~ (all_0_8_8 = all_0_10_10)
% 8.20/2.50 | (33) ~ (all_0_2_2 = e1)
% 8.20/2.50 | (34) ~ (all_0_1_1 = e0)
% 8.20/2.50 | (35) op(all_0_15_15, e2) = e0
% 8.20/2.50 | (36) all_0_1_1 = e3 | all_0_4_4 = e3 | all_0_9_9 = e3 | all_0_14_14 = e3
% 8.20/2.50 | (37) ~ (all_0_12_12 = all_0_13_13)
% 8.20/2.51 | (38) ~ (all_0_6_6 = e0)
% 8.20/2.51 | (39) ~ (all_0_16_16 = all_0_17_17)
% 8.20/2.51 | (40) ~ (all_0_16_16 = e4) | ( ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)) | ( ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1)) | ( ~ (all_0_7_7 = e4) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_10_10 = e1) & ~ (all_0_11_11 = e0)) | ( ~ (all_0_13_13 = e3) & ~ (all_0_14_14 = e2) & ~ (all_0_15_15 = e0))
% 8.20/2.51 | (41) ~ (all_0_10_10 = e2)
% 8.20/2.51 | (42) ~ (all_0_0_0 = all_0_8_8)
% 8.20/2.51 | (43) ~ (all_0_7_7 = all_0_11_11)
% 8.20/2.51 | (44) ~ (all_0_4_4 = all_0_9_9)
% 8.20/2.51 | (45) all_0_7_7 = e4 | all_0_8_8 = e4 | all_0_9_9 = e4 | all_0_11_11 = e4
% 8.20/2.51 | (46) op(e1, e2) = all_0_14_14
% 8.20/2.51 | (47) ~ (all_0_12_12 = all_0_15_15)
% 8.20/2.51 | (48) op(all_0_14_14, all_0_10_10) = e2
% 8.20/2.51 | (49) ~ (all_0_3_3 = all_0_7_7)
% 8.20/2.51 | (50) op(all_0_7_7, all_0_1_1) = e4
% 8.20/2.51 | (51) all_0_0_0 = e2 | all_0_8_8 = e2 | all_0_13_13 = e2
% 8.20/2.51 | (52) op(e3, e1) = all_0_5_5
% 8.20/2.51 | (53) all_0_0_0 = e3 | all_0_1_1 = e3
% 8.20/2.51 | (54) ~ (e2 = e0)
% 8.20/2.51 | (55) all_0_8_8 = e1 | all_0_9_9 = e1 | all_0_10_10 = e1 | all_0_11_11 = e1
% 8.20/2.51 | (56) op(all_0_16_16, all_0_2_2) = e4
% 8.20/2.51 | (57) op(e0, e1) = e2
% 8.20/2.51 | (58) all_0_8_8 = e1 | all_0_13_13 = e1 | all_0_17_17 = e1
% 8.20/2.51 | (59) op(e4, e2) = all_0_1_1
% 8.20/2.51 | (60) all_0_0_0 = e3 | all_0_8_8 = e3 | all_0_13_13 = e3
% 8.20/2.51 | (61) all_0_12_12 = e3 | all_0_12_12 = e2 | all_0_12_12 = e0
% 8.20/2.51 | (62) op(e3, e0) = all_0_6_6
% 8.20/2.51 | (63) all_0_2_2 = e4 | all_0_6_6 = e4 | all_0_11_11 = e4
% 8.20/2.51 | (64) op(all_0_2_2, all_0_16_16) = e0
% 8.20/2.51 | (65) ~ (e3 = e0)
% 8.20/2.51 | (66) ~ (all_0_3_3 = all_0_5_5)
% 8.20/2.51 | (67) ~ (all_0_5_5 = all_0_10_10)
% 8.20/2.51 | (68) ~ (all_0_7_7 = e1)
% 8.20/2.51 | (69) ~ (all_0_12_12 = e1)
% 8.20/2.51 | (70) all_0_17_17 = e1 | all_0_18_18 = e1
% 8.20/2.51 | (71) ~ (all_0_8_8 = all_0_11_11)
% 8.20/2.51 | (72) all_0_5_5 = e1 | all_0_10_10 = e1
% 8.20/2.51 | (73) ~ (all_0_1_1 = all_0_9_9)
% 8.20/2.51 | (74) all_0_5_5 = e3 | all_0_5_5 = e1
% 8.20/2.51 | (75) op(e2, e2) = all_0_9_9
% 8.20/2.51 | (76) op(all_0_13_13, all_0_5_5) = e3
% 8.20/2.51 | (77) all_0_16_16 = e4 | all_0_16_16 = e0
% 8.20/2.51 | (78) ~ (all_0_1_1 = all_0_14_14)
% 8.20/2.51 | (79) op(e3, e4) = all_0_3_3
% 8.20/2.51 | (80) op(all_0_18_18, all_0_11_11) = e2
% 8.20/2.51 | (81) all_0_18_18 = e4 | all_0_18_18 = e1 | all_0_18_18 = e0
% 8.20/2.51 | (82) ~ (all_0_15_15 = e4)
% 8.20/2.51 | (83) ~ (all_0_3_3 = all_0_4_4)
% 8.20/2.51 | (84) all_0_16_16 = e0 | all_0_18_18 = e0
% 8.20/2.51 | (85) ~ (all_0_17_17 = e2)
% 8.20/2.51 | (86) ~ (all_0_18_18 = e2)
% 8.20/2.51 | (87) all_0_7_7 = e0 | all_0_12_12 = e0 | all_0_16_16 = e0
% 8.20/2.51 | (88) op(e0, e4) = all_0_16_16
% 8.20/2.51 | (89) all_0_7_7 = e4 | all_0_7_7 = e3 | all_0_7_7 = e2 | all_0_7_7 = e0
% 8.20/2.51 | (90) ~ (all_0_0_0 = all_0_17_17)
% 8.20/2.51 | (91) all_0_14_14 = e3 | all_0_14_14 = e2 | all_0_14_14 = e1 | all_0_14_14 = e0
% 8.20/2.51 | (92) all_0_0_0 = e2 | all_0_1_1 = e2 | all_0_2_2 = e2
% 8.20/2.51 | (93) ~ (all_0_14_14 = all_0_15_15)
% 8.20/2.51 | (94) ~ (all_0_3_3 = e0)
% 8.20/2.51 | (95) all_0_3_3 = e3 | all_0_4_4 = e3 | all_0_5_5 = e3
% 8.20/2.51 | (96) op(all_0_10_10, all_0_14_14) = e1
% 8.20/2.51 | (97) op(all_0_11_11, all_0_18_18) = e0
% 8.20/2.51 | (98) ~ (all_0_18_18 = e3)
% 8.20/2.51 | (99) all_0_9_9 = e4 | all_0_9_9 = e3 | all_0_9_9 = e2 | all_0_9_9 = e1 | all_0_9_9 = e0
% 8.20/2.51 | (100) all_0_6_6 = e1 | all_0_11_11 = e1 | all_0_15_15 = e1
% 8.20/2.52 | (101) ~ (all_0_1_1 = all_0_4_4)
% 8.20/2.52 | (102) all_0_12_12 = e0 | all_0_14_14 = e0 | all_0_15_15 = e0
% 8.20/2.52 | (103) ~ (all_0_1_1 = all_0_18_18)
% 8.20/2.52 | (104) all_0_7_7 = e3 | all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3
% 8.20/2.52 | (105) ~ (all_0_0_0 = all_0_1_1)
% 8.20/2.52 | (106) ~ (all_0_9_9 = all_0_14_14)
% 8.20/2.52 | (107) ~ (all_0_13_13 = e4)
% 8.20/2.52 | (108) all_0_4_4 = e1 | all_0_9_9 = e1 | all_0_14_14 = e1 | all_0_18_18 = e1
% 8.20/2.52 | (109) ~ (all_0_4_4 = all_0_5_5)
% 8.20/2.52 | (110) op(e2, e4) = all_0_7_7
% 8.20/2.52 | (111) op(all_0_1_1, all_0_7_7) = e2
% 8.20/2.52 | (112) op(all_0_12_12, e0) = e4
% 8.20/2.52 | (113) ~ (e1 = e0)
% 8.20/2.52 | (114) ~ (all_0_11_11 = all_0_15_15)
% 8.20/2.52 | (115) ~ (e3 = e1)
% 8.20/2.52 | (116) ~ (all_0_10_10 = e4)
% 8.20/2.52 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 8.20/2.52 | (118) ~ (all_0_3_3 = all_0_16_16)
% 8.20/2.52 | (119) ~ (e2 = e1)
% 8.20/2.52 | (120) all_0_8_8 = e4 | all_0_8_8 = e3 | all_0_8_8 = e2 | all_0_8_8 = e1
% 8.20/2.52 | (121) ~ (all_0_7_7 = all_0_10_10)
% 8.20/2.52 | (122) all_0_3_3 = e3 | all_0_7_7 = e3 | all_0_12_12 = e3
% 8.20/2.52 | (123) op(all_0_9_9, all_0_9_9) = e2
% 8.20/2.52 | (124) all_0_13_13 = e1 | all_0_14_14 = e1 | all_0_15_15 = e1
% 8.20/2.52 | (125) ~ (all_0_13_13 = all_0_15_15)
% 8.20/2.52 | (126) ~ (all_0_4_4 = all_0_6_6)
% 8.20/2.52 | (127) all_0_11_11 = e0 | all_0_15_15 = e0
% 8.20/2.52 | (128) all_0_3_3 = e4 | all_0_4_4 = e4 | all_0_6_6 = e4
% 8.20/2.52 | (129) all_0_3_3 = e2 | all_0_4_4 = e2 | all_0_6_6 = e2
% 8.20/2.52 | (130) op(e1, e3) = all_0_13_13
% 8.20/2.52 | (131) ~ (all_0_16_16 = e1)
% 8.20/2.52 | (132) op(e3, e3) = e0
% 8.20/2.52 | (133) all_0_5_5 = e3 | all_0_10_10 = e3
% 8.20/2.52 | (134) all_0_7_7 = e2 | all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_11_11 = e2
% 8.20/2.52 | (135) op(e4, e3) = all_0_0_0
% 8.20/2.52 | (136) all_0_1_1 = e4 | all_0_4_4 = e4 | all_0_9_9 = e4 | all_0_18_18 = e4
% 8.20/2.52 | (137) op(e4, e0) = all_0_2_2
% 8.20/2.52 | (138) ~ (all_0_1_1 = e1)
% 8.20/2.52 | (139) ~ (all_0_10_10 = e0)
% 8.20/2.52 | (140) ~ (all_0_4_4 = all_0_14_14)
% 8.20/2.52 | (141) ~ (all_0_0_0 = all_0_2_2)
% 8.20/2.52 | (142) all_0_6_6 = e4 | all_0_6_6 = e2 | all_0_6_6 = e1
% 8.20/2.52 | (143) ~ (all_0_0_0 = e0)
% 8.20/2.52 | (144) ~ (all_0_1_1 = all_0_2_2)
% 8.20/2.52 | (145) op(e4, e4) = e1
% 8.20/2.52 | (146) ~ (all_0_2_2 = e3)
% 8.20/2.52 | (147) ~ (all_0_3_3 = all_0_12_12)
% 8.20/2.52 | (148) ~ (all_0_2_2 = all_0_6_6)
% 8.20/2.52 | (149) ~ (all_0_9_9 = all_0_18_18)
% 8.20/2.52 | (150) all_0_0_0 = e4 | all_0_0_0 = e3 | all_0_0_0 = e2
% 8.20/2.52 | (151) op(e0, e2) = all_0_18_18
% 8.20/2.52 | (152) op(e0, all_0_12_12) = e1
% 8.20/2.52 | (153) all_0_0_0 = e4 | all_0_1_1 = e4 | all_0_2_2 = e4
% 8.20/2.52 | (154) op(e2, e3) = all_0_8_8
% 8.20/2.52 | (155) op(e0, e0) = e3
% 8.20/2.52 | (156) ~ (all_0_14_14 = all_0_18_18)
% 8.20/2.52 | (157) ~ (all_0_4_4 = e0)
% 8.20/2.52 | (158) ~ (all_0_3_3 = e1)
% 8.20/2.52 | (159) ~ (all_0_13_13 = e0)
% 8.20/2.52 | (160) all_0_9_9 = e0 | all_0_14_14 = e0 | all_0_18_18 = e0
% 8.20/2.52 | (161) ~ (all_0_5_5 = e0)
% 8.20/2.52 | (162) all_0_1_1 = e4 | all_0_1_1 = e3 | all_0_1_1 = e2
% 8.20/2.52 | (163) ~ (all_0_5_5 = e2)
% 8.20/2.52 | (164) op(e1, e0) = all_0_15_15
% 8.20/2.52 | (165) ~ (all_0_10_10 = all_0_11_11)
% 8.20/2.52 | (166) ~ (all_0_7_7 = all_0_12_12)
% 8.20/2.52 | (167) ~ (all_0_16_16 = e2)
% 8.20/2.52 | (168) all_0_12_12 = e2 | all_0_13_13 = e2 | all_0_14_14 = e2 | all_0_15_15 = e2
% 8.20/2.52 | (169) ~ (all_0_4_4 = all_0_18_18)
% 8.20/2.52 | (170) ~ (all_0_14_14 = e4)
% 8.20/2.52 | (171) all_0_7_7 = e0 | all_0_9_9 = e0 | all_0_11_11 = e0
% 8.20/2.52 | (172) ~ (all_0_2_2 = all_0_11_11)
% 8.20/2.52 | (173) op(e2, e1) = all_0_10_10
% 8.20/2.52 | (174) all_0_10_10 = e3 | all_0_10_10 = e1
% 8.20/2.52 | (175) ~ (all_0_12_12 = e4)
% 8.20/2.52 | (176) all_0_1_1 = e2 | all_0_4_4 = e2 | all_0_9_9 = e2 | all_0_14_14 = e2
% 8.20/2.52 | (177) all_0_15_15 = e2 | all_0_15_15 = e1 | all_0_15_15 = e0
% 8.20/2.52 | (178) ~ (all_0_16_16 = e3)
% 8.20/2.52 | (179) all_0_12_12 = e3 | all_0_13_13 = e3 | all_0_14_14 = e3
% 8.20/2.52 | (180) op(all_0_5_5, all_0_13_13) = e1
% 8.20/2.52 | (181) ~ (all_0_5_5 = all_0_6_6)
% 8.20/2.52 | (182) ~ (e3 = e2)
% 8.20/2.52 | (183) ~ (all_0_8_8 = all_0_13_13)
% 8.20/2.52 | (184) op(all_0_4_4, all_0_8_8) = e2
% 8.20/2.52 | (185) ~ (all_0_3_3 = all_0_6_6)
% 8.20/2.53 | (186) op(all_0_17_17, all_0_6_6) = e3
% 8.20/2.53 | (187) all_0_3_3 = e4 | all_0_3_3 = e3 | all_0_3_3 = e2
% 8.20/2.53 | (188) op(e3, e2) = all_0_4_4
% 8.20/2.53 | (189) ~ (all_0_17_17 = e3)
% 8.20/2.53 | (190) op(e2, all_0_15_15) = e1
% 8.20/2.53 | (191) ~ (e4 = e2)
% 8.20/2.53 | (192) ~ (all_0_12_12 = all_0_14_14)
% 8.20/2.53 | (193) ~ (all_0_8_8 = all_0_9_9)
% 8.20/2.53 | (194) ~ (all_0_5_5 = e3) | ( ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)) | ( ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0)) | ( ~ (all_0_2_2 = e4) & ~ (all_0_11_11 = e2) & ~ (all_0_15_15 = e1)) | ( ~ (all_0_3_3 = e3) & ~ (all_0_7_7 = e2) & ~ (all_0_16_16 = e0))
% 8.20/2.53 | (195) ~ (all_0_0_0 = all_0_13_13)
% 8.20/2.53 | (196) ~ (all_0_6_6 = all_0_11_11)
% 8.20/2.53 | (197) ~ (all_0_7_7 = all_0_9_9)
% 8.20/2.53 | (198) ~ (all_0_6_6 = e3)
% 8.20/2.53 | (199) all_0_11_11 = e4 | all_0_11_11 = e2 | all_0_11_11 = e1 | all_0_11_11 = e0
% 8.20/2.53 | (200) ~ (all_0_7_7 = all_0_16_16)
% 8.20/2.53 | (201) ~ (all_0_12_12 = all_0_16_16)
% 8.20/2.53 | (202) op(all_0_6_6, all_0_17_17) = e0
% 8.20/2.53 | (203) ~ (all_0_17_17 = e0)
% 8.20/2.53 | (204) op(e1, e4) = all_0_12_12
% 8.20/2.53 | (205) all_0_3_3 = e2 | all_0_7_7 = e2 | all_0_12_12 = e2
% 8.20/2.53 | (206) ~ (e4 = e1)
% 8.20/2.53 | (207) ~ (all_0_9_9 = all_0_10_10)
% 8.20/2.53 | (208) op(e2, e0) = all_0_11_11
% 8.20/2.53 | (209) ~ (all_0_13_13 = all_0_14_14)
% 8.20/2.53 | (210) all_0_4_4 = e1 | all_0_5_5 = e1 | all_0_6_6 = e1
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (24), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (211) all_0_2_2 = e2
% 8.20/2.53 |
% 8.20/2.53 | Equations (211) can reduce 141 to:
% 8.20/2.53 | (212) ~ (all_0_0_0 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Equations (211) can reduce 148 to:
% 8.20/2.53 | (213) ~ (all_0_6_6 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Simplifying 213 yields:
% 8.20/2.53 | (214) ~ (all_0_6_6 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Equations (211) can reduce 172 to:
% 8.20/2.53 | (215) ~ (all_0_11_11 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Simplifying 215 yields:
% 8.20/2.53 | (216) ~ (all_0_11_11 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Equations (211) can reduce 7 to:
% 8.20/2.53 | (217) ~ (all_0_15_15 = e2)
% 8.20/2.53 |
% 8.20/2.53 | Simplifying 217 yields:
% 8.20/2.53 | (218) ~ (all_0_15_15 = e2)
% 8.20/2.53 |
% 8.20/2.53 | From (211) and (64) follows:
% 8.20/2.53 | (219) op(e2, all_0_16_16) = e0
% 8.20/2.53 |
% 8.20/2.53 | From (211) and (56) follows:
% 8.20/2.53 | (220) op(all_0_16_16, e2) = e4
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (11), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (221) all_0_17_17 = e4
% 8.20/2.53 |
% 8.20/2.53 | Equations (221) can reduce 90 to:
% 8.20/2.53 | (222) ~ (all_0_0_0 = e4)
% 8.20/2.53 |
% 8.20/2.53 | Equations (221) can reduce 39 to:
% 8.20/2.53 | (223) ~ (all_0_16_16 = e4)
% 8.20/2.53 |
% 8.20/2.53 | Equations (221) can reduce 85 to:
% 8.20/2.53 | (191) ~ (e4 = e2)
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (77), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (225) all_0_16_16 = e4
% 8.20/2.53 |
% 8.20/2.53 | Equations (225) can reduce 223 to:
% 8.20/2.53 | (226) $false
% 8.20/2.53 |
% 8.20/2.53 |-The branch is then unsatisfiable
% 8.20/2.53 |-Branch two:
% 8.20/2.53 | (223) ~ (all_0_16_16 = e4)
% 8.20/2.53 | (228) all_0_16_16 = e0
% 8.20/2.53 |
% 8.20/2.53 | From (228) and (220) follows:
% 8.20/2.53 | (229) op(e0, e2) = e4
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (70), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (230) all_0_17_17 = e1
% 8.20/2.53 |
% 8.20/2.53 | Combining equations (230,221) yields a new equation:
% 8.20/2.53 | (231) e4 = e1
% 8.20/2.53 |
% 8.20/2.53 | Equations (231) can reduce 206 to:
% 8.20/2.53 | (226) $false
% 8.20/2.53 |
% 8.20/2.53 |-The branch is then unsatisfiable
% 8.20/2.53 |-Branch two:
% 8.20/2.53 | (233) ~ (all_0_17_17 = e1)
% 8.20/2.53 | (234) all_0_18_18 = e1
% 8.20/2.53 |
% 8.20/2.53 | Equations (234) can reduce 103 to:
% 8.20/2.53 | (138) ~ (all_0_1_1 = e1)
% 8.20/2.53 |
% 8.20/2.53 | From (234) and (151) follows:
% 8.20/2.53 | (236) op(e0, e2) = e1
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (153), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (237) all_0_0_0 = e4
% 8.20/2.53 |
% 8.20/2.53 | Equations (237) can reduce 222 to:
% 8.20/2.53 | (226) $false
% 8.20/2.53 |
% 8.20/2.53 |-The branch is then unsatisfiable
% 8.20/2.53 |-Branch two:
% 8.20/2.53 | (222) ~ (all_0_0_0 = e4)
% 8.20/2.53 | (240) all_0_1_1 = e4 | all_0_2_2 = e4
% 8.20/2.53 |
% 8.20/2.53 +-Applying beta-rule and splitting (240), into two cases.
% 8.20/2.53 |-Branch one:
% 8.20/2.53 | (241) all_0_1_1 = e4
% 8.20/2.53 |
% 8.20/2.53 | Equations (241) can reduce 138 to:
% 8.20/2.53 | (206) ~ (e4 = e1)
% 8.20/2.53 |
% 8.20/2.53 | Instantiating formula (117) with e0, e2, e1, e4 and discharging atoms op(e0, e2) = e4, op(e0, e2) = e1, yields:
% 8.20/2.53 | (231) e4 = e1
% 8.20/2.53 |
% 8.20/2.53 | Equations (231) can reduce 206 to:
% 8.20/2.53 | (226) $false
% 8.20/2.53 |
% 8.20/2.53 |-The branch is then unsatisfiable
% 8.20/2.53 |-Branch two:
% 8.20/2.54 | (245) ~ (all_0_1_1 = e4)
% 8.20/2.54 | (246) all_0_2_2 = e4
% 8.20/2.54 |
% 8.20/2.54 | Combining equations (246,211) yields a new equation:
% 8.20/2.54 | (247) e4 = e2
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 247 yields:
% 8.20/2.54 | (248) e4 = e2
% 8.20/2.54 |
% 8.20/2.54 | Equations (248) can reduce 191 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (250) ~ (all_0_17_17 = e4)
% 8.20/2.54 | (230) all_0_17_17 = e1
% 8.20/2.54 |
% 8.20/2.54 | Equations (230) can reduce 21 to:
% 8.20/2.54 | (252) ~ (all_0_13_13 = e1)
% 8.20/2.54 |
% 8.20/2.54 | Equations (230) can reduce 12 to:
% 8.20/2.54 | (253) ~ (all_0_18_18 = e1)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 253 yields:
% 8.20/2.54 | (254) ~ (all_0_18_18 = e1)
% 8.20/2.54 |
% 8.20/2.54 | From (230) and (186) follows:
% 8.20/2.54 | (255) op(e1, all_0_6_6) = e3
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (77), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (225) all_0_16_16 = e4
% 8.20/2.54 |
% 8.20/2.54 | Equations (225) can reduce 201 to:
% 8.20/2.54 | (175) ~ (all_0_12_12 = e4)
% 8.20/2.54 |
% 8.20/2.54 | From (225) and (220) follows:
% 8.20/2.54 | (258) op(e4, e2) = e4
% 8.20/2.54 |
% 8.20/2.54 | From (225) and (219) follows:
% 8.20/2.54 | (259) op(e2, e4) = e0
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (84), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (228) all_0_16_16 = e0
% 8.20/2.54 |
% 8.20/2.54 | Combining equations (225,228) yields a new equation:
% 8.20/2.54 | (261) e4 = e0
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 261 yields:
% 8.20/2.54 | (262) e4 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (262) can reduce 5 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (264) ~ (all_0_16_16 = e0)
% 8.20/2.54 | (265) all_0_18_18 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (265) can reduce 156 to:
% 8.20/2.54 | (266) ~ (all_0_14_14 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Instantiating formula (117) with e4, e2, e4, all_0_1_1 and discharging atoms op(e4, e2) = all_0_1_1, op(e4, e2) = e4, yields:
% 8.20/2.54 | (241) all_0_1_1 = e4
% 8.20/2.54 |
% 8.20/2.54 | Instantiating formula (117) with e2, e4, e0, all_0_7_7 and discharging atoms op(e2, e4) = all_0_7_7, op(e2, e4) = e0, yields:
% 8.20/2.54 | (268) all_0_7_7 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (241) can reduce 105 to:
% 8.20/2.54 | (222) ~ (all_0_0_0 = e4)
% 8.20/2.54 |
% 8.20/2.54 | Equations (241) can reduce 138 to:
% 8.20/2.54 | (206) ~ (e4 = e1)
% 8.20/2.54 |
% 8.20/2.54 | Equations (268) can reduce 166 to:
% 8.20/2.54 | (271) ~ (all_0_12_12 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 271 yields:
% 8.20/2.54 | (272) ~ (all_0_12_12 = e0)
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (150), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (273) all_0_0_0 = e2
% 8.20/2.54 |
% 8.20/2.54 | Equations (273) can reduce 212 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (212) ~ (all_0_0_0 = e2)
% 8.20/2.54 | (276) all_0_0_0 = e4 | all_0_0_0 = e3
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (102), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (277) all_0_12_12 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (277) can reduce 272 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (272) ~ (all_0_12_12 = e0)
% 8.20/2.54 | (280) all_0_14_14 = e0 | all_0_15_15 = e0
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (276), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (237) all_0_0_0 = e4
% 8.20/2.54 |
% 8.20/2.54 | Equations (237) can reduce 222 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (222) ~ (all_0_0_0 = e4)
% 8.20/2.54 | (284) all_0_0_0 = e3
% 8.20/2.54 |
% 8.20/2.54 | Equations (284) can reduce 195 to:
% 8.20/2.54 | (285) ~ (all_0_13_13 = e3)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 285 yields:
% 8.20/2.54 | (286) ~ (all_0_13_13 = e3)
% 8.20/2.54 |
% 8.20/2.54 | Equations (284) can reduce 222 to:
% 8.20/2.54 | (287) ~ (e4 = e3)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 287 yields:
% 8.20/2.54 | (28) ~ (e4 = e3)
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (16), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (289) all_0_13_13 = e2
% 8.20/2.54 |
% 8.20/2.54 | Equations (289) can reduce 183 to:
% 8.20/2.54 | (290) ~ (all_0_8_8 = e2)
% 8.20/2.54 |
% 8.20/2.54 | Equations (289) can reduce 125 to:
% 8.20/2.54 | (217) ~ (all_0_15_15 = e2)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 217 yields:
% 8.20/2.54 | (218) ~ (all_0_15_15 = e2)
% 8.20/2.54 |
% 8.20/2.54 | Equations (289) can reduce 286 to:
% 8.20/2.54 | (293) ~ (e3 = e2)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 293 yields:
% 8.20/2.54 | (182) ~ (e3 = e2)
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (120), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (295) all_0_8_8 = e2
% 8.20/2.54 |
% 8.20/2.54 | Equations (295) can reduce 290 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (290) ~ (all_0_8_8 = e2)
% 8.20/2.54 | (298) all_0_8_8 = e4 | all_0_8_8 = e3 | all_0_8_8 = e1
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (280), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (299) all_0_14_14 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (299) can reduce 266 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.54 |-The branch is then unsatisfiable
% 8.20/2.54 |-Branch two:
% 8.20/2.54 | (266) ~ (all_0_14_14 = e0)
% 8.20/2.54 | (302) all_0_15_15 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (302) can reduce 47 to:
% 8.20/2.54 | (272) ~ (all_0_12_12 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Equations (302) can reduce 6 to:
% 8.20/2.54 | (304) ~ (e3 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 304 yields:
% 8.20/2.54 | (65) ~ (e3 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Equations (302) can reduce 218 to:
% 8.20/2.54 | (306) ~ (e2 = e0)
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 306 yields:
% 8.20/2.54 | (54) ~ (e2 = e0)
% 8.20/2.54 |
% 8.20/2.54 +-Applying beta-rule and splitting (134), into two cases.
% 8.20/2.54 |-Branch one:
% 8.20/2.54 | (308) all_0_7_7 = e2
% 8.20/2.54 |
% 8.20/2.54 | Combining equations (308,268) yields a new equation:
% 8.20/2.54 | (309) e2 = e0
% 8.20/2.54 |
% 8.20/2.54 | Simplifying 309 yields:
% 8.20/2.54 | (310) e2 = e0
% 8.20/2.54 |
% 8.20/2.54 | Equations (310) can reduce 54 to:
% 8.20/2.54 | (226) $false
% 8.20/2.54 |
% 8.20/2.55 |-The branch is then unsatisfiable
% 8.20/2.55 |-Branch two:
% 8.20/2.55 | (312) ~ (all_0_7_7 = e2)
% 8.20/2.55 | (313) all_0_8_8 = e2 | all_0_9_9 = e2 | all_0_11_11 = e2
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (313), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (295) all_0_8_8 = e2
% 8.20/2.55 |
% 8.20/2.55 | Equations (295) can reduce 290 to:
% 8.20/2.55 | (226) $false
% 8.20/2.55 |
% 8.20/2.55 |-The branch is then unsatisfiable
% 8.20/2.55 |-Branch two:
% 8.20/2.55 | (290) ~ (all_0_8_8 = e2)
% 8.20/2.55 | (317) all_0_9_9 = e2 | all_0_11_11 = e2
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (317), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (318) all_0_9_9 = e2
% 8.20/2.55 |
% 8.20/2.55 | Equations (318) can reduce 44 to:
% 8.20/2.55 | (319) ~ (all_0_4_4 = e2)
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (129), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (320) all_0_3_3 = e2
% 8.20/2.55 |
% 8.20/2.55 | Equations (320) can reduce 147 to:
% 8.20/2.55 | (321) ~ (all_0_12_12 = e2)
% 8.20/2.55 |
% 8.20/2.55 | Simplifying 321 yields:
% 8.20/2.55 | (322) ~ (all_0_12_12 = e2)
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (9), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (237) all_0_0_0 = e4
% 8.20/2.55 |
% 8.20/2.55 | Combining equations (237,284) yields a new equation:
% 8.20/2.55 | (324) e4 = e3
% 8.20/2.55 |
% 8.20/2.55 | Simplifying 324 yields:
% 8.20/2.55 | (325) e4 = e3
% 8.20/2.55 |
% 8.20/2.55 | Equations (325) can reduce 28 to:
% 8.20/2.55 | (226) $false
% 8.20/2.55 |
% 8.20/2.55 |-The branch is then unsatisfiable
% 8.20/2.55 |-Branch two:
% 8.20/2.55 | (222) ~ (all_0_0_0 = e4)
% 8.20/2.55 | (328) all_0_8_8 = e4 | all_0_17_17 = e4
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (40), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (223) ~ (all_0_16_16 = e4)
% 8.20/2.55 |
% 8.20/2.55 | Equations (225) can reduce 223 to:
% 8.20/2.55 | (226) $false
% 8.20/2.55 |
% 8.20/2.55 |-The branch is then unsatisfiable
% 8.20/2.55 |-Branch two:
% 8.20/2.55 | (225) all_0_16_16 = e4
% 8.20/2.55 | (332) ( ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)) | ( ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1)) | ( ~ (all_0_7_7 = e4) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_10_10 = e1) & ~ (all_0_11_11 = e0)) | ( ~ (all_0_13_13 = e3) & ~ (all_0_14_14 = e2) & ~ (all_0_15_15 = e0))
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (332), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (333) ( ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)) | ( ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1)) | ( ~ (all_0_7_7 = e4) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_10_10 = e1) & ~ (all_0_11_11 = e0))
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (333), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (334) ( ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)) | ( ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1))
% 8.20/2.55 |
% 8.20/2.55 +-Applying beta-rule and splitting (334), into two cases.
% 8.20/2.55 |-Branch one:
% 8.20/2.55 | (335) ~ (all_0_0_0 = e3) & ~ (all_0_1_1 = e2)
% 8.20/2.55 |
% 8.20/2.55 | Applying alpha-rule on (335) yields:
% 8.20/2.55 | (336) ~ (all_0_0_0 = e3)
% 8.20/2.55 | (337) ~ (all_0_1_1 = e2)
% 8.20/2.55 |
% 8.20/2.55 | Equations (284) can reduce 336 to:
% 8.47/2.55 | (226) $false
% 8.47/2.55 |
% 8.47/2.55 |-The branch is then unsatisfiable
% 8.47/2.55 |-Branch two:
% 8.47/2.55 | (339) ~ (all_0_3_3 = e4) & ~ (all_0_4_4 = e2) & ~ (all_0_5_5 = e1)
% 8.47/2.55 |
% 8.47/2.55 | Applying alpha-rule on (339) yields:
% 8.47/2.55 | (340) ~ (all_0_3_3 = e4)
% 8.47/2.55 | (319) ~ (all_0_4_4 = e2)
% 8.47/2.55 | (342) ~ (all_0_5_5 = e1)
% 8.47/2.55 |
% 8.47/2.55 +-Applying beta-rule and splitting (122), into two cases.
% 8.47/2.55 |-Branch one:
% 8.47/2.55 | (343) all_0_3_3 = e3
% 8.47/2.55 |
% 8.47/2.55 | Combining equations (343,320) yields a new equation:
% 8.47/2.55 | (344) e3 = e2
% 8.47/2.55 |
% 8.47/2.55 | Simplifying 344 yields:
% 8.47/2.55 | (345) e3 = e2
% 8.47/2.55 |
% 8.47/2.55 | Equations (345) can reduce 182 to:
% 8.47/2.55 | (226) $false
% 8.47/2.55 |
% 8.47/2.55 |-The branch is then unsatisfiable
% 8.47/2.55 |-Branch two:
% 8.47/2.55 | (347) ~ (all_0_3_3 = e3)
% 8.47/2.55 | (348) all_0_7_7 = e3 | all_0_12_12 = e3
% 8.47/2.55 |
% 8.47/2.55 +-Applying beta-rule and splitting (328), into two cases.
% 8.47/2.55 |-Branch one:
% 8.47/2.55 | (349) all_0_8_8 = e4
% 8.47/2.55 |
% 8.47/2.55 +-Applying beta-rule and splitting (348), into two cases.
% 8.47/2.55 |-Branch one:
% 8.47/2.55 | (350) all_0_7_7 = e3
% 8.47/2.55 |
% 8.47/2.55 | Combining equations (350,268) yields a new equation:
% 8.47/2.55 | (351) e3 = e0
% 8.47/2.55 |
% 8.47/2.55 | Simplifying 351 yields:
% 8.47/2.55 | (352) e3 = e0
% 8.47/2.55 |
% 8.47/2.55 | Equations (352) can reduce 65 to:
% 8.47/2.55 | (226) $false
% 8.47/2.55 |
% 8.47/2.55 |-The branch is then unsatisfiable
% 8.47/2.55 |-Branch two:
% 8.47/2.55 | (354) ~ (all_0_7_7 = e3)
% 8.47/2.55 | (355) all_0_12_12 = e3
% 8.47/2.55 |
% 8.47/2.55 | Equations (355) can reduce 175 to:
% 8.47/2.55 | (287) ~ (e4 = e3)
% 8.47/2.55 |
% 8.47/2.55 | Simplifying 287 yields:
% 8.47/2.55 | (28) ~ (e4 = e3)
% 8.47/2.55 |
% 8.47/2.55 | Equations (355) can reduce 322 to:
% 8.48/2.55 | (182) ~ (e3 = e2)
% 8.48/2.55 |
% 8.48/2.55 | Equations (355) can reduce 272 to:
% 8.48/2.55 | (65) ~ (e3 = e0)
% 8.48/2.55 |
% 8.48/2.55 +-Applying beta-rule and splitting (36), into two cases.
% 8.48/2.55 |-Branch one:
% 8.48/2.55 | (360) all_0_1_1 = e3
% 8.48/2.55 |
% 8.48/2.55 | Combining equations (360,241) yields a new equation:
% 8.48/2.55 | (325) e4 = e3
% 8.48/2.55 |
% 8.48/2.55 | Equations (325) can reduce 28 to:
% 8.48/2.55 | (226) $false
% 8.48/2.55 |
% 8.48/2.55 |-The branch is then unsatisfiable
% 8.48/2.55 |-Branch two:
% 8.48/2.55 | (363) ~ (all_0_1_1 = e3)
% 8.48/2.55 | (364) all_0_4_4 = e3 | all_0_9_9 = e3 | all_0_14_14 = e3
% 8.48/2.55 |
% 8.48/2.55 | Equations (241) can reduce 363 to:
% 8.48/2.55 | (28) ~ (e4 = e3)
% 8.48/2.55 |
% 8.48/2.55 +-Applying beta-rule and splitting (104), into two cases.
% 8.48/2.55 |-Branch one:
% 8.48/2.55 | (350) all_0_7_7 = e3
% 8.48/2.55 |
% 8.48/2.55 | Combining equations (350,268) yields a new equation:
% 8.48/2.55 | (351) e3 = e0
% 8.48/2.55 |
% 8.48/2.55 | Simplifying 351 yields:
% 8.48/2.55 | (352) e3 = e0
% 8.48/2.55 |
% 8.48/2.55 | Equations (352) can reduce 65 to:
% 8.48/2.55 | (226) $false
% 8.48/2.55 |
% 8.48/2.55 |-The branch is then unsatisfiable
% 8.48/2.55 |-Branch two:
% 8.48/2.55 | (354) ~ (all_0_7_7 = e3)
% 8.48/2.55 | (371) all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.55 |
% 8.48/2.55 +-Applying beta-rule and splitting (371), into two cases.
% 8.48/2.55 |-Branch one:
% 8.48/2.55 | (372) all_0_8_8 = e3
% 8.48/2.55 |
% 8.48/2.55 | Combining equations (372,349) yields a new equation:
% 8.48/2.55 | (325) e4 = e3
% 8.48/2.55 |
% 8.48/2.55 | Equations (325) can reduce 28 to:
% 8.48/2.55 | (226) $false
% 8.48/2.55 |
% 8.48/2.55 |-The branch is then unsatisfiable
% 8.48/2.55 |-Branch two:
% 8.48/2.55 | (375) ~ (all_0_8_8 = e3)
% 8.48/2.55 | (376) all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.55 |
% 8.48/2.55 +-Applying beta-rule and splitting (376), into two cases.
% 8.48/2.55 |-Branch one:
% 8.48/2.55 | (377) all_0_9_9 = e3
% 8.48/2.55 |
% 8.48/2.55 | Combining equations (318,377) yields a new equation:
% 8.48/2.55 | (345) e3 = e2
% 8.48/2.55 |
% 8.48/2.55 | Equations (345) can reduce 182 to:
% 8.48/2.55 | (226) $false
% 8.48/2.55 |
% 8.48/2.55 |-The branch is then unsatisfiable
% 8.48/2.55 |-Branch two:
% 8.48/2.55 | (380) ~ (all_0_9_9 = e3)
% 8.48/2.55 | (381) all_0_10_10 = e3
% 8.48/2.55 |
% 8.48/2.55 | Equations (381) can reduce 67 to:
% 8.48/2.55 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.55 |
% 8.48/2.55 +-Applying beta-rule and splitting (74), into two cases.
% 8.48/2.55 |-Branch one:
% 8.48/2.55 | (383) all_0_5_5 = e3
% 8.48/2.55 |
% 8.48/2.55 | Equations (383) can reduce 382 to:
% 8.48/2.55 | (226) $false
% 8.48/2.55 |
% 8.48/2.55 |-The branch is then unsatisfiable
% 8.48/2.55 |-Branch two:
% 8.48/2.55 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.55 | (386) all_0_5_5 = e1
% 8.48/2.55 |
% 8.48/2.56 | Equations (386) can reduce 342 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (388) ~ (all_0_8_8 = e4)
% 8.48/2.56 | (221) all_0_17_17 = e4
% 8.48/2.56 |
% 8.48/2.56 | Combining equations (221,230) yields a new equation:
% 8.48/2.56 | (390) e4 = e1
% 8.48/2.56 |
% 8.48/2.56 | Simplifying 390 yields:
% 8.48/2.56 | (231) e4 = e1
% 8.48/2.56 |
% 8.48/2.56 | Equations (231) can reduce 206 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (393) ~ (all_0_7_7 = e4) & ~ (all_0_8_8 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_10_10 = e1) & ~ (all_0_11_11 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Applying alpha-rule on (393) yields:
% 8.48/2.56 | (394) ~ (all_0_7_7 = e4)
% 8.48/2.56 | (395) ~ (all_0_10_10 = e1)
% 8.48/2.56 | (396) ~ (all_0_9_9 = e2)
% 8.48/2.56 | (397) ~ (all_0_11_11 = e0)
% 8.48/2.56 | (375) ~ (all_0_8_8 = e3)
% 8.48/2.56 |
% 8.48/2.56 | Equations (318) can reduce 396 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (400) ~ (all_0_13_13 = e3) & ~ (all_0_14_14 = e2) & ~ (all_0_15_15 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Applying alpha-rule on (400) yields:
% 8.48/2.56 | (286) ~ (all_0_13_13 = e3)
% 8.48/2.56 | (402) ~ (all_0_14_14 = e2)
% 8.48/2.56 | (403) ~ (all_0_15_15 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Equations (302) can reduce 403 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (405) ~ (all_0_3_3 = e2)
% 8.48/2.56 | (406) all_0_4_4 = e2 | all_0_6_6 = e2
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (406), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (407) all_0_4_4 = e2
% 8.48/2.56 |
% 8.48/2.56 | Equations (407) can reduce 319 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (319) ~ (all_0_4_4 = e2)
% 8.48/2.56 | (410) all_0_6_6 = e2
% 8.48/2.56 |
% 8.48/2.56 | Equations (410) can reduce 214 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (396) ~ (all_0_9_9 = e2)
% 8.48/2.56 | (413) all_0_11_11 = e2
% 8.48/2.56 |
% 8.48/2.56 | Equations (413) can reduce 216 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (415) ~ (all_0_13_13 = e2)
% 8.48/2.56 | (416) all_0_13_13 = e3 | all_0_13_13 = e1
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (416), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (417) all_0_13_13 = e3
% 8.48/2.56 |
% 8.48/2.56 | Equations (417) can reduce 286 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (286) ~ (all_0_13_13 = e3)
% 8.48/2.56 | (420) all_0_13_13 = e1
% 8.48/2.56 |
% 8.48/2.56 | Equations (420) can reduce 252 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (223) ~ (all_0_16_16 = e4)
% 8.48/2.56 | (228) all_0_16_16 = e0
% 8.48/2.56 |
% 8.48/2.56 | Equations (228) can reduce 13 to:
% 8.48/2.56 | (424) ~ (all_0_18_18 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Simplifying 424 yields:
% 8.48/2.56 | (425) ~ (all_0_18_18 = e0)
% 8.48/2.56 |
% 8.48/2.56 | From (228) and (219) follows:
% 8.48/2.56 | (426) op(e2, e0) = e0
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (81), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (427) all_0_18_18 = e4
% 8.48/2.56 |
% 8.48/2.56 | Equations (427) can reduce 103 to:
% 8.48/2.56 | (245) ~ (all_0_1_1 = e4)
% 8.48/2.56 |
% 8.48/2.56 | Equations (427) can reduce 156 to:
% 8.48/2.56 | (170) ~ (all_0_14_14 = e4)
% 8.48/2.56 |
% 8.48/2.56 | Equations (427) can reduce 98 to:
% 8.48/2.56 | (28) ~ (e4 = e3)
% 8.48/2.56 |
% 8.48/2.56 | Equations (427) can reduce 86 to:
% 8.48/2.56 | (191) ~ (e4 = e2)
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (153), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (237) all_0_0_0 = e4
% 8.48/2.56 |
% 8.48/2.56 | Equations (237) can reduce 212 to:
% 8.48/2.56 | (191) ~ (e4 = e2)
% 8.48/2.56 |
% 8.48/2.56 | Equations (237) can reduce 143 to:
% 8.48/2.56 | (5) ~ (e4 = e0)
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (53), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (284) all_0_0_0 = e3
% 8.48/2.56 |
% 8.48/2.56 | Combining equations (284,237) yields a new equation:
% 8.48/2.56 | (325) e4 = e3
% 8.48/2.56 |
% 8.48/2.56 | Equations (325) can reduce 28 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (336) ~ (all_0_0_0 = e3)
% 8.48/2.56 | (360) all_0_1_1 = e3
% 8.48/2.56 |
% 8.48/2.56 | Equations (360) can reduce 101 to:
% 8.48/2.56 | (440) ~ (all_0_4_4 = e3)
% 8.48/2.56 |
% 8.48/2.56 | Simplifying 440 yields:
% 8.48/2.56 | (441) ~ (all_0_4_4 = e3)
% 8.48/2.56 |
% 8.48/2.56 | Equations (360) can reduce 73 to:
% 8.48/2.56 | (442) ~ (all_0_9_9 = e3)
% 8.48/2.56 |
% 8.48/2.56 | Simplifying 442 yields:
% 8.48/2.56 | (380) ~ (all_0_9_9 = e3)
% 8.48/2.56 |
% 8.48/2.56 | From (360) and (111) follows:
% 8.48/2.56 | (444) op(e3, all_0_7_7) = e2
% 8.48/2.56 |
% 8.48/2.56 | Instantiating formula (117) with e2, e0, e0, all_0_11_11 and discharging atoms op(e2, e0) = all_0_11_11, op(e2, e0) = e0, yields:
% 8.48/2.56 | (445) all_0_11_11 = e0
% 8.48/2.56 |
% 8.48/2.56 | Equations (445) can reduce 196 to:
% 8.48/2.56 | (38) ~ (all_0_6_6 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Equations (445) can reduce 26 to:
% 8.48/2.56 | (447) ~ (all_0_9_9 = e0)
% 8.48/2.56 |
% 8.48/2.56 | Equations (445) can reduce 165 to:
% 8.48/2.56 | (139) ~ (all_0_10_10 = e0)
% 8.48/2.56 |
% 8.48/2.56 +-Applying beta-rule and splitting (160), into two cases.
% 8.48/2.56 |-Branch one:
% 8.48/2.56 | (449) all_0_9_9 = e0
% 8.48/2.56 |
% 8.48/2.56 | Equations (449) can reduce 447 to:
% 8.48/2.56 | (226) $false
% 8.48/2.56 |
% 8.48/2.56 |-The branch is then unsatisfiable
% 8.48/2.56 |-Branch two:
% 8.48/2.56 | (447) ~ (all_0_9_9 = e0)
% 8.48/2.57 | (452) all_0_14_14 = e0 | all_0_18_18 = e0
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (452), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (299) all_0_14_14 = e0
% 8.48/2.57 |
% 8.48/2.57 | Equations (299) can reduce 209 to:
% 8.48/2.57 | (159) ~ (all_0_13_13 = e0)
% 8.48/2.57 |
% 8.48/2.57 | Equations (299) can reduce 93 to:
% 8.48/2.57 | (455) ~ (all_0_15_15 = e0)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 455 yields:
% 8.48/2.57 | (403) ~ (all_0_15_15 = e0)
% 8.48/2.57 |
% 8.48/2.57 | Equations (299) can reduce 170 to:
% 8.48/2.57 | (457) ~ (e4 = e0)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 457 yields:
% 8.48/2.57 | (5) ~ (e4 = e0)
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (177), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (459) all_0_15_15 = e2
% 8.48/2.57 |
% 8.48/2.57 | Equations (459) can reduce 218 to:
% 8.48/2.57 | (226) $false
% 8.48/2.57 |
% 8.48/2.57 |-The branch is then unsatisfiable
% 8.48/2.57 |-Branch two:
% 8.48/2.57 | (218) ~ (all_0_15_15 = e2)
% 8.48/2.57 | (462) all_0_15_15 = e1 | all_0_15_15 = e0
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (45), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (463) all_0_7_7 = e4
% 8.48/2.57 |
% 8.48/2.57 | Equations (463) can reduce 121 to:
% 8.48/2.57 | (464) ~ (all_0_10_10 = e4)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 464 yields:
% 8.48/2.57 | (116) ~ (all_0_10_10 = e4)
% 8.48/2.57 |
% 8.48/2.57 | Equations (463) can reduce 166 to:
% 8.48/2.57 | (466) ~ (all_0_12_12 = e4)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 466 yields:
% 8.48/2.57 | (175) ~ (all_0_12_12 = e4)
% 8.48/2.57 |
% 8.48/2.57 | From (463) and (444) follows:
% 8.48/2.57 | (468) op(e3, e4) = e2
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (462), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (469) all_0_15_15 = e1
% 8.48/2.57 |
% 8.48/2.57 | Equations (469) can reduce 4 to:
% 8.48/2.57 | (470) ~ (all_0_6_6 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Equations (469) can reduce 47 to:
% 8.48/2.57 | (69) ~ (all_0_12_12 = e1)
% 8.48/2.57 |
% 8.48/2.57 | From (469) and (190) follows:
% 8.48/2.57 | (472) op(e2, e1) = e1
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (142), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (410) all_0_6_6 = e2
% 8.48/2.57 |
% 8.48/2.57 | Equations (410) can reduce 214 to:
% 8.48/2.57 | (226) $false
% 8.48/2.57 |
% 8.48/2.57 |-The branch is then unsatisfiable
% 8.48/2.57 |-Branch two:
% 8.48/2.57 | (214) ~ (all_0_6_6 = e2)
% 8.48/2.57 | (476) all_0_6_6 = e4 | all_0_6_6 = e1
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (476), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (477) all_0_6_6 = e4
% 8.48/2.57 |
% 8.48/2.57 | Equations (477) can reduce 185 to:
% 8.48/2.57 | (340) ~ (all_0_3_3 = e4)
% 8.48/2.57 |
% 8.48/2.57 | Equations (477) can reduce 126 to:
% 8.48/2.57 | (479) ~ (all_0_4_4 = e4)
% 8.48/2.57 |
% 8.48/2.57 | Equations (477) can reduce 181 to:
% 8.48/2.57 | (15) ~ (all_0_5_5 = e4)
% 8.48/2.57 |
% 8.48/2.57 | From (477) and (255) follows:
% 8.48/2.57 | (481) op(e1, e4) = e3
% 8.48/2.57 |
% 8.48/2.57 | Instantiating formula (117) with e3, e4, e2, all_0_3_3 and discharging atoms op(e3, e4) = all_0_3_3, op(e3, e4) = e2, yields:
% 8.48/2.57 | (320) all_0_3_3 = e2
% 8.48/2.57 |
% 8.48/2.57 | Instantiating formula (117) with e2, e1, e1, all_0_10_10 and discharging atoms op(e2, e1) = all_0_10_10, op(e2, e1) = e1, yields:
% 8.48/2.57 | (483) all_0_10_10 = e1
% 8.48/2.57 |
% 8.48/2.57 | Instantiating formula (117) with e1, e4, e3, all_0_12_12 and discharging atoms op(e1, e4) = all_0_12_12, op(e1, e4) = e3, yields:
% 8.48/2.57 | (355) all_0_12_12 = e3
% 8.48/2.57 |
% 8.48/2.57 | Equations (320) can reduce 83 to:
% 8.48/2.57 | (485) ~ (all_0_4_4 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 485 yields:
% 8.48/2.57 | (319) ~ (all_0_4_4 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Equations (320) can reduce 66 to:
% 8.48/2.57 | (487) ~ (all_0_5_5 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 487 yields:
% 8.48/2.57 | (163) ~ (all_0_5_5 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Equations (320) can reduce 340 to:
% 8.48/2.57 | (489) ~ (e4 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 489 yields:
% 8.48/2.57 | (191) ~ (e4 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Equations (483) can reduce 32 to:
% 8.48/2.57 | (491) ~ (all_0_8_8 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Equations (483) can reduce 207 to:
% 8.48/2.57 | (492) ~ (all_0_9_9 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Equations (483) can reduce 116 to:
% 8.48/2.57 | (493) ~ (e4 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 493 yields:
% 8.48/2.57 | (206) ~ (e4 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Equations (483) can reduce 139 to:
% 8.48/2.57 | (113) ~ (e1 = e0)
% 8.48/2.57 |
% 8.48/2.57 | Equations (355) can reduce 37 to:
% 8.48/2.57 | (285) ~ (all_0_13_13 = e3)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 285 yields:
% 8.48/2.57 | (286) ~ (all_0_13_13 = e3)
% 8.48/2.57 |
% 8.48/2.57 | Equations (355) can reduce 175 to:
% 8.48/2.57 | (287) ~ (e4 = e3)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 287 yields:
% 8.48/2.57 | (28) ~ (e4 = e3)
% 8.48/2.57 |
% 8.48/2.57 | Equations (355) can reduce 69 to:
% 8.48/2.57 | (115) ~ (e3 = e1)
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (16), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (289) all_0_13_13 = e2
% 8.48/2.57 |
% 8.48/2.57 | Equations (289) can reduce 286 to:
% 8.48/2.57 | (293) ~ (e3 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 293 yields:
% 8.48/2.57 | (182) ~ (e3 = e2)
% 8.48/2.57 |
% 8.48/2.57 | Equations (289) can reduce 159 to:
% 8.48/2.57 | (54) ~ (e2 = e0)
% 8.48/2.57 |
% 8.48/2.57 +-Applying beta-rule and splitting (210), into two cases.
% 8.48/2.57 |-Branch one:
% 8.48/2.57 | (505) all_0_4_4 = e1
% 8.48/2.57 |
% 8.48/2.57 | Equations (505) can reduce 441 to:
% 8.48/2.57 | (506) ~ (e3 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Simplifying 506 yields:
% 8.48/2.57 | (115) ~ (e3 = e1)
% 8.48/2.57 |
% 8.48/2.57 | Equations (505) can reduce 319 to:
% 8.48/2.57 | (508) ~ (e2 = e1)
% 8.48/2.57 |
% 8.48/2.58 | Simplifying 508 yields:
% 8.48/2.58 | (119) ~ (e2 = e1)
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (133), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (383) all_0_5_5 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (383) can reduce 163 to:
% 8.48/2.58 | (182) ~ (e3 = e2)
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (176), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (512) all_0_1_1 = e2
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (512,360) yields a new equation:
% 8.48/2.58 | (345) e3 = e2
% 8.48/2.58 |
% 8.48/2.58 | Equations (345) can reduce 182 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (337) ~ (all_0_1_1 = e2)
% 8.48/2.58 | (516) all_0_4_4 = e2 | all_0_9_9 = e2 | all_0_14_14 = e2
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (99), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (318) all_0_9_9 = e2
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (194), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.58 |
% 8.48/2.58 | Equations (383) can reduce 382 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (383) all_0_5_5 = e3
% 8.48/2.58 | (521) ( ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)) | ( ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0)) | ( ~ (all_0_2_2 = e4) & ~ (all_0_11_11 = e2) & ~ (all_0_15_15 = e1)) | ( ~ (all_0_3_3 = e3) & ~ (all_0_7_7 = e2) & ~ (all_0_16_16 = e0))
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (521), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (522) ( ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)) | ( ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0)) | ( ~ (all_0_2_2 = e4) & ~ (all_0_11_11 = e2) & ~ (all_0_15_15 = e1))
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (522), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (523) ( ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)) | ( ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0))
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (523), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (524) ~ (all_0_0_0 = e4) & ~ (all_0_8_8 = e2) & ~ (all_0_13_13 = e1)
% 8.48/2.58 |
% 8.48/2.58 | Applying alpha-rule on (524) yields:
% 8.48/2.58 | (222) ~ (all_0_0_0 = e4)
% 8.48/2.58 | (290) ~ (all_0_8_8 = e2)
% 8.48/2.58 | (252) ~ (all_0_13_13 = e1)
% 8.48/2.58 |
% 8.48/2.58 | Equations (237) can reduce 222 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (529) ~ (all_0_1_1 = e4) & ~ (all_0_4_4 = e3) & ~ (all_0_9_9 = e2) & ~ (all_0_14_14 = e1) & ~ (all_0_18_18 = e0)
% 8.48/2.58 |
% 8.48/2.58 | Applying alpha-rule on (529) yields:
% 8.48/2.58 | (425) ~ (all_0_18_18 = e0)
% 8.48/2.58 | (396) ~ (all_0_9_9 = e2)
% 8.48/2.58 | (245) ~ (all_0_1_1 = e4)
% 8.48/2.58 | (441) ~ (all_0_4_4 = e3)
% 8.48/2.58 | (534) ~ (all_0_14_14 = e1)
% 8.48/2.58 |
% 8.48/2.58 | Equations (318) can reduce 396 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (536) ~ (all_0_2_2 = e4) & ~ (all_0_11_11 = e2) & ~ (all_0_15_15 = e1)
% 8.48/2.58 |
% 8.48/2.58 | Applying alpha-rule on (536) yields:
% 8.48/2.58 | (537) ~ (all_0_2_2 = e4)
% 8.48/2.58 | (216) ~ (all_0_11_11 = e2)
% 8.48/2.58 | (539) ~ (all_0_15_15 = e1)
% 8.48/2.58 |
% 8.48/2.58 | Equations (469) can reduce 539 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (541) ~ (all_0_3_3 = e3) & ~ (all_0_7_7 = e2) & ~ (all_0_16_16 = e0)
% 8.48/2.58 |
% 8.48/2.58 | Applying alpha-rule on (541) yields:
% 8.48/2.58 | (347) ~ (all_0_3_3 = e3)
% 8.48/2.58 | (312) ~ (all_0_7_7 = e2)
% 8.48/2.58 | (264) ~ (all_0_16_16 = e0)
% 8.48/2.58 |
% 8.48/2.58 | Equations (228) can reduce 264 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (396) ~ (all_0_9_9 = e2)
% 8.48/2.58 | (547) all_0_9_9 = e4 | all_0_9_9 = e3 | all_0_9_9 = e1 | all_0_9_9 = e0
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (516), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (407) all_0_4_4 = e2
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (505,407) yields a new equation:
% 8.48/2.58 | (549) e2 = e1
% 8.48/2.58 |
% 8.48/2.58 | Equations (549) can reduce 119 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (319) ~ (all_0_4_4 = e2)
% 8.48/2.58 | (552) all_0_9_9 = e2 | all_0_14_14 = e2
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (552), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (318) all_0_9_9 = e2
% 8.48/2.58 |
% 8.48/2.58 | Equations (318) can reduce 396 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (396) ~ (all_0_9_9 = e2)
% 8.48/2.58 | (556) all_0_14_14 = e2
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (299,556) yields a new equation:
% 8.48/2.58 | (310) e2 = e0
% 8.48/2.58 |
% 8.48/2.58 | Equations (310) can reduce 54 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.58 | (381) all_0_10_10 = e3
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (483,381) yields a new equation:
% 8.48/2.58 | (561) e3 = e1
% 8.48/2.58 |
% 8.48/2.58 | Equations (561) can reduce 115 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (563) ~ (all_0_4_4 = e1)
% 8.48/2.58 | (564) all_0_5_5 = e1 | all_0_6_6 = e1
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (104), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (350) all_0_7_7 = e3
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (463,350) yields a new equation:
% 8.48/2.58 | (324) e4 = e3
% 8.48/2.58 |
% 8.48/2.58 | Simplifying 324 yields:
% 8.48/2.58 | (325) e4 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (325) can reduce 28 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (354) ~ (all_0_7_7 = e3)
% 8.48/2.58 | (371) all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (463) can reduce 354 to:
% 8.48/2.58 | (28) ~ (e4 = e3)
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (60), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (284) all_0_0_0 = e3
% 8.48/2.58 |
% 8.48/2.58 | Combining equations (284,237) yields a new equation:
% 8.48/2.58 | (325) e4 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (325) can reduce 28 to:
% 8.48/2.58 | (226) $false
% 8.48/2.58 |
% 8.48/2.58 |-The branch is then unsatisfiable
% 8.48/2.58 |-Branch two:
% 8.48/2.58 | (336) ~ (all_0_0_0 = e3)
% 8.48/2.58 | (576) all_0_8_8 = e3 | all_0_13_13 = e3
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (371), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (372) all_0_8_8 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (372) can reduce 491 to:
% 8.48/2.58 | (115) ~ (e3 = e1)
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (133), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (383) all_0_5_5 = e3
% 8.48/2.58 |
% 8.48/2.58 | Equations (383) can reduce 109 to:
% 8.48/2.58 | (441) ~ (all_0_4_4 = e3)
% 8.48/2.58 |
% 8.48/2.58 +-Applying beta-rule and splitting (10), into two cases.
% 8.48/2.58 |-Branch one:
% 8.48/2.58 | (407) all_0_4_4 = e2
% 8.48/2.59 |
% 8.48/2.59 | Equations (407) can reduce 319 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (319) ~ (all_0_4_4 = e2)
% 8.48/2.59 | (584) all_0_4_4 = e4 | all_0_4_4 = e3 | all_0_4_4 = e1
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (584), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (585) all_0_4_4 = e4
% 8.48/2.59 |
% 8.48/2.59 | Equations (585) can reduce 479 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (479) ~ (all_0_4_4 = e4)
% 8.48/2.59 | (588) all_0_4_4 = e3 | all_0_4_4 = e1
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (588), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (589) all_0_4_4 = e3
% 8.48/2.59 |
% 8.48/2.59 | Equations (589) can reduce 441 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (441) ~ (all_0_4_4 = e3)
% 8.48/2.59 | (505) all_0_4_4 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (505) can reduce 563 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.59 | (381) all_0_10_10 = e3
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (483,381) yields a new equation:
% 8.48/2.59 | (561) e3 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (561) can reduce 115 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (375) ~ (all_0_8_8 = e3)
% 8.48/2.59 | (376) all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (576), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (372) all_0_8_8 = e3
% 8.48/2.59 |
% 8.48/2.59 | Equations (372) can reduce 375 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (375) ~ (all_0_8_8 = e3)
% 8.48/2.59 | (417) all_0_13_13 = e3
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (289,417) yields a new equation:
% 8.48/2.59 | (345) e3 = e2
% 8.48/2.59 |
% 8.48/2.59 | Equations (345) can reduce 182 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (415) ~ (all_0_13_13 = e2)
% 8.48/2.59 | (416) all_0_13_13 = e3 | all_0_13_13 = e1
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (133), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (383) all_0_5_5 = e3
% 8.48/2.59 |
% 8.48/2.59 | Equations (383) can reduce 109 to:
% 8.48/2.59 | (441) ~ (all_0_4_4 = e3)
% 8.48/2.59 |
% 8.48/2.59 | Equations (383) can reduce 15 to:
% 8.48/2.59 | (287) ~ (e4 = e3)
% 8.48/2.59 |
% 8.48/2.59 | Simplifying 287 yields:
% 8.48/2.59 | (28) ~ (e4 = e3)
% 8.48/2.59 |
% 8.48/2.59 | Equations (383) can reduce 163 to:
% 8.48/2.59 | (182) ~ (e3 = e2)
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (51), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (273) all_0_0_0 = e2
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (273,237) yields a new equation:
% 8.48/2.59 | (248) e4 = e2
% 8.48/2.59 |
% 8.48/2.59 | Equations (248) can reduce 191 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (212) ~ (all_0_0_0 = e2)
% 8.48/2.59 | (617) all_0_8_8 = e2 | all_0_13_13 = e2
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (617), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (295) all_0_8_8 = e2
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (108), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (505) all_0_4_4 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (505) can reduce 441 to:
% 8.48/2.59 | (506) ~ (e3 = e1)
% 8.48/2.59 |
% 8.48/2.59 | Simplifying 506 yields:
% 8.48/2.59 | (115) ~ (e3 = e1)
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (104), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (350) all_0_7_7 = e3
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (350,463) yields a new equation:
% 8.48/2.59 | (325) e4 = e3
% 8.48/2.59 |
% 8.48/2.59 | Equations (325) can reduce 28 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (354) ~ (all_0_7_7 = e3)
% 8.48/2.59 | (371) all_0_8_8 = e3 | all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (371), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (372) all_0_8_8 = e3
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (295,372) yields a new equation:
% 8.48/2.59 | (345) e3 = e2
% 8.48/2.59 |
% 8.48/2.59 | Equations (345) can reduce 182 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (375) ~ (all_0_8_8 = e3)
% 8.48/2.59 | (376) all_0_9_9 = e3 | all_0_10_10 = e3
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (376), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (377) all_0_9_9 = e3
% 8.48/2.59 |
% 8.48/2.59 | Equations (377) can reduce 380 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (380) ~ (all_0_9_9 = e3)
% 8.48/2.59 | (381) all_0_10_10 = e3
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (483,381) yields a new equation:
% 8.48/2.59 | (561) e3 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (561) can reduce 115 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (563) ~ (all_0_4_4 = e1)
% 8.48/2.59 | (639) all_0_9_9 = e1 | all_0_14_14 = e1 | all_0_18_18 = e1
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (639), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (640) all_0_9_9 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (640) can reduce 492 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (492) ~ (all_0_9_9 = e1)
% 8.48/2.59 | (643) all_0_14_14 = e1 | all_0_18_18 = e1
% 8.48/2.59 |
% 8.48/2.59 +-Applying beta-rule and splitting (643), into two cases.
% 8.48/2.59 |-Branch one:
% 8.48/2.59 | (644) all_0_14_14 = e1
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (299,644) yields a new equation:
% 8.48/2.59 | (645) e1 = e0
% 8.48/2.59 |
% 8.48/2.59 | Equations (645) can reduce 113 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (534) ~ (all_0_14_14 = e1)
% 8.48/2.59 | (234) all_0_18_18 = e1
% 8.48/2.59 |
% 8.48/2.59 | Combining equations (234,427) yields a new equation:
% 8.48/2.59 | (231) e4 = e1
% 8.48/2.59 |
% 8.48/2.59 | Equations (231) can reduce 206 to:
% 8.48/2.59 | (226) $false
% 8.48/2.59 |
% 8.48/2.59 |-The branch is then unsatisfiable
% 8.48/2.59 |-Branch two:
% 8.48/2.59 | (290) ~ (all_0_8_8 = e2)
% 8.48/2.59 | (289) all_0_13_13 = e2
% 8.48/2.60 |
% 8.48/2.60 | Equations (289) can reduce 415 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (382) ~ (all_0_5_5 = e3)
% 8.48/2.60 | (381) all_0_10_10 = e3
% 8.48/2.60 |
% 8.48/2.60 | Combining equations (483,381) yields a new equation:
% 8.48/2.60 | (561) e3 = e1
% 8.48/2.60 |
% 8.48/2.60 | Equations (561) can reduce 115 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (658) ~ (all_0_6_6 = e4)
% 8.48/2.60 | (659) all_0_6_6 = e1
% 8.48/2.60 |
% 8.48/2.60 | Equations (659) can reduce 470 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (539) ~ (all_0_15_15 = e1)
% 8.48/2.60 | (302) all_0_15_15 = e0
% 8.48/2.60 |
% 8.48/2.60 | Equations (302) can reduce 403 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (394) ~ (all_0_7_7 = e4)
% 8.48/2.60 | (665) all_0_8_8 = e4 | all_0_9_9 = e4 | all_0_11_11 = e4
% 8.48/2.60 |
% 8.48/2.60 +-Applying beta-rule and splitting (63), into two cases.
% 8.48/2.60 |-Branch one:
% 8.48/2.60 | (246) all_0_2_2 = e4
% 8.48/2.60 |
% 8.48/2.60 | Combining equations (211,246) yields a new equation:
% 8.48/2.60 | (248) e4 = e2
% 8.48/2.60 |
% 8.48/2.60 | Equations (248) can reduce 191 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (537) ~ (all_0_2_2 = e4)
% 8.48/2.60 | (670) all_0_6_6 = e4 | all_0_11_11 = e4
% 8.48/2.60 |
% 8.48/2.60 +-Applying beta-rule and splitting (670), into two cases.
% 8.48/2.60 |-Branch one:
% 8.48/2.60 | (477) all_0_6_6 = e4
% 8.48/2.60 |
% 8.48/2.60 | Equations (477) can reduce 185 to:
% 8.48/2.60 | (340) ~ (all_0_3_3 = e4)
% 8.48/2.60 |
% 8.48/2.60 | Equations (477) can reduce 38 to:
% 8.48/2.60 | (5) ~ (e4 = e0)
% 8.48/2.60 |
% 8.48/2.60 +-Applying beta-rule and splitting (18), into two cases.
% 8.48/2.60 |-Branch one:
% 8.48/2.60 | (674) all_0_3_3 = e4
% 8.48/2.60 |
% 8.48/2.60 | Equations (674) can reduce 340 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (340) ~ (all_0_3_3 = e4)
% 8.48/2.60 | (677) all_0_7_7 = e4 | all_0_16_16 = e4
% 8.48/2.60 |
% 8.48/2.60 +-Applying beta-rule and splitting (677), into two cases.
% 8.48/2.60 |-Branch one:
% 8.48/2.60 | (463) all_0_7_7 = e4
% 8.48/2.60 |
% 8.48/2.60 | Equations (463) can reduce 394 to:
% 8.48/2.60 | (226) $false
% 8.48/2.60 |
% 8.48/2.60 |-The branch is then unsatisfiable
% 8.48/2.60 |-Branch two:
% 8.48/2.60 | (394) ~ (all_0_7_7 = e4)
% 8.48/2.60 | (225) all_0_16_16 = e4
% 8.48/2.60 |
% 8.48/2.60 | Combining equations (225,228) yields a new equation:
% 8.48/2.60 | (261) e4 = e0
% 8.48/2.60 |
% 8.48/2.60 | Simplifying 261 yields:
% 8.48/2.60 | (262) e4 = e0
% 8.48/2.60 |
% 8.67/2.60 | Equations (262) can reduce 5 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (658) ~ (all_0_6_6 = e4)
% 8.67/2.60 | (686) all_0_11_11 = e4
% 8.67/2.60 |
% 8.67/2.60 | Combining equations (445,686) yields a new equation:
% 8.67/2.60 | (262) e4 = e0
% 8.67/2.60 |
% 8.67/2.60 | Equations (262) can reduce 5 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (266) ~ (all_0_14_14 = e0)
% 8.67/2.60 | (265) all_0_18_18 = e0
% 8.67/2.60 |
% 8.67/2.60 | Combining equations (427,265) yields a new equation:
% 8.67/2.60 | (261) e4 = e0
% 8.67/2.60 |
% 8.67/2.60 | Simplifying 261 yields:
% 8.67/2.60 | (262) e4 = e0
% 8.67/2.60 |
% 8.67/2.60 | Equations (262) can reduce 5 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (222) ~ (all_0_0_0 = e4)
% 8.67/2.60 | (240) all_0_1_1 = e4 | all_0_2_2 = e4
% 8.67/2.60 |
% 8.67/2.60 +-Applying beta-rule and splitting (240), into two cases.
% 8.67/2.60 |-Branch one:
% 8.67/2.60 | (241) all_0_1_1 = e4
% 8.67/2.60 |
% 8.67/2.60 | Equations (241) can reduce 245 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (245) ~ (all_0_1_1 = e4)
% 8.67/2.60 | (246) all_0_2_2 = e4
% 8.67/2.60 |
% 8.67/2.60 | Combining equations (246,211) yields a new equation:
% 8.67/2.60 | (247) e4 = e2
% 8.67/2.60 |
% 8.67/2.60 | Simplifying 247 yields:
% 8.67/2.60 | (248) e4 = e2
% 8.67/2.60 |
% 8.67/2.60 | Equations (248) can reduce 191 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (703) ~ (all_0_18_18 = e4)
% 8.67/2.60 | (704) all_0_18_18 = e1 | all_0_18_18 = e0
% 8.67/2.60 |
% 8.67/2.60 +-Applying beta-rule and splitting (704), into two cases.
% 8.67/2.60 |-Branch one:
% 8.67/2.60 | (234) all_0_18_18 = e1
% 8.67/2.60 |
% 8.67/2.60 | Equations (234) can reduce 254 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (254) ~ (all_0_18_18 = e1)
% 8.67/2.60 | (265) all_0_18_18 = e0
% 8.67/2.60 |
% 8.67/2.60 | Equations (265) can reduce 425 to:
% 8.67/2.60 | (226) $false
% 8.67/2.60 |
% 8.67/2.60 |-The branch is then unsatisfiable
% 8.67/2.60 |-Branch two:
% 8.67/2.60 | (710) ~ (all_0_2_2 = e2)
% 8.67/2.60 | (246) all_0_2_2 = e4
% 8.67/2.60 |
% 8.67/2.60 | Equations (246) can reduce 148 to:
% 8.67/2.60 | (712) ~ (all_0_6_6 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Simplifying 712 yields:
% 8.67/2.60 | (658) ~ (all_0_6_6 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Equations (246) can reduce 172 to:
% 8.67/2.60 | (714) ~ (all_0_11_11 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Simplifying 714 yields:
% 8.67/2.60 | (715) ~ (all_0_11_11 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Equations (246) can reduce 3 to:
% 8.67/2.60 | (5) ~ (e4 = e0)
% 8.67/2.60 |
% 8.67/2.60 | From (246) and (64) follows:
% 8.67/2.60 | (717) op(e4, all_0_16_16) = e0
% 8.67/2.60 |
% 8.67/2.60 | From (246) and (56) follows:
% 8.67/2.60 | (718) op(all_0_16_16, e4) = e4
% 8.67/2.60 |
% 8.67/2.60 +-Applying beta-rule and splitting (77), into two cases.
% 8.67/2.60 |-Branch one:
% 8.67/2.60 | (225) all_0_16_16 = e4
% 8.67/2.60 |
% 8.67/2.60 | Equations (225) can reduce 118 to:
% 8.67/2.60 | (340) ~ (all_0_3_3 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Equations (225) can reduce 200 to:
% 8.67/2.60 | (394) ~ (all_0_7_7 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Equations (225) can reduce 39 to:
% 8.67/2.60 | (722) ~ (all_0_17_17 = e4)
% 8.67/2.60 |
% 8.67/2.60 | Simplifying 722 yields:
% 8.67/2.60 | (250) ~ (all_0_17_17 = e4)
% 8.67/2.60 |
% 8.67/2.60 | From (225) and (718) follows:
% 8.67/2.61 | (724) op(e4, e4) = e4
% 8.67/2.61 |
% 8.67/2.61 | From (225) and (717) follows:
% 8.67/2.61 | (725) op(e4, e4) = e0
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (11), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (221) all_0_17_17 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (221) can reduce 250 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (250) ~ (all_0_17_17 = e4)
% 8.67/2.61 | (230) all_0_17_17 = e1
% 8.67/2.61 |
% 8.67/2.61 | Equations (230) can reduce 12 to:
% 8.67/2.61 | (253) ~ (all_0_18_18 = e1)
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 253 yields:
% 8.67/2.61 | (254) ~ (all_0_18_18 = e1)
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (84), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (228) all_0_16_16 = e0
% 8.67/2.61 |
% 8.67/2.61 | Combining equations (225,228) yields a new equation:
% 8.67/2.61 | (261) e4 = e0
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 261 yields:
% 8.67/2.61 | (262) e4 = e0
% 8.67/2.61 |
% 8.67/2.61 | Equations (262) can reduce 5 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (264) ~ (all_0_16_16 = e0)
% 8.67/2.61 | (265) all_0_18_18 = e0
% 8.67/2.61 |
% 8.67/2.61 | Equations (265) can reduce 254 to:
% 8.67/2.61 | (738) ~ (e1 = e0)
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 738 yields:
% 8.67/2.61 | (113) ~ (e1 = e0)
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (128), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (674) all_0_3_3 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (674) can reduce 340 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (340) ~ (all_0_3_3 = e4)
% 8.67/2.61 | (743) all_0_4_4 = e4 | all_0_6_6 = e4
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (743), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (585) all_0_4_4 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (585) can reduce 44 to:
% 8.67/2.61 | (745) ~ (all_0_9_9 = e4)
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 745 yields:
% 8.67/2.61 | (746) ~ (all_0_9_9 = e4)
% 8.67/2.61 |
% 8.67/2.61 | From (585) and (184) follows:
% 8.67/2.61 | (747) op(e4, all_0_8_8) = e2
% 8.67/2.61 |
% 8.67/2.61 | From (585) and (8) follows:
% 8.67/2.61 | (748) op(all_0_8_8, e4) = e3
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (45), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (463) all_0_7_7 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (463) can reduce 394 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (394) ~ (all_0_7_7 = e4)
% 8.67/2.61 | (665) all_0_8_8 = e4 | all_0_9_9 = e4 | all_0_11_11 = e4
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (665), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (349) all_0_8_8 = e4
% 8.67/2.61 |
% 8.67/2.61 | From (349) and (748) follows:
% 8.67/2.61 | (754) op(e4, e4) = e3
% 8.67/2.61 |
% 8.67/2.61 | From (349) and (747) follows:
% 8.67/2.61 | (755) op(e4, e4) = e2
% 8.67/2.61 |
% 8.67/2.61 | Instantiating formula (117) with e4, e4, e4, e1 and discharging atoms op(e4, e4) = e4, op(e4, e4) = e1, yields:
% 8.67/2.61 | (231) e4 = e1
% 8.67/2.61 |
% 8.67/2.61 | Instantiating formula (117) with e4, e4, e3, e4 and discharging atoms op(e4, e4) = e4, op(e4, e4) = e3, yields:
% 8.67/2.61 | (325) e4 = e3
% 8.67/2.61 |
% 8.67/2.61 | Instantiating formula (117) with e4, e4, e2, e3 and discharging atoms op(e4, e4) = e3, op(e4, e4) = e2, yields:
% 8.67/2.61 | (345) e3 = e2
% 8.67/2.61 |
% 8.67/2.61 | Instantiating formula (117) with e4, e4, e0, e3 and discharging atoms op(e4, e4) = e3, op(e4, e4) = e0, yields:
% 8.67/2.61 | (352) e3 = e0
% 8.67/2.61 |
% 8.67/2.61 | Combining equations (325,231) yields a new equation:
% 8.67/2.61 | (760) e3 = e1
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 760 yields:
% 8.67/2.61 | (561) e3 = e1
% 8.67/2.61 |
% 8.67/2.61 | Combining equations (352,345) yields a new equation:
% 8.67/2.61 | (310) e2 = e0
% 8.67/2.61 |
% 8.67/2.61 | Combining equations (561,345) yields a new equation:
% 8.67/2.61 | (549) e2 = e1
% 8.67/2.61 |
% 8.67/2.61 | Combining equations (310,549) yields a new equation:
% 8.67/2.61 | (645) e1 = e0
% 8.67/2.61 |
% 8.67/2.61 | Equations (645) can reduce 113 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (388) ~ (all_0_8_8 = e4)
% 8.67/2.61 | (767) all_0_9_9 = e4 | all_0_11_11 = e4
% 8.67/2.61 |
% 8.67/2.61 +-Applying beta-rule and splitting (767), into two cases.
% 8.67/2.61 |-Branch one:
% 8.67/2.61 | (768) all_0_9_9 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (768) can reduce 746 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (746) ~ (all_0_9_9 = e4)
% 8.67/2.61 | (686) all_0_11_11 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (686) can reduce 715 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (479) ~ (all_0_4_4 = e4)
% 8.67/2.61 | (477) all_0_6_6 = e4
% 8.67/2.61 |
% 8.67/2.61 | Equations (477) can reduce 658 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 |-Branch two:
% 8.67/2.61 | (223) ~ (all_0_16_16 = e4)
% 8.67/2.61 | (228) all_0_16_16 = e0
% 8.67/2.61 |
% 8.67/2.61 | Equations (228) can reduce 223 to:
% 8.67/2.61 | (457) ~ (e4 = e0)
% 8.67/2.61 |
% 8.67/2.61 | Simplifying 457 yields:
% 8.67/2.61 | (5) ~ (e4 = e0)
% 8.67/2.61 |
% 8.67/2.61 | From (228) and (718) follows:
% 8.67/2.61 | (780) op(e0, e4) = e4
% 8.67/2.61 |
% 8.67/2.61 | From (228) and (88) follows:
% 8.67/2.61 | (781) op(e0, e4) = e0
% 8.67/2.61 |
% 8.67/2.61 | Instantiating formula (117) with e0, e4, e0, e4 and discharging atoms op(e0, e4) = e4, op(e0, e4) = e0, yields:
% 8.67/2.61 | (262) e4 = e0
% 8.67/2.61 |
% 8.67/2.61 | Equations (262) can reduce 5 to:
% 8.67/2.61 | (226) $false
% 8.67/2.61 |
% 8.67/2.61 |-The branch is then unsatisfiable
% 8.67/2.61 % SZS output end Proof for theBenchmark
% 8.67/2.61
% 8.67/2.61 1986ms
%------------------------------------------------------------------------------